diff --git a/velox/CMakeLists.txt b/velox/CMakeLists.txt
index 45d6a454054..b63feee4517 100644
--- a/velox/CMakeLists.txt
+++ b/velox/CMakeLists.txt
@@ -26,6 +26,7 @@ add_subdirectory(external/date)
 add_subdirectory(external/tzdb)
 add_subdirectory(external/md5)
 add_subdirectory(external/hdfs)
+add_subdirectory(external/theta)
 #
 
 # examples depend on expression
diff --git a/velox/external/theta/BinomialBounds.h b/velox/external/theta/BinomialBounds.h
new file mode 100644
index 00000000000..53c561552eb
--- /dev/null
+++ b/velox/external/theta/BinomialBounds.h
@@ -0,0 +1,1032 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "velox/common/base/Exceptions.h"
+#include <algorithm>
+#include <cmath>
+#include <stdexcept>
+
+/*
+ * This class enables the estimation of error bounds given a sample set size,
+ * the sampling probability theta, the number of standard deviations and a
+ * simple noDataSeen flag. This can be used to estimate error bounds for fixed
+ * threshold sampling as well as the error bounds calculations for sketches.
+ *
+ * author Alexander Saydakov
+ * author Lee Rhodes
+ * author Kevin Lang
+ */
+
+namespace facebook::velox::common::theta {
+
+static constexpr double deltaOfNumStdDevs[] = {
+    0.5000000000000000000, // not actually using this value
+    0.1586553191586026479,
+    0.0227502618904135701,
+    0.0013498126861731796};
+
+static constexpr double lbEquivTable[] = {
+    1.0,
+    2.0,
+    3.0, // fake values for k = 0
+    0.78733703534118149,
+    3.14426768537558132,
+    13.56789685109913535, // k = 1
+    0.94091379266077979,
+    2.64699271711145911,
+    6.29302733018320737, // k = 2
+    0.96869128474958188,
+    2.46531676590527127,
+    4.97375283467403051, // k = 3
+    0.97933572521046131,
+    2.37418810664669877,
+    4.44899975481712318, // k = 4
+    0.98479165917274258,
+    2.31863116255024693,
+    4.16712379778553554, // k = 5
+    0.98806033915698777,
+    2.28075536565225434,
+    3.99010556144099837, // k = 6
+    0.99021896790580399,
+    2.25302005857281529,
+    3.86784477136922078, // k = 7
+    0.99174267079089873,
+    2.23168103978522936,
+    3.77784896945266269, // k = 8
+    0.99287147837287648,
+    2.21465899260871879,
+    3.70851932988722410, // k = 9
+    0.99373900046805375,
+    2.20070155496262032,
+    3.65326029076638292, // k = 10
+    0.99442519013851438,
+    2.18900651202670815,
+    3.60803817612955413, // k = 11
+    0.99498066823221620,
+    2.17903457780744247,
+    3.57024330407946877, // k = 12
+    0.99543899410224412,
+    2.17040883161922693,
+    3.53810982030634591, // k = 13
+    0.99582322541263579,
+    2.16285726913676513,
+    3.51039837124298515, // k = 14
+    0.99614973311747690,
+    2.15617827879603396,
+    3.48621230377099778, // k = 15
+    0.99643042892560629,
+    2.15021897666090922,
+    3.46488605693562590, // k = 16
+    0.99667418783778317,
+    2.14486114872480016,
+    3.44591466064832730, // k = 17
+    0.99688774875812669,
+    2.14001181420209718,
+    3.42890765690452781, // k = 18
+    0.99707632299691795,
+    2.13559675336844634,
+    3.41355809420343803, // k = 19
+    0.99724399084971083,
+    2.13155592217421486,
+    3.39962113251016262, // k = 20
+    0.99739400151915447,
+    2.12784018863251845,
+    3.38689892877548004, // k = 21
+    0.99752896842633731,
+    2.12440890875851096,
+    3.37522975271599535, // k = 22
+    0.99765101725122918,
+    2.12122815311133195,
+    3.36448003577621080, // k = 23
+    0.99776189496810730,
+    2.11826934724291505,
+    3.35453840911279144, // k = 24
+    0.99786304821586214,
+    2.11550823850916458,
+    3.34531123809287578, // k = 25
+    0.99795568665180667,
+    2.11292409529477254,
+    3.33671916527694634, // k = 26
+    0.99804083063483517,
+    2.11049908609763293,
+    3.32869446834217797, // k = 27
+    0.99811933910984862,
+    2.10821776918189130,
+    3.32117898316676019, // k = 28
+    0.99819195457286014,
+    2.10606671027090897,
+    3.31412243534683171, // k = 29
+    0.99825930555178388,
+    2.10403415237001923,
+    3.30748113008135647, // k = 30
+    0.99832193858154028,
+    2.10210975877822648,
+    3.30121691946897045, // k = 31
+    0.99838032666573895,
+    2.10028440670842542,
+    3.29529629751144171, // k = 32
+    0.99843488390555990,
+    2.09855000145353188,
+    3.28968974413223236, // k = 33
+    0.99848596721417948,
+    2.09689934193824001,
+    3.28437111460505093, // k = 34
+    0.99853390005924325,
+    2.09532599155502908,
+    3.27931717312372939, // k = 35
+    0.99857895741078551,
+    2.09382418262592296,
+    3.27450718840060517, // k = 36
+    0.99862138880970974,
+    2.09238872751677718,
+    3.26992261182860489, // k = 37
+    0.99866141580770318,
+    2.09101494715108061,
+    3.26554677962434425, // k = 38
+    0.99869923565267982,
+    2.08969860402822860,
+    3.26136468165239535, // k = 39
+    0.99873502010169091,
+    2.08843585627218431,
+    3.25736275677081721, // k = 40
+    0.99876893292508839,
+    2.08722321436752623,
+    3.25352872241415980, // k = 41
+    0.99880111078502409,
+    2.08605749165553789,
+    3.24985141664350863, // k = 42
+    0.99883168573342118,
+    2.08493577529222307,
+    3.24632068399498053, // k = 43
+    0.99886077231613513,
+    2.08385540129560809,
+    3.24292724848112357, // k = 44
+    0.99888847451828155,
+    2.08281392374021834,
+    3.23966263299664092, // k = 45
+    0.99891488795844907,
+    2.08180908991394631,
+    3.23651906111521726, // k = 46
+    0.99894010085196783,
+    2.08083882998420222,
+    3.23348939240611344, // k = 47
+    0.99896419358239541,
+    2.07990122528650545,
+    3.23056705515594444, // k = 48
+    0.99898723510594323,
+    2.07899450946285924,
+    3.22774598963252402, // k = 49
+    0.99900929266780736,
+    2.07811704477046533,
+    3.22502059972006805, // k = 50
+    0.99903043086155208,
+    2.07726730587160091,
+    3.22238570890294795, // k = 51
+    0.99905070073845081,
+    2.07644388314946582,
+    3.21983651940365689, // k = 52
+    0.99907015770423868,
+    2.07564546080757850,
+    3.21736857351049821, // k = 53
+    0.99908884779227947,
+    2.07487081196367740,
+    3.21497773796417619, // k = 54
+    0.99910681586905525,
+    2.07411879634256024,
+    3.21266015316183484, // k = 55
+    0.99912410177549305,
+    2.07338834403498140,
+    3.21041222805715165, // k = 56
+    0.99914074347179849,
+    2.07267845454973099,
+    3.20823061166797174, // k = 57
+    0.99915677607464204,
+    2.07198819052374006,
+    3.20611216970604573, // k = 58
+    0.99917223149395795,
+    2.07131667846186929,
+    3.20405396962596001, // k = 59
+    0.99918714153457699,
+    2.07066309019154460,
+    3.20205326110445299, // k = 60
+    0.99920153247185794,
+    2.07002665203046377,
+    3.20010746990493544, // k = 61
+    0.99921543193525508,
+    2.06940663431663552,
+    3.19821417453343315, // k = 62
+    0.99922886570365677,
+    2.06880235245998279,
+    3.19637109973109546, // k = 63
+    0.99924185357357942,
+    2.06821315729285971,
+    3.19457610621114441, // k = 64
+    0.99925441845175555,
+    2.06763843812092318,
+    3.19282717869864996, // k = 65
+    0.99926658263325407,
+    2.06707761824370095,
+    3.19112241228646099, // k = 66
+    0.99927836173816331,
+    2.06653015295219689,
+    3.18946001739936946, // k = 67
+    0.99928977431994781,
+    2.06599552505539918,
+    3.18783829446098821, // k = 68
+    0.99930083753795884,
+    2.06547324585920933,
+    3.18625564538041317, // k = 69
+    0.99931156864562354,
+    2.06496285191821016,
+    3.18471055124089730, // k = 70
+    0.99932197985521043,
+    2.06446390392778767,
+    3.18320157510865442, // k = 71
+    0.99933208559809827,
+    2.06397598606787369,
+    3.18172735837393361, // k = 72
+    0.99934190032416836,
+    2.06349869971447220,
+    3.18028661102792398, // k = 73
+    0.99935143390791836,
+    2.06303166975550312,
+    3.17887810481605015, // k = 74
+    0.99936070171270330,
+    2.06257453607466346,
+    3.17750067581857820, // k = 75
+    0.99936971103502970,
+    2.06212696042919674,
+    3.17615321728274580, // k = 76
+    0.99937847392385493,
+    2.06168861430600714,
+    3.17483467831510779, // k = 77
+    0.99938700168914352,
+    2.06125918927764928,
+    3.17354405480557489, // k = 78
+    0.99939530099953799,
+    2.06083838987589729,
+    3.17228039269048168, // k = 79
+    0.99940338278830154,
+    2.06042593411496000,
+    3.17104278166036124, // k = 80
+    0.99941125463777780,
+    2.06002155276328835,
+    3.16983035274597569, // k = 81
+    0.99941892470027938,
+    2.05962498741951094,
+    3.16864227952240185, // k = 82
+    0.99942640059737187,
+    2.05923599161263837,
+    3.16747776846497686, // k = 83
+    0.99943368842187397,
+    2.05885433061945378,
+    3.16633606416374391, // k = 84
+    0.99944079790603269,
+    2.05847977868873500,
+    3.16521644518826406, // k = 85
+    0.99944773295734990,
+    2.05811212058944193,
+    3.16411821883858124, // k = 86
+    0.99945450059186669,
+    2.05775114781260982,
+    3.16304072400711789, // k = 87
+    0.99946110646314423,
+    2.05739666442039493,
+    3.16198332650733960, // k = 88
+    0.99946755770463369,
+    2.05704847678819647,
+    3.16094541781455973, // k = 89
+    0.99947385746861528,
+    2.05670640500335367,
+    3.15992641851471490, // k = 90
+    0.99948001256305474,
+    2.05637027420314666,
+    3.15892576988736096, // k = 91
+    0.99948602689656241,
+    2.05603991286400856,
+    3.15794293484717059, // k = 92
+    0.99949190674294641,
+    2.05571516158917689,
+    3.15697740043813724, // k = 93
+    0.99949765436329585,
+    2.05539586490317561,
+    3.15602867309343083, // k = 94
+    0.99950327557880314,
+    2.05508187237845164,
+    3.15509627710042651, // k = 95
+    0.99950877461972709,
+    2.05477304104951486,
+    3.15417975753007340, // k = 96
+    0.99951415481862682,
+    2.05446923022574879,
+    3.15327867462917766, // k = 97
+    0.99951942042375208,
+    2.05417030908833453,
+    3.15239260700215596, // k = 98
+    0.99952457390890004,
+    2.05387614661762541,
+    3.15152114915238712, // k = 99
+    0.99952962005008317,
+    2.05358662050909402,
+    3.15066390921020911, // k = 100
+    0.99953456216121594,
+    2.05330161104427589,
+    3.14982051097524618, // k = 101
+    0.99953940176368405,
+    2.05302100378725072,
+    3.14899059183684926, // k = 102
+    0.99954414373920031,
+    2.05274468493067275,
+    3.14817379948561893, // k = 103
+    0.99954879047621148,
+    2.05247255013657082,
+    3.14736979964868624, // k = 104
+    0.99955334485656522,
+    2.05220449388099269,
+    3.14657826610371671, // k = 105
+    0.99955780993869325,
+    2.05194041831310869,
+    3.14579888316276879, // k = 106
+    0.99956218652590678,
+    2.05168022402710903,
+    3.14503134811607765, // k = 107
+    0.99956647932785359,
+    2.05142381889103831,
+    3.14427536967733090, // k = 108
+    0.99957069025060719,
+    2.05117111251445294,
+    3.14353066260227365, // k = 109
+    0.99957482032178291,
+    2.05092201793428330,
+    3.14279695558593630, // k = 110
+    0.99957887261450651,
+    2.05067645094720774,
+    3.14207398336887422, // k = 111
+    0.99958284988383639,
+    2.05043432833224415,
+    3.14136149076028914, // k = 112
+    0.99958675435604505,
+    2.05019557189746138,
+    3.14065923143530767, // k = 113
+    0.99959058650074439,
+    2.04996010556124020,
+    3.13996696426707445, // k = 114
+    0.99959434898201494,
+    2.04972785368377686,
+    3.13928445867830419, // k = 115
+    0.99959804437042976,
+    2.04949874512311681,
+    3.13861149103462367, // k = 116
+    0.99960167394553423,
+    2.04927271043337100,
+    3.13794784369528656, // k = 117
+    0.99960523957651048,
+    2.04904968140490951,
+    3.13729330661277572, // k = 118
+    0.99960874253329735,
+    2.04882959397491504,
+    3.13664767767019725, // k = 119
+    0.99961218434327748,
+    2.04861238220240693,
+    3.13601075688413289 // k = 120
+};
+
+static constexpr double ubEquivTable[] = {
+    1.0,
+    2.0,
+    3.0, // fake values for k = 0
+    0.99067760836669549,
+    1.75460517119302040,
+    2.48055626001627161, // k = 1
+    0.99270518097577565,
+    1.78855957509907171,
+    2.53863835259832626, // k = 2
+    0.99402032633599902,
+    1.81047286499563143,
+    2.57811676180597260, // k = 3
+    0.99492607629539975,
+    1.82625928017762362,
+    2.60759550546498531, // k = 4
+    0.99558653966013821,
+    1.83839160339161367,
+    2.63086812358551470, // k = 5
+    0.99608981951632813,
+    1.84812399034444752,
+    2.64993712523727254, // k = 6
+    0.99648648035983456,
+    1.85617372053235385,
+    2.66598485907860550, // k = 7
+    0.99680750790483330,
+    1.86298655802610824,
+    2.67976541374471822, // k = 8
+    0.99707292880049181,
+    1.86885682585270274,
+    2.69178781407745760, // k = 9
+    0.99729614928489241,
+    1.87398826101983218,
+    2.70241106542158604, // k = 10
+    0.99748667952445658,
+    1.87852708449801753,
+    2.71189717290596377, // k = 11
+    0.99765127712748836,
+    1.88258159501103250,
+    2.72044290303773550, // k = 12
+    0.99779498340305395,
+    1.88623391878036273,
+    2.72819957382063194, // k = 13
+    0.99792160418357412,
+    1.88954778748873764,
+    2.73528576807902368, // k = 14
+    0.99803398604944960,
+    1.89257337682371940,
+    2.74179612106766513, // k = 15
+    0.99813449883217231,
+    1.89535099316557876,
+    2.74780718300419835, // k = 16
+    0.99822494122659577,
+    1.89791339232732525,
+    2.75338173141955167, // k = 17
+    0.99830679915913834,
+    1.90028752122407241,
+    2.75857186416826039, // k = 18
+    0.99838117410831728,
+    1.90249575897183831,
+    2.76342117562634826, // k = 19
+    0.99844913407071090,
+    1.90455689090418900,
+    2.76796659454200267, // k = 20
+    0.99851147736424650,
+    1.90648682834171268,
+    2.77223944710058845, // k = 21
+    0.99856879856019987,
+    1.90829917277082473,
+    2.77626682032629901, // k = 22
+    0.99862183849734265,
+    1.91000561415842185,
+    2.78007199816156003, // k = 23
+    0.99867096266018507,
+    1.91161621560812023,
+    2.78367524259661536, // k = 24
+    0.99871656986212543,
+    1.91313978579765376,
+    2.78709435016625662, // k = 25
+    0.99875907577771272,
+    1.91458400425526065,
+    2.79034488416175463, // k = 26
+    0.99879885565047744,
+    1.91595563175945927,
+    2.79344064132371273, // k = 27
+    0.99883610756373287,
+    1.91726064301425936,
+    2.79639384757751941, // k = 28
+    0.99887095169674467,
+    1.91850441099725799,
+    2.79921543574803877, // k = 29
+    0.99890379414739527,
+    1.91969155477030995,
+    2.80191513182441554, // k = 30
+    0.99893466279047516,
+    1.92082633358913313,
+    2.80450167352080371, // k = 31
+    0.99896392088177777,
+    1.92191254955568525,
+    2.80698295731653502, // k = 32
+    0.99899147889385631,
+    1.92295362479495680,
+    2.80936614404217266, // k = 33
+    0.99901764688726757,
+    1.92395267400968351,
+    2.81165765979318394, // k = 34
+    0.99904238606342233,
+    1.92491244978191389,
+    2.81386337393604435, // k = 35
+    0.99906590152386343,
+    1.92583552644848055,
+    2.81598868034527072, // k = 36
+    0.99908829040739988,
+    1.92672418013918900,
+    2.81803841726804194, // k = 37
+    0.99910959420023460,
+    1.92758051694144683,
+    2.82001709302821268, // k = 38
+    0.99912996403594434,
+    1.92840654943159961,
+    2.82192875763732332, // k = 39
+    0.99914930224576892,
+    1.92920397044028391,
+    2.82377730628954282, // k = 40
+    0.99916781270195543,
+    1.92997447498220254,
+    2.82556612075063640, // k = 41
+    0.99918553179077207,
+    1.93071949211818605,
+    2.82729843191989971, // k = 42
+    0.99920250730914972,
+    1.93144048613876862,
+    2.82897728689417249, // k = 43
+    0.99921873345181211,
+    1.93213870990595638,
+    2.83060537017752267, // k = 44
+    0.99923435180002684,
+    1.93281536508689555,
+    2.83218527795750674, // k = 45
+    0.99924930425362390,
+    1.93347145882316340,
+    2.83371938965598247, // k = 46
+    0.99926370394567243,
+    1.93410820221384938,
+    2.83520990872793277, // k = 47
+    0.99927750755296074,
+    1.93472643138986200,
+    2.83665891945119597, // k = 48
+    0.99929082941537217,
+    1.93532697329771963,
+    2.83806833931606661, // k = 49
+    0.99930366295501472,
+    1.93591074716263734,
+    2.83943997143404658, // k = 50
+    0.99931598804721489,
+    1.93647857274021362,
+    2.84077557836653227, // k = 51
+    0.99932789059798210,
+    1.93703110239354714,
+    2.84207662106302905, // k = 52
+    0.99933946180485123,
+    1.93756904936378760,
+    2.84334468086129277, // k = 53
+    0.99935053819703512,
+    1.93809302131219852,
+    2.84458116874117195, // k = 54
+    0.99936126637970801,
+    1.93860365411038060,
+    2.84578731838604426, // k = 55
+    0.99937166229284458,
+    1.93910149816429112,
+    2.84696443486512862, // k = 56
+    0.99938169190727422,
+    1.93958709548454067,
+    2.84811369085281285, // k = 57
+    0.99939136927613959,
+    1.94006085573701625,
+    2.84923617230361970, // k = 58
+    0.99940074328745254,
+    1.94052339623206649,
+    2.85033291216254270, // k = 59
+    0.99940993070470086,
+    1.94097508636855309,
+    2.85140492437699322, // k = 60
+    0.99941868577388959,
+    1.94141633372043998,
+    2.85245314430358121, // k = 61
+    0.99942734443487780,
+    1.94184757038001976,
+    2.85347839582286156, // k = 62
+    0.99943556385736088,
+    1.94226915100517772,
+    2.85448160365493209, // k = 63
+    0.99944374522542034,
+    1.94268143723749631,
+    2.85546346373061510, // k = 64
+    0.99945159955424856,
+    1.94308482059116727,
+    2.85642486111805738, // k = 65
+    0.99945915301904620,
+    1.94347956957849988,
+    2.85736639994965458, // k = 66
+    0.99946660663832176,
+    1.94386600964031686,
+    2.85828887832701639, // k = 67
+    0.99947383703224091,
+    1.94424436597356021,
+    2.85919278275500233, // k = 68
+    0.99948075442870277,
+    1.94461502153473020,
+    2.86007887186090670, // k = 69
+    0.99948766082269458,
+    1.94497821937304138,
+    2.86094774077355396, // k = 70
+    0.99949422748713346,
+    1.94533411296001191,
+    2.86179981848076181, // k = 71
+    0.99950070756119658,
+    1.94568300035135167,
+    2.86263579405672886, // k = 72
+    0.99950704321753392,
+    1.94602523449961495,
+    2.86345610449197352, // k = 73
+    0.99951320334216121,
+    1.94636083782822311,
+    2.86426125541271404, // k = 74
+    0.99951920293474927,
+    1.94669011080745236,
+    2.86505169255406145, // k = 75
+    0.99952501670378524,
+    1.94701327348536779,
+    2.86582788270862920, // k = 76
+    0.99953071209267819,
+    1.94733044372333097,
+    2.86659027602854621, // k = 77
+    0.99953632734991515,
+    1.94764180764266825,
+    2.86733927778843167, // k = 78
+    0.99954171164873173,
+    1.94794766430732125,
+    2.86807526143834934, // k = 79
+    0.99954699274462655,
+    1.94824807472994621,
+    2.86879864789403882, // k = 80
+    0.99955216611081710,
+    1.94854317889829076,
+    2.86950970901679625, // k = 81
+    0.99955730019613043,
+    1.94883320227168610,
+    2.87020887436986527, // k = 82
+    0.99956213770650493,
+    1.94911826561721568,
+    2.87089648477021342, // k = 83
+    0.99956704264963037,
+    1.94939848545763539,
+    2.87157281693902178, // k = 84
+    0.99957166306481327,
+    1.94967401618316671,
+    2.87223821840905202, // k = 85
+    0.99957632713136491,
+    1.94994497791333288,
+    2.87289293193450135, // k = 86
+    0.99958087233392234,
+    1.95021155752212394,
+    2.87353731228213860, // k = 87
+    0.99958532555996271,
+    1.95047376805584349,
+    2.87417154907075201, // k = 88
+    0.99958956246481989,
+    1.95073180380688882,
+    2.87479599765507032, // k = 89
+    0.99959389351869277,
+    1.95098572880579013,
+    2.87541081987382086, // k = 90
+    0.99959807862052230,
+    1.95123574036898617,
+    2.87601637401948551, // k = 91
+    0.99960214057801977,
+    1.95148186921983324,
+    2.87661283691068093, // k = 92
+    0.99960607527256684,
+    1.95172415829728152,
+    2.87720042968334155, // k = 93
+    0.99960996433179616,
+    1.95196280898670693,
+    2.87777936649376898, // k = 94
+    0.99961379137860717,
+    1.95219787713926962,
+    2.87834989933620022, // k = 95
+    0.99961756088146103,
+    1.95242944583677058,
+    2.87891216133900230, // k = 96
+    0.99962125605327401,
+    1.95265762420910960,
+    2.87946647367488140, // k = 97
+    0.99962486179100551,
+    1.95288245314810638,
+    2.88001290210658567, // k = 98
+    0.99962843240297161,
+    1.95310404286672679,
+    2.88055166523392359, // k = 99
+    0.99963187276145504,
+    1.95332251980147475,
+    2.88108300006589957, // k = 100
+    0.99963525453173929,
+    1.95353785898848287,
+    2.88160703591438505, // k = 101
+    0.99963855412988778,
+    1.95375019354571577,
+    2.88212393551896184, // k = 102
+    0.99964190254169694,
+    1.95395953472205974,
+    2.88263389761985422, // k = 103
+    0.99964506565942202,
+    1.95416607430155409,
+    2.88313700661564098, // k = 104
+    0.99964834424233118,
+    1.95436972855640079,
+    2.88363350163803034, // k = 105
+    0.99965136548857458,
+    1.95457068540693513,
+    2.88412349413960101, // k = 106
+    0.99965436594726498,
+    1.95476896383092935,
+    2.88460710620208260, // k = 107
+    0.99965736463468602,
+    1.95496457504532373,
+    2.88508450078833789, // k = 108
+    0.99966034130443404,
+    1.95515761150707590,
+    2.88555580586194083, // k = 109
+    0.99966326130828520,
+    1.95534810382198998,
+    2.88602118761679094, // k = 110
+    0.99966601446035952,
+    1.95553622237747504,
+    2.88648066384146773, // k = 111
+    0.99966887679593697,
+    1.95572186728168163,
+    2.88693444915907094, // k = 112
+    0.99967161286551232,
+    1.95590523410490391,
+    2.88738271495714116, // k = 113
+    0.99967435412270333,
+    1.95608626483223702,
+    2.88782540459769166, // k = 114
+    0.99967701261934394,
+    1.95626497627117146,
+    2.88826277189363623, // k = 115
+    0.99967963265157778,
+    1.95644153684824573,
+    2.88869486674335008, // k = 116
+    0.99968216317182623,
+    1.95661589936000269,
+    2.88912184353694101, // k = 117
+    0.99968479674396349,
+    1.95678821614791332,
+    2.88954376359643561, // k = 118
+    0.99968729031337489,
+    1.95695842061650183,
+    2.88996069422501023, // k = 119
+    0.99968963358631413,
+    1.95712651709766305,
+    2.89037285320668502 // k = 120
+};
+
+class BinomialBounds {
+ public:
+  static double getLowerBound(
+      unsigned long long numSamples,
+      double theta,
+      unsigned numStdDevs) {
+    checkTheta(theta);
+    checkNumStdDevs(numStdDevs);
+    const double estimate = numSamples / theta;
+    const double lb =
+        computeApproxBinomialLowerBound(numSamples, theta, numStdDevs);
+    return std::min(estimate, std::max(static_cast<double>(numSamples), lb));
+  }
+
+  static double getUpperBound(
+      unsigned long long numSamples,
+      double theta,
+      unsigned numStdDevs) {
+    checkTheta(theta);
+    checkNumStdDevs(numStdDevs);
+    const double estimate = numSamples / theta;
+    const double ub =
+        computeApproxBinomialUpperBound(numSamples, theta, numStdDevs);
+    return std::max(estimate, ub);
+  }
+
+ private:
+  // our "classic" bounds, but now with continuity correction
+  static double contClassicLb(
+      unsigned long long numSamples,
+      double theta,
+      double numStdDevs) {
+    const double n_hat = (numSamples - 0.5) / theta;
+    const double b = numStdDevs * std::sqrt((1.0 - theta) / theta);
+    const double d = 0.5 * b * std::sqrt((b * b) + (4.0 * n_hat));
+    const double center = n_hat + (0.5 * (b * b));
+    return (center - d);
+  }
+
+  // our "classic" bounds, but now with continuity correction
+  static double contClassicUb(
+      unsigned long long numSamples,
+      double theta,
+      double numStdSevs) {
+    const double n_hat = (numSamples + 0.5) / theta;
+    const double b = numStdSevs * std::sqrt((1.0 - theta) / theta);
+    const double d = 0.5 * b * std::sqrt((b * b) + (4.0 * n_hat));
+    const double center = n_hat + (0.5 * (b * b));
+    return (center + d);
+  }
+
+  // This is a special purpose calculator for NStar, using a computational
+  // strategy inspired by its Bayesian definition. It is only appropriate
+  // for a very limited set of inputs. However, the procedure
+  // compute_approx_binomial_lower_bound() below does in fact only call it for
+  // suitably limited inputs. Outside of this limited range, two different bad
+  // things will happen. First, because we are not using logarithms, the values
+  // of intermediate quantities will exceed the dynamic range of doubles.
+  // Second, even if that problem were fixed, the running time of this procedure
+  // is essentially linear in est = (numSamples / p), and that can be Very, Very
+  // Big.
+  static unsigned long long
+  specialNStar(unsigned long long numSamples, double p, double delta) {
+    const double q = 1.0 - p;
+    // Use a different algorithm if the following is true; this one will be too
+    // slow, or worse.
+    if ((numSamples / p) >= 500.0)
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "out of range",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+    double cur_term =
+        std::pow(p, numSamples); // curTerm = posteriorProbability (k, k, p)
+    if (cur_term <= 1e-100)
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "out of range",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/); // sanity check for non-use of logarithms
+    double tot = cur_term;
+    unsigned long long m = numSamples;
+    while (tot <= delta) { // this test can fail even the first time
+      cur_term = (cur_term * q * (m)) / ((m + 1) - numSamples);
+      tot += cur_term;
+      m += 1;
+    }
+    // we have reached a state where tot > delta, so back up one
+    return (m - 1);
+  }
+
+  //  The following procedure has very limited applicability.
+  //  The above remarks about special_n_star() also apply here.
+  static unsigned long long
+  specialNPrimeB(unsigned long long numSamples, double p, double delta) {
+    const double q = 1.0 - p;
+    const double oneMinusDelta = 1.0 - delta;
+    double curTerm =
+        std::pow(p, numSamples); // curTerm = posteriorProbability (k, k, p)
+    if (curTerm <= 1e-100)
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "out of range",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/); // sanity check for non-use of logarithms
+    double tot = curTerm;
+    unsigned long long m = numSamples;
+    while (tot < oneMinusDelta) {
+      curTerm = (curTerm * q * (m)) / ((m + 1) - numSamples);
+      tot += curTerm;
+      m += 1;
+    }
+    return m; // no need to back up
+  }
+
+  static unsigned long long
+  specialNPrimeF(unsigned long long numSamples, double p, double delta) {
+    // Use a different algorithm if the following is true; this one will be too
+    // slow, or worse.
+    if ((numSamples / p) >= 500.0)
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "out of range",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/); // A super-small delta could also make it slow.
+    return specialNPrimeB(numSamples + 1, p, delta);
+  }
+
+  // The following computes an approximation to the lower bound of a Frequentist
+  // confidence interval based on the tails of the Binomial distribution.
+  static double computeApproxBinomialLowerBound(
+      unsigned long long numSamples,
+      double theta,
+      unsigned numStdDevs) {
+    if (theta == 1)
+      return static_cast<double>(numSamples);
+    if (numSamples == 0)
+      return 0;
+    if (numSamples == 1) {
+      const double delta = deltaOfNumStdDevs[numStdDevs];
+      const double rawLb = std::log(1 - delta) / std::log(1 - theta);
+      return std::floor(rawLb); // round down
+    }
+    if (numSamples > 120) {
+      // plenty of samples, so gaussian approximation to binomial distribution
+      // isn't too bad
+      const double rawLb = contClassicLb(numSamples, theta, numStdDevs);
+      return (rawLb - 0.5); // fake round down
+    }
+    // at this point we know 2 <= num_samples <= 120
+    if (theta > (1 - 1e-5)) { // empirically-determined threshold
+      return static_cast<double>(numSamples);
+    }
+    if (theta < (numSamples / 360.0)) { // empirically-determined threshold
+      // here we use the Gaussian approximation, but with a modified
+      // num_std_devs
+      const unsigned index =
+          3 * static_cast<unsigned>(numSamples) + (numStdDevs - 1);
+      const double rawLb =
+          contClassicLb(numSamples, theta, lbEquivTable[index]);
+      return rawLb - 0.5; // fake round down
+    }
+    // This is the most difficult range to approximate; we will compute an
+    // "exact" LB. We know that est <= 360, so specialNStar() shouldn't be
+    // ridiculously slow.
+    const double delta = deltaOfNumStdDevs[numStdDevs];
+    return static_cast<double>(
+        specialNStar(numSamples, theta, delta)); // no need to round
+  }
+
+  // The following computes an approximation to the upper bound of a Frequentist
+  // confidence interval based on the tails of the Binomial distribution.
+  static double computeApproxBinomialUpperBound(
+      unsigned long long numSamples,
+      double theta,
+      unsigned numStdDevs) {
+    if (theta == 1)
+      return static_cast<double>(numSamples);
+    if (numSamples == 0) {
+      const double delta = deltaOfNumStdDevs[numStdDevs];
+      const double raw_ub = std::log(delta) / std::log(1 - theta);
+      return std::ceil(raw_ub); // round up
+    }
+    if (numSamples > 120) {
+      // plenty of samples, so gaussian approximation to binomial distribution
+      // isn't too bad
+      const double raw_ub = contClassicUb(numSamples, theta, numStdDevs);
+      return (raw_ub + 0.5); // fake round up
+    }
+    // at this point we know 2 <= num_samples <= 120
+    if (theta > (1 - 1e-5)) { // empirically-determined threshold
+      return static_cast<double>(numSamples + 1);
+    }
+    if (theta < (numSamples / 360.0)) { // empirically-determined threshold
+      // here we use the Gaussian approximation, but with a modified
+      // num_std_devs
+      const unsigned index =
+          3 * static_cast<unsigned>(numSamples) + (numStdDevs - 1);
+      const double raw_ub =
+          contClassicUb(numSamples, theta, ubEquivTable[index]);
+      return raw_ub + 0.5; // fake round up
+    }
+    // This is the most difficult range to approximate; we will compute an
+    // "exact" UB. We know that est <= 360, so specialNPrimeF() shouldn't be
+    // ridiculously slow.
+    const double delta = deltaOfNumStdDevs[numStdDevs];
+    return static_cast<double>(
+        specialNPrimeF(numSamples, theta, delta)); // no need to round
+  }
+
+  static void checkTheta(double theta) {
+    if (theta < 0 || theta > 1) {
+      throw VeloxUserError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "theta must be in [0, 1]",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+    }
+  }
+
+  static void checkNumStdDevs(unsigned numStdDevs) {
+    if (numStdDevs < 1 || numStdDevs > 3) {
+      throw VeloxUserError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "num_std_devs must be 1, 2 or 3",
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+    }
+  }
+};
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/BitPacking.h b/velox/external/theta/BitPacking.h
new file mode 100644
index 00000000000..e964e1316a8
--- /dev/null
+++ b/velox/external/theta/BitPacking.h
@@ -0,0 +1,6552 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "velox/common/base/Exceptions.h"
+
+#include <memory>
+#include <string>
+
+namespace facebook::velox::common::theta {
+
+static inline uint8_t
+packBits(uint64_t value, uint8_t bits, uint8_t*& ptr, uint8_t offset) {
+  if (offset > 0) {
+    const uint8_t chunkBits = 8 - offset;
+    const uint8_t mask = (1 << chunkBits) - 1;
+    if (bits < chunkBits) {
+      *ptr |= (value << (chunkBits - bits)) & mask;
+      return offset + bits;
+    }
+    *ptr++ |= (value >> (bits - chunkBits)) & mask;
+    bits -= chunkBits;
+  }
+  while (bits >= 8) {
+    *ptr++ = static_cast<uint8_t>(value >> (bits - 8));
+    bits -= 8;
+  }
+  if (bits > 0) {
+    *ptr = static_cast<uint8_t>(value << (8 - bits));
+    return bits;
+  }
+  return 0;
+}
+
+static inline uint8_t
+unpackBits(uint64_t& value, uint8_t bits, const uint8_t*& ptr, uint8_t offset) {
+  const uint8_t availBits = 8 - offset;
+  const uint8_t chunkBits = std::min(availBits, bits);
+  const uint8_t mask = (1 << chunkBits) - 1;
+  value = (*ptr >> (availBits - chunkBits)) & mask;
+  ptr += availBits == chunkBits;
+  offset = (offset + chunkBits) & 7;
+  bits -= chunkBits;
+  while (bits >= 8) {
+    value <<= 8;
+    value |= *ptr++;
+    bits -= 8;
+  }
+  if (bits > 0) {
+    value <<= bits;
+    value |= *ptr >> (8 - bits);
+    return bits;
+  }
+  return offset;
+}
+
+// pack given number of bits from a block of 8 64-bit values into bytes
+// we don't need 0 and 64 bits
+// we assume that higher bits (which we are not packing) are zeros
+// this assumption allows to avoid masking operations
+
+static inline void packBits1(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr |= static_cast<uint8_t>(values[1] << 6);
+  *ptr |= static_cast<uint8_t>(values[2] << 5);
+  *ptr |= static_cast<uint8_t>(values[3] << 4);
+  *ptr |= static_cast<uint8_t>(values[4] << 3);
+  *ptr |= static_cast<uint8_t>(values[5] << 2);
+  *ptr |= static_cast<uint8_t>(values[6] << 1);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits2(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr |= static_cast<uint8_t>(values[1] << 4);
+  *ptr |= static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3]);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr |= static_cast<uint8_t>(values[5] << 4);
+  *ptr |= static_cast<uint8_t>(values[6] << 2);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits3(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr |= static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr |= static_cast<uint8_t>(values[3] << 4);
+  *ptr |= static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr |= static_cast<uint8_t>(values[6] << 3);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits4(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1]);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3]);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5]);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits5(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr |= static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr |= static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits6(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3]);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits7(const uint64_t* values, uint8_t* ptr) {
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr |= static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits8(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0]);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits9(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits10(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits11(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits12(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits13(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits14(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits15(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits16(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits17(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits18(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits19(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 15);
+
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits20(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits21(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 19);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits22(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits23(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 21);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 19);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits24(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits25(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 19);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 21);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 23);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits26(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 24);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits27(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 19);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 25);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 23);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 26);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 21);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits28(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits29(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 21);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 26);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 23);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 15);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 28);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 25);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 17);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 22);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 27);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 19);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits30(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits31(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits32(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits33(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits34(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits35(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits36(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits37(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits38(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits39(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits40(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits41(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits42(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits43(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits44(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits45(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits46(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits47(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits48(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits49(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits50(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits51(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits52(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits53(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits54(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits55(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 53);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits56(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[0]);
+
+  *ptr++ = static_cast<uint8_t>(values[1] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[2]);
+
+  *ptr++ = static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[4]);
+
+  *ptr++ = static_cast<uint8_t>(values[5] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[6]);
+
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits57(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[0] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[2] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 53);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[4] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 55);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[6] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits58(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[0] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[2] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[4] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[6] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits59(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[0] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 57);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[2] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 55);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[4] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 58);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 53);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[6] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits60(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[0] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[1]);
+
+  *ptr++ = static_cast<uint8_t>(values[2] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[2] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[4] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[5]);
+
+  *ptr++ = static_cast<uint8_t>(values[6] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[6] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits61(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 53);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[0] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 58);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[1] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 55);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[2] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 60);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 57);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[4] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[5] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 59);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[6] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits62(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[0] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 60);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[1] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 58);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[2] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 8);
+  *ptr++ = static_cast<uint8_t>(values[3]);
+
+  *ptr++ = static_cast<uint8_t>(values[4] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[4] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 60);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[5] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 58);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[6] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void packBits63(const uint64_t* values, uint8_t* ptr) {
+  *ptr++ = static_cast<uint8_t>(values[0] >> 55);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 47);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 39);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 31);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 23);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 15);
+  *ptr++ = static_cast<uint8_t>(values[0] >> 7);
+
+  *ptr = static_cast<uint8_t>(values[0] << 1);
+  *ptr++ |= static_cast<uint8_t>(values[1] >> 62);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 54);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 46);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 38);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 30);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 22);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 14);
+  *ptr++ = static_cast<uint8_t>(values[1] >> 6);
+
+  *ptr = static_cast<uint8_t>(values[1] << 2);
+  *ptr++ |= static_cast<uint8_t>(values[2] >> 61);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 53);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 45);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 37);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 29);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 21);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 13);
+  *ptr++ = static_cast<uint8_t>(values[2] >> 5);
+
+  *ptr = static_cast<uint8_t>(values[2] << 3);
+  *ptr++ |= static_cast<uint8_t>(values[3] >> 60);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 52);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 44);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 36);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 28);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 20);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 12);
+  *ptr++ = static_cast<uint8_t>(values[3] >> 4);
+
+  *ptr = static_cast<uint8_t>(values[3] << 4);
+  *ptr++ |= static_cast<uint8_t>(values[4] >> 59);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 51);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 43);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 35);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 27);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 19);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 11);
+  *ptr++ = static_cast<uint8_t>(values[4] >> 3);
+
+  *ptr = static_cast<uint8_t>(values[4] << 5);
+  *ptr++ |= static_cast<uint8_t>(values[5] >> 58);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 50);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 42);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 34);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 26);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 18);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 10);
+  *ptr++ = static_cast<uint8_t>(values[5] >> 2);
+
+  *ptr = static_cast<uint8_t>(values[5] << 6);
+  *ptr++ |= static_cast<uint8_t>(values[6] >> 57);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 49);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 41);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 33);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 25);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 17);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 9);
+  *ptr++ = static_cast<uint8_t>(values[6] >> 1);
+
+  *ptr = static_cast<uint8_t>(values[6] << 7);
+  *ptr++ |= static_cast<uint8_t>(values[7] >> 56);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 48);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 40);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 32);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 24);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 16);
+  *ptr++ = static_cast<uint8_t>(values[7] >> 8);
+  *ptr = static_cast<uint8_t>(values[7]);
+}
+
+static inline void unpackBits1(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 7;
+  values[1] = (*ptr >> 6) & 1;
+  values[2] = (*ptr >> 5) & 1;
+  values[3] = (*ptr >> 4) & 1;
+  values[4] = (*ptr >> 3) & 1;
+  values[5] = (*ptr >> 2) & 1;
+  values[6] = (*ptr >> 1) & 1;
+  values[7] = *ptr & 1;
+}
+
+static inline void unpackBits2(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 6;
+  values[1] = (*ptr >> 4) & 3;
+  values[2] = (*ptr >> 2) & 3;
+  values[3] = *ptr++ & 3;
+  values[4] = *ptr >> 6;
+  values[5] = (*ptr >> 4) & 3;
+  values[6] = (*ptr >> 2) & 3;
+  values[7] = *ptr & 3;
+}
+
+static inline void unpackBits3(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 5;
+  values[1] = (*ptr >> 2) & 7;
+  values[2] = (*ptr++ & 3) << 1;
+  values[2] |= *ptr >> 7;
+  values[3] = (*ptr >> 4) & 7;
+  values[4] = (*ptr >> 1) & 7;
+  values[5] = (*ptr++ & 1) << 2;
+  values[5] |= *ptr >> 6;
+  values[6] = (*ptr >> 3) & 7;
+  values[7] = *ptr & 7;
+}
+
+static inline void unpackBits4(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 4;
+  values[1] = *ptr++ & 0xf;
+  values[2] = *ptr >> 4;
+  values[3] = *ptr++ & 0xf;
+  values[4] = *ptr >> 4;
+  values[5] = *ptr++ & 0xf;
+  values[6] = *ptr >> 4;
+  values[7] = *ptr & 0xf;
+}
+
+static inline void unpackBits5(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 3;
+
+  values[1] = (*ptr++ & 7) << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr >> 1) & 0x1f;
+
+  values[3] = (*ptr++ & 1) << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = (*ptr >> 2) & 0x1f;
+
+  values[6] = (*ptr++ & 3) << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = *ptr & 0x1f;
+}
+
+static inline void unpackBits6(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 2;
+
+  values[1] = (*ptr++ & 3) << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = *ptr++ & 0x3f;
+
+  values[4] = *ptr >> 2;
+
+  values[5] = (*ptr++ & 3) << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = *ptr & 0x3f;
+}
+
+static inline void unpackBits7(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr >> 1;
+
+  values[1] = (*ptr++ & 1) << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = (*ptr++ & 3) << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = (*ptr++ & 7) << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = (*ptr++ & 0x1f) << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = *ptr & 0x7f;
+}
+
+static inline void unpackBits8(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++;
+  values[1] = *ptr++;
+  values[2] = *ptr++;
+  values[3] = *ptr++;
+  values[4] = *ptr++;
+  values[5] = *ptr++;
+  values[6] = *ptr++;
+  values[7] = *ptr;
+}
+
+static inline void unpackBits9(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = (*ptr++ & 0x7f) << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = (*ptr++ & 0x1f) << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = (*ptr++ & 7) << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = (*ptr++ & 3) << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = (*ptr++ & 1) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits10(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = (*ptr++ & 0x3f) << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = (*ptr++ & 3) << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = (*ptr++ & 0x3f) << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = (*ptr++ & 3) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits11(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = (*ptr++ & 0x1f) << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = (*ptr++ & 3) << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = (*ptr++ & 0x7f) << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = (*ptr++ & 1) << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = (*ptr++ & 7) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits12(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = (*ptr++ & 0xf) << 8;
+  values[1] |= *ptr++;
+
+  values[2] = *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = (*ptr++ & 0xf) << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = (*ptr++ & 0xf) << 8;
+  values[5] |= *ptr++;
+
+  values[6] = *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = (*ptr++ & 0xf) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits13(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = (*ptr++ & 7) << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = (*ptr++ & 1) << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = (*ptr++ & 0x7f) << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = (*ptr++ & 3) << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = (*ptr++ & 0x1f) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits14(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = (*ptr++ & 3) << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = (*ptr++ & 0x3f) << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = (*ptr++ & 3) << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = (*ptr++ & 0x3f) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits15(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = (*ptr++ & 1) << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = (*ptr++ & 3) << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = (*ptr++ & 7) << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = (*ptr++ & 0x1f) << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = (*ptr++ & 0x7f) << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits16(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits17(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = (*ptr++ & 0x7f) << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = (*ptr++ & 0x1f) << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = (*ptr++ & 7) << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = (*ptr++ & 3) << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = (*ptr++ & 1) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits18(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = (*ptr++ & 0x3f) << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = (*ptr++ & 3) << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = (*ptr++ & 0x3f) << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = (*ptr++ & 3) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits19(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = (*ptr++ & 0x1f) << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = (*ptr++ & 3) << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = (*ptr++ & 0x7f) << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = (*ptr++ & 1) << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = (*ptr++ & 7) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits20(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = (*ptr++ & 0xf) << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = (*ptr++ & 0xf) << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = (*ptr++ & 0xf) << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = (*ptr++ & 0xf) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits21(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = (*ptr++ & 7) << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = (*ptr++ & 1) << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = (*ptr++ & 0x7f) << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = (*ptr++ & 3) << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = (*ptr++ & 0x1f) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits22(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = (*ptr++ & 3) << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = (*ptr++ & 0x3f) << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = (*ptr++ & 3) << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = (*ptr++ & 0x3f) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits23(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = (*ptr++ & 1) << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = (*ptr++ & 3) << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = (*ptr++ & 7) << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = (*ptr++ & 0x1f) << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = (*ptr++ & 0x7f) << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits24(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 16;
+  values[0] |= *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = *ptr++ << 16;
+  values[2] |= *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = *ptr++ << 16;
+  values[4] |= *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = *ptr++ << 16;
+  values[6] |= *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits25(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 17;
+  values[0] |= *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = (*ptr++ & 0x7f) << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 19;
+  values[2] |= *ptr++ << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = (*ptr++ & 0x1f) << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 21;
+  values[4] |= *ptr++ << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = (*ptr++ & 7) << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = (*ptr++ & 3) << 23;
+  values[6] |= *ptr++ << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 1) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits26(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 18;
+  values[0] |= *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = (*ptr++ & 0x3f) << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = (*ptr++ & 0xf) << 22;
+  values[2] |= *ptr++ << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 3) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 18;
+  values[4] |= *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = (*ptr++ & 0x3f) << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = (*ptr++ & 0xf) << 22;
+  values[6] |= *ptr++ << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 3) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits27(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 19;
+  values[0] |= *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = (*ptr++ & 0x1f) << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 25;
+  values[2] |= *ptr++ << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = (*ptr++ & 0x7f) << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = (*ptr++ & 0xf) << 23;
+  values[4] |= *ptr++ << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 1) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = (*ptr++ & 0x3f) << 21;
+  values[6] |= *ptr++ << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 7) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits28(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 20;
+  values[0] |= *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0xf) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = *ptr++ << 20;
+  values[2] |= *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0xf) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 20;
+  values[4] |= *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0xf) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = *ptr++ << 20;
+  values[6] |= *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0xf) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits29(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 21;
+  values[0] |= *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 7) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = (*ptr++ & 0x3f) << 23;
+  values[2] |= *ptr++ << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 1) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 25;
+  values[4] |= *ptr++ << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = (*ptr++ & 0x7f) << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 27;
+  values[6] |= *ptr++ << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x1f) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits30(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 22;
+  values[0] |= *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 3) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 26;
+  values[2] |= *ptr++ << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x3f) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = *ptr++ << 22;
+  values[4] |= *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 3) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 26;
+  values[6] |= *ptr++ << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x3f) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits31(uint64_t* values, const uint8_t* ptr) {
+  values[0] = *ptr++ << 23;
+  values[0] |= *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 1) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 29;
+  values[2] |= *ptr++ << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 7) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 27;
+  values[4] |= *ptr++ << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x1f) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 25;
+  values[6] |= *ptr++ << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x7f) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits32(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 24;
+  values[0] |= *ptr++ << 16;
+  values[0] |= *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = static_cast<uint64_t>(*ptr++) << 24;
+  values[2] |= *ptr++ << 16;
+  values[2] |= *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = static_cast<uint64_t>(*ptr++) << 24;
+  values[4] |= *ptr++ << 16;
+  values[4] |= *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = static_cast<uint64_t>(*ptr++) << 24;
+  values[6] |= *ptr++ << 16;
+  values[6] |= *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits33(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 25;
+  values[0] |= *ptr++ << 17;
+  values[0] |= *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x7f) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 27;
+  values[2] |= *ptr++ << 19;
+  values[2] |= *ptr++ << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x1f) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 29;
+  values[4] |= *ptr++ << 21;
+  values[4] |= *ptr++ << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 7) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 31;
+  values[6] |= *ptr++ << 23;
+  values[6] |= *ptr++ << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 1) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits34(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 26;
+  values[0] |= *ptr++ << 18;
+  values[0] |= *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x3f) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 30;
+  values[2] |= *ptr++ << 22;
+  values[2] |= *ptr++ << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 3) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 26;
+  values[4] |= *ptr++ << 18;
+  values[4] |= *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x3f) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 30;
+  values[6] |= *ptr++ << 22;
+  values[6] |= *ptr++ << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 3) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr++;
+}
+
+static inline void unpackBits35(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 27;
+  values[0] |= *ptr++ << 19;
+  values[0] |= *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x1f) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 33;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[2] |= *ptr++ << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x7f) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 31;
+  values[4] |= *ptr++ << 23;
+  values[4] |= *ptr++ << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 1) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 29;
+  values[6] |= *ptr++ << 21;
+  values[6] |= *ptr++ << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 7) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits36(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 28;
+  values[0] |= *ptr++ << 20;
+  values[0] |= *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0xf) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = static_cast<uint64_t>(*ptr++) << 28;
+  values[2] |= *ptr++ << 20;
+  values[2] |= *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0xf) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 28;
+  values[4] |= *ptr++ << 20;
+  values[4] |= *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0xf) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = static_cast<uint64_t>(*ptr++) << 28;
+  values[6] |= *ptr++ << 20;
+  values[6] |= *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0xf) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits37(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 29;
+  values[0] |= *ptr++ << 21;
+  values[0] |= *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 7) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 31;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 23;
+  values[2] |= *ptr++ << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 1) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 33;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[4] |= *ptr++ << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x7f) << 30;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 35;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[6] |= *ptr++ << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x1f) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits38(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 30;
+  values[0] |= *ptr++ << 22;
+  values[0] |= *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 3) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 34;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[2] |= *ptr++ << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x3f) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 30;
+  values[4] |= *ptr++ << 22;
+  values[4] |= *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 3) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 34;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[6] |= *ptr++ << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x3f) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits39(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 31;
+  values[0] |= *ptr++ << 23;
+  values[0] |= *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 1) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 37;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[2] |= *ptr++ << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 7) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 35;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[4] |= *ptr++ << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x1f) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 33;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[6] |= *ptr++ << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x7f) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits40(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 32;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[0] |= *ptr++ << 16;
+  values[0] |= *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = static_cast<uint64_t>(*ptr++) << 32;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[2] |= *ptr++ << 16;
+  values[2] |= *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = static_cast<uint64_t>(*ptr++) << 32;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[4] |= *ptr++ << 16;
+  values[4] |= *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = static_cast<uint64_t>(*ptr++) << 32;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[6] |= *ptr++ << 16;
+  values[6] |= *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits41(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 33;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[0] |= *ptr++ << 17;
+  values[0] |= *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x7f) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 35;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[2] |= *ptr++ << 19;
+  values[2] |= *ptr++ << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x1f) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 37;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[4] |= *ptr++ << 21;
+  values[4] |= *ptr++ << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 7) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 39;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[6] |= *ptr++ << 23;
+  values[6] |= *ptr++ << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 1) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits42(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 34;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[0] |= *ptr++ << 18;
+  values[0] |= *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x3f) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 38;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[2] |= *ptr++ << 22;
+  values[2] |= *ptr++ << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 3) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 34;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[4] |= *ptr++ << 18;
+  values[4] |= *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x3f) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 38;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[6] |= *ptr++ << 22;
+  values[6] |= *ptr++ << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 3) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits43(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 35;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[0] |= *ptr++ << 19;
+  values[0] |= *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x1f) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 41;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[2] |= *ptr++ << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x7f) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 39;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[4] |= *ptr++ << 23;
+  values[4] |= *ptr++ << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 1) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 37;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[6] |= *ptr++ << 21;
+  values[6] |= *ptr++ << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 7) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits44(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 36;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[0] |= *ptr++ << 20;
+  values[0] |= *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0xf) << 40;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = static_cast<uint64_t>(*ptr++) << 36;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[2] |= *ptr++ << 20;
+  values[2] |= *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0xf) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 36;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[4] |= *ptr++ << 20;
+  values[4] |= *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0xf) << 40;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = static_cast<uint64_t>(*ptr++) << 36;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[6] |= *ptr++ << 20;
+  values[6] |= *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0xf) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits45(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 37;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[0] |= *ptr++ << 21;
+  values[0] |= *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 7) << 42;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 39;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 23;
+  values[2] |= *ptr++ << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 1) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 41;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[4] |= *ptr++ << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x7f) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 43;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[6] |= *ptr++ << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x1f) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits46(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 38;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[0] |= *ptr++ << 22;
+  values[0] |= *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 3) << 44;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 42;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[2] |= *ptr++ << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x3f) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 38;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[4] |= *ptr++ << 22;
+  values[4] |= *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 3) << 44;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 42;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[6] |= *ptr++ << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x3f) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits47(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 39;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[0] |= *ptr++ << 23;
+  values[0] |= *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 1) << 46;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 45;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[2] |= *ptr++ << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 7) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 43;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[4] |= *ptr++ << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x1f) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 41;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[6] |= *ptr++ << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x7f) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits48(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 40;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[0] |= *ptr++ << 16;
+  values[0] |= *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = static_cast<uint64_t>(*ptr++) << 40;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = static_cast<uint64_t>(*ptr++) << 40;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[2] |= *ptr++ << 16;
+  values[2] |= *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = static_cast<uint64_t>(*ptr++) << 40;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[4] |= *ptr++ << 16;
+  values[4] |= *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = static_cast<uint64_t>(*ptr++) << 40;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = static_cast<uint64_t>(*ptr++) << 40;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[6] |= *ptr++ << 16;
+  values[6] |= *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits49(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 41;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[0] |= *ptr++ << 17;
+  values[0] |= *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x7f) << 42;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 43;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[2] |= *ptr++ << 19;
+  values[2] |= *ptr++ << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x1f) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 45;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[4] |= *ptr++ << 21;
+  values[4] |= *ptr++ << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 7) << 46;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 47;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[6] |= *ptr++ << 23;
+  values[6] |= *ptr++ << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 1) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits50(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 42;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[0] |= *ptr++ << 18;
+  values[0] |= *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x3f) << 44;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 46;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[2] |= *ptr++ << 22;
+  values[2] |= *ptr++ << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 3) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 42;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[4] |= *ptr++ << 18;
+  values[4] |= *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x3f) << 44;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 46;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[6] |= *ptr++ << 22;
+  values[6] |= *ptr++ << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 3) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits51(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 43;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[0] |= *ptr++ << 19;
+  values[0] |= *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x1f) << 46;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 49;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[2] |= *ptr++ << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x7f) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 47;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[4] |= *ptr++ << 23;
+  values[4] |= *ptr++ << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 1) << 50;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 45;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[6] |= *ptr++ << 21;
+  values[6] |= *ptr++ << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 7) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits52(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 44;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[0] |= *ptr++ << 20;
+  values[0] |= *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0xf) << 48;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = static_cast<uint64_t>(*ptr++) << 44;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[2] |= *ptr++ << 20;
+  values[2] |= *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0xf) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 44;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[4] |= *ptr++ << 20;
+  values[4] |= *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0xf) << 48;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = static_cast<uint64_t>(*ptr++) << 44;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[6] |= *ptr++ << 20;
+  values[6] |= *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0xf) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits53(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 45;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[0] |= *ptr++ << 21;
+  values[0] |= *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 7) << 50;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 47;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 23;
+  values[2] |= *ptr++ << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 1) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 49;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[4] |= *ptr++ << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x7f) << 46;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 51;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[6] |= *ptr++ << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x1f) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits54(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 46;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[0] |= *ptr++ << 22;
+  values[0] |= *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 3) << 52;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 50;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[2] |= *ptr++ << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x3f) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 46;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[4] |= *ptr++ << 22;
+  values[4] |= *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 3) << 52;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 50;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[6] |= *ptr++ << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x3f) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr++;
+}
+
+static inline void unpackBits55(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 47;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[0] |= *ptr++ << 23;
+  values[0] |= *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 1) << 54;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 53;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 45;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[2] |= *ptr++ << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 7) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 51;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[4] |= *ptr++ << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x1f) << 50;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 49;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[6] |= *ptr++ << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x7f) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits56(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 48;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[0] |= *ptr++ << 16;
+  values[0] |= *ptr++ << 8;
+  values[0] |= *ptr++;
+  values[1] = static_cast<uint64_t>(*ptr++) << 48;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+  values[2] = static_cast<uint64_t>(*ptr++) << 48;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[2] |= *ptr++ << 16;
+  values[2] |= *ptr++ << 8;
+  values[2] |= *ptr++;
+  values[3] = static_cast<uint64_t>(*ptr++) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+  values[4] = static_cast<uint64_t>(*ptr++) << 48;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[4] |= *ptr++ << 16;
+  values[4] |= *ptr++ << 8;
+  values[4] |= *ptr++;
+  values[5] = static_cast<uint64_t>(*ptr++) << 48;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+  values[6] = static_cast<uint64_t>(*ptr++) << 48;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[6] |= *ptr++ << 16;
+  values[6] |= *ptr++ << 8;
+  values[6] |= *ptr++;
+  values[7] = static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits57(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 49;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[0] |= *ptr++ << 17;
+  values[0] |= *ptr++ << 9;
+  values[0] |= *ptr++ << 1;
+  values[0] |= *ptr >> 7;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x7f) << 50;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 51;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[2] |= *ptr++ << 19;
+  values[2] |= *ptr++ << 11;
+  values[2] |= *ptr++ << 3;
+  values[2] |= *ptr >> 5;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x1f) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 53;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 45;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[4] |= *ptr++ << 21;
+  values[4] |= *ptr++ << 13;
+  values[4] |= *ptr++ << 5;
+  values[4] |= *ptr >> 3;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 7) << 54;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 55;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 47;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[6] |= *ptr++ << 23;
+  values[6] |= *ptr++ << 15;
+  values[6] |= *ptr++ << 7;
+  values[6] |= *ptr >> 1;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 1) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits58(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 50;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[0] |= *ptr++ << 18;
+  values[0] |= *ptr++ << 10;
+  values[0] |= *ptr++ << 2;
+  values[0] |= *ptr >> 6;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x3f) << 52;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 54;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[2] |= *ptr++ << 22;
+  values[2] |= *ptr++ << 14;
+  values[2] |= *ptr++ << 6;
+  values[2] |= *ptr >> 2;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 3) << 56;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 50;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[4] |= *ptr++ << 18;
+  values[4] |= *ptr++ << 10;
+  values[4] |= *ptr++ << 2;
+  values[4] |= *ptr >> 6;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x3f) << 52;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 54;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[6] |= *ptr++ << 22;
+  values[6] |= *ptr++ << 14;
+  values[6] |= *ptr++ << 6;
+  values[6] |= *ptr >> 2;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 3) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr++;
+}
+
+static inline void unpackBits59(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 51;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[0] |= *ptr++ << 19;
+  values[0] |= *ptr++ << 11;
+  values[0] |= *ptr++ << 3;
+  values[0] |= *ptr >> 5;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0x1f) << 54;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 57;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 49;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[2] |= *ptr++ << 17;
+  values[2] |= *ptr++ << 9;
+  values[2] |= *ptr++ << 1;
+  values[2] |= *ptr >> 7;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x7f) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 55;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 47;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[4] |= *ptr++ << 23;
+  values[4] |= *ptr++ << 15;
+  values[4] |= *ptr++ << 7;
+  values[4] |= *ptr >> 1;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 1) << 58;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 50;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 53;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 45;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[6] |= *ptr++ << 21;
+  values[6] |= *ptr++ << 13;
+  values[6] |= *ptr++ << 5;
+  values[6] |= *ptr >> 3;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 7) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits60(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 52;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[0] |= *ptr++ << 20;
+  values[0] |= *ptr++ << 12;
+  values[0] |= *ptr++ << 4;
+  values[0] |= *ptr >> 4;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 0xf) << 56;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[1] |= *ptr++ << 16;
+  values[1] |= *ptr++ << 8;
+  values[1] |= *ptr++;
+
+  values[2] = static_cast<uint64_t>(*ptr++) << 52;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[2] |= *ptr++ << 20;
+  values[2] |= *ptr++ << 12;
+  values[2] |= *ptr++ << 4;
+  values[2] |= *ptr >> 4;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0xf) << 56;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 52;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[4] |= *ptr++ << 20;
+  values[4] |= *ptr++ << 12;
+  values[4] |= *ptr++ << 4;
+  values[4] |= *ptr >> 4;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0xf) << 56;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[5] |= *ptr++ << 16;
+  values[5] |= *ptr++ << 8;
+  values[5] |= *ptr++;
+
+  values[6] = static_cast<uint64_t>(*ptr++) << 52;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[6] |= *ptr++ << 20;
+  values[6] |= *ptr++ << 12;
+  values[6] |= *ptr++ << 4;
+  values[6] |= *ptr >> 4;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0xf) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits61(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 53;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 45;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[0] |= *ptr++ << 21;
+  values[0] |= *ptr++ << 13;
+  values[0] |= *ptr++ << 5;
+  values[0] |= *ptr >> 3;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 7) << 58;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 50;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[1] |= *ptr++ << 18;
+  values[1] |= *ptr++ << 10;
+  values[1] |= *ptr++ << 2;
+  values[1] |= *ptr >> 6;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0x3f) << 55;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 47;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[2] |= *ptr++ << 23;
+  values[2] |= *ptr++ << 15;
+  values[2] |= *ptr++ << 7;
+  values[2] |= *ptr >> 1;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 1) << 60;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 57;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 49;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[4] |= *ptr++ << 17;
+  values[4] |= *ptr++ << 9;
+  values[4] |= *ptr++ << 1;
+  values[4] |= *ptr >> 7;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x7f) << 54;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[5] |= *ptr++ << 22;
+  values[5] |= *ptr++ << 14;
+  values[5] |= *ptr++ << 6;
+  values[5] |= *ptr >> 2;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 3) << 59;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 51;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[6] |= *ptr++ << 19;
+  values[6] |= *ptr++ << 11;
+  values[6] |= *ptr++ << 3;
+  values[6] |= *ptr >> 5;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x1f) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits62(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 54;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[0] |= *ptr++ << 22;
+  values[0] |= *ptr++ << 14;
+  values[0] |= *ptr++ << 6;
+  values[0] |= *ptr >> 2;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 3) << 60;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 52;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[1] |= *ptr++ << 20;
+  values[1] |= *ptr++ << 12;
+  values[1] |= *ptr++ << 4;
+  values[1] |= *ptr >> 4;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 0xf) << 58;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 50;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[2] |= *ptr++ << 18;
+  values[2] |= *ptr++ << 10;
+  values[2] |= *ptr++ << 2;
+  values[2] |= *ptr >> 6;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 0x3f) << 56;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[3] |= *ptr++ << 16;
+  values[3] |= *ptr++ << 8;
+  values[3] |= *ptr++;
+
+  values[4] = static_cast<uint64_t>(*ptr++) << 54;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[4] |= *ptr++ << 22;
+  values[4] |= *ptr++ << 14;
+  values[4] |= *ptr++ << 6;
+  values[4] |= *ptr >> 2;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 3) << 60;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 52;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[5] |= *ptr++ << 20;
+  values[5] |= *ptr++ << 12;
+  values[5] |= *ptr++ << 4;
+  values[5] |= *ptr >> 4;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0xf) << 58;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 50;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[6] |= *ptr++ << 18;
+  values[6] |= *ptr++ << 10;
+  values[6] |= *ptr++ << 2;
+  values[6] |= *ptr >> 6;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x3f) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void unpackBits63(uint64_t* values, const uint8_t* ptr) {
+  values[0] = static_cast<uint64_t>(*ptr++) << 55;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 47;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 39;
+  values[0] |= static_cast<uint64_t>(*ptr++) << 31;
+  values[0] |= *ptr++ << 23;
+  values[0] |= *ptr++ << 15;
+  values[0] |= *ptr++ << 7;
+  values[0] |= *ptr >> 1;
+
+  values[1] = static_cast<uint64_t>(*ptr++ & 1) << 62;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 54;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 46;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 38;
+  values[1] |= static_cast<uint64_t>(*ptr++) << 30;
+  values[1] |= *ptr++ << 22;
+  values[1] |= *ptr++ << 14;
+  values[1] |= *ptr++ << 6;
+  values[1] |= *ptr >> 2;
+
+  values[2] = static_cast<uint64_t>(*ptr++ & 3) << 61;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 53;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 45;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 37;
+  values[2] |= static_cast<uint64_t>(*ptr++) << 29;
+  values[2] |= *ptr++ << 21;
+  values[2] |= *ptr++ << 13;
+  values[2] |= *ptr++ << 5;
+  values[2] |= *ptr >> 3;
+
+  values[3] = static_cast<uint64_t>(*ptr++ & 7) << 60;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 52;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 44;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 36;
+  values[3] |= static_cast<uint64_t>(*ptr++) << 28;
+  values[3] |= *ptr++ << 20;
+  values[3] |= *ptr++ << 12;
+  values[3] |= *ptr++ << 4;
+  values[3] |= *ptr >> 4;
+
+  values[4] = static_cast<uint64_t>(*ptr++ & 0xf) << 59;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 51;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 43;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 35;
+  values[4] |= static_cast<uint64_t>(*ptr++) << 27;
+  values[4] |= *ptr++ << 19;
+  values[4] |= *ptr++ << 11;
+  values[4] |= *ptr++ << 3;
+  values[4] |= *ptr >> 5;
+
+  values[5] = static_cast<uint64_t>(*ptr++ & 0x1f) << 58;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 50;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 42;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 34;
+  values[5] |= static_cast<uint64_t>(*ptr++) << 26;
+  values[5] |= *ptr++ << 18;
+  values[5] |= *ptr++ << 10;
+  values[5] |= *ptr++ << 2;
+  values[5] |= *ptr >> 6;
+
+  values[6] = static_cast<uint64_t>(*ptr++ & 0x3f) << 57;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 49;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 41;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 33;
+  values[6] |= static_cast<uint64_t>(*ptr++) << 25;
+  values[6] |= *ptr++ << 17;
+  values[6] |= *ptr++ << 9;
+  values[6] |= *ptr++ << 1;
+  values[6] |= *ptr >> 7;
+
+  values[7] = static_cast<uint64_t>(*ptr++ & 0x7f) << 56;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 48;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 40;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 32;
+  values[7] |= static_cast<uint64_t>(*ptr++) << 24;
+  values[7] |= *ptr++ << 16;
+  values[7] |= *ptr++ << 8;
+  values[7] |= *ptr;
+}
+
+static inline void
+packBitsBlock8(const uint64_t* values, uint8_t* ptr, uint8_t bits) {
+  switch (bits) {
+    case 1:
+      packBits1(values, ptr);
+      break;
+    case 2:
+      packBits2(values, ptr);
+      break;
+    case 3:
+      packBits3(values, ptr);
+      break;
+    case 4:
+      packBits4(values, ptr);
+      break;
+    case 5:
+      packBits5(values, ptr);
+      break;
+    case 6:
+      packBits6(values, ptr);
+      break;
+    case 7:
+      packBits7(values, ptr);
+      break;
+    case 8:
+      packBits8(values, ptr);
+      break;
+    case 9:
+      packBits9(values, ptr);
+      break;
+    case 10:
+      packBits10(values, ptr);
+      break;
+    case 11:
+      packBits11(values, ptr);
+      break;
+    case 12:
+      packBits12(values, ptr);
+      break;
+    case 13:
+      packBits13(values, ptr);
+      break;
+    case 14:
+      packBits14(values, ptr);
+      break;
+    case 15:
+      packBits15(values, ptr);
+      break;
+    case 16:
+      packBits16(values, ptr);
+      break;
+    case 17:
+      packBits17(values, ptr);
+      break;
+    case 18:
+      packBits18(values, ptr);
+      break;
+    case 19:
+      packBits19(values, ptr);
+      break;
+    case 20:
+      packBits20(values, ptr);
+      break;
+    case 21:
+      packBits21(values, ptr);
+      break;
+    case 22:
+      packBits22(values, ptr);
+      break;
+    case 23:
+      packBits23(values, ptr);
+      break;
+    case 24:
+      packBits24(values, ptr);
+      break;
+    case 25:
+      packBits25(values, ptr);
+      break;
+    case 26:
+      packBits26(values, ptr);
+      break;
+    case 27:
+      packBits27(values, ptr);
+      break;
+    case 28:
+      packBits28(values, ptr);
+      break;
+    case 29:
+      packBits29(values, ptr);
+      break;
+    case 30:
+      packBits30(values, ptr);
+      break;
+    case 31:
+      packBits31(values, ptr);
+      break;
+    case 32:
+      packBits32(values, ptr);
+      break;
+    case 33:
+      packBits33(values, ptr);
+      break;
+    case 34:
+      packBits34(values, ptr);
+      break;
+    case 35:
+      packBits35(values, ptr);
+      break;
+    case 36:
+      packBits36(values, ptr);
+      break;
+    case 37:
+      packBits37(values, ptr);
+      break;
+    case 38:
+      packBits38(values, ptr);
+      break;
+    case 39:
+      packBits39(values, ptr);
+      break;
+    case 40:
+      packBits40(values, ptr);
+      break;
+    case 41:
+      packBits41(values, ptr);
+      break;
+    case 42:
+      packBits42(values, ptr);
+      break;
+    case 43:
+      packBits43(values, ptr);
+      break;
+    case 44:
+      packBits44(values, ptr);
+      break;
+    case 45:
+      packBits45(values, ptr);
+      break;
+    case 46:
+      packBits46(values, ptr);
+      break;
+    case 47:
+      packBits47(values, ptr);
+      break;
+    case 48:
+      packBits48(values, ptr);
+      break;
+    case 49:
+      packBits49(values, ptr);
+      break;
+    case 50:
+      packBits50(values, ptr);
+      break;
+    case 51:
+      packBits51(values, ptr);
+      break;
+    case 52:
+      packBits52(values, ptr);
+      break;
+    case 53:
+      packBits53(values, ptr);
+      break;
+    case 54:
+      packBits54(values, ptr);
+      break;
+    case 55:
+      packBits55(values, ptr);
+      break;
+    case 56:
+      packBits56(values, ptr);
+      break;
+    case 57:
+      packBits57(values, ptr);
+      break;
+    case 58:
+      packBits58(values, ptr);
+      break;
+    case 59:
+      packBits59(values, ptr);
+      break;
+    case 60:
+      packBits60(values, ptr);
+      break;
+    case 61:
+      packBits61(values, ptr);
+      break;
+    case 62:
+      packBits62(values, ptr);
+      break;
+    case 63:
+      packBits63(values, ptr);
+      break;
+    default:
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "wrong number of bits in packBitsBlock8: " + std::to_string(bits),
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+  }
+}
+
+static inline void
+unpackBitsBlock8(uint64_t* values, const uint8_t* ptr, uint8_t bits) {
+  switch (bits) {
+    case 1:
+      unpackBits1(values, ptr);
+      break;
+    case 2:
+      unpackBits2(values, ptr);
+      break;
+    case 3:
+      unpackBits3(values, ptr);
+      break;
+    case 4:
+      unpackBits4(values, ptr);
+      break;
+    case 5:
+      unpackBits5(values, ptr);
+      break;
+    case 6:
+      unpackBits6(values, ptr);
+      break;
+    case 7:
+      unpackBits7(values, ptr);
+      break;
+    case 8:
+      unpackBits8(values, ptr);
+      break;
+    case 9:
+      unpackBits9(values, ptr);
+      break;
+    case 10:
+      unpackBits10(values, ptr);
+      break;
+    case 11:
+      unpackBits11(values, ptr);
+      break;
+    case 12:
+      unpackBits12(values, ptr);
+      break;
+    case 13:
+      unpackBits13(values, ptr);
+      break;
+    case 14:
+      unpackBits14(values, ptr);
+      break;
+    case 15:
+      unpackBits15(values, ptr);
+      break;
+    case 16:
+      unpackBits16(values, ptr);
+      break;
+    case 17:
+      unpackBits17(values, ptr);
+      break;
+    case 18:
+      unpackBits18(values, ptr);
+      break;
+    case 19:
+      unpackBits19(values, ptr);
+      break;
+    case 20:
+      unpackBits20(values, ptr);
+      break;
+    case 21:
+      unpackBits21(values, ptr);
+      break;
+    case 22:
+      unpackBits22(values, ptr);
+      break;
+    case 23:
+      unpackBits23(values, ptr);
+      break;
+    case 24:
+      unpackBits24(values, ptr);
+      break;
+    case 25:
+      unpackBits25(values, ptr);
+      break;
+    case 26:
+      unpackBits26(values, ptr);
+      break;
+    case 27:
+      unpackBits27(values, ptr);
+      break;
+    case 28:
+      unpackBits28(values, ptr);
+      break;
+    case 29:
+      unpackBits29(values, ptr);
+      break;
+    case 30:
+      unpackBits30(values, ptr);
+      break;
+    case 31:
+      unpackBits31(values, ptr);
+      break;
+    case 32:
+      unpackBits32(values, ptr);
+      break;
+    case 33:
+      unpackBits33(values, ptr);
+      break;
+    case 34:
+      unpackBits34(values, ptr);
+      break;
+    case 35:
+      unpackBits35(values, ptr);
+      break;
+    case 36:
+      unpackBits36(values, ptr);
+      break;
+    case 37:
+      unpackBits37(values, ptr);
+      break;
+    case 38:
+      unpackBits38(values, ptr);
+      break;
+    case 39:
+      unpackBits39(values, ptr);
+      break;
+    case 40:
+      unpackBits40(values, ptr);
+      break;
+    case 41:
+      unpackBits41(values, ptr);
+      break;
+    case 42:
+      unpackBits42(values, ptr);
+      break;
+    case 43:
+      unpackBits43(values, ptr);
+      break;
+    case 44:
+      unpackBits44(values, ptr);
+      break;
+    case 45:
+      unpackBits45(values, ptr);
+      break;
+    case 46:
+      unpackBits46(values, ptr);
+      break;
+    case 47:
+      unpackBits47(values, ptr);
+      break;
+    case 48:
+      unpackBits48(values, ptr);
+      break;
+    case 49:
+      unpackBits49(values, ptr);
+      break;
+    case 50:
+      unpackBits50(values, ptr);
+      break;
+    case 51:
+      unpackBits51(values, ptr);
+      break;
+    case 52:
+      unpackBits52(values, ptr);
+      break;
+    case 53:
+      unpackBits53(values, ptr);
+      break;
+    case 54:
+      unpackBits54(values, ptr);
+      break;
+    case 55:
+      unpackBits55(values, ptr);
+      break;
+    case 56:
+      unpackBits56(values, ptr);
+      break;
+    case 57:
+      unpackBits57(values, ptr);
+      break;
+    case 58:
+      unpackBits58(values, ptr);
+      break;
+    case 59:
+      unpackBits59(values, ptr);
+      break;
+    case 60:
+      unpackBits60(values, ptr);
+      break;
+    case 61:
+      unpackBits61(values, ptr);
+      break;
+    case 62:
+      unpackBits62(values, ptr);
+      break;
+    case 63:
+      unpackBits63(values, ptr);
+      break;
+    default:
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "wrong number of bits in unpackBitsBlock8: " + std::to_string(bits),
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+  }
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/CMakeLists.txt b/velox/external/theta/CMakeLists.txt
new file mode 100644
index 00000000000..9f6182f5e2f
--- /dev/null
+++ b/velox/external/theta/CMakeLists.txt
@@ -0,0 +1,29 @@
+# Copyright (c) Facebook, Inc. and its affiliates.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#     http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+velox_add_library(
+  velox_common_theta
+        CompactThetaSketchParser.cpp
+        ThetaUpdateSketchBase.cpp
+        ThetaSketch.cpp
+        ThetaUnionBase.cpp
+        ThetaUnion.cpp)
+
+velox_link_libraries(
+  velox_common_theta
+  PUBLIC velox_memory
+  PRIVATE velox_exception)
+
+if(${VELOX_BUILD_TESTING})
+  add_subdirectory(tests)
+endif()
diff --git a/velox/external/theta/CommonDefs.h b/velox/external/theta/CommonDefs.h
new file mode 100644
index 00000000000..b5ba42dde07
--- /dev/null
+++ b/velox/external/theta/CommonDefs.h
@@ -0,0 +1,131 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <chrono>
+#include <cstdint>
+#include <iostream>
+#include <memory>
+#include <random>
+#include <string>
+#include <thread>
+
+namespace facebook::velox::common::theta {
+
+static const uint64_t DEFAULT_SEED = 9001;
+
+enum resizeFactor { X1 = 0, X2, X4, X8 };
+
+template <typename A>
+using string = std::basic_string<
+    char,
+    std::char_traits<char>,
+    typename std::allocator_traits<A>::template rebind_alloc<char>>;
+
+// common random declarations
+namespace randomUtils {
+static std::random_device rd; // possibly unsafe in MinGW with GCC < 9.2
+static thread_local std::mt19937_64 rand(rd());
+static thread_local std::uniform_real_distribution<> next_double(0.0, 1.0);
+static thread_local std::uniform_int_distribution<uint64_t> next_uint64(
+    0,
+    UINT64_MAX);
+
+// thread-safe random bit
+static thread_local std::independent_bits_engine<std::mt19937, 1, uint32_t>
+    random_bit(static_cast<uint32_t>(
+        std::chrono::system_clock::now().time_since_epoch().count() +
+        std::hash<std::thread::id>{}(std::this_thread::get_id())));
+
+inline void overrideSeed(uint64_t s) {
+  rand.seed(s);
+}
+} // namespace randomUtils
+
+// utility function to hide unused compiler warning
+// usually has no additional cost
+template <typename T>
+void unused(T&&...) {}
+
+// common helping functions
+// TODO: find a better place for them
+
+constexpr uint8_t log2(uint32_t n) {
+  return (n > 1) ? 1 + log2(n >> 1) : 0;
+}
+
+constexpr uint8_t lgSizeFromCount(uint32_t n, double load_factor) {
+  return log2(n) +
+      ((n > static_cast<uint32_t>((1 << (log2(n) + 1)) * load_factor)) ? 2 : 1);
+}
+
+// stream helpers to hide casts
+template <typename T>
+static inline T read(std::istream& is) {
+  T value;
+  is.read(reinterpret_cast<char*>(&value), sizeof(T));
+  return value;
+}
+
+template <typename T>
+static inline void read(std::istream& is, T* ptr, size_t size_bytes) {
+  is.read(reinterpret_cast<char*>(ptr), size_bytes);
+}
+
+template <typename T>
+static inline void write(std::ostream& os, T value) {
+  os.write(reinterpret_cast<const char*>(&value), sizeof(T));
+}
+
+template <typename T>
+static inline void write(std::ostream& os, const T* ptr, size_t size_bytes) {
+  os.write(reinterpret_cast<const char*>(ptr), size_bytes);
+}
+
+template <typename T>
+T byteswap(T value) {
+  char* ptr = static_cast<char*>(static_cast<void*>(&value));
+  const int len = sizeof(T);
+  for (size_t i = 0; i < len / 2; ++i) {
+    std::swap(ptr[i], ptr[len - i - 1]);
+  }
+  return value;
+}
+
+template <typename T>
+static inline T readBigEndian(std::istream& is) {
+  T value;
+  is.read(reinterpret_cast<char*>(&value), sizeof(T));
+  return byteswap(value);
+}
+
+// wrapper for iterators to implement operator-> returning temporary value
+template <typename T>
+class returnValueHolder {
+ public:
+  returnValueHolder(T value) : value_(value) {}
+  const T* operator->() const {
+    return std::addressof(value_);
+  }
+
+ private:
+  T value_;
+};
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/CompactThetaSketchParser.cpp b/velox/external/theta/CompactThetaSketchParser.cpp
new file mode 100644
index 00000000000..1925f311d71
--- /dev/null
+++ b/velox/external/theta/CompactThetaSketchParser.cpp
@@ -0,0 +1,261 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#ifndef COMPACT_THETA_SKETCH_PARSER_CPP
+#define COMPACT_THETA_SKETCH_PARSER_CPP
+
+#include "CompactThetaSketchParser.h"
+#include "MurmurHash3.h"
+#include "ThetaHelpers.h"
+
+#include <iomanip>
+#include <sstream>
+
+namespace facebook::velox::common::theta {
+
+template <bool dummy>
+auto CompactThetaSketchParser<dummy>::parse(
+    const void* ptr,
+    size_t size,
+    uint64_t seed,
+    bool dump_on_error) -> CompactThetaSketchData {
+  checkMemorySize(ptr, size, 8, dump_on_error);
+  checker<true>::checkSketchType(
+      reinterpret_cast<const uint8_t*>(ptr)[COMPACT_SKETCH_TYPE_BYTE],
+      COMPACT_SKETCH_TYPE);
+  uint8_t serial_version =
+      reinterpret_cast<const uint8_t*>(ptr)[COMPACT_SKETCH_SERIAL_VERSION_BYTE];
+  switch (serial_version) {
+    case 4: {
+      // version 4 sketches are ordered and always have entries (single item in
+      // exact mode is v3)
+      const uint16_t seed_hash =
+          reinterpret_cast<const uint16_t*>(ptr)[COMPACT_SKETCH_SEED_HASH_U16];
+      checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+      const bool has_theta = reinterpret_cast<const uint8_t*>(
+                                 ptr)[COMPACT_SKETCH_PRE_LONGS_BYTE] > 1;
+      uint64_t theta = ThetaConstants::MAX_THETA;
+      if (has_theta) {
+        checkMemorySize(ptr, size, 16, dump_on_error);
+        theta =
+            reinterpret_cast<const uint64_t*>(ptr)[COMPACT_SKETCH_V4_THETA_U64];
+      }
+      const uint8_t num_entries_bytes = reinterpret_cast<const uint8_t*>(
+          ptr)[COMPACT_SKETCH_V4_NUM_ENTRIES_BYTES_BYTE];
+      size_t data_offset_bytes = has_theta
+          ? COMPACT_SKETCH_V4_PACKED_DATA_ESTIMATION_BYTE
+          : COMPACT_SKETCH_V4_PACKED_DATA_EXACT_BYTE;
+      checkMemorySize(
+          ptr, size, data_offset_bytes + num_entries_bytes, dump_on_error);
+      uint32_t num_entries = 0;
+      const uint8_t* num_entries_ptr =
+          reinterpret_cast<const uint8_t*>(ptr) + data_offset_bytes;
+      for (unsigned i = 0; i < num_entries_bytes; ++i) {
+        num_entries |= (*num_entries_ptr++) << (i << 3);
+      }
+      data_offset_bytes += num_entries_bytes;
+      const uint8_t entry_bits = reinterpret_cast<const uint8_t*>(
+          ptr)[COMPACT_SKETCH_V4_ENTRY_BITS_BYTE];
+      const size_t expected_bits = entry_bits * num_entries;
+      const size_t expected_size_bytes =
+          data_offset_bytes + wholeBytesToHoldBits(expected_bits);
+      checkMemorySize(ptr, size, expected_size_bytes, dump_on_error);
+      return {
+          false,
+          true,
+          seed_hash,
+          num_entries,
+          theta,
+          reinterpret_cast<const uint8_t*>(ptr) + data_offset_bytes,
+          entry_bits};
+    }
+    case 3: {
+      uint64_t theta = ThetaConstants::MAX_THETA;
+      const uint16_t seed_hash =
+          reinterpret_cast<const uint16_t*>(ptr)[COMPACT_SKETCH_SEED_HASH_U16];
+      if (reinterpret_cast<const uint8_t*>(ptr)[COMPACT_SKETCH_FLAGS_BYTE] &
+          (1 << COMPACT_SKETCH_IS_EMPTY_FLAG)) {
+        return {true, true, seed_hash, 0, theta, nullptr, 64};
+      }
+      checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+      const bool has_theta = reinterpret_cast<const uint8_t*>(
+                                 ptr)[COMPACT_SKETCH_PRE_LONGS_BYTE] > 2;
+      if (has_theta) {
+        checkMemorySize(
+            ptr,
+            size,
+            (COMPACT_SKETCH_THETA_U64 + 1) * sizeof(uint64_t),
+            dump_on_error);
+        theta =
+            reinterpret_cast<const uint64_t*>(ptr)[COMPACT_SKETCH_THETA_U64];
+      }
+      if (reinterpret_cast<const uint8_t*>(
+              ptr)[COMPACT_SKETCH_PRE_LONGS_BYTE] == 1) {
+        checkMemorySize(ptr, size, 16, dump_on_error);
+        return {
+            false,
+            true,
+            seed_hash,
+            1,
+            theta,
+            reinterpret_cast<const uint64_t*>(ptr) +
+                COMPACT_SKETCH_SINGLE_ENTRY_U64,
+            64};
+      }
+      const uint32_t num_entries = reinterpret_cast<const uint32_t*>(
+          ptr)[COMPACT_SKETCH_NUM_ENTRIES_U32];
+      const size_t entries_start_u64 = has_theta
+          ? COMPACT_SKETCH_ENTRIES_ESTIMATION_U64
+          : COMPACT_SKETCH_ENTRIES_EXACT_U64;
+      const uint64_t* entries =
+          reinterpret_cast<const uint64_t*>(ptr) + entries_start_u64;
+      const size_t expected_size_bytes =
+          (entries_start_u64 + num_entries) * sizeof(uint64_t);
+      checkMemorySize(ptr, size, expected_size_bytes, dump_on_error);
+      const bool is_ordered =
+          reinterpret_cast<const uint8_t*>(ptr)[COMPACT_SKETCH_FLAGS_BYTE] &
+          (1 << COMPACT_SKETCH_IS_ORDERED_FLAG);
+      return {false, is_ordered, seed_hash, num_entries, theta, entries, 64};
+    }
+    case 1: {
+      uint16_t seed_hash = compute_seed_hash(seed);
+      const uint32_t num_entries = reinterpret_cast<const uint32_t*>(
+          ptr)[COMPACT_SKETCH_NUM_ENTRIES_U32];
+      uint64_t theta =
+          reinterpret_cast<const uint64_t*>(ptr)[COMPACT_SKETCH_THETA_U64];
+      bool is_empty =
+          (num_entries == 0) && (theta == ThetaConstants::MAX_THETA);
+      if (is_empty)
+        return {true, true, seed_hash, 0, theta, nullptr, 64};
+      const uint64_t* entries = reinterpret_cast<const uint64_t*>(ptr) +
+          COMPACT_SKETCH_ENTRIES_ESTIMATION_U64;
+      const size_t expected_size_bytes =
+          (COMPACT_SKETCH_ENTRIES_ESTIMATION_U64 + num_entries) *
+          sizeof(uint64_t);
+      checkMemorySize(ptr, size, expected_size_bytes, dump_on_error);
+      return {false, true, seed_hash, num_entries, theta, entries, 64};
+    }
+    case 2: {
+      uint8_t preamble_size =
+          reinterpret_cast<const uint8_t*>(ptr)[COMPACT_SKETCH_PRE_LONGS_BYTE];
+      const uint16_t seed_hash =
+          reinterpret_cast<const uint16_t*>(ptr)[COMPACT_SKETCH_SEED_HASH_U16];
+      checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+      if (preamble_size == 1) {
+        return {
+            true, true, seed_hash, 0, ThetaConstants::MAX_THETA, nullptr, 64};
+      } else if (preamble_size == 2) {
+        const uint32_t num_entries = reinterpret_cast<const uint32_t*>(
+            ptr)[COMPACT_SKETCH_NUM_ENTRIES_U32];
+        if (num_entries == 0) {
+          return {
+              true, true, seed_hash, 0, ThetaConstants::MAX_THETA, nullptr, 64};
+        } else {
+          const size_t expected_size_bytes = (preamble_size + num_entries) << 3;
+          checkMemorySize(ptr, size, expected_size_bytes, dump_on_error);
+          const uint64_t* entries = reinterpret_cast<const uint64_t*>(ptr) +
+              COMPACT_SKETCH_ENTRIES_EXACT_U64;
+          return {
+              false,
+              true,
+              seed_hash,
+              num_entries,
+              ThetaConstants::MAX_THETA,
+              entries,
+              64};
+        }
+      } else if (preamble_size == 3) {
+        const uint32_t num_entries = reinterpret_cast<const uint32_t*>(
+            ptr)[COMPACT_SKETCH_NUM_ENTRIES_U32];
+        uint64_t theta =
+            reinterpret_cast<const uint64_t*>(ptr)[COMPACT_SKETCH_THETA_U64];
+        bool is_empty =
+            (num_entries == 0) && (theta == ThetaConstants::MAX_THETA);
+        if (is_empty)
+          return {true, true, seed_hash, 0, theta, nullptr, 64};
+        const uint64_t* entries = reinterpret_cast<const uint64_t*>(ptr) +
+            COMPACT_SKETCH_ENTRIES_ESTIMATION_U64;
+        const size_t expected_size_bytes =
+            (COMPACT_SKETCH_ENTRIES_ESTIMATION_U64 + num_entries) *
+            sizeof(uint64_t);
+        checkMemorySize(ptr, size, expected_size_bytes, dump_on_error);
+        return {false, true, seed_hash, num_entries, theta, entries, 64};
+      } else {
+        throw VeloxUserError(
+            __FILE__,
+            __LINE__,
+            __FUNCTION__,
+            "",
+            " longs of premable, but expected 1, 2, or 3",
+            error_source::kErrorSourceUser,
+            error_code::kInvalidArgument,
+            false /*retriable*/);
+      }
+    }
+    default:
+      throw VeloxUserError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "unsupported serial version " + std::to_string(serial_version),
+          error_source::kErrorSourceUser,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+  }
+}
+
+template <bool dummy>
+void CompactThetaSketchParser<dummy>::checkMemorySize(
+    const void* ptr,
+    size_t actual_bytes,
+    size_t expected_bytes,
+    bool dump_on_error) {
+  if (actual_bytes < expected_bytes) {
+    auto msg = "at least " + std::to_string(expected_bytes) +
+        " bytes expected, actual " + std::to_string(actual_bytes) +
+        (dump_on_error
+             ? (", sketch dump: " +
+                hexDump(reinterpret_cast<const uint8_t*>(ptr), actual_bytes))
+             : "");
+    throw VeloxUserError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        msg,
+        error_source::kErrorSourceUser,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+}
+
+template <bool dummy>
+std::string CompactThetaSketchParser<dummy>::hexDump(
+    const uint8_t* ptr,
+    size_t size) {
+  std::stringstream s;
+  s << std::hex << std::setfill('0') << std::uppercase;
+  for (size_t i = 0; i < size; ++i)
+    s << std::setw(2) << (ptr[i] & 0xff);
+  return s.str();
+}
+
+} // namespace facebook::velox::common::theta
+
+#endif
diff --git a/velox/external/theta/CompactThetaSketchParser.h b/velox/external/theta/CompactThetaSketchParser.h
new file mode 100644
index 00000000000..64867ed61c5
--- /dev/null
+++ b/velox/external/theta/CompactThetaSketchParser.h
@@ -0,0 +1,82 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+#pragma once
+
+#include <string>
+
+namespace facebook::velox::common::theta {
+
+template <typename T>
+T wholeBytesToHoldBits(T bits) {
+  static_assert(std::is_integral<T>::value, "integral type expected");
+  return (bits >> 3) + ((bits & 7) > 0);
+}
+
+template <bool dummy>
+class CompactThetaSketchParser {
+ public:
+  struct CompactThetaSketchData {
+    bool isEmpty;
+    bool isOrdered;
+    uint16_t seedHash;
+    uint32_t numEntries;
+    uint64_t theta;
+    const void* entriesStartPtr;
+    uint8_t entryBits;
+  };
+
+  static CompactThetaSketchData parse(
+      const void* ptr,
+      size_t size,
+      uint64_t seed,
+      bool dump_on_error = false);
+
+ private:
+  // offsets are in sizeof(type)
+  static const size_t COMPACT_SKETCH_PRE_LONGS_BYTE = 0;
+  static const size_t COMPACT_SKETCH_SERIAL_VERSION_BYTE = 1;
+  static const size_t COMPACT_SKETCH_TYPE_BYTE = 2;
+  static const size_t COMPACT_SKETCH_FLAGS_BYTE = 5;
+  static const size_t COMPACT_SKETCH_SEED_HASH_U16 = 3;
+  static const size_t COMPACT_SKETCH_SINGLE_ENTRY_U64 = 1; // ver 3
+  static const size_t COMPACT_SKETCH_NUM_ENTRIES_U32 = 2; // ver 1-3
+  static const size_t COMPACT_SKETCH_ENTRIES_EXACT_U64 = 2; // ver 1-3
+  static const size_t COMPACT_SKETCH_ENTRIES_ESTIMATION_U64 = 3; // ver 1-3
+  static const size_t COMPACT_SKETCH_THETA_U64 = 2; // ver 1-3
+  static const size_t COMPACT_SKETCH_V4_ENTRY_BITS_BYTE = 3;
+  static const size_t COMPACT_SKETCH_V4_NUM_ENTRIES_BYTES_BYTE = 4;
+  static const size_t COMPACT_SKETCH_V4_THETA_U64 = 1;
+  static const size_t COMPACT_SKETCH_V4_PACKED_DATA_EXACT_BYTE = 8;
+  static const size_t COMPACT_SKETCH_V4_PACKED_DATA_ESTIMATION_BYTE = 16;
+
+  static const uint8_t COMPACT_SKETCH_IS_EMPTY_FLAG = 2;
+  static const uint8_t COMPACT_SKETCH_IS_ORDERED_FLAG = 4;
+
+  static const uint8_t COMPACT_SKETCH_TYPE = 3;
+
+  static void checkMemorySize(
+      const void* ptr,
+      size_t actual_bytes,
+      size_t expected_bytes,
+      bool dump_on_error);
+  static std::string hexDump(const uint8_t* ptr, size_t size);
+};
+
+} // namespace facebook::velox::common::theta
+
+#include "CompactThetaSketchParser.cpp"
diff --git a/velox/external/theta/ConditionalForward.h b/velox/external/theta/ConditionalForward.h
new file mode 100644
index 00000000000..f90e920fddb
--- /dev/null
+++ b/velox/external/theta/ConditionalForward.h
@@ -0,0 +1,81 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <iterator>
+#include <type_traits>
+
+namespace facebook::velox::common::theta {
+
+// Forward type T2 as rvalue reference if type T1 is rvalue reference
+
+template <typename T1, typename T2>
+using fwdType = typename std::conditional<
+    std::is_lvalue_reference<T1>::value,
+    T2,
+    typename std::remove_reference<T2>::type&&>::type;
+
+template <typename T1, typename T2>
+fwdType<T1, T2> conditionalForward(T2&& value) {
+  return std::forward<fwdType<T1, T2>>(std::forward<T2>(value));
+}
+
+// Forward container as iterators
+
+template <typename Container>
+auto forwardBegin(Container&& c) -> typename std::enable_if<
+    std::is_lvalue_reference<Container>::value ||
+        std::is_same<
+            typename std::remove_reference<Container>::type::const_iterator,
+            decltype(c.begin())>::value,
+    decltype(c.begin())>::type {
+  return c.begin();
+}
+
+template <typename Container>
+auto forwardBegin(Container&& c) -> typename std::enable_if<
+    !std::is_lvalue_reference<Container>::value &&
+        !std::is_same<
+            typename std::remove_reference<Container>::type::const_iterator,
+            decltype(c.begin())>::value,
+    decltype(std::make_move_iterator(c.begin()))>::type {
+  return std::make_move_iterator(c.begin());
+}
+
+template <typename Container>
+auto forwardEnd(Container&& c) -> typename std::enable_if<
+    std::is_lvalue_reference<Container>::value ||
+        std::is_same<
+            typename std::remove_reference<Container>::type::const_iterator,
+            decltype(c.begin())>::value,
+    decltype(c.end())>::type {
+  return c.end();
+}
+
+template <typename Container>
+auto forwardEnd(Container&& c) -> typename std::enable_if<
+    !std::is_lvalue_reference<Container>::value &&
+        !std::is_same<
+            typename std::remove_reference<Container>::type::const_iterator,
+            decltype(c.begin())>::value,
+    decltype(std::make_move_iterator(c.end()))>::type {
+  return std::make_move_iterator(c.end());
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/CountZeros.h b/velox/external/theta/CountZeros.h
new file mode 100644
index 00000000000..c898b16a52d
--- /dev/null
+++ b/velox/external/theta/CountZeros.h
@@ -0,0 +1,109 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <cstdint>
+
+namespace facebook::velox::common::theta {
+
+static const uint8_t byteLeadingZerosTable[256] = {
+    8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3,
+    3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
+    2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1,
+    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+    1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
+    1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
+    0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0};
+
+static const uint8_t byteTrailingZerosTable[256] = {
+    8, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0,
+    3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 6, 0, 1, 0, 2, 0, 1, 0,
+    3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+    5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0,
+    3, 0, 1, 0, 2, 0, 1, 0, 7, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0,
+    3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+    6, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 4, 0, 1, 0, 2, 0, 1, 0,
+    3, 0, 1, 0, 2, 0, 1, 0, 5, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0,
+    4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0};
+
+static const uint64_t FCLZ_MASK_56 = 0x00ffffffffffffff;
+static const uint64_t FCLZ_MASK_48 = 0x0000ffffffffffff;
+static const uint64_t FCLZ_MASK_40 = 0x000000ffffffffff;
+static const uint64_t FCLZ_MASK_32 = 0x00000000ffffffff;
+static const uint64_t FCLZ_MASK_24 = 0x0000000000ffffff;
+static const uint64_t FCLZ_MASK_16 = 0x000000000000ffff;
+static const uint64_t FCLZ_MASK_08 = 0x00000000000000ff;
+
+static inline uint8_t countLeadingZerosInU64(uint64_t input) {
+  if (input > FCLZ_MASK_56)
+    return byteLeadingZerosTable[(input >> 56) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_48)
+    return 8 + byteLeadingZerosTable[(input >> 48) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_40)
+    return 16 + byteLeadingZerosTable[(input >> 40) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_32)
+    return 24 + byteLeadingZerosTable[(input >> 32) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_24)
+    return 32 + byteLeadingZerosTable[(input >> 24) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_16)
+    return 40 + byteLeadingZerosTable[(input >> 16) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_08)
+    return 48 + byteLeadingZerosTable[(input >> 8) & FCLZ_MASK_08];
+  if (true)
+    return 56 + byteLeadingZerosTable[(input)&FCLZ_MASK_08];
+}
+
+static inline uint8_t countLeadingZerosInU32(uint32_t input) {
+  if (input > FCLZ_MASK_24)
+    return byteLeadingZerosTable[(input >> 24) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_16)
+    return 8 + byteLeadingZerosTable[(input >> 16) & FCLZ_MASK_08];
+  if (input > FCLZ_MASK_08)
+    return 16 + byteLeadingZerosTable[(input >> 8) & FCLZ_MASK_08];
+  if (true)
+    return 24 + byteLeadingZerosTable[(input)&FCLZ_MASK_08];
+}
+
+static inline uint8_t countTrailingZerosInU32(uint32_t input) {
+  for (int i = 0; i < 4; i++) {
+    const int byte = input & 0xff;
+    if (byte != 0)
+      return static_cast<uint8_t>((i << 3) + byteLeadingZerosTable[byte]);
+    input >>= 8;
+  }
+  return 32;
+}
+
+static inline uint8_t countTrailingZerosInU64(uint64_t input) {
+  for (int i = 0; i < 8; i++) {
+    const int byte = input & 0xff;
+    if (byte != 0)
+      return static_cast<uint8_t>((i << 3) + byteLeadingZerosTable[byte]);
+    input >>= 8;
+  }
+  return 64;
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/MemoryOperations.h b/velox/external/theta/MemoryOperations.h
new file mode 100644
index 00000000000..81c2e972b3f
--- /dev/null
+++ b/velox/external/theta/MemoryOperations.h
@@ -0,0 +1,90 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "velox/common/base/Exceptions.h"
+#include <cstring>
+#include <exception>
+#include <iostream>
+#include <memory>
+#include <string>
+
+namespace facebook::velox::common::theta {
+
+static inline void ensureMinimumMemory(
+    size_t bytes_available,
+    size_t min_needed) {
+  if (bytes_available < min_needed) {
+    auto msg = "Insufficient buffer size detected: bytes available " +
+        std::to_string(bytes_available) + ", minimum needed " +
+        std::to_string(min_needed);
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        msg,
+        error_source::kErrorSourceUser,
+        error_code::kGenericUserError,
+        false /*retriable*/);
+  }
+}
+
+static inline void checkMemorySize(size_t requested_index, size_t capacity) {
+  if (requested_index > capacity) {
+    auto msg = "Attempt to access memory beyond limits: requested index " +
+        std::to_string(requested_index) + ", capacity " +
+        std::to_string(capacity);
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        msg,
+        error_source::kErrorSourceUser,
+        error_code::kGenericUserError,
+        false /*retriable*/);
+  }
+}
+
+// note: size is in bytes, not items
+static inline size_t copyFromMem(const void* src, void* dst, size_t size) {
+  memcpy(dst, src, size);
+  return size;
+}
+
+// note: size is in bytes, not items
+static inline size_t copyToMem(const void* src, void* dst, size_t size) {
+  memcpy(dst, src, size);
+  return size;
+}
+
+template <typename T>
+static inline size_t copyFromMem(const void* src, T& item) {
+  memcpy(&item, src, sizeof(T));
+  return sizeof(T);
+}
+
+template <typename T>
+static inline size_t copyToMem(T item, void* dst) {
+  memcpy(dst, &item, sizeof(T));
+  return sizeof(T);
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/MurmurHash3.h b/velox/external/theta/MurmurHash3.h
new file mode 100644
index 00000000000..bc5dd67fd76
--- /dev/null
+++ b/velox/external/theta/MurmurHash3.h
@@ -0,0 +1,221 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+// Minimally modified from Austin Applebee's code:
+//  * Removed MurmurHash3_x86_32 and MurmurHash3_x86_128
+//  * Changed input seed in MurmurHash3_x64_128 to uint64_t
+//  * Define and use HashState reference to return result
+//  * Made entire hash function defined inline
+//  * Added compute_seed_hash
+//-----------------------------------------------------------------------------
+// MurmurHash3 was written by Austin Appleby, and is placed in the public
+// domain. The author hereby disclaims copyright to this source code.
+
+// Note - The x86 and x64 versions do _not_ produce the same results, as the
+// algorithms are optimized for their respective platforms. You can still
+// compile and run any of them on any platform, but your performance with the
+// non-native version will be less than optimal.
+
+#pragma once
+
+#include <cstring>
+
+//-----------------------------------------------------------------------------
+// Platform-specific functions and macros
+
+// Microsoft Visual Studio
+
+#if defined(_MSC_VER)
+
+typedef unsigned char uint8_t;
+typedef unsigned int uint32_t;
+typedef unsigned __int64 uint64_t;
+
+#define MURMUR3_FORCE_INLINE __forceinline
+
+#include <stdlib.h>
+
+#define MURMUR3_ROTL64(x, y) _rotl64(x, y)
+
+#define MURMUR3_BIG_CONSTANT(x) (x)
+
+// Other compilers
+
+#else // defined(_MSC_VER)
+
+#include <stdint.h>
+
+#define MURMUR3_FORCE_INLINE inline __attribute__((always_inline))
+
+inline uint64_t rotl64(uint64_t x, int8_t r) {
+  return (x << r) | (x >> (64 - r));
+}
+
+#define MURMUR3_ROTL64(x, y) rotl64(x, y)
+
+#define MURMUR3_BIG_CONSTANT(x) (x##LLU)
+
+#endif // !defined(_MSC_VER)
+
+//-----------------------------------------------------------------------------
+
+//-----------------------------------------------------------------------------
+// Return type - Using C++ reference for return type which should allow better
+// compiler optimization than a void* pointer
+typedef struct {
+  uint64_t h1;
+  uint64_t h2;
+} HashState;
+
+//-----------------------------------------------------------------------------
+// Block read - if your platform needs to do endian-swapping or can only
+// handle aligned reads, do the conversion here
+
+MURMUR3_FORCE_INLINE uint64_t getblock64(const uint8_t* p, size_t i) {
+  uint64_t res;
+  memcpy(&res, p + i * sizeof(uint64_t), sizeof(res));
+  return res;
+}
+
+//-----------------------------------------------------------------------------
+// Finalization mix - force all bits of a hash block to avalanche
+
+MURMUR3_FORCE_INLINE uint64_t fmix64(uint64_t k) {
+  k ^= k >> 33;
+  k *= MURMUR3_BIG_CONSTANT(0xff51afd7ed558ccd);
+  k ^= k >> 33;
+  k *= MURMUR3_BIG_CONSTANT(0xc4ceb9fe1a85ec53);
+  k ^= k >> 33;
+
+  return k;
+}
+
+MURMUR3_FORCE_INLINE void MurmurHash3_x64_128(
+    const void* key,
+    size_t lenBytes,
+    uint64_t seed,
+    HashState& out) {
+  static const uint64_t c1 = MURMUR3_BIG_CONSTANT(0x87c37b91114253d5);
+  static const uint64_t c2 = MURMUR3_BIG_CONSTANT(0x4cf5ad432745937f);
+
+  const uint8_t* data = (const uint8_t*)key;
+
+  out.h1 = seed;
+  out.h2 = seed;
+
+  // Number of full 128-bit blocks of 16 bytes.
+  // Possible exclusion of a remainder of up to 15 bytes.
+  const size_t nblocks = lenBytes >> 4; // bytes / 16
+
+  // Process the 128-bit blocks (the body) into the hash
+  for (size_t i = 0; i < nblocks; ++i) { // 16 bytes per block
+    uint64_t k1 = getblock64(data, i * 2 + 0);
+    uint64_t k2 = getblock64(data, i * 2 + 1);
+
+    k1 *= c1;
+    k1 = MURMUR3_ROTL64(k1, 31);
+    k1 *= c2;
+    out.h1 ^= k1;
+    out.h1 = MURMUR3_ROTL64(out.h1, 27);
+    out.h1 += out.h2;
+    out.h1 = out.h1 * 5 + 0x52dce729;
+
+    k2 *= c2;
+    k2 = MURMUR3_ROTL64(k2, 33);
+    k2 *= c1;
+    out.h2 ^= k2;
+    out.h2 = MURMUR3_ROTL64(out.h2, 31);
+    out.h2 += out.h1;
+    out.h2 = out.h2 * 5 + 0x38495ab5;
+  }
+
+  // tail
+  const uint8_t* tail = (const uint8_t*)(data + (nblocks << 4));
+
+  uint64_t k1 = 0;
+  uint64_t k2 = 0;
+
+  switch (lenBytes & 15) {
+    case 15:
+      k2 ^= ((uint64_t)tail[14]) << 48; // falls through
+    case 14:
+      k2 ^= ((uint64_t)tail[13]) << 40; // falls through
+    case 13:
+      k2 ^= ((uint64_t)tail[12]) << 32; // falls through
+    case 12:
+      k2 ^= ((uint64_t)tail[11]) << 24; // falls through
+    case 11:
+      k2 ^= ((uint64_t)tail[10]) << 16; // falls through
+    case 10:
+      k2 ^= ((uint64_t)tail[9]) << 8; // falls through
+    case 9:
+      k2 ^= ((uint64_t)tail[8]) << 0;
+      k2 *= c2;
+      k2 = MURMUR3_ROTL64(k2, 33);
+      k2 *= c1;
+      out.h2 ^= k2;
+      // falls through
+    case 8:
+      k1 ^= ((uint64_t)tail[7]) << 56; // falls through
+    case 7:
+      k1 ^= ((uint64_t)tail[6]) << 48; // falls through
+    case 6:
+      k1 ^= ((uint64_t)tail[5]) << 40; // falls through
+    case 5:
+      k1 ^= ((uint64_t)tail[4]) << 32; // falls through
+    case 4:
+      k1 ^= ((uint64_t)tail[3]) << 24; // falls through
+    case 3:
+      k1 ^= ((uint64_t)tail[2]) << 16; // falls through
+    case 2:
+      k1 ^= ((uint64_t)tail[1]) << 8; // falls through
+    case 1:
+      k1 ^= ((uint64_t)tail[0]) << 0;
+      k1 *= c1;
+      k1 = MURMUR3_ROTL64(k1, 31);
+      k1 *= c2;
+      out.h1 ^= k1;
+  };
+
+  //----------
+  // finalization
+
+  out.h1 ^= lenBytes;
+  out.h2 ^= lenBytes;
+
+  out.h1 += out.h2;
+  out.h2 += out.h1;
+
+  out.h1 = fmix64(out.h1);
+  out.h2 = fmix64(out.h2);
+
+  out.h1 += out.h2;
+  out.h2 += out.h1;
+}
+
+//-----------------------------------------------------------------------------
+
+MURMUR3_FORCE_INLINE uint16_t compute_seed_hash(uint64_t seed) {
+  HashState hashes;
+  MurmurHash3_x64_128(&seed, sizeof(seed), 0, hashes);
+  return static_cast<uint16_t>(hashes.h1 & 0xffff);
+}
+
+#undef MURMUR3_FORCE_INLINE
+#undef MURMUR3_ROTL64
+#undef MURMUR3_BIG_CONSTANT
diff --git a/velox/external/theta/Serde.h b/velox/external/theta/Serde.h
new file mode 100644
index 00000000000..3215e62a866
--- /dev/null
+++ b/velox/external/theta/Serde.h
@@ -0,0 +1,297 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <cstring>
+#include <exception>
+#include <iostream>
+#include <memory>
+#include <string>
+
+#include "MemoryOperations.h"
+#include "velox/common/base/Exceptions.h"
+
+namespace facebook::velox::common::theta {
+
+/// Interface for serializing and deserializing items
+template <typename T, typename Enable = void>
+struct serde {
+  /**
+   * Stream serialization
+   * @param os output stream
+   * @param items pointer to array of items
+   * @param num number of items
+   */
+  void serialize(std::ostream& os, const T* items, unsigned num) const;
+
+  /**
+   * Stream deserialization
+   * @param is input stream
+   * @param items pointer to array of items (items in the array are allocated
+   * but not initialized)
+   * @param num number of items
+   */
+  void deserialize(std::istream& is, T* items, unsigned num) const;
+
+  /**
+   * Raw bytes serialization
+   * @param ptr pointer to output buffer
+   * @param capacity size of the buffer in bytes
+   * @param items pointer to array of items
+   * @param num number of items
+   */
+  size_t serialize(void* ptr, size_t capacity, const T* items, unsigned num)
+      const;
+
+  /**
+   * Raw bytes deserialization
+   * @param ptr pointer to input buffer
+   * @param capacity size of the buffer in bytes
+   * @param items pointer to array of items (items in the array are allocated
+   * but not initialized)
+   * @param num number of items
+   */
+  size_t deserialize(const void* ptr, size_t capacity, T* items, unsigned num)
+      const;
+
+  /**
+   * Size of the given item
+   * @param item to be sized
+   * @return size of the given item in bytes
+   */
+  size_t size_of_item(const T& item) const;
+};
+
+/// serde for all fixed-size arithmetic types (int and float of different
+/// sizes). in particular, kll_sketch<int64_t> should produce sketches
+/// binary-compatible with LongsSketch and ItemsSketch<Long> with
+/// ArrayOfLongsSerDe in Java
+template <typename T>
+struct serde<T, typename std::enable_if<std::is_arithmetic<T>::value>::type> {
+  /// @copydoc serde::serialize
+  void serialize(std::ostream& os, const T* items, unsigned num) const {
+    bool failure = false;
+    try {
+      os.write(reinterpret_cast<const char*>(items), sizeof(T) * num);
+    } catch (std::ostream::failure&) {
+      failure = true;
+    }
+    if (failure || !os.good()) {
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error writing to std::ostream with " + std::to_string(num) +
+              " items",
+          error_source::kErrorSourceUser,
+          error_code::kGenericUserError,
+          false /*retriable*/);
+    }
+  }
+
+  void deserialize(std::istream& is, T* items, unsigned num) const {
+    bool failure = false;
+    try {
+      is.read((char*)items, sizeof(T) * num);
+    } catch (std::istream::failure&) {
+      failure = true;
+    }
+    if (failure || !is.good()) {
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error reading from std::istream with " + std::to_string(num) +
+              " items",
+          error_source::kErrorSourceUser,
+          error_code::kGenericUserError,
+          false /*retriable*/);
+    }
+  }
+
+  /// @copydoc serde::serialize(void*,size_t,const T*,unsigned) const
+  size_t serialize(void* ptr, size_t capacity, const T* items, unsigned num)
+      const {
+    const size_t bytes_written = sizeof(T) * num;
+    checkMemorySize(bytes_written, capacity);
+    memcpy(ptr, items, bytes_written);
+    return bytes_written;
+  }
+
+  /// @copydoc serde::deserialize(const void*,size_t,T*,unsigned) const
+  size_t deserialize(const void* ptr, size_t capacity, T* items, unsigned num)
+      const {
+    const size_t bytes_read = sizeof(T) * num;
+    checkMemorySize(bytes_read, capacity);
+    memcpy(items, ptr, bytes_read);
+    return bytes_read;
+  }
+
+  /// @copydoc serde::size_of_item
+  size_t size_of_item(const T& item) const {
+    unused(item);
+    return sizeof(T);
+  }
+};
+
+/// serde for std::string items.
+/// This should produce sketches binary-compatible with
+/// ItemsSketch<String> with ArrayOfStringsSerDe in Java.
+/// The length of each string is stored as a 32-bit integer (historically),
+/// which may be too wasteful. Treat this as an example.
+template <>
+struct serde<std::string> {
+  /// @copydoc serde::serialize
+  void serialize(std::ostream& os, const std::string* items, unsigned num)
+      const {
+    unsigned i = 0;
+    bool failure = false;
+    try {
+      for (; i < num && os.good(); i++) {
+        uint32_t length = static_cast<uint32_t>(items[i].size());
+        os.write((char*)&length, sizeof(length));
+        os.write(items[i].c_str(), length);
+      }
+    } catch (std::ostream::failure&) {
+      failure = true;
+    }
+    if (failure || !os.good()) {
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error writing to std::ostream at item " + std::to_string(i),
+          error_source::kErrorSourceUser,
+          error_code::kGenericUserError,
+          false /*retriable*/);
+    }
+  }
+
+  /// @copydoc serde::deserialize
+  void deserialize(std::istream& is, std::string* items, unsigned num) const {
+    unsigned i = 0;
+    bool failure = false;
+    try {
+      for (; i < num; i++) {
+        uint32_t length;
+        is.read((char*)&length, sizeof(length));
+        if (!is.good()) {
+          break;
+        }
+        std::string str;
+        str.reserve(length);
+        for (uint32_t j = 0; j < length; j++) {
+          str.push_back(static_cast<char>(is.get()));
+        }
+        if (!is.good()) {
+          break;
+        }
+        new (&items[i]) std::string(std::move(str));
+      }
+    } catch (std::istream::failure&) {
+      failure = true;
+    }
+    if (failure || !is.good()) {
+      // clean up what we've already allocated
+      for (unsigned j = 0; j < i; ++j) {
+        items[j].~basic_string();
+      }
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error reading from std::istream at item " + std::to_string(i),
+          error_source::kErrorSourceUser,
+          error_code::kGenericUserError,
+          false /*retriable*/);
+    }
+  }
+
+  /// @copydoc serde::serialize(void*,size_t,const T*,unsigned) const
+  size_t serialize(
+      void* ptr,
+      size_t capacity,
+      const std::string* items,
+      unsigned num) const {
+    size_t bytes_written = 0;
+    for (unsigned i = 0; i < num; ++i) {
+      const uint32_t length = static_cast<uint32_t>(items[i].size());
+      const size_t new_bytes = length + sizeof(length);
+      checkMemorySize(bytes_written + new_bytes, capacity);
+      memcpy(ptr, &length, sizeof(length));
+      ptr = static_cast<char*>(ptr) + sizeof(uint32_t);
+      memcpy(ptr, items[i].c_str(), length);
+      ptr = static_cast<char*>(ptr) + length;
+      bytes_written += new_bytes;
+    }
+    return bytes_written;
+  }
+
+  /// @copydoc serde::deserialize(const void*,size_t,T*,unsigned) const
+  size_t deserialize(
+      const void* ptr,
+      size_t capacity,
+      std::string* items,
+      unsigned num) const {
+    size_t bytes_read = 0;
+    unsigned i = 0;
+    bool failure = false;
+    for (; i < num && !failure; ++i) {
+      uint32_t length;
+      if (bytes_read + sizeof(length) > capacity) {
+        bytes_read += sizeof(length); // we'll use this to report the error
+        failure = true;
+        break;
+      }
+      memcpy(&length, ptr, sizeof(length));
+      ptr = static_cast<const char*>(ptr) + sizeof(uint32_t);
+      bytes_read += sizeof(length);
+
+      if (bytes_read + length > capacity) {
+        bytes_read += length; // we'll use this to report the error
+        failure = true;
+        break;
+      }
+      new (&items[i]) std::string(static_cast<const char*>(ptr), length);
+      ptr = static_cast<const char*>(ptr) + length;
+      bytes_read += length;
+    }
+
+    if (failure) {
+      // clean up what we've already allocated
+      for (unsigned j = 0; j < i; ++j)
+        items[j].~basic_string();
+      // using this for a consistent error message
+      checkMemorySize(bytes_read, capacity);
+    }
+
+    return bytes_read;
+  }
+
+  /// @copydoc serde::size_of_item
+  size_t size_of_item(const std::string& item) const {
+    return sizeof(uint32_t) + item.size();
+  }
+};
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/ThetaComparators.h b/velox/external/theta/ThetaComparators.h
new file mode 100644
index 00000000000..e35eb96578c
--- /dev/null
+++ b/velox/external/theta/ThetaComparators.h
@@ -0,0 +1,48 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <utility>
+
+namespace facebook::velox::common::theta {
+
+template <typename ExtractKey>
+struct compareByKey {
+  template <typename Entry1, typename Entry2>
+  bool operator()(Entry1&& a, Entry2&& b) const {
+    return ExtractKey()(std::forward<Entry1>(a)) <
+        ExtractKey()(std::forward<Entry2>(b));
+  }
+};
+
+// less than
+
+template <typename Key, typename Entry, typename ExtractKey>
+class KeyLessThan {
+ public:
+  explicit KeyLessThan(const Key& key) : key(key) {}
+  bool operator()(const Entry& entry) const {
+    return ExtractKey()(entry) < this->key;
+  }
+
+ private:
+  Key key;
+};
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/ThetaConstants.h b/velox/external/theta/ThetaConstants.h
new file mode 100644
index 00000000000..e59a2b6c61f
--- /dev/null
+++ b/velox/external/theta/ThetaConstants.h
@@ -0,0 +1,43 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <climits>
+#include "CommonDefs.h"
+
+namespace facebook::velox::common::theta {
+
+/// Theta constants
+namespace ThetaConstants {
+/// hash table resize factor
+using resizeFactor = facebook::velox::common::theta::resizeFactor;
+/// default resize factor
+const resizeFactor DEFAULT_RESIZE_FACTOR = resizeFactor::X8;
+
+/// max theta - signed max for compatibility with Java
+const uint64_t MAX_THETA = LLONG_MAX;
+/// min log2 of K
+const uint8_t MIN_LG_K = 5;
+/// max log2 of K
+const uint8_t MAX_LG_K = 26;
+/// default log2 of K
+const uint8_t DEFAULT_LG_K = 12;
+} // namespace ThetaConstants
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/ThetaHelpers.h b/velox/external/theta/ThetaHelpers.h
new file mode 100644
index 00000000000..27c32f8cb10
--- /dev/null
+++ b/velox/external/theta/ThetaHelpers.h
@@ -0,0 +1,83 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <stdexcept>
+#include <string>
+
+#include "ThetaConstants.h"
+#include "velox/common/base/Exceptions.h"
+
+namespace facebook::velox::common::theta {
+
+template <typename T>
+static void checkValue(T actual, T expected, const char* description) {
+  if (actual != expected) {
+    auto msg = std::string(description) + " mismatch: expected " +
+        std::to_string(expected) + ", actual " + std::to_string(actual);
+    throw VeloxUserError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        msg,
+        error_source::kErrorSourceUser,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+}
+
+template <bool dummy>
+class checker {
+ public:
+  static void checkSerialVersion(uint8_t actual, uint8_t expected) {
+    checkValue(actual, expected, "serial version");
+  }
+  static void checkSketchFamily(uint8_t actual, uint8_t expected) {
+    checkValue(actual, expected, "sketch family");
+  }
+  static void checkSketchType(uint8_t actual, uint8_t expected) {
+    checkValue(actual, expected, "sketch type");
+  }
+  static void checkSeedHash(uint16_t actual, uint16_t expected) {
+    checkValue(actual, expected, "seed hash");
+  }
+};
+
+template <bool dummy>
+class ThetaBuildHelper {
+ public:
+  // consistent way of initializing theta from p
+  // avoids multiplication if p == 1 since it might not yield MAX_THETA exactly
+  static uint64_t startingThetaFromP(float p) {
+    if (p < 1)
+      return static_cast<uint64_t>(
+          static_cast<double>(ThetaConstants::MAX_THETA) * p);
+    return ThetaConstants::MAX_THETA;
+  }
+
+  static uint8_t
+  startingSubMultiple(uint8_t lg_tgt, uint8_t lg_min, uint8_t lg_rf) {
+    return (lg_tgt <= lg_min) ? lg_min
+        : (lg_rf == 0)        ? lg_tgt
+                              : ((lg_tgt - lg_min) % lg_rf) + lg_min;
+  }
+};
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/ThetaSketch.cpp b/velox/external/theta/ThetaSketch.cpp
new file mode 100644
index 00000000000..e72929268f7
--- /dev/null
+++ b/velox/external/theta/ThetaSketch.cpp
@@ -0,0 +1,1122 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#ifndef THETA_SKETCH_CPP
+#define THETA_SKETCH_CPP
+
+#include <sstream>
+#include <vector>
+
+#include "BinomialBounds.h"
+#include "BitPacking.h"
+#include "CompactThetaSketchParser.h"
+#include "CountZeros.h"
+#include "MemoryOperations.h"
+#include "ThetaSketch.h"
+#include "velox/common/base/Exceptions.h"
+
+namespace facebook::velox::common::theta {
+
+template <typename A>
+bool BaseThetaSketchAlloc<A>::isEstimationMode() const {
+  return getTheta64() < ThetaConstants::MAX_THETA && !isEmpty();
+}
+
+template <typename A>
+double BaseThetaSketchAlloc<A>::getTheta() const {
+  return static_cast<double>(getTheta64()) /
+      static_cast<double>(ThetaConstants::MAX_THETA);
+}
+
+template <typename A>
+double BaseThetaSketchAlloc<A>::getEstimate() const {
+  return getNumRetained() / getTheta();
+}
+
+template <typename A>
+double BaseThetaSketchAlloc<A>::getLowerBound(uint8_t num_std_devs) const {
+  if (!isEstimationMode())
+    return getNumRetained();
+  return BinomialBounds::getLowerBound(
+      getNumRetained(), getTheta(), num_std_devs);
+}
+
+template <typename A>
+double BaseThetaSketchAlloc<A>::getUpperBound(uint8_t num_std_devs) const {
+  if (!isEstimationMode())
+    return getNumRetained();
+  return BinomialBounds::getUpperBound(
+      getNumRetained(), getTheta(), num_std_devs);
+}
+
+template <typename A>
+string<A> BaseThetaSketchAlloc<A>::toString(bool print_details) const {
+  // Using a temporary stream for implementation here does not comply with
+  // AllocatorAwareContainer requirements. The stream does not support passing
+  // an allocator instance, and alternatives are complicated.
+  std::ostringstream os;
+  os << "### Theta sketch summary:" << std::endl;
+  os << "   num retained entries : " << this->getNumRetained() << std::endl;
+  os << "   seed hash            : " << this->getSeedHash() << std::endl;
+  os << "   empty?               : " << (this->isEmpty() ? "true" : "false")
+     << std::endl;
+  os << "   ordered?             : " << (this->isOrdered() ? "true" : "false")
+     << std::endl;
+  os << "   estimation mode?     : "
+     << (this->isEstimationMode() ? "true" : "false") << std::endl;
+  os << "   theta (fraction)     : " << this->getTheta() << std::endl;
+  os << "   theta (raw 64-bit)   : " << this->getTheta64() << std::endl;
+  os << "   estimate             : " << this->getEstimate() << std::endl;
+  os << "   lower bound 95% conf : " << this->getLowerBound(2) << std::endl;
+  os << "   upper bound 95% conf : " << this->getUpperBound(2) << std::endl;
+  printSpecifics(os);
+  os << "### End sketch summary" << std::endl;
+  if (print_details) {
+    printItems(os);
+  }
+  return string<A>(os.str().c_str(), this->getAllocator());
+}
+
+template <typename A>
+void ThetaSketchAlloc<A>::printItems(std::ostringstream& os) const {
+  os << "### Retained entries" << std::endl;
+  for (const auto& hash : *this) {
+    os << hash << std::endl;
+  }
+  os << "### End retained entries" << std::endl;
+}
+
+// update sketch
+
+template <typename A>
+UpdateThetaSketchAlloc<A>::UpdateThetaSketchAlloc(
+    uint8_t lgCurSize,
+    uint8_t lgNomSize,
+    resizeFactor rf,
+    float p,
+    uint64_t theta,
+    uint64_t seed,
+    const A& allocator)
+    : table_(lgCurSize, lgNomSize, rf, p, theta, seed, allocator) {}
+
+template <typename A>
+A UpdateThetaSketchAlloc<A>::getAllocator() const {
+  return table_.allocator_;
+}
+
+template <typename A>
+bool UpdateThetaSketchAlloc<A>::isEmpty() const {
+  return table_.isEmpty_;
+}
+
+template <typename A>
+bool UpdateThetaSketchAlloc<A>::isOrdered() const {
+  return table_.numEntries_ > 1 ? false : true;
+}
+
+template <typename A>
+uint64_t UpdateThetaSketchAlloc<A>::getTheta64() const {
+  return isEmpty() ? ThetaConstants::MAX_THETA : table_.theta_;
+}
+
+template <typename A>
+uint32_t UpdateThetaSketchAlloc<A>::getNumRetained() const {
+  return table_.numEntries_;
+}
+
+template <typename A>
+uint16_t UpdateThetaSketchAlloc<A>::getSeedHash() const {
+  return compute_seed_hash(table_.seed_);
+}
+
+template <typename A>
+uint8_t UpdateThetaSketchAlloc<A>::getLgK() const {
+  return table_.lgNomSize_;
+}
+
+template <typename A>
+auto UpdateThetaSketchAlloc<A>::getRf() const -> resizeFactor {
+  return table_.rf_;
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(uint64_t value) {
+  update(&value, sizeof(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(int64_t value) {
+  update(&value, sizeof(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(uint32_t value) {
+  update(static_cast<int32_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(int32_t value) {
+  update(static_cast<int64_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(uint16_t value) {
+  update(static_cast<int16_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(int16_t value) {
+  update(static_cast<int64_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(uint8_t value) {
+  update(static_cast<int8_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(int8_t value) {
+  update(static_cast<int64_t>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(double value) {
+  update(canonical_double(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(float value) {
+  update(static_cast<double>(value));
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(const std::string& value) {
+  if (value.empty())
+    return;
+  update(value.c_str(), value.length());
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::update(const void* data, size_t length) {
+  const uint64_t hash = table_.hashAndScreen(data, length);
+  if (hash == 0)
+    return;
+  auto result = table_.find(hash);
+  if (!result.second) {
+    table_.insert(result.first, hash);
+  }
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::trim() {
+  table_.trim();
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::reset() {
+  table_.reset();
+}
+
+template <typename A>
+auto UpdateThetaSketchAlloc<A>::begin() -> iterator {
+  return iterator(table_.entries_, 1 << table_.lgCurSize_, 0);
+}
+
+template <typename A>
+auto UpdateThetaSketchAlloc<A>::end() -> iterator {
+  return iterator(nullptr, 0, 1 << table_.lgCurSize_);
+}
+
+template <typename A>
+auto UpdateThetaSketchAlloc<A>::begin() const -> const_iterator {
+  return const_iterator(table_.entries_, 1 << table_.lgCurSize_, 0);
+}
+
+template <typename A>
+auto UpdateThetaSketchAlloc<A>::end() const -> const_iterator {
+  return const_iterator(nullptr, 0, 1 << table_.lgCurSize_);
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> UpdateThetaSketchAlloc<A>::compact(
+    bool ordered) const {
+  return CompactThetaSketchAlloc<A>(*this, ordered);
+}
+
+template <typename A>
+void UpdateThetaSketchAlloc<A>::printSpecifics(std::ostringstream& os) const {
+  os << "   lg nominal size      : " << static_cast<int>(table_.lgNomSize_)
+     << std::endl;
+  os << "   lg current size      : " << static_cast<int>(table_.lgCurSize_)
+     << std::endl;
+  os << "   resize factor        : " << (1 << table_.rf_) << std::endl;
+}
+
+// builder
+
+template <typename A>
+UpdateThetaSketchAlloc<A>::builder::builder(const A& allocator)
+    : ThetaBaseBuilder<builder, A>(allocator) {}
+
+template <typename A>
+UpdateThetaSketchAlloc<A> UpdateThetaSketchAlloc<A>::builder::build() const {
+  return UpdateThetaSketchAlloc(
+      this->startingLgSize(),
+      this->lg_k_,
+      this->rf_,
+      this->p_,
+      this->startingTheta(),
+      this->seed_,
+      this->allocator_);
+}
+
+// compact sketch
+
+template <typename A>
+template <typename Other>
+CompactThetaSketchAlloc<A>::CompactThetaSketchAlloc(
+    const Other& other,
+    bool ordered)
+    : isEmpty_(other.isEmpty()),
+      isOrdered_(other.isOrdered() || ordered),
+      seedHash_(other.getSeedHash()),
+      theta_(other.getTheta64()),
+      entries_(other.getAllocator()) {
+  if (!other.isEmpty()) {
+    entries_.reserve(other.getNumRetained());
+    std::copy(other.begin(), other.end(), std::back_inserter(entries_));
+    if (ordered && !other.isOrdered())
+      std::sort(entries_.begin(), entries_.end());
+  }
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A>::CompactThetaSketchAlloc(
+    bool isEmpty,
+    bool isOrdered,
+    uint16_t seedHash,
+    uint64_t theta,
+    std::vector<uint64_t, A>&& entries)
+    : isEmpty_(isEmpty),
+      isOrdered_(isOrdered || (entries.size() <= 1ULL)),
+      seedHash_(seedHash),
+      theta_(theta),
+      entries_(std::move(entries)) {}
+
+template <typename A>
+A CompactThetaSketchAlloc<A>::getAllocator() const {
+  return entries_.get_allocator();
+}
+
+template <typename A>
+bool CompactThetaSketchAlloc<A>::isEmpty() const {
+  return isEmpty_;
+}
+
+template <typename A>
+bool CompactThetaSketchAlloc<A>::isOrdered() const {
+  return isOrdered_;
+}
+
+template <typename A>
+uint64_t CompactThetaSketchAlloc<A>::getTheta64() const {
+  return theta_;
+}
+
+template <typename A>
+uint32_t CompactThetaSketchAlloc<A>::getNumRetained() const {
+  return static_cast<uint32_t>(entries_.size());
+}
+
+template <typename A>
+uint16_t CompactThetaSketchAlloc<A>::getSeedHash() const {
+  return seedHash_;
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::begin() -> iterator {
+  return iterator(entries_.data(), static_cast<uint32_t>(entries_.size()), 0);
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::end() -> iterator {
+  return iterator(nullptr, 0, static_cast<uint32_t>(entries_.size()));
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::begin() const -> const_iterator {
+  return const_iterator(
+      entries_.data(), static_cast<uint32_t>(entries_.size()), 0);
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::end() const -> const_iterator {
+  return const_iterator(nullptr, 0, static_cast<uint32_t>(entries_.size()));
+}
+
+template <typename A>
+void CompactThetaSketchAlloc<A>::printSpecifics(std::ostringstream&) const {}
+
+template <typename A>
+uint8_t CompactThetaSketchAlloc<A>::getPreambleLongs(bool compressed) const {
+  if (compressed) {
+    return this->isEstimationMode() ? 2 : 1;
+  }
+  return this->isEstimationMode()               ? 3
+      : this->isEmpty() || entries_.size() == 1 ? 1
+                                                : 2;
+}
+
+template <typename A>
+size_t CompactThetaSketchAlloc<A>::getMaxSerializedSizeBytes(uint8_t lg_k) {
+  return sizeof(uint64_t) *
+      (3 + UpdateThetaSketchAlloc<A>::ThetaTable::getCapacity(lg_k + 1, lg_k));
+}
+
+template <typename A>
+size_t CompactThetaSketchAlloc<A>::getSerializedSizeBytes(
+    bool compressed) const {
+  if (compressed && isSuitableForCompression()) {
+    return getCompressedSerializedSizeBytes(
+        computeEntryBits(), getNumEntriesBytes());
+  }
+  return sizeof(uint64_t) * getPreambleLongs(false) +
+      sizeof(uint64_t) * entries_.size();
+}
+
+// store num_entries as whole bytes since whole-byte blocks will follow (most
+// probably)
+template <typename A>
+uint8_t CompactThetaSketchAlloc<A>::getNumEntriesBytes() const {
+  return wholeBytesToHoldBits<uint8_t>(
+      32 - countLeadingZerosInU32(static_cast<uint32_t>(entries_.size())));
+}
+
+template <typename A>
+size_t CompactThetaSketchAlloc<A>::getCompressedSerializedSizeBytes(
+    uint8_t entry_bits,
+    uint8_t num_entries_bytes) const {
+  const size_t compressed_bits = entry_bits * entries_.size();
+  return sizeof(uint64_t) * getPreambleLongs(true) + num_entries_bytes +
+      wholeBytesToHoldBits(compressed_bits);
+}
+
+template <typename A>
+void CompactThetaSketchAlloc<A>::serialize(std::ostream& os) const {
+  const uint8_t preamble_longs = this->isEstimationMode() ? 3
+      : this->isEmpty() || entries_.size() == 1           ? 1
+                                                          : 2;
+  write(os, preamble_longs);
+  write(os, UNCOMPRESSED_SERIAL_VERSION);
+  write(os, SKETCH_TYPE);
+  write<uint16_t>(os, 0); // unused
+  const uint8_t flags_byte(
+      (1 << flags::IS_COMPACT) | (1 << flags::IS_READ_ONLY) |
+      (this->isEmpty() ? 1 << flags::IS_EMPTY : 0) |
+      (this->isOrdered() ? 1 << flags::IS_ORDERED : 0));
+  write(os, flags_byte);
+  write(os, getSeedHash());
+  if (preamble_longs > 1) {
+    write(os, static_cast<uint32_t>(entries_.size()));
+    write<uint32_t>(os, 0); // unused
+  }
+  if (this->isEstimationMode())
+    write(os, this->theta_);
+  if (entries_.size() > 0)
+    write(os, entries_.data(), entries_.size() * sizeof(uint64_t));
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::serialize(unsigned header_size_bytes) const
+    -> vector_bytes {
+  const size_t size = getSerializedSizeBytes() + header_size_bytes;
+  vector_bytes bytes(size, 0, entries_.get_allocator());
+  uint8_t* ptr = bytes.data() + header_size_bytes;
+  const uint8_t preamble_longs = getPreambleLongs(false);
+  *ptr++ = preamble_longs;
+  *ptr++ = UNCOMPRESSED_SERIAL_VERSION;
+  *ptr++ = SKETCH_TYPE;
+  ptr += sizeof(uint16_t); // unused
+  const uint8_t flags_byte(
+      (1 << flags::IS_COMPACT) | (1 << flags::IS_READ_ONLY) |
+      (this->isEmpty() ? 1 << flags::IS_EMPTY : 0) |
+      (this->isOrdered() ? 1 << flags::IS_ORDERED : 0));
+  *ptr++ = flags_byte;
+  ptr += copyToMem(getSeedHash(), ptr);
+  if (preamble_longs > 1) {
+    ptr += copyToMem(static_cast<uint32_t>(entries_.size()), ptr);
+    ptr += sizeof(uint32_t); // unused
+  }
+  if (this->isEstimationMode())
+    ptr += copyToMem(theta_, ptr);
+  if (entries_.size() > 0)
+    ptr += copyToMem(entries_.data(), ptr, entries_.size() * sizeof(uint64_t));
+  return bytes;
+}
+
+template <typename A>
+bool CompactThetaSketchAlloc<A>::isSuitableForCompression() const {
+  if (!this->isOrdered() || entries_.size() == 0 ||
+      (entries_.size() == 1 && !this->isEstimationMode()))
+    return false;
+  return true;
+}
+
+template <typename A>
+void CompactThetaSketchAlloc<A>::serializeCompressed(std::ostream& os) const {
+  if (isSuitableForCompression())
+    return serializeVersion4(os);
+  return serialize(os);
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::serializeCompressed(
+    unsigned header_size_bytes) const -> vector_bytes {
+  if (isSuitableForCompression())
+    return serializeVersion4(header_size_bytes);
+  return serialize(header_size_bytes);
+}
+
+template <typename A>
+uint8_t CompactThetaSketchAlloc<A>::computeEntryBits() const {
+  // compression is based on leading zeros in deltas between ordered hash values
+  // assumes ordered sketch
+  uint64_t previous = 0;
+  uint64_t ored = 0;
+  for (const uint64_t entry : entries_) {
+    const uint64_t delta = entry - previous;
+    ored |= delta;
+    previous = entry;
+  }
+  return 64 - countLeadingZerosInU64(ored);
+}
+
+template <typename A>
+void CompactThetaSketchAlloc<A>::serializeVersion4(std::ostream& os) const {
+  const uint8_t preamble_longs = this->isEstimationMode() ? 2 : 1;
+  const uint8_t entry_bits = computeEntryBits();
+  const uint8_t num_entries_bytes = getNumEntriesBytes();
+
+  write(os, preamble_longs);
+  write(os, COMPRESSED_SERIAL_VERSION);
+  write(os, SKETCH_TYPE);
+  write(os, entry_bits);
+  write(os, num_entries_bytes);
+  const uint8_t flags_byte(
+      (1 << flags::IS_COMPACT) | (1 << flags::IS_READ_ONLY) |
+      (1 << flags::IS_ORDERED));
+  write(os, flags_byte);
+  write(os, getSeedHash());
+  if (this->isEstimationMode())
+    write(os, this->theta_);
+  uint32_t num_entries = static_cast<uint32_t>(entries_.size());
+  for (unsigned i = 0; i < num_entries_bytes; ++i) {
+    write<uint8_t>(os, num_entries & 0xff);
+    num_entries >>= 8;
+  }
+
+  uint64_t previous = 0;
+  uint64_t deltas[8];
+  vector_bytes buffer(
+      entry_bits,
+      0,
+      entries_.get_allocator()); // block of 8 entries takes entry_bits bytes
+
+  // pack blocks of 8 deltas
+  unsigned i;
+  for (i = 0; i + 7 < entries_.size(); i += 8) {
+    for (unsigned j = 0; j < 8; ++j) {
+      deltas[j] = entries_[i + j] - previous;
+      previous = entries_[i + j];
+    }
+    packBitsBlock8(deltas, buffer.data(), entry_bits);
+    write(os, buffer.data(), buffer.size());
+  }
+
+  // pack extra deltas if fewer than 8 of them left
+  if (i < entries_.size()) {
+    uint8_t offset = 0;
+    uint8_t* ptr = buffer.data();
+    for (; i < entries_.size(); ++i) {
+      const uint64_t delta = entries_[i] - previous;
+      previous = entries_[i];
+      offset = packBits(delta, entry_bits, ptr, offset);
+    }
+    if (offset > 0)
+      ++ptr;
+    write(os, buffer.data(), ptr - buffer.data());
+  }
+}
+
+template <typename A>
+auto CompactThetaSketchAlloc<A>::serializeVersion4(
+    unsigned header_size_bytes) const -> vector_bytes {
+  const uint8_t entry_bits = computeEntryBits();
+  const uint8_t num_entries_bytes = getNumEntriesBytes();
+  const size_t size =
+      getCompressedSerializedSizeBytes(entry_bits, num_entries_bytes) +
+      header_size_bytes;
+  vector_bytes bytes(size, 0, entries_.get_allocator());
+  uint8_t* ptr = bytes.data() + header_size_bytes;
+
+  *ptr++ = getPreambleLongs(true);
+  *ptr++ = COMPRESSED_SERIAL_VERSION;
+  *ptr++ = SKETCH_TYPE;
+  *ptr++ = entry_bits;
+  *ptr++ = num_entries_bytes;
+  const uint8_t flags_byte(
+      (1 << flags::IS_COMPACT) | (1 << flags::IS_READ_ONLY) |
+      (1 << flags::IS_ORDERED));
+  *ptr++ = flags_byte;
+  ptr += copyToMem(getSeedHash(), ptr);
+  if (this->isEstimationMode()) {
+    ptr += copyToMem(theta_, ptr);
+  }
+  uint32_t num_entries = static_cast<uint32_t>(entries_.size());
+  for (unsigned i = 0; i < num_entries_bytes; ++i) {
+    *ptr++ = num_entries & 0xff;
+    num_entries >>= 8;
+  }
+
+  uint64_t previous = 0;
+  uint64_t deltas[8];
+
+  // pack blocks of 8 deltas
+  unsigned i;
+  for (i = 0; i + 7 < entries_.size(); i += 8) {
+    for (unsigned j = 0; j < 8; ++j) {
+      deltas[j] = entries_[i + j] - previous;
+      previous = entries_[i + j];
+    }
+    packBitsBlock8(deltas, ptr, entry_bits);
+    ptr += entry_bits;
+  }
+
+  // pack extra deltas if fewer than 8 of them left
+  uint8_t offset = 0;
+  for (; i < entries_.size(); ++i) {
+    const uint64_t delta = entries_[i] - previous;
+    previous = entries_[i];
+    offset = packBits(delta, entry_bits, ptr, offset);
+  }
+  return bytes;
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserialize(
+    std::istream& is,
+    uint64_t seed,
+    const A& allocator) {
+  const auto preamble_longs = read<uint8_t>(is);
+  const auto serial_version = read<uint8_t>(is);
+  const auto type = read<uint8_t>(is);
+  checker<true>::checkSketchType(type, SKETCH_TYPE);
+  switch (serial_version) {
+    case 4:
+      return deserializeV4(preamble_longs, is, seed, allocator);
+    case 3:
+      return deserializeV3(preamble_longs, is, seed, allocator);
+    case 1:
+      return deserializeV1(preamble_longs, is, seed, allocator);
+    case 2:
+      return deserializeV2(preamble_longs, is, seed, allocator);
+    default:
+      throw VeloxUserError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "unexpected sketch serialization version " +
+              std::to_string(serial_version),
+          error_source::kErrorSourceRuntime,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+  }
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserializeV1(
+    uint8_t,
+    std::istream& is,
+    uint64_t seed,
+    const A& allocator) {
+  const auto seed_hash = compute_seed_hash(seed);
+  read<uint8_t>(is); // unused
+  read<uint32_t>(is); // unused
+  const auto num_entries = read<uint32_t>(is);
+  read<uint32_t>(is); // unused
+  const auto theta = read<uint64_t>(is);
+  std::vector<uint64_t, A> entries(num_entries, 0, allocator);
+  bool isEmpty = (num_entries == 0) && (theta == ThetaConstants::MAX_THETA);
+  if (!isEmpty)
+    read(is, entries.data(), sizeof(uint64_t) * entries.size());
+  if (!is.good()) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "error reading from std::istream",
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  return CompactThetaSketchAlloc(
+      isEmpty, true, seed_hash, theta, std::move(entries));
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserializeV2(
+    uint8_t preamble_longs,
+    std::istream& is,
+    uint64_t seed,
+    const A& allocator) {
+  read<uint8_t>(is); // unused
+  read<uint16_t>(is); // unused
+  const uint16_t seed_hash = read<uint16_t>(is);
+  checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+  if (preamble_longs == 1) {
+    if (!is.good()) {
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error reading from std::istream",
+          error_source::kErrorSourceRuntime,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+    }
+    std::vector<uint64_t, A> entries(0, 0, allocator);
+    return CompactThetaSketchAlloc(
+        true, true, seed_hash, ThetaConstants::MAX_THETA, std::move(entries));
+  } else if (preamble_longs == 2) {
+    const uint32_t num_entries = read<uint32_t>(is);
+    read<uint32_t>(is); // unused
+    std::vector<uint64_t, A> entries(num_entries, 0, allocator);
+    if (num_entries == 0) {
+      return CompactThetaSketchAlloc(
+          true, true, seed_hash, ThetaConstants::MAX_THETA, std::move(entries));
+    }
+    read(is, entries.data(), entries.size() * sizeof(uint64_t));
+    if (!is.good()) {
+      throw VeloxRuntimeError(
+          __FILE__,
+          __LINE__,
+          __FUNCTION__,
+          "",
+          "error reading from std::istream",
+          error_source::kErrorSourceRuntime,
+          error_code::kInvalidArgument,
+          false /*retriable*/);
+    }
+    return CompactThetaSketchAlloc(
+        false, true, seed_hash, ThetaConstants::MAX_THETA, std::move(entries));
+  } else if (preamble_longs == 3) {
+    const uint32_t num_entries = read<uint32_t>(is);
+    read<uint32_t>(is); // unused
+    const auto theta = read<uint64_t>(is);
+    bool isEmpty = (num_entries == 0) && (theta == ThetaConstants::MAX_THETA);
+    std::vector<uint64_t, A> entries(num_entries, 0, allocator);
+    if (isEmpty) {
+      if (!is.good()) {
+        throw VeloxRuntimeError(
+            __FILE__,
+            __LINE__,
+            __FUNCTION__,
+            "",
+            "error reading from std::istream",
+            error_source::kErrorSourceRuntime,
+            error_code::kInvalidArgument,
+            false /*retriable*/);
+      }
+      return CompactThetaSketchAlloc(
+          true, true, seed_hash, theta, std::move(entries));
+    } else {
+      read(is, entries.data(), sizeof(uint64_t) * entries.size());
+      if (!is.good()) {
+        throw VeloxRuntimeError(
+            __FILE__,
+            __LINE__,
+            __FUNCTION__,
+            "",
+            "error reading from std::istream",
+            error_source::kErrorSourceRuntime,
+            error_code::kInvalidArgument,
+            false /*retriable*/);
+      }
+      return CompactThetaSketchAlloc(
+          false, true, seed_hash, theta, std::move(entries));
+    }
+  } else {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        std::to_string(preamble_longs) +
+            " longs of premable, but expected 1, 2, or 3",
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserializeV3(
+    uint8_t preamble_longs,
+    std::istream& is,
+    uint64_t seed,
+    const A& allocator) {
+  read<uint16_t>(is); // unused
+  const auto flags_byte = read<uint8_t>(is);
+  const auto seed_hash = read<uint16_t>(is);
+  const bool isEmpty = flags_byte & (1 << flags::IS_EMPTY);
+  if (!isEmpty)
+    checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+  uint64_t theta = ThetaConstants::MAX_THETA;
+  uint32_t num_entries = 0;
+  if (!isEmpty) {
+    if (preamble_longs == 1) {
+      num_entries = 1;
+    } else {
+      num_entries = read<uint32_t>(is);
+      read<uint32_t>(is); // unused
+      if (preamble_longs > 2)
+        theta = read<uint64_t>(is);
+    }
+  }
+  std::vector<uint64_t, A> entries(num_entries, 0, allocator);
+  if (!isEmpty)
+    read(is, entries.data(), sizeof(uint64_t) * entries.size());
+  const bool isOrdered = flags_byte & (1 << flags::IS_ORDERED);
+  if (!is.good()) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "error reading from std::istream",
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  return CompactThetaSketchAlloc(
+      isEmpty, isOrdered, seed_hash, theta, std::move(entries));
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserializeV4(
+    uint8_t preamble_longs,
+    std::istream& is,
+    uint64_t seed,
+    const A& allocator) {
+  const auto entry_bits = read<uint8_t>(is);
+  const auto num_entries_bytes = read<uint8_t>(is);
+  const auto flags_byte = read<uint8_t>(is);
+  const auto seed_hash = read<uint16_t>(is);
+  const bool isEmpty = flags_byte & (1 << flags::IS_EMPTY);
+  if (!isEmpty)
+    checker<true>::checkSeedHash(seed_hash, compute_seed_hash(seed));
+  uint64_t theta = ThetaConstants::MAX_THETA;
+  if (preamble_longs > 1)
+    theta = read<uint64_t>(is);
+  uint32_t num_entries = 0;
+  for (unsigned i = 0; i < num_entries_bytes; ++i) {
+    num_entries |= read<uint8_t>(is) << (i << 3);
+  }
+  vector_bytes buffer(
+      entry_bits, 0, allocator); // block of 8 entries takes entry_bits bytes
+  std::vector<uint64_t, A> entries(num_entries, 0, allocator);
+
+  // unpack blocks of 8 deltas
+  unsigned i;
+  for (i = 0; i + 7 < num_entries; i += 8) {
+    read(is, buffer.data(), buffer.size());
+    unpackBitsBlock8(&entries[i], buffer.data(), entry_bits);
+  }
+  // unpack extra deltas if fewer than 8 of them left
+  if (i < num_entries)
+    read(
+        is,
+        buffer.data(),
+        wholeBytesToHoldBits((num_entries - i) * entry_bits));
+  if (!is.good()) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "error reading from std::istream",
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  const uint8_t* ptr = buffer.data();
+  uint8_t offset = 0;
+  for (; i < num_entries; ++i) {
+    offset = unpackBits(entries[i], entry_bits, ptr, offset);
+  }
+  // undo deltas
+  uint64_t previous = 0;
+  for (i = 0; i < num_entries; ++i) {
+    entries[i] += previous;
+    previous = entries[i];
+  }
+  const bool isOrdered = flags_byte & (1 << flags::IS_ORDERED);
+  return CompactThetaSketchAlloc(
+      isEmpty, isOrdered, seed_hash, theta, std::move(entries));
+}
+
+template <typename A>
+CompactThetaSketchAlloc<A> CompactThetaSketchAlloc<A>::deserialize(
+    const void* bytes,
+    size_t size,
+    uint64_t seed,
+    const A& allocator) {
+  auto data = CompactThetaSketchParser<true>::parse(bytes, size, seed, false);
+  if (data.entryBits == 64) { // versions 1 to 3
+    const uint64_t* entries =
+        reinterpret_cast<const uint64_t*>(data.entriesStartPtr);
+    return CompactThetaSketchAlloc(
+        data.isEmpty,
+        data.isOrdered,
+        data.seedHash,
+        data.theta,
+        std::vector<uint64_t, A>(
+            entries, entries + data.numEntries, allocator));
+  } else { // version 4
+    std::vector<uint64_t, A> entries(data.numEntries, 0, allocator);
+    const uint8_t* ptr = reinterpret_cast<const uint8_t*>(data.entriesStartPtr);
+    // unpack blocks of 8 deltas
+    unsigned i;
+    for (i = 0; i + 7 < data.numEntries; i += 8) {
+      unpackBitsBlock8(&entries[i], ptr, data.entryBits);
+      ptr += data.entryBits;
+    }
+    // unpack extra deltas if fewer than 8 of them left
+    uint8_t offset = 0;
+    for (; i < data.numEntries; ++i) {
+      offset = unpackBits(entries[i], data.entryBits, ptr, offset);
+    }
+    // undo deltas
+    uint64_t previous = 0;
+    for (i = 0; i < data.numEntries; ++i) {
+      entries[i] += previous;
+      previous = entries[i];
+    }
+    return CompactThetaSketchAlloc(
+        data.isEmpty,
+        data.isOrdered,
+        data.seedHash,
+        data.theta,
+        std::move(entries));
+  }
+}
+
+// wrapped compact sketch
+
+template <typename A>
+WrappedCompactThetaSketchAlloc<A>::WrappedCompactThetaSketchAlloc(
+    const data_type& data)
+    : data_(data) {}
+
+template <typename A>
+const WrappedCompactThetaSketchAlloc<A> WrappedCompactThetaSketchAlloc<A>::wrap(
+    const void* bytes,
+    size_t size,
+    uint64_t seed,
+    bool dump_on_error) {
+  return WrappedCompactThetaSketchAlloc(
+      CompactThetaSketchParser<true>::parse(bytes, size, seed, dump_on_error));
+}
+
+template <typename A>
+A WrappedCompactThetaSketchAlloc<A>::getAllocator() const {
+  return A();
+}
+
+template <typename A>
+bool WrappedCompactThetaSketchAlloc<A>::isEmpty() const {
+  return data_.isEmpty;
+}
+
+template <typename A>
+bool WrappedCompactThetaSketchAlloc<A>::isOrdered() const {
+  return data_.isOrdered;
+}
+
+template <typename A>
+uint64_t WrappedCompactThetaSketchAlloc<A>::getTheta64() const {
+  return data_.theta;
+}
+
+template <typename A>
+uint32_t WrappedCompactThetaSketchAlloc<A>::getNumRetained() const {
+  return data_.numEntries;
+}
+
+template <typename A>
+uint16_t WrappedCompactThetaSketchAlloc<A>::getSeedHash() const {
+  return data_.seedHash;
+}
+
+template <typename A>
+auto WrappedCompactThetaSketchAlloc<A>::begin() const -> const_iterator {
+  return const_iterator(
+      data_.entriesStartPtr, data_.entryBits, data_.numEntries, 0);
+}
+
+template <typename A>
+auto WrappedCompactThetaSketchAlloc<A>::end() const -> const_iterator {
+  return const_iterator(
+      data_.entriesStartPtr,
+      data_.entryBits,
+      data_.numEntries,
+      data_.numEntries);
+}
+
+template <typename A>
+void WrappedCompactThetaSketchAlloc<A>::printSpecifics(
+    std::ostringstream&) const {}
+
+template <typename A>
+void WrappedCompactThetaSketchAlloc<A>::printItems(
+    std::ostringstream& os) const {
+  os << "### Retained entries" << std::endl;
+  for (const auto hash : *this) {
+    os << hash << std::endl;
+  }
+  os << "### End retained entries" << std::endl;
+}
+
+// assumes index == 0 or index == num_entries
+template <typename Allocator>
+WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::const_iterator(
+    const void* ptr,
+    uint8_t entry_bits,
+    uint32_t num_entries,
+    uint32_t index)
+    : ptr_(ptr),
+      entry_bits_(entry_bits),
+      num_entries_(num_entries),
+      index_(index),
+      previous_(0),
+      is_block_mode_(num_entries_ >= 8),
+      offset_(0) {
+  if (entry_bits == 64) { // no compression
+    ptr_ = reinterpret_cast<const uint64_t*>(ptr) + index;
+  } else if (index < num_entries) {
+    if (is_block_mode_) {
+      unpack8();
+    } else {
+      unpack1();
+    }
+  }
+}
+
+template <typename Allocator>
+auto WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator++()
+    -> const_iterator& {
+  if (entry_bits_ == 64) { // no compression
+    ptr_ = reinterpret_cast<const uint64_t*>(ptr_) + 1;
+    return *this;
+  }
+  if (++index_ < num_entries_) {
+    if (is_block_mode_) {
+      if ((index_ & 7) == 0) {
+        if (num_entries_ - index_ >= 8) {
+          unpack8();
+        } else {
+          is_block_mode_ = false;
+          unpack1();
+        }
+      }
+    } else {
+      unpack1();
+    }
+  }
+  return *this;
+}
+
+template <typename Allocator>
+void WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::unpack1() {
+  const uint32_t i = index_ & 7;
+  offset_ = unpackBits(
+      buffer_[i],
+      entry_bits_,
+      reinterpret_cast<const uint8_t*&>(ptr_),
+      offset_);
+  buffer_[i] += previous_;
+  previous_ = buffer_[i];
+}
+
+template <typename Allocator>
+void WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::unpack8() {
+  unpackBitsBlock8(
+      buffer_, reinterpret_cast<const uint8_t*>(ptr_), entry_bits_);
+  ptr_ = reinterpret_cast<const uint8_t*>(ptr_) + entry_bits_;
+  for (int i = 0; i < 8; ++i) {
+    buffer_[i] += previous_;
+    previous_ = buffer_[i];
+  }
+}
+
+template <typename Allocator>
+auto WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator++(int)
+    -> const_iterator {
+  const_iterator tmp(*this);
+  operator++();
+  return tmp;
+}
+
+template <typename Allocator>
+bool WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator!=(
+    const const_iterator& other) const {
+  if (entry_bits_ == 64)
+    return ptr_ != other.ptr_;
+  return index_ != other.index_;
+}
+
+template <typename Allocator>
+bool WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator==(
+    const const_iterator& other) const {
+  if (entry_bits_ == 64)
+    return ptr_ == other.ptr_;
+  return index_ == other.index_;
+}
+
+template <typename Allocator>
+auto WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator*()
+    const -> reference {
+  if (entry_bits_ == 64)
+    return *reinterpret_cast<const uint64_t*>(ptr_);
+  return buffer_[index_ & 7];
+}
+
+template <typename Allocator>
+auto WrappedCompactThetaSketchAlloc<Allocator>::const_iterator::operator->()
+    const -> pointer {
+  if (entry_bits_ == 64)
+    return reinterpret_cast<const uint64_t*>(ptr_);
+  return buffer_ + (index_ & 7);
+}
+
+} // namespace facebook::velox::common::theta
+
+#endif
diff --git a/velox/external/theta/ThetaSketch.h b/velox/external/theta/ThetaSketch.h
new file mode 100644
index 00000000000..ff31a2c064e
--- /dev/null
+++ b/velox/external/theta/ThetaSketch.h
@@ -0,0 +1,699 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "CompactThetaSketchParser.h"
+#include "ThetaUpdateSketchBase.h"
+
+namespace facebook::velox::common::theta {
+
+// forward declarations
+template <typename A>
+class ThetaSketchAlloc;
+template <typename A>
+class UpdateThetaSketchAlloc;
+template <typename A>
+class CompactThetaSketchAlloc;
+template <typename A>
+class WrappedCompactThetaSketchAlloc;
+
+/// Theta sketch alias with default allocator
+using thetaSketch = ThetaSketchAlloc<std::allocator<uint64_t>>;
+/// Update Theta sketch alias with default allocator
+using updateThetaSketch = UpdateThetaSketchAlloc<std::allocator<uint64_t>>;
+/// Compact Theta sketch alias with default allocator
+using compactThetaSketch = CompactThetaSketchAlloc<std::allocator<uint64_t>>;
+/// Wrapped Compact Theta sketch alias with default allocator
+using wrappedCompactThetaSketch =
+    WrappedCompactThetaSketchAlloc<std::allocator<uint64_t>>;
+
+/// Abstract base class for Theta sketch
+template <typename Allocator = std::allocator<uint64_t>>
+class BaseThetaSketchAlloc {
+ public:
+  virtual ~BaseThetaSketchAlloc() = default;
+
+  /**
+   * @return allocator
+   */
+  virtual Allocator getAllocator() const = 0;
+
+  /**
+   * @return true if this sketch represents an empty set (not the same as no
+   * retained entries!)
+   */
+  virtual bool isEmpty() const = 0;
+
+  /**
+   * @return estimate of the distinct count of the input stream
+   */
+  double getEstimate() const;
+
+  /**
+   * Returns the approximate lower error bound given a number of standard
+   * deviations. This parameter is similar to the number of standard deviations
+   * of the normal distribution and corresponds to approximately 67%, 95% and
+   * 99% confidence intervals.
+   * @param num_std_devs number of Standard Deviations (1, 2 or 3)
+   * @return the lower bound
+   */
+  double getLowerBound(uint8_t num_std_devs) const;
+
+  /**
+   * Returns the approximate upper error bound given a number of standard
+   * deviations. This parameter is similar to the number of standard deviations
+   * of the normal distribution and corresponds to approximately 67%, 95% and
+   * 99% confidence intervals.
+   * @param num_std_devs number of Standard Deviations (1, 2 or 3)
+   * @return the upper bound
+   */
+  double getUpperBound(uint8_t num_std_devs) const;
+
+  /**
+   * @return true if the sketch is in estimation mode (as opposed to exact mode)
+   */
+  bool isEstimationMode() const;
+
+  /**
+   * @return theta as a fraction from 0 to 1 (effective sampling rate)
+   */
+  double getTheta() const;
+
+  /**
+   * @return theta as a positive integer between 0 and LLONG_MAX
+   */
+  virtual uint64_t getTheta64() const = 0;
+
+  /**
+   * @return the number of retained entries in the sketch
+   */
+  virtual uint32_t getNumRetained() const = 0;
+
+  /**
+   * @return hash of the seed that was used to hash the input
+   */
+  virtual uint16_t getSeedHash() const = 0;
+
+  /**
+   * @return true if retained entries are ordered
+   */
+  virtual bool isOrdered() const = 0;
+
+  /**
+   * Provides a human-readable summary of this sketch as a string
+   * @param print_items if true include the list of items retained by the sketch
+   * @return sketch summary as a string
+   */
+  virtual string<Allocator> toString(bool print_items = false) const;
+
+ protected:
+  virtual void printSpecifics(std::ostringstream& os) const = 0;
+  virtual void printItems(std::ostringstream& os) const = 0;
+};
+
+/// Base class for the Theta Sketch, a generalization of the Kth Minimum Value
+/// (KMV) sketch.
+template <typename Allocator = std::allocator<uint64_t>>
+class ThetaSketchAlloc : public BaseThetaSketchAlloc<Allocator> {
+ public:
+  using Entry = uint64_t;
+  using ExtractKey = trivialExtractKey;
+  using iterator = ThetaIterator<Entry, ExtractKey>;
+  using const_iterator = ThetaConstIterator<Entry, ExtractKey>;
+
+  virtual ~ThetaSketchAlloc() = default;
+
+  /**
+   * Iterator over hash values in this sketch.
+   * @return begin iterator
+   */
+  virtual iterator begin() = 0;
+
+  /**
+   * Iterator pointing past the valid range.
+   * Not to be incremented or dereferenced.
+   * @return end iterator
+   */
+  virtual iterator end() = 0;
+
+  /**
+   * Const iterator over hash values in this sketch.
+   * @return begin iterator
+   */
+  virtual const_iterator begin() const = 0;
+
+  /**
+   * Const iterator pointing past the valid range.
+   * Not to be incremented or dereferenced.
+   * @return end iterator
+   */
+  virtual const_iterator end() const = 0;
+
+ protected:
+  virtual void printItems(std::ostringstream& os) const;
+};
+
+// forward declaration
+template <typename A>
+class CompactThetaSketchAlloc;
+
+/**
+ * Update Theta sketch.
+ * The purpose of this class is to build a Theta sketch from input data via the
+ * update() methods. There is no constructor. Use builder instead.
+ */
+template <typename Allocator = std::allocator<uint64_t>>
+class UpdateThetaSketchAlloc : public ThetaSketchAlloc<Allocator> {
+ public:
+  using Base = ThetaSketchAlloc<Allocator>;
+  using Entry = typename Base::Entry;
+  using ExtractKey = typename Base::ExtractKey;
+  using iterator = typename Base::iterator;
+  using const_iterator = typename Base::const_iterator;
+  using ThetaTable = ThetaUpdateSketchBase<Entry, ExtractKey, Allocator>;
+  using resizeFactor = typename ThetaTable::resizeFactor;
+
+  // No constructor here. Use builder instead.
+  class builder;
+
+  /**
+   * Copy constructor
+   * @param other sketch to be copied
+   */
+  UpdateThetaSketchAlloc(const UpdateThetaSketchAlloc& other) = default;
+
+  /**
+   * Move constructor
+   * @param other sketch to be moved
+   */
+  UpdateThetaSketchAlloc(UpdateThetaSketchAlloc&& other) noexcept = default;
+
+  virtual ~UpdateThetaSketchAlloc() = default;
+
+  /**
+   * Copy assignment
+   * @param other sketch to be copied
+   * @return reference to this sketch
+   */
+  UpdateThetaSketchAlloc& operator=(const UpdateThetaSketchAlloc& other) =
+      default;
+
+  /**
+   * Move assignment
+   * @param other sketch to be moved
+   * @return reference to this sketch
+   */
+  UpdateThetaSketchAlloc& operator=(UpdateThetaSketchAlloc&& other) = default;
+
+  virtual Allocator getAllocator() const override;
+  virtual bool isEmpty() const override;
+  virtual bool isOrdered() const override;
+  virtual uint16_t getSeedHash() const override;
+  virtual uint64_t getTheta64() const override;
+  virtual uint32_t getNumRetained() const override;
+
+  /**
+   * @return configured nominal number of entries in the sketch
+   */
+  uint8_t getLgK() const;
+
+  /**
+   * @return configured resize factor of the sketch
+   */
+  resizeFactor getRf() const;
+
+  /**
+   * Update this sketch with a given string.
+   * @param value string to update the sketch with
+   */
+  void update(const std::string& value);
+
+  /**
+   * Update this sketch with a given unsigned 64-bit integer.
+   * @param value uint64_t to update the sketch with
+   */
+  void update(uint64_t value);
+
+  /**
+   * Update this sketch with a given signed 64-bit integer.
+   * @param value int64_t to update the sketch with
+   */
+  void update(int64_t value);
+
+  /**
+   * Update this sketch with a given unsigned 32-bit integer.
+   * For compatibility with Java implementation.
+   * @param value uint32_t to update the sketch with
+   */
+  void update(uint32_t value);
+
+  /**
+   * Update this sketch with a given signed 32-bit integer.
+   * For compatibility with Java implementation.
+   * @param value int32_t to update the sketch with
+   */
+  void update(int32_t value);
+
+  /**
+   * Update this sketch with a given unsigned 16-bit integer.
+   * For compatibility with Java implementation.
+   * @param value uint16_t to update the sketch with
+   */
+  void update(uint16_t value);
+
+  /**
+   * Update this sketch with a given signed 16-bit integer.
+   * For compatibility with Java implementation.
+   * @param value int16_t to update the sketch with
+   */
+  void update(int16_t value);
+
+  /**
+   * Update this sketch with a given unsigned 8-bit integer.
+   * For compatibility with Java implementation.
+   * @param value uint8_t to update the sketch with
+   */
+  void update(uint8_t value);
+
+  /**
+   * Update this sketch with a given signed 8-bit integer.
+   * For compatibility with Java implementation.
+   * @param value int8_t to update the sketch with
+   */
+  void update(int8_t value);
+
+  /**
+   * Update this sketch with a given double-precision floating point value.
+   * For compatibility with Java implementation.
+   * @param value double to update the sketch with
+   */
+  void update(double value);
+
+  /**
+   * Update this sketch with a given floating point value.
+   * For compatibility with Java implementation.
+   * @param value float to update the sketch with
+   */
+  void update(float value);
+
+  /**
+   * Update this sketch with given data of any type.
+   * This is a "universal" update that covers all cases above,
+   * but may produce different hashes.
+   * Be very careful to hash input values consistently using the same approach
+   * both over time and on different platforms
+   * and while passing sketches between C++ environment and Java environment.
+   * Otherwise two sketches that should represent overlapping sets will be
+   * disjoint For instance, for signed 32-bit values call update(int32_t) method
+   * above, which does widening conversion to int64_t, if compatibility with
+   * Java is expected
+   * @param data pointer to the data
+   * @param length of the data in bytes
+   */
+  void update(const void* data, size_t length);
+
+  /**
+   * Remove retained entries in excess of the nominal size k (if any)
+   */
+  void trim();
+
+  /**
+   * Reset the sketch to the initial empty state
+   */
+  void reset();
+
+  /**
+   * Converts this sketch to a compact sketch (ordered or unordered).
+   * @param ordered optional flag to specify if an ordered sketch should be
+   * produced
+   * @return compact sketch
+   */
+  CompactThetaSketchAlloc<Allocator> compact(bool ordered = true) const;
+
+  virtual iterator begin() override;
+  virtual iterator end() override;
+  virtual const_iterator begin() const override;
+  virtual const_iterator end() const override;
+
+ private:
+  ThetaTable table_;
+
+  // for builder
+  UpdateThetaSketchAlloc(
+      uint8_t lg_cur_size,
+      uint8_t lg_nom_size,
+      resizeFactor rf,
+      float p,
+      uint64_t theta,
+      uint64_t seed,
+      const Allocator& allocator);
+
+  virtual void printSpecifics(std::ostringstream& os) const override;
+};
+
+/**
+ * Compact Theta sketch.
+ * This is an immutable form of the Theta sketch, the form that can be
+ * serialized and deserialized.
+ */
+template <typename Allocator = std::allocator<uint64_t>>
+class CompactThetaSketchAlloc : public ThetaSketchAlloc<Allocator> {
+ public:
+  using Base = ThetaSketchAlloc<Allocator>;
+  using iterator = typename Base::iterator;
+  using const_iterator = typename Base::const_iterator;
+  using AllocBytes =
+      typename std::allocator_traits<Allocator>::template rebind_alloc<uint8_t>;
+  using vector_bytes = std::vector<uint8_t, AllocBytes>;
+
+  static const uint8_t UNCOMPRESSED_SERIAL_VERSION = 3;
+  static const uint8_t COMPRESSED_SERIAL_VERSION = 4;
+  static const uint8_t SKETCH_TYPE = 3;
+
+  // Instances of this type can be obtained:
+  // - by compacting an update_theta_sketch_alloc
+  // - as a result of a set operation
+  // - by deserializing a previously serialized compact sketch
+
+  /**
+   * Copy constructor.
+   * Constructs a compact sketch from any other type of Theta sketch
+   * @param other sketch to be constructed from
+   * @param ordered if true make the resulting sketch ordered
+   */
+  template <typename Other>
+  CompactThetaSketchAlloc(const Other& other, bool ordered);
+
+  /**
+   * Copy constructor
+   * @param other sketch to be copied
+   */
+  CompactThetaSketchAlloc(const CompactThetaSketchAlloc& other) = default;
+
+  /**
+   * Move constructor
+   * @param other sketch to be moved
+   */
+  CompactThetaSketchAlloc(CompactThetaSketchAlloc&& other) noexcept = default;
+
+  virtual ~CompactThetaSketchAlloc() = default;
+
+  /**
+   * Copy assignment
+   * @param other sketch to be copied
+   * @return reference to this sketch
+   */
+  CompactThetaSketchAlloc& operator=(const CompactThetaSketchAlloc& other) =
+      default;
+
+  /**
+   * Move assignment
+   * @param other sketch to be moved
+   * @return reference to this sketch
+   */
+  CompactThetaSketchAlloc& operator=(CompactThetaSketchAlloc&& other) = default;
+
+  virtual Allocator getAllocator() const override;
+  virtual bool isEmpty() const override;
+  virtual bool isOrdered() const override;
+  virtual uint64_t getTheta64() const override;
+  virtual uint32_t getNumRetained() const override;
+  virtual uint16_t getSeedHash() const override;
+
+  /**
+   * Computes maximum serialized size in bytes
+   * @param lg_k nominal number of entries in the sketch
+   */
+  static size_t getMaxSerializedSizeBytes(uint8_t lg_k);
+
+  /**
+   * Computes size in bytes required to serialize the current state of the
+   * sketch. Computing compressed size is expensive. It takes iterating over all
+   * retained hashes, and the actual serialization will have to look at them
+   * again.
+   * @param compressed if true compressed size is returned (if applicable)
+   */
+  size_t getSerializedSizeBytes(bool compressed = false) const;
+
+  /**
+   * This method serializes the sketch into a given stream in a binary form
+   * @param os output stream
+   */
+  void serialize(std::ostream& os) const;
+
+  /**
+   * This method serializes the sketch as a vector of bytes.
+   * An optional header can be reserved in front of the sketch.
+   * It is an uninitialized space of a given size.
+   * This header is used in Datasketches PostgreSQL extension.
+   * @param header_size_bytes space to reserve in front of the sketch
+   */
+  vector_bytes serialize(unsigned header_size_bytes = 0) const;
+
+  /**
+   * This method serializes the sketch into a given stream in a compressed
+   * binary form. Compression is applied to ordered sketches except empty and
+   * single item. For unordered, empty and single item sketches this method is
+   * equivalent to serialize()
+   * @param os output stream
+   */
+  void serializeCompressed(std::ostream& os) const;
+
+  /**
+   * This method serializes the sketch as a vector of bytes.
+   * An optional header can be reserved in front of the sketch.
+   * It is an uninitialized space of a given size.
+   * This header is used in Datasketches PostgreSQL extension.
+   * Compression is applied to ordered sketches except empty and single item.
+   * For unordered, empty and single item sketches this method is equivalent to
+   * serialize()
+   * @param header_size_bytes space to reserve in front of the sketch
+   */
+  vector_bytes serializeCompressed(unsigned header_size_bytes = 0) const;
+
+  virtual iterator begin() override;
+  virtual iterator end() override;
+  virtual const_iterator begin() const override;
+  virtual const_iterator end() const override;
+
+  /**
+   * This method deserializes a sketch from a given stream.
+   * @param is input stream
+   * @param seed the seed for the hash function that was used to create the
+   * sketch
+   * @param allocator instance of an Allocator
+   * @return an instance of the sketch
+   */
+  static CompactThetaSketchAlloc deserialize(
+      std::istream& is,
+      uint64_t seed = DEFAULT_SEED,
+      const Allocator& allocator = Allocator());
+
+  /**
+   * This method deserializes a sketch from a given array of bytes.
+   * @param bytes pointer to the array of bytes
+   * @param size the size of the array
+   * @param seed the seed for the hash function that was used to create the
+   * sketch
+   * @param allocator instance of an Allocator
+   * @return an instance of the sketch
+   */
+  static CompactThetaSketchAlloc deserialize(
+      const void* bytes,
+      size_t size,
+      uint64_t seed = DEFAULT_SEED,
+      const Allocator& allocator = Allocator());
+
+ private:
+  enum flags { IS_BIG_ENDIAN, IS_READ_ONLY, IS_EMPTY, IS_COMPACT, IS_ORDERED };
+
+  bool isEmpty_;
+  bool isOrdered_;
+  uint16_t seedHash_;
+  uint64_t theta_;
+  std::vector<uint64_t, Allocator> entries_;
+
+  uint8_t getPreambleLongs(bool compressed) const;
+  bool isSuitableForCompression() const;
+  uint8_t computeEntryBits() const;
+  uint8_t getNumEntriesBytes() const;
+  size_t getCompressedSerializedSizeBytes(
+      uint8_t entry_bits,
+      uint8_t num_entries_bytes) const;
+  void serializeVersion4(std::ostream& os) const;
+  vector_bytes serializeVersion4(unsigned header_size_bytes = 0) const;
+
+  static CompactThetaSketchAlloc deserializeV1(
+      uint8_t preamble_longs,
+      std::istream& is,
+      uint64_t seed,
+      const Allocator& allocator);
+  static CompactThetaSketchAlloc deserializeV2(
+      uint8_t preamble_longs,
+      std::istream& is,
+      uint64_t seed,
+      const Allocator& allocator);
+  static CompactThetaSketchAlloc deserializeV3(
+      uint8_t preamble_longs,
+      std::istream& is,
+      uint64_t seed,
+      const Allocator& allocator);
+  static CompactThetaSketchAlloc deserializeV4(
+      uint8_t preamble_longs,
+      std::istream& is,
+      uint64_t seed,
+      const Allocator& allocator);
+
+  virtual void printSpecifics(std::ostringstream& os) const override;
+
+  template <
+      typename E,
+      typename EK,
+      typename P,
+      typename S,
+      typename CS,
+      typename A>
+  friend class ThetaUnionBase;
+  template <
+      typename E,
+      typename EK,
+      typename P,
+      typename S,
+      typename CS,
+      typename A>
+  friend class ThetaIntersectionBase;
+  template <typename E, typename EK, typename CS, typename A>
+  friend class ThetaSetDifferenceBase;
+  CompactThetaSketchAlloc(
+      bool is_empty,
+      bool is_ordered,
+      uint16_t seed_hash,
+      uint64_t theta,
+      std::vector<uint64_t, Allocator>&& entries);
+};
+
+/// Update Theta sketch builder
+template <typename Allocator>
+class UpdateThetaSketchAlloc<Allocator>::builder
+    : public ThetaBaseBuilder<builder, Allocator> {
+ public:
+  /**
+   * Constructor
+   * @param allocator
+   */
+  builder(const Allocator& allocator = Allocator());
+  /// @return instance of Update Theta sketch
+  UpdateThetaSketchAlloc build() const;
+};
+
+/**
+ * Wrapped Compact Theta sketch.
+ * This is to wrap a buffer containing a serialized compact sketch and use it in
+ * a set operation avoiding some cost of deserialization. It does not take the
+ * ownership of the buffer.
+ */
+template <typename Allocator = std::allocator<uint64_t>>
+class WrappedCompactThetaSketchAlloc : public BaseThetaSketchAlloc<Allocator> {
+ public:
+  class const_iterator;
+
+  virtual Allocator getAllocator() const override;
+  virtual bool isEmpty() const override;
+  virtual bool isOrdered() const override;
+  virtual uint64_t getTheta64() const override;
+  virtual uint32_t getNumRetained() const override;
+  virtual uint16_t getSeedHash() const override;
+
+  /**
+   * Const iterator over hash values in this sketch.
+   * @return begin iterator
+   */
+  const_iterator begin() const;
+
+  /**
+   * Const iterator pointing past the valid range.
+   * Not to be incremented or dereferenced.
+   * @return end iterator
+   */
+  const_iterator end() const;
+
+  /**
+   * This method wraps a serialized compact sketch as an array of bytes.
+   * @param bytes pointer to the array of bytes
+   * @param size the size of the array
+   * @param seed the seed for the hash function that was used to create the
+   * sketch
+   * @param dump_on_error if true prints hex dump of the input
+   * @return an instance of the sketch
+   */
+  static const WrappedCompactThetaSketchAlloc wrap(
+      const void* bytes,
+      size_t size,
+      uint64_t seed = DEFAULT_SEED,
+      bool dump_on_error = false);
+
+ protected:
+  virtual void printSpecifics(std::ostringstream& os) const override;
+  virtual void printItems(std::ostringstream& os) const override;
+
+ private:
+  using data_type = CompactThetaSketchParser<true>::CompactThetaSketchData;
+  data_type data_;
+
+  WrappedCompactThetaSketchAlloc(const data_type& data);
+};
+
+template <typename Allocator>
+class WrappedCompactThetaSketchAlloc<Allocator>::const_iterator {
+ public:
+  using iterator_category = std::input_iterator_tag;
+  using value_type = const uint64_t;
+  using difference_type = void;
+  using pointer = value_type*;
+  using reference = uint64_t;
+
+  const_iterator(
+      const void* ptr,
+      uint8_t entry_bits,
+      uint32_t num_entries,
+      uint32_t index);
+  const_iterator& operator++();
+  const_iterator operator++(int);
+  bool operator==(const const_iterator& other) const;
+  bool operator!=(const const_iterator& other) const;
+  reference operator*() const;
+  pointer operator->() const;
+
+ private:
+  const void* ptr_;
+  uint8_t entry_bits_;
+  uint32_t num_entries_;
+  uint32_t index_;
+  uint64_t previous_;
+  bool is_block_mode_;
+  uint8_t offset_;
+  uint64_t buffer_[8];
+
+  inline void unpack1();
+  inline void unpack8();
+};
+
+} // namespace facebook::velox::common::theta
+
+#include "ThetaSketch.cpp"
diff --git a/velox/external/theta/ThetaUnion.cpp b/velox/external/theta/ThetaUnion.cpp
new file mode 100644
index 00000000000..d26dad88c75
--- /dev/null
+++ b/velox/external/theta/ThetaUnion.cpp
@@ -0,0 +1,79 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#ifndef THETA_UNION_CPP
+#define THETA_UNION_CPP
+
+#include "ThetaUnion.h"
+
+namespace facebook::velox::common::theta {
+
+template <typename A>
+ThetaUnionAlloc<A>::ThetaUnionAlloc(
+    uint8_t lgCurSize,
+    uint8_t lgNomSize,
+    resizeFactor rf,
+    float p,
+    uint64_t theta,
+    uint64_t seed,
+    const A& allocator)
+    : state_(
+          lgCurSize,
+          lgNomSize,
+          rf,
+          p,
+          theta,
+          seed,
+          nop_policy(),
+          allocator) {}
+
+template <typename A>
+template <typename FwdSketch>
+void ThetaUnionAlloc<A>::update(FwdSketch&& sketch) {
+  state_.update(std::forward<FwdSketch>(sketch));
+}
+
+template <typename A>
+auto ThetaUnionAlloc<A>::getResult(bool ordered) const -> CompactSketch {
+  return state_.getResult(ordered);
+}
+
+template <typename A>
+void ThetaUnionAlloc<A>::reset() {
+  state_.reset();
+}
+
+template <typename A>
+ThetaUnionAlloc<A>::builder::builder(const A& allocator)
+    : ThetaBaseBuilder<builder, A>(allocator) {}
+
+template <typename A>
+auto ThetaUnionAlloc<A>::builder::build() const -> ThetaUnionAlloc {
+  return ThetaUnionAlloc(
+      this->startingLgSize(),
+      this->lg_k_,
+      this->rf_,
+      this->p_,
+      this->startingTheta(),
+      this->seed_,
+      this->allocator_);
+}
+
+} // namespace facebook::velox::common::theta
+
+#endif
diff --git a/velox/external/theta/ThetaUnion.h b/velox/external/theta/ThetaUnion.h
new file mode 100644
index 00000000000..e9e3cb54e3d
--- /dev/null
+++ b/velox/external/theta/ThetaUnion.h
@@ -0,0 +1,113 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "Serde.h"
+#include "ThetaSketch.h"
+#include "ThetaUnionBase.h"
+
+namespace facebook::velox::common::theta {
+
+// forward declaration
+template <typename A>
+class ThetaUnionAlloc;
+
+// alias with default allocator for convenience
+using ThetaUnion = ThetaUnionAlloc<std::allocator<uint64_t>>;
+
+/**
+ * Theta Union.
+ * Computes union of Theta sketches. There is no constructor. Use builder
+ * instead.
+ */
+template <typename Allocator = std::allocator<uint64_t>>
+class ThetaUnionAlloc {
+ public:
+  using Entry = uint64_t;
+  using ExtractKey = trivialExtractKey;
+  using Sketch = ThetaSketchAlloc<Allocator>;
+  using CompactSketch = CompactThetaSketchAlloc<Allocator>;
+  using resizeFactor = ThetaConstants::resizeFactor;
+
+  // there is no payload in Theta sketch entry
+  struct nop_policy {
+    void operator()(uint64_t internal_entry, uint64_t incoming_entry) const {
+      unused(internal_entry);
+      unused(incoming_entry);
+    }
+  };
+  using State = ThetaUnionBase<
+      Entry,
+      ExtractKey,
+      nop_policy,
+      Sketch,
+      CompactSketch,
+      Allocator>;
+
+  // No constructor here. Use builder instead.
+  class builder;
+
+  /**
+   * Update the union with a given sketch
+   * @param sketch to update the union with
+   */
+  template <typename FwdSketch>
+  void update(FwdSketch&& sketch);
+
+  /**
+   * Produces a copy of the current state of the union as a compact sketch.
+   * @param ordered optional flag to specify if an ordered sketch should be
+   * produced
+   * @return the result of the union
+   */
+  CompactSketch getResult(bool ordered = true) const;
+
+  /// Reset the union to the initial empty state
+  void reset();
+
+ private:
+  State state_;
+
+  // for builder
+  ThetaUnionAlloc(
+      uint8_t lg_cur_size,
+      uint8_t lg_nom_size,
+      resizeFactor rf,
+      float p,
+      uint64_t theta,
+      uint64_t seed,
+      const Allocator& allocator);
+};
+
+/// Theta union builder
+template <typename A>
+class ThetaUnionAlloc<A>::builder : public ThetaBaseBuilder<builder, A> {
+ public:
+  builder(const A& allocator = A());
+
+  /**
+   * Create an instance of the union with predefined parameters.
+   * @return an instance of the union
+   */
+  ThetaUnionAlloc<A> build() const;
+};
+
+} // namespace facebook::velox::common::theta
+
+#include "ThetaUnion.cpp"
diff --git a/velox/external/theta/ThetaUnionBase.cpp b/velox/external/theta/ThetaUnionBase.cpp
new file mode 100644
index 00000000000..4567bd46e32
--- /dev/null
+++ b/velox/external/theta/ThetaUnionBase.cpp
@@ -0,0 +1,168 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#ifndef THETA_UNION_BASE_CPP
+#define THETA_UNION_BASE_CPP
+
+#include <algorithm>
+
+#include "ConditionalForward.h"
+#include "ThetaUnionBase.h"
+#include "velox/common/base/Exceptions.h"
+
+namespace facebook::velox::common::theta {
+
+template <
+    typename EN,
+    typename EK,
+    typename P,
+    typename S,
+    typename CS,
+    typename A>
+ThetaUnionBase<EN, EK, P, S, CS, A>::ThetaUnionBase(
+    uint8_t lg_cur_size,
+    uint8_t lg_nom_size,
+    resizeFactor rf,
+    float p,
+    uint64_t theta,
+    uint64_t seed,
+    const P& policy,
+    const A& allocator)
+    : policy_(policy),
+      table_(lg_cur_size, lg_nom_size, rf, p, theta, seed, allocator),
+      union_theta_(table_.theta_) {}
+
+template <
+    typename EN,
+    typename EK,
+    typename P,
+    typename S,
+    typename CS,
+    typename A>
+template <typename SS>
+void ThetaUnionBase<EN, EK, P, S, CS, A>::update(SS&& sketch) {
+  if (sketch.isEmpty())
+    return;
+  if (sketch.getSeedHash() != compute_seed_hash(table_.seed_)) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "seed hash mismatch",
+        error_source::kErrorSourceRuntime,
+        error_code::kUnknown,
+        false /*retriable*/);
+  }
+  table_.isEmpty_ = false;
+  union_theta_ = std::min(union_theta_, sketch.getTheta64());
+  for (auto&& entry : sketch) {
+    const uint64_t hash = EK()(entry);
+    if (hash < union_theta_ && hash < table_.theta_) {
+      auto result = table_.find(hash);
+      if (!result.second) {
+        table_.insert(result.first, conditionalForward<SS>(entry));
+      } else {
+        policy_(*result.first, conditionalForward<SS>(entry));
+      }
+    } else {
+      if (sketch.isOrdered())
+        break; // early stop
+    }
+  }
+  union_theta_ = std::min(union_theta_, table_.theta_);
+}
+
+template <
+    typename EN,
+    typename EK,
+    typename P,
+    typename S,
+    typename CS,
+    typename A>
+CS ThetaUnionBase<EN, EK, P, S, CS, A>::getResult(bool ordered) const {
+  std::vector<EN, A> entries(table_.allocator_);
+  if (table_.isEmpty_)
+    return CS(
+        true,
+        true,
+        compute_seed_hash(table_.seed_),
+        union_theta_,
+        std::move(entries));
+  entries.reserve(table_.numEntries_);
+  uint64_t theta = std::min(union_theta_, table_.theta_);
+  const uint32_t nominal_num = 1 << table_.lgNomSize_;
+  if (union_theta_ >= table_.theta_) {
+    std::copy_if(
+        table_.begin(),
+        table_.end(),
+        std::back_inserter(entries),
+        keyNotZero<EN, EK>());
+  } else {
+    std::copy_if(
+        table_.begin(),
+        table_.end(),
+        std::back_inserter(entries),
+        keyNotZeroLessThan<uint64_t, EN, EK>(theta));
+  }
+  if (entries.size() > nominal_num) {
+    std::nth_element(
+        entries.begin(),
+        entries.begin() + nominal_num,
+        entries.end(),
+        comparator());
+    theta = EK()(entries[nominal_num]);
+    entries.erase(entries.begin() + nominal_num, entries.end());
+    entries.shrink_to_fit();
+  }
+  if (ordered)
+    std::sort(entries.begin(), entries.end(), comparator());
+  return CS(
+      table_.isEmpty_,
+      ordered,
+      compute_seed_hash(table_.seed_),
+      theta,
+      std::move(entries));
+}
+
+template <
+    typename EN,
+    typename EK,
+    typename P,
+    typename S,
+    typename CS,
+    typename A>
+const P& ThetaUnionBase<EN, EK, P, S, CS, A>::getPolicy() const {
+  return policy_;
+}
+
+template <
+    typename EN,
+    typename EK,
+    typename P,
+    typename S,
+    typename CS,
+    typename A>
+void ThetaUnionBase<EN, EK, P, S, CS, A>::reset() {
+  table_.reset();
+  union_theta_ = table_.theta_;
+}
+
+} // namespace facebook::velox::common::theta
+
+#endif
diff --git a/velox/external/theta/ThetaUnionBase.h b/velox/external/theta/ThetaUnionBase.h
new file mode 100644
index 00000000000..1d25f060191
--- /dev/null
+++ b/velox/external/theta/ThetaUnionBase.h
@@ -0,0 +1,65 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include "ThetaUpdateSketchBase.h"
+
+namespace facebook::velox::common::theta {
+
+template <
+    typename Entry,
+    typename ExtractKey,
+    typename Policy,
+    typename Sketch,
+    typename CompactSketch,
+    typename Allocator>
+class ThetaUnionBase {
+ public:
+  using hashTable = ThetaUpdateSketchBase<Entry, ExtractKey, Allocator>;
+  using resizeFactor = typename hashTable::resizeFactor;
+  using comparator = compareByKey<ExtractKey>;
+
+  ThetaUnionBase(
+      uint8_t lg_cur_size,
+      uint8_t lg_nom_size,
+      resizeFactor rf,
+      float p,
+      uint64_t theta,
+      uint64_t seed,
+      const Policy& policy,
+      const Allocator& allocator);
+
+  template <typename FwdSketch>
+  void update(FwdSketch&& sketch);
+
+  CompactSketch getResult(bool ordered = true) const;
+
+  const Policy& getPolicy() const;
+
+  void reset();
+
+ private:
+  Policy policy_;
+  hashTable table_;
+  uint64_t union_theta_;
+};
+
+} // namespace facebook::velox::common::theta
+
+#include "ThetaUnionBase.cpp"
diff --git a/velox/external/theta/ThetaUpdateSketchBase.cpp b/velox/external/theta/ThetaUpdateSketchBase.cpp
new file mode 100644
index 00000000000..591c6a084a0
--- /dev/null
+++ b/velox/external/theta/ThetaUpdateSketchBase.cpp
@@ -0,0 +1,530 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#ifndef THETA_UPDATE_SKETCH_BASE_CPP
+#define THETA_UPDATE_SKETCH_BASE_CPP
+
+#include <algorithm>
+#include <iostream>
+#include <sstream>
+#include <stdexcept>
+
+#include "ThetaHelpers.h"
+#include "ThetaUpdateSketchBase.h"
+#include "velox/common/base/Exceptions.h"
+
+namespace facebook::velox::common::theta {
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>::ThetaUpdateSketchBase(
+    uint8_t lgCurSize,
+    uint8_t lgNomSize,
+    resizeFactor rf,
+    float p,
+    uint64_t theta,
+    uint64_t seed,
+    const A& allocator,
+    bool isEmpty)
+    : allocator_(allocator),
+      isEmpty_(isEmpty),
+      lgCurSize_(lgCurSize),
+      lgNomSize_(lgNomSize),
+      rf_(rf),
+      p_(p),
+      numEntries_(0),
+      theta_(theta),
+      seed_(seed),
+      entries_(nullptr) {
+  if (lgCurSize > 0) {
+    const size_t size = 1ULL << lgCurSize;
+    entries_ = allocator_.allocate(size);
+    for (size_t i = 0; i < size; ++i)
+      EK()(entries_[i]) = 0;
+  }
+}
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>::ThetaUpdateSketchBase(
+    const ThetaUpdateSketchBase& other)
+    : allocator_(other.allocator_),
+      isEmpty_(other.isEmpty_),
+      lgCurSize_(other.lgCurSize_),
+      lgNomSize_(other.lgNomSize_),
+      rf_(other.rf_),
+      p_(other.p_),
+      numEntries_(other.numEntries_),
+      theta_(other.theta_),
+      seed_(other.seed_),
+      entries_(nullptr) {
+  if (other.entries_ != nullptr) {
+    const size_t size = 1ULL << lgCurSize_;
+    entries_ = allocator_.allocate(size);
+    for (size_t i = 0; i < size; ++i) {
+      if (EK()(other.entries_[i]) != 0) {
+        new (&entries_[i]) EN(other.entries_[i]);
+      } else {
+        EK()(entries_[i]) = 0;
+      }
+    }
+  }
+}
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>::ThetaUpdateSketchBase(
+    ThetaUpdateSketchBase&& other) noexcept
+    : allocator_(std::move(other.allocator_)),
+      isEmpty_(other.isEmpty_),
+      lgCurSize_(other.lgCurSize_),
+      lgNomSize_(other.lgNomSize_),
+      rf_(other.rf_),
+      p_(other.p_),
+      numEntries_(other.numEntries_),
+      theta_(other.theta_),
+      seed_(other.seed_),
+      entries_(other.entries_) {
+  other.entries_ = nullptr;
+}
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>::~ThetaUpdateSketchBase() {
+  if (entries_ != nullptr) {
+    const size_t size = 1ULL << lgCurSize_;
+    for (size_t i = 0; i < size; ++i) {
+      if (EK()(entries_[i]) != 0)
+        entries_[i].~EN();
+    }
+    allocator_.deallocate(entries_, size);
+  }
+}
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>& ThetaUpdateSketchBase<EN, EK, A>::operator=(
+    const ThetaUpdateSketchBase& other) {
+  ThetaUpdateSketchBase<EN, EK, A> copy(other);
+  std::swap(allocator_, copy.allocator_);
+  std::swap(isEmpty_, copy.isEmpty_);
+  std::swap(lgCurSize_, copy.lgCurSize_);
+  std::swap(lgNomSize_, copy.lgNomSize_);
+  std::swap(rf_, copy.rf_);
+  std::swap(p_, copy.p_);
+  std::swap(numEntries_, copy.numEntries_);
+  std::swap(theta_, copy.theta_);
+  std::swap(seed_, copy.seed_);
+  std::swap(entries_, copy.entries_);
+  return *this;
+}
+
+template <typename EN, typename EK, typename A>
+ThetaUpdateSketchBase<EN, EK, A>& ThetaUpdateSketchBase<EN, EK, A>::operator=(
+    ThetaUpdateSketchBase&& other) {
+  std::swap(allocator_, other.allocator_);
+  std::swap(isEmpty_, other.isEmpty_);
+  std::swap(lgCurSize_, other.lgCurSize_);
+  std::swap(lgNomSize_, other.lgNomSize_);
+  std::swap(rf_, other.rf_);
+  std::swap(p_, other.p_);
+  std::swap(numEntries_, other.numEntries_);
+  std::swap(theta_, other.theta_);
+  std::swap(seed_, other.seed_);
+  std::swap(entries_, other.entries_);
+  return *this;
+}
+
+template <typename EN, typename EK, typename A>
+uint64_t ThetaUpdateSketchBase<EN, EK, A>::hashAndScreen(
+    const void* data,
+    size_t length) {
+  isEmpty_ = false;
+  const uint64_t hash = computeHash(data, length, seed_);
+  if (hash >= theta_)
+    return 0; // hash == 0 is reserved to mark empty slots in the table
+  return hash;
+}
+
+template <typename EN, typename EK, typename A>
+auto ThetaUpdateSketchBase<EN, EK, A>::find(uint64_t key) const
+    -> std::pair<iterator, bool> {
+  return find(entries_, lgCurSize_, key);
+}
+
+template <typename EN, typename EK, typename A>
+auto ThetaUpdateSketchBase<EN, EK, A>::find(
+    EN* entries,
+    uint8_t lg_size,
+    uint64_t key) -> std::pair<iterator, bool> {
+  const uint32_t size = 1 << lg_size;
+  const uint32_t mask = size - 1;
+  const uint32_t stride = getStride(key, lg_size);
+  uint32_t index = static_cast<uint32_t>(key) & mask;
+  // search for duplicate or zero
+  const uint32_t loop_index = index;
+  do {
+    const uint64_t probe = EK()(entries[index]);
+    if (probe == 0) {
+      return std::pair<iterator, bool>(&entries[index], false);
+    } else if (probe == key) {
+      return std::pair<iterator, bool>(&entries[index], true);
+    }
+    index = (index + stride) & mask;
+  } while (index != loop_index);
+  throw VeloxRuntimeError(
+      __FILE__,
+      __LINE__,
+      __FUNCTION__,
+      "",
+      "key not found and no empty slots!",
+      error_source::kErrorSourceRuntime,
+      error_code::kInvalidArgument,
+      false /*retriable*/);
+}
+
+template <typename EN, typename EK, typename A>
+template <typename Fwd>
+void ThetaUpdateSketchBase<EN, EK, A>::insert(iterator it, Fwd&& entry) {
+  new (it) EN(std::forward<Fwd>(entry));
+  ++numEntries_;
+  if (numEntries_ > getCapacity(lgCurSize_, lgNomSize_)) {
+    if (lgCurSize_ <= lgNomSize_) {
+      resize();
+    } else {
+      rebuild();
+    }
+  }
+}
+
+template <typename EN, typename EK, typename A>
+auto ThetaUpdateSketchBase<EN, EK, A>::begin() const -> iterator {
+  return entries_;
+}
+
+template <typename EN, typename EK, typename A>
+auto ThetaUpdateSketchBase<EN, EK, A>::end() const -> iterator {
+  return entries_ + (1ULL << lgCurSize_);
+}
+
+template <typename EN, typename EK, typename A>
+uint32_t ThetaUpdateSketchBase<EN, EK, A>::getCapacity(
+    uint8_t lg_cur_size,
+    uint8_t lg_nom_size) {
+  const double fraction =
+      (lg_cur_size <= lg_nom_size) ? RESIZE_THRESHOLD : REBUILD_THRESHOLD;
+  return static_cast<uint32_t>(std::floor(fraction * (1 << lg_cur_size)));
+}
+
+template <typename EN, typename EK, typename A>
+uint32_t ThetaUpdateSketchBase<EN, EK, A>::getStride(
+    uint64_t key,
+    uint8_t lg_size) {
+  // odd and independent of index assuming lg_size lowest bits of the key were
+  // used for the index
+  return (2 * static_cast<uint32_t>((key >> lg_size) & STRIDE_MASK)) + 1;
+}
+
+template <typename EN, typename EK, typename A>
+void ThetaUpdateSketchBase<EN, EK, A>::resize() {
+  const size_t old_size = 1ULL << lgCurSize_;
+  const uint8_t lg_new_size =
+      std::min<uint8_t>(lgCurSize_ + static_cast<uint8_t>(rf_), lgNomSize_ + 1);
+  const size_t new_size = 1ULL << lg_new_size;
+  EN* new_entries = allocator_.allocate(new_size);
+  for (size_t i = 0; i < new_size; ++i)
+    EK()(new_entries[i]) = 0;
+  for (size_t i = 0; i < old_size; ++i) {
+    const uint64_t key = EK()(entries_[i]);
+    if (key != 0) {
+      // always finds an empty slot in a larger table
+      new (find(new_entries, lg_new_size, key).first)
+          EN(std::move(entries_[i]));
+      entries_[i].~EN();
+      EK()(entries_[i]) = 0;
+    }
+  }
+  std::swap(entries_, new_entries);
+  lgCurSize_ = lg_new_size;
+  allocator_.deallocate(new_entries, old_size);
+}
+
+// assumes number of entries > nominal size
+template <typename EN, typename EK, typename A>
+void ThetaUpdateSketchBase<EN, EK, A>::rebuild() {
+  const size_t size = 1ULL << lgCurSize_;
+  const uint32_t nominal_size = 1 << lgNomSize_;
+
+  // empty entries have uninitialized payloads
+  // TODO: avoid this for empty or trivial payloads (arithmetic types)
+  consolidateNonEmpty(entries_, size, numEntries_);
+
+  std::nth_element(
+      entries_, entries_ + nominal_size, entries_ + numEntries_, comparator());
+  this->theta_ = EK()(entries_[nominal_size]);
+  EN* old_entries = entries_;
+  const size_t num_old_entries = numEntries_;
+  entries_ = allocator_.allocate(size);
+  for (size_t i = 0; i < size; ++i)
+    EK()(entries_[i]) = 0;
+  numEntries_ = nominal_size;
+  // relies on consolidating non-empty entries to the front
+  for (size_t i = 0; i < nominal_size; ++i) {
+    new (find(EK()(old_entries[i])).first) EN(std::move(old_entries[i]));
+    old_entries[i].~EN();
+  }
+  for (size_t i = nominal_size; i < num_old_entries; ++i)
+    old_entries[i].~EN();
+  allocator_.deallocate(old_entries, size);
+}
+
+template <typename EN, typename EK, typename A>
+void ThetaUpdateSketchBase<EN, EK, A>::trim() {
+  if (numEntries_ > static_cast<uint32_t>(1 << lgNomSize_))
+    rebuild();
+}
+
+template <typename EN, typename EK, typename A>
+void ThetaUpdateSketchBase<EN, EK, A>::reset() {
+  const size_t cur_size = 1ULL << lgCurSize_;
+  for (size_t i = 0; i < cur_size; ++i) {
+    if (EK()(entries_[i]) != 0) {
+      entries_[i].~EN();
+      EK()(entries_[i]) = 0;
+    }
+  }
+  const uint8_t starting_lg_size = ThetaBuildHelper<true>::startingSubMultiple(
+      lgNomSize_ + 1, ThetaConstants::MIN_LG_K, static_cast<uint8_t>(rf_));
+  if (starting_lg_size != lgCurSize_) {
+    allocator_.deallocate(entries_, cur_size);
+    lgCurSize_ = starting_lg_size;
+    const size_t new_size = 1ULL << starting_lg_size;
+    entries_ = allocator_.allocate(new_size);
+    for (size_t i = 0; i < new_size; ++i)
+      EK()(entries_[i]) = 0;
+  }
+  numEntries_ = 0;
+  theta_ = ThetaBuildHelper<true>::startingThetaFromP(p_);
+  isEmpty_ = true;
+}
+
+template <typename EN, typename EK, typename A>
+void ThetaUpdateSketchBase<EN, EK, A>::consolidateNonEmpty(
+    EN* entries,
+    size_t size,
+    size_t num) {
+  // find the first empty slot
+  size_t i = 0;
+  while (i < size) {
+    if (EK()(entries[i]) == 0)
+      break;
+    ++i;
+  }
+  // scan the rest and move non-empty entries to the front
+  for (size_t j = i + 1; j < size; ++j) {
+    if (EK()(entries[j]) != 0) {
+      new (&entries[i]) EN(std::move(entries[j]));
+      entries[j].~EN();
+      EK()(entries[j]) = 0;
+      ++i;
+      if (i == num)
+        break;
+    }
+  }
+}
+
+// builder
+
+template <typename Derived, typename Allocator>
+ThetaBaseBuilder<Derived, Allocator>::ThetaBaseBuilder(
+    const Allocator& allocator)
+    : allocator_(allocator),
+      lg_k_(ThetaConstants::DEFAULT_LG_K),
+      rf_(ThetaConstants::DEFAULT_RESIZE_FACTOR),
+      p_(1),
+      seed_(DEFAULT_SEED) {}
+
+template <typename Derived, typename Allocator>
+Derived& ThetaBaseBuilder<Derived, Allocator>::set_lg_k(uint8_t lg_k) {
+  if (lg_k < ThetaConstants::MIN_LG_K) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "lg_k must not be less than " +
+            std::to_string(ThetaConstants::MIN_LG_K) + ": " + std::to_string(lg_k),
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  if (lg_k > ThetaConstants::MAX_LG_K) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "lg_k must not be greater than " +
+            std::to_string(ThetaConstants::MAX_LG_K) + ": " + std::to_string(lg_k),
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  lg_k_ = lg_k;
+  return static_cast<Derived&>(*this);
+}
+
+template <typename Derived, typename Allocator>
+Derived& ThetaBaseBuilder<Derived, Allocator>::setResizeFactor(
+    resizeFactor rf) {
+  rf_ = rf;
+  return static_cast<Derived&>(*this);
+}
+
+template <typename Derived, typename Allocator>
+Derived& ThetaBaseBuilder<Derived, Allocator>::setP(float p) {
+  if (p <= 0 || p > 1) {
+    throw VeloxRuntimeError(
+        __FILE__,
+        __LINE__,
+        __FUNCTION__,
+        "",
+        "sampling probability must be between 0 and 1",
+        error_source::kErrorSourceRuntime,
+        error_code::kInvalidArgument,
+        false /*retriable*/);
+  }
+  p_ = p;
+  return static_cast<Derived&>(*this);
+}
+
+template <typename Derived, typename Allocator>
+Derived& ThetaBaseBuilder<Derived, Allocator>::setSeed(uint64_t seed) {
+  seed_ = seed;
+  return static_cast<Derived&>(*this);
+}
+
+template <typename Derived, typename Allocator>
+uint64_t ThetaBaseBuilder<Derived, Allocator>::startingTheta() const {
+  return ThetaBuildHelper<true>::startingThetaFromP(p_);
+}
+
+template <typename Derived, typename Allocator>
+uint8_t ThetaBaseBuilder<Derived, Allocator>::startingLgSize() const {
+  return ThetaBuildHelper<true>::startingSubMultiple(
+      lg_k_ + 1, ThetaConstants::MIN_LG_K, static_cast<uint8_t>(rf_));
+}
+
+// iterator
+
+template <typename Entry, typename ExtractKey>
+ThetaIterator<Entry, ExtractKey>::ThetaIterator(
+    Entry* entries,
+    uint32_t size,
+    uint32_t index)
+    : entries_(entries), size_(size), index_(index) {
+  while (index_ < size_ && ExtractKey()(entries_[index_]) == 0)
+    ++index_;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaIterator<Entry, ExtractKey>::operator++() -> ThetaIterator& {
+  ++index_;
+  while (index_ < size_ && ExtractKey()(entries_[index_]) == 0)
+    ++index_;
+  return *this;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaIterator<Entry, ExtractKey>::operator++(int) -> ThetaIterator {
+  ThetaIterator tmp(*this);
+  operator++();
+  return tmp;
+}
+
+template <typename Entry, typename ExtractKey>
+bool ThetaIterator<Entry, ExtractKey>::operator!=(
+    const ThetaIterator& other) const {
+  return index_ != other.index_;
+}
+
+template <typename Entry, typename ExtractKey>
+bool ThetaIterator<Entry, ExtractKey>::operator==(
+    const ThetaIterator& other) const {
+  return index_ == other.index_;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaIterator<Entry, ExtractKey>::operator*() const -> reference {
+  return entries_[index_];
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaIterator<Entry, ExtractKey>::operator->() const -> pointer {
+  return entries_ + index_;
+}
+
+// const iterator
+
+template <typename Entry, typename ExtractKey>
+ThetaConstIterator<Entry, ExtractKey>::ThetaConstIterator(
+    const Entry* entries,
+    uint32_t size,
+    uint32_t index)
+    : entries_(entries), size_(size), index_(index) {
+  while (index_ < size_ && ExtractKey()(entries_[index_]) == 0)
+    ++index_;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaConstIterator<Entry, ExtractKey>::operator++()
+    -> ThetaConstIterator& {
+  ++index_;
+  while (index_ < size_ && ExtractKey()(entries_[index_]) == 0)
+    ++index_;
+  return *this;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaConstIterator<Entry, ExtractKey>::operator++(int)
+    -> ThetaConstIterator {
+  ThetaConstIterator tmp(*this);
+  operator++();
+  return tmp;
+}
+
+template <typename Entry, typename ExtractKey>
+bool ThetaConstIterator<Entry, ExtractKey>::operator!=(
+    const ThetaConstIterator& other) const {
+  return index_ != other.index_;
+}
+
+template <typename Entry, typename ExtractKey>
+bool ThetaConstIterator<Entry, ExtractKey>::operator==(
+    const ThetaConstIterator& other) const {
+  return index_ == other.index_;
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaConstIterator<Entry, ExtractKey>::operator*() const -> reference {
+  return entries_[index_];
+}
+
+template <typename Entry, typename ExtractKey>
+auto ThetaConstIterator<Entry, ExtractKey>::operator->() const -> pointer {
+  return entries_ + index_;
+}
+
+} // namespace facebook::velox::common::theta
+
+#endif
diff --git a/velox/external/theta/ThetaUpdateSketchBase.h b/velox/external/theta/ThetaUpdateSketchBase.h
new file mode 100644
index 00000000000..e0c98928173
--- /dev/null
+++ b/velox/external/theta/ThetaUpdateSketchBase.h
@@ -0,0 +1,258 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <cmath>
+#include <iterator>
+
+#include "MurmurHash3.h"
+#include "ThetaComparators.h"
+#include "ThetaConstants.h"
+
+namespace facebook::velox::common::theta {
+
+template <typename Entry, typename ExtractKey, typename Allocator>
+struct ThetaUpdateSketchBase {
+  using resizeFactor = ThetaConstants::resizeFactor;
+  using comparator = compareByKey<ExtractKey>;
+
+  ThetaUpdateSketchBase(
+      uint8_t lg_cur_size,
+      uint8_t lg_nom_size,
+      resizeFactor rf,
+      float p,
+      uint64_t theta,
+      uint64_t seed,
+      const Allocator& allocator,
+      bool is_empty = true);
+  ThetaUpdateSketchBase(const ThetaUpdateSketchBase& other);
+  ThetaUpdateSketchBase(ThetaUpdateSketchBase&& other) noexcept;
+  ~ThetaUpdateSketchBase();
+  ThetaUpdateSketchBase& operator=(const ThetaUpdateSketchBase& other);
+  ThetaUpdateSketchBase& operator=(ThetaUpdateSketchBase&& other);
+
+  using iterator = Entry*;
+
+  inline uint64_t hashAndScreen(const void* data, size_t length);
+
+  inline std::pair<iterator, bool> find(uint64_t key) const;
+  static inline std::pair<iterator, bool>
+  find(Entry* entries, uint8_t lg_size, uint64_t key);
+
+  template <typename FwdEntry>
+  inline void insert(iterator it, FwdEntry&& entry);
+
+  iterator begin() const;
+  iterator end() const;
+
+  // resize threshold = 0.5 tuned for speed
+  static constexpr double RESIZE_THRESHOLD = 0.5;
+  // hash table rebuild threshold = 15/16
+  static constexpr double REBUILD_THRESHOLD = 15.0 / 16.0;
+
+  static constexpr uint8_t STRIDE_HASH_BITS = 7;
+  static constexpr uint32_t STRIDE_MASK = (1 << STRIDE_HASH_BITS) - 1;
+
+  Allocator allocator_;
+  bool isEmpty_;
+  uint8_t lgCurSize_;
+  uint8_t lgNomSize_;
+  resizeFactor rf_;
+  float p_;
+  uint32_t numEntries_;
+  uint64_t theta_;
+  uint64_t seed_;
+  Entry* entries_;
+
+  void resize();
+  void rebuild();
+  void trim();
+  void reset();
+
+  static inline uint32_t getCapacity(uint8_t lg_cur_size, uint8_t lg_nom_size);
+  static inline uint32_t getStride(uint64_t key, uint8_t lg_size);
+  static void consolidateNonEmpty(Entry* entries, size_t size, size_t num);
+};
+
+/// Theta base builder
+template <typename Derived, typename Allocator>
+class ThetaBaseBuilder {
+ public:
+  /**
+   * Creates and instance of the builder with default parameters.
+   * @param allocator instance of an Allocator to pass to created sketches
+   */
+  ThetaBaseBuilder(const Allocator& allocator);
+
+  /**
+   * Set log2(k), where k is a nominal number of entries in the sketch
+   * @param lg_k base 2 logarithm of nominal number of entries
+   * @return this builder
+   */
+  Derived& set_lg_k(uint8_t lg_k);
+
+  /**
+   * Set resize factor for the internal hash table (defaults to 8)
+   * @param rf resize factor
+   * @return this builder
+   */
+  Derived& setResizeFactor(resizeFactor rf);
+
+  /**
+   * Set sampling probability (initial theta). The default is 1, so the sketch
+   * retains all entries until it reaches the limit, at which point it goes into
+   * the estimation mode and reduces the effective sampling probability (theta)
+   * as necessary.
+   * @param p sampling probability
+   * @return this builder
+   */
+  Derived& setP(float p);
+
+  /**
+   * Set the seed for the hash function. Should be used carefully if needed.
+   * Sketches produced with different seed are not compatible
+   * and cannot be mixed in set operations.
+   * @param seed hash seed
+   * @return this builder
+   */
+  Derived& setSeed(uint64_t seed);
+
+ protected:
+  Allocator allocator_;
+  uint8_t lg_k_;
+  resizeFactor rf_;
+  float p_;
+  uint64_t seed_;
+
+  uint64_t startingTheta() const;
+  uint8_t startingLgSize() const;
+};
+
+// key extractor
+
+struct trivialExtractKey {
+  template <typename T>
+  auto operator()(T&& entry) const -> decltype(std::forward<T>(entry)) {
+    return std::forward<T>(entry);
+  }
+};
+
+// key not zero
+
+template <typename Entry, typename ExtractKey>
+class keyNotZero {
+ public:
+  bool operator()(const Entry& entry) const {
+    return ExtractKey()(entry) != 0;
+  }
+};
+
+template <typename Key, typename Entry, typename ExtractKey>
+class keyNotZeroLessThan {
+ public:
+  explicit keyNotZeroLessThan(const Key& key) : key(key) {}
+  bool operator()(const Entry& entry) const {
+    return ExtractKey()(entry) != 0 && ExtractKey()(entry) < this->key;
+  }
+
+ private:
+  Key key;
+};
+
+// MurMur3 hash functions
+
+static inline uint64_t
+computeHash(const void* data, size_t length, uint64_t seed) {
+  HashState hashes;
+  MurmurHash3_x64_128(data, length, seed, hashes);
+  return (
+      hashes.h1 >>
+      1); // Java implementation does unsigned shift >>> to make values positive
+}
+
+// iterators
+
+template <typename Entry, typename ExtractKey>
+class ThetaIterator {
+ public:
+  using iterator_category = std::input_iterator_tag;
+  using value_type = Entry;
+  using difference_type = std::ptrdiff_t;
+  using pointer = Entry*;
+  using reference = Entry&;
+
+  ThetaIterator(Entry* entries, uint32_t size, uint32_t index);
+  ThetaIterator& operator++();
+  ThetaIterator operator++(int);
+  bool operator==(const ThetaIterator& other) const;
+  bool operator!=(const ThetaIterator& other) const;
+  reference operator*() const;
+  pointer operator->() const;
+
+ private:
+  Entry* entries_;
+  uint32_t size_;
+  uint32_t index_;
+};
+
+template <typename Entry, typename ExtractKey>
+class ThetaConstIterator {
+ public:
+  using iterator_category = std::input_iterator_tag;
+  using value_type = const Entry;
+  using difference_type = std::ptrdiff_t;
+  using pointer = const Entry*;
+  using reference = const Entry&;
+
+  ThetaConstIterator(const Entry* entries, uint32_t size, uint32_t index);
+  ThetaConstIterator& operator++();
+  ThetaConstIterator operator++(int);
+  bool operator==(const ThetaConstIterator& other) const;
+  bool operator!=(const ThetaConstIterator& other) const;
+  reference operator*() const;
+  pointer operator->() const;
+
+ private:
+  const Entry* entries_;
+  uint32_t size_;
+  uint32_t index_;
+};
+
+// double value canonicalization for compatibility with Java
+static inline int64_t canonical_double(double value) {
+  union {
+    int64_t long_value;
+    double double_value;
+  } long_double_union;
+
+  if (value == 0.0) {
+    long_double_union.double_value = 0.0; // canonicalize -0.0 to 0.0
+  } else if (std::isnan(value)) {
+    long_double_union.long_value =
+        0x7ff8000000000000L; // canonicalize NaN using value from Java's
+                             // Double.doubleToLongBits()
+  } else {
+    long_double_union.double_value = value;
+  }
+  return long_double_union.long_value;
+}
+
+} // namespace facebook::velox::common::theta
+
+#include "ThetaUpdateSketchBase.cpp"
diff --git a/velox/external/theta/tests/BitPackingTest.cpp b/velox/external/theta/tests/BitPackingTest.cpp
new file mode 100644
index 00000000000..0eff4caed1e
--- /dev/null
+++ b/velox/external/theta/tests/BitPackingTest.cpp
@@ -0,0 +1,133 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+// Adapted from Apache DataSketches
+
+#include "velox/external/theta/BitPacking.h"
+
+#include <gtest/gtest.h>
+
+namespace facebook::velox::common::theta {
+
+// for every number of bits from 1 to 63
+// generate pseudo-random data, pack, unpack and compare
+
+// inverse golden ratio (0.618.. of max uint64_t)
+static const uint64_t IGOLDEN64 = 0x9e3779b97f4a7c13ULL;
+
+TEST(BitPackingTest, packUnpackBits) {
+  uint64_t value = 0xaa55aa55aa55aa55ULL; // arbitrary starting value
+  for (int m = 0; m < 10000; ++m) {
+    for (uint8_t bits = 1; bits <= 63; ++bits) {
+      int n = 8;
+      const uint64_t mask = (1ULL << bits) - 1;
+      std::vector<uint64_t> input(n, 0);
+      for (int i = 0; i < n; ++i) {
+        input[i] = value & mask;
+        value += IGOLDEN64;
+      }
+      std::vector<uint8_t> bytes(n * sizeof(uint64_t), 0);
+      uint8_t offset = 0;
+      uint8_t* ptr = bytes.data();
+      for (int i = 0; i < n; ++i) {
+        offset = packBits(input[i], bits, ptr, offset);
+      }
+
+      std::vector<uint64_t> output(n, 0);
+      offset = 0;
+      const uint8_t* cptr = bytes.data();
+      for (int i = 0; i < n; ++i) {
+        offset = unpackBits(output[i], bits, cptr, offset);
+      }
+      for (int i = 0; i < n; ++i) {
+        EXPECT_EQ(input[i], output[i]);
+      }
+    }
+  }
+}
+
+TEST(BitPackingTest, packUnpackBlocks) {
+  uint64_t value = 0xaa55aa55aa55aa55ULL; // arbitrary starting value
+  for (int n = 0; n < 10000; ++n) {
+    for (uint8_t bits = 1; bits <= 63; ++bits) {
+      const uint64_t mask = (1ULL << bits) - 1;
+      std::vector<uint64_t> input(8, 0);
+      for (int i = 0; i < 8; ++i) {
+        input[i] = value & mask;
+        value += IGOLDEN64;
+      }
+      std::vector<uint8_t> bytes(bits, 0);
+      packBitsBlock8(input.data(), bytes.data(), bits);
+      std::vector<uint64_t> output(8, 0);
+      unpackBitsBlock8(output.data(), bytes.data(), bits);
+      for (int i = 0; i < 8; ++i) {
+        EXPECT_EQ(input[i], output[i]);
+      }
+    }
+  }
+}
+
+TEST(BitPackingTest, packBitsUnpackBlocks) {
+  uint64_t value = 0; // arbitrary starting value
+  for (int m = 0; m < 10000; ++m) {
+    for (uint8_t bits = 1; bits <= 63; ++bits) {
+      const uint64_t mask = (1ULL << bits) - 1;
+      std::vector<uint64_t> input(8, 0);
+      for (int i = 0; i < 8; ++i) {
+        input[i] = value & mask;
+        value += IGOLDEN64;
+      }
+      std::vector<uint8_t> bytes(bits, 0);
+      uint8_t offset = 0;
+      uint8_t* ptr = bytes.data();
+      for (int i = 0; i < 8; ++i) {
+        offset = packBits(input[i], bits, ptr, offset);
+      }
+      std::vector<uint64_t> output(8, 0);
+      unpackBitsBlock8(output.data(), bytes.data(), bits);
+      for (int i = 0; i < 8; ++i) {
+        EXPECT_EQ(input[i], output[i]);
+      }
+    }
+  }
+}
+
+TEST(BitPackingTest, packBlocksUnpackBits) {
+  uint64_t value = 111; // arbitrary starting value
+  for (int m = 0; m < 10000; ++m) {
+    for (uint8_t bits = 1; bits <= 63; ++bits) {
+      const uint64_t mask = (1ULL << bits) - 1;
+      std::vector<uint64_t> input(8, 0);
+      for (int i = 0; i < 8; ++i) {
+        input[i] = value & mask;
+        value += IGOLDEN64;
+      }
+      std::vector<uint8_t> bytes(bits, 0);
+      packBitsBlock8(input.data(), bytes.data(), bits);
+      std::vector<uint64_t> output(8, 0);
+      uint8_t offset = 0;
+      const uint8_t* cptr = bytes.data();
+      for (int i = 0; i < 8; ++i) {
+        offset = unpackBits(output[i], bits, cptr, offset);
+      }
+      for (int i = 0; i < 8; ++i) {
+        EXPECT_EQ(input[i], output[i]);
+      }
+    }
+  }
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/tests/CMakeLists.txt b/velox/external/theta/tests/CMakeLists.txt
new file mode 100644
index 00000000000..431e13e1ce9
--- /dev/null
+++ b/velox/external/theta/tests/CMakeLists.txt
@@ -0,0 +1,32 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+add_executable(
+  velox_common_theta_test
+        ThetaSketchTest.cpp
+        ThetaUnionTest.cpp
+        BitPackingTest.cpp
+        TestUtils.h)
+
+add_test(NAME velox_common_theta_test COMMAND velox_common_theta_test)
+
+target_link_libraries(
+  velox_common_theta_test
+  PRIVATE velox_common_theta GTest::gtest GTest::gtest_main)
+
+file(COPY test_sketch_files
+     DESTINATION ${CMAKE_CURRENT_BINARY_DIR})
diff --git a/velox/external/theta/tests/TestUtils.h b/velox/external/theta/tests/TestUtils.h
new file mode 100644
index 00000000000..a9055b521ab
--- /dev/null
+++ b/velox/external/theta/tests/TestUtils.h
@@ -0,0 +1,204 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#pragma once
+
+#include <string>
+#include <type_traits>
+#include "velox/common/base/Exceptions.h"
+
+namespace {
+class Approx {
+ private:
+  bool marginComparison(double lhs, double rhs, double margin) const {
+    return (lhs + margin >= rhs) && (rhs + margin >= lhs);
+  }
+
+  bool equalityComparisonImpl(const double other) const {
+    // First try with fixed margin, then compute margin based on epsilon, scale
+    // and Approx's value Thanks to Richard Harris for his help refining the
+    // scaled margin value
+    return marginComparison(m_value, other, m_margin) ||
+        marginComparison(
+               m_value,
+               other,
+               m_epsilon *
+                   (m_scale + std::fabs(std::isinf(m_value) ? 0 : m_value)));
+  }
+  // Validates the new margin (margin >= 0)
+  // out-of-line to avoid including stdexcept in the header
+  void setMargin(double newMargin) {
+    VELOX_CHECK(
+        newMargin >= 0,
+        "Invalid Approx::margin: {} Approx::Margin has to be non-negative.",
+        newMargin);
+    m_margin = newMargin;
+  }
+
+  // Validates the new epsilon (0 < epsilon < 1)
+  // out-of-line to avoid including stdexcept in the header
+  void setEpsilon(double newEpsilon) {
+    VELOX_CHECK(
+        newEpsilon >= 0 && newEpsilon <= 1.0,
+        "Invalid Approx::epsilon: {} Approx::epsilon has to be in [0, 1]",
+        newEpsilon);
+    m_epsilon = newEpsilon;
+  }
+
+ public:
+  explicit Approx(double value)
+      : m_epsilon(std::numeric_limits<float>::epsilon() * 100),
+        m_margin(0.0),
+        m_scale(0.0),
+        m_value(value) {}
+
+  static Approx custom() {
+    return Approx(0);
+  }
+
+  Approx operator-() const {
+    auto temp(*this);
+    temp.m_value = -temp.m_value;
+    return temp;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  Approx operator()(T const& value) const {
+    Approx approx(static_cast<double>(value));
+    approx.m_epsilon = m_epsilon;
+    approx.m_margin = m_margin;
+    approx.m_scale = m_scale;
+    return approx;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  explicit Approx(T const& value) : Approx(static_cast<double>(value)) {}
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator==(const T& lhs, Approx const& rhs) {
+    auto lhs_v = static_cast<double>(lhs);
+    return rhs.equalityComparisonImpl(lhs_v);
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator==(Approx const& lhs, const T& rhs) {
+    return operator==(rhs, lhs);
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator!=(T const& lhs, Approx const& rhs) {
+    return !operator==(lhs, rhs);
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator!=(Approx const& lhs, T const& rhs) {
+    return !operator==(rhs, lhs);
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator<=(T const& lhs, Approx const& rhs) {
+    return static_cast<double>(lhs) < rhs.m_value || lhs == rhs;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator<=(Approx const& lhs, T const& rhs) {
+    return lhs.m_value < static_cast<double>(rhs) || lhs == rhs;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator>=(T const& lhs, Approx const& rhs) {
+    return static_cast<double>(lhs) > rhs.m_value || lhs == rhs;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  friend bool operator>=(Approx const& lhs, T const& rhs) {
+    return lhs.m_value > static_cast<double>(rhs) || lhs == rhs;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  Approx& epsilon(T const& newEpsilon) {
+    double epsilonAsDouble = static_cast<double>(newEpsilon);
+    setEpsilon(epsilonAsDouble);
+    return *this;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  Approx& margin(T const& newMargin) {
+    double marginAsDouble = static_cast<double>(newMargin);
+    setMargin(marginAsDouble);
+    return *this;
+  }
+
+  template <
+      typename T,
+      typename = typename std::enable_if<
+          std::is_constructible<double, T>::value>::type>
+  Approx& scale(T const& newScale) {
+    m_scale = static_cast<double>(newScale);
+    return *this;
+  }
+
+  std::string toString() const {
+    std::stringstream rss;
+    rss << "Approx( " << m_value << " )";
+    return rss.str();
+  }
+
+ private:
+  double m_epsilon;
+  double m_margin;
+  double m_scale;
+  double m_value;
+};
+} // namespace
diff --git a/velox/external/theta/tests/ThetaSketchTest.cpp b/velox/external/theta/tests/ThetaSketchTest.cpp
new file mode 100644
index 00000000000..fb5ee1fced2
--- /dev/null
+++ b/velox/external/theta/tests/ThetaSketchTest.cpp
@@ -0,0 +1,773 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#include "velox/external/theta/ThetaSketch.h"
+#include "TestUtils.h"
+
+#include <gtest/gtest.h>
+#include <fstream>
+#include <istream>
+#include <sstream>
+#include <stdexcept>
+#include <vector>
+
+namespace facebook::velox::common::theta {
+
+const std::string inputPath = "test_sketch_files/";
+
+TEST(ThetaSketch, Empty) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  EXPECT_TRUE(update_sketch.isEmpty());
+  EXPECT_FALSE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(update_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.isOrdered());
+
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  EXPECT_TRUE(compact_sketch.isEmpty());
+  EXPECT_FALSE(compact_sketch.isEstimationMode());
+  EXPECT_TRUE(compact_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(compact_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(compact_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(compact_sketch.getUpperBound(1) == 0.0);
+  EXPECT_TRUE(compact_sketch.isOrdered());
+
+  // empty is forced to be ordered
+  EXPECT_TRUE(update_sketch.compact(false).isOrdered());
+}
+
+TEST(ThetaSketch, NonEmptyNoRetainedKeys) {
+  updateThetaSketch update_sketch =
+      updateThetaSketch::builder().setP(0.001f).build();
+  update_sketch.update(1);
+  EXPECT_TRUE(update_sketch.getNumRetained() == 0);
+  EXPECT_FALSE(update_sketch.isEmpty());
+  EXPECT_TRUE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) > 0);
+
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  EXPECT_TRUE(compact_sketch.getNumRetained() == 0);
+  EXPECT_FALSE(compact_sketch.isEmpty());
+  EXPECT_TRUE(compact_sketch.isEstimationMode());
+  EXPECT_TRUE(compact_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(compact_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(compact_sketch.getUpperBound(1) > 0);
+
+  update_sketch.reset();
+  EXPECT_TRUE(update_sketch.isEmpty());
+  EXPECT_FALSE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(update_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) == 0.0);
+}
+
+TEST(ThetaSketch, SingleItem) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  update_sketch.update(1);
+  EXPECT_FALSE(update_sketch.isEmpty());
+  EXPECT_FALSE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(update_sketch.getEstimate() == 1.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 1.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) == 1.0);
+  EXPECT_TRUE(update_sketch.isOrdered()); // one item is ordered
+
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  EXPECT_FALSE(compact_sketch.isEmpty());
+  EXPECT_FALSE(compact_sketch.isEstimationMode());
+  EXPECT_TRUE(compact_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(compact_sketch.getEstimate() == 1.0);
+  EXPECT_TRUE(compact_sketch.getLowerBound(1) == 1.0);
+  EXPECT_TRUE(compact_sketch.getUpperBound(1) == 1.0);
+  EXPECT_TRUE(compact_sketch.isOrdered());
+
+  // single item is forced to be ordered
+  EXPECT_TRUE(update_sketch.compact(false).isOrdered());
+}
+
+TEST(ThetaSketch, ResizeExact) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  for (int i = 0; i < 2000; i++)
+    update_sketch.update(i);
+  EXPECT_FALSE(update_sketch.isEmpty());
+  EXPECT_FALSE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(update_sketch.getEstimate() == 2000.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 2000.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) == 2000.0);
+  EXPECT_FALSE(update_sketch.isOrdered());
+
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  EXPECT_FALSE(compact_sketch.isEmpty());
+  EXPECT_FALSE(compact_sketch.isEstimationMode());
+  EXPECT_TRUE(compact_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(compact_sketch.getEstimate() == 2000.0);
+  EXPECT_TRUE(compact_sketch.getLowerBound(1) == 2000.0);
+  EXPECT_TRUE(compact_sketch.getUpperBound(1) == 2000.0);
+  EXPECT_TRUE(compact_sketch.isOrdered());
+
+  update_sketch.reset();
+  EXPECT_TRUE(update_sketch.isEmpty());
+  EXPECT_FALSE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() == 1.0);
+  EXPECT_TRUE(update_sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(update_sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) == 0.0);
+  EXPECT_TRUE(update_sketch.isOrdered());
+}
+
+TEST(ThetaSketch, estimation) {
+  updateThetaSketch update_sketch =
+      updateThetaSketch::builder()
+          .setResizeFactor(updateThetaSketch::resizeFactor::X1)
+          .build();
+  const int n = 8000;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+  // std::cerr << update_sketch.to_string();
+  EXPECT_FALSE(update_sketch.isEmpty());
+  EXPECT_TRUE(update_sketch.isEstimationMode());
+  EXPECT_TRUE(update_sketch.getTheta() < 1.0);
+  EXPECT_TRUE(
+      update_sketch.getEstimate() == Approx((double)n).margin(n * 0.01));
+  EXPECT_TRUE(update_sketch.getLowerBound(1) < n);
+  EXPECT_TRUE(update_sketch.getUpperBound(1) > n);
+
+  const uint32_t k = 1 << ThetaConstants::DEFAULT_LG_K;
+  EXPECT_TRUE(update_sketch.getNumRetained() >= k);
+  update_sketch.trim();
+  EXPECT_TRUE(update_sketch.getNumRetained() == k);
+
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  EXPECT_FALSE(compact_sketch.isEmpty());
+  EXPECT_TRUE(compact_sketch.isOrdered());
+  EXPECT_TRUE(compact_sketch.isEstimationMode());
+  EXPECT_TRUE(compact_sketch.getTheta() < 1.0);
+  EXPECT_TRUE(
+      compact_sketch.getEstimate() == Approx((double)n).margin(n * 0.01));
+  EXPECT_TRUE(compact_sketch.getLowerBound(1) < n);
+  EXPECT_TRUE(compact_sketch.getUpperBound(1) > n);
+}
+
+TEST(ThetaSketch, DeserializeCompactV1EmptyFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(inputPath + "theta_compact_empty_from_java_v1.sk", std::ios::binary);
+  auto sketch = compactThetaSketch::deserialize(is);
+  EXPECT_TRUE(sketch.isEmpty());
+  EXPECT_FALSE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.getNumRetained() == 0);
+  EXPECT_TRUE(sketch.getTheta() == 1.0);
+  EXPECT_TRUE(sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(sketch.getUpperBound(1) == 0.0);
+}
+
+TEST(ThetaSketch, DeserializeCompactV2EmptyFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(inputPath + "theta_compact_empty_from_java_v2.sk", std::ios::binary);
+  auto sketch = compactThetaSketch::deserialize(is);
+  EXPECT_TRUE(sketch.isEmpty());
+  EXPECT_FALSE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.getNumRetained() == 0);
+  EXPECT_TRUE(sketch.getTheta() == 1.0);
+  EXPECT_TRUE(sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(sketch.getUpperBound(1) == 0.0);
+}
+
+TEST(ThetaSketch, DeserializeCompactV1EstimationFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_estimation_from_java_v1.sk", std::ios::binary);
+  auto sketch = compactThetaSketch::deserialize(is);
+  EXPECT_FALSE(sketch.isEmpty());
+  EXPECT_TRUE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.isOrdered());
+  EXPECT_TRUE(sketch.getNumRetained() == 4342);
+  EXPECT_TRUE(sketch.getTheta() == Approx(0.531700444213199).margin(1e-10));
+  EXPECT_TRUE(sketch.getEstimate() == Approx(8166.25234614053).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) == Approx(7996.956955317471).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) == Approx(8339.090301078124).margin(1e-10));
+
+  // the same construction process in Java must have produced exactly the same
+  // sketch
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+  EXPECT_TRUE(sketch.getNumRetained() == update_sketch.getNumRetained());
+  EXPECT_TRUE(
+      sketch.getTheta() == Approx(update_sketch.getTheta()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getEstimate() ==
+      Approx(update_sketch.getEstimate()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(1) ==
+      Approx(update_sketch.getLowerBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(1) ==
+      Approx(update_sketch.getUpperBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) ==
+      Approx(update_sketch.getLowerBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) ==
+      Approx(update_sketch.getUpperBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(3) ==
+      Approx(update_sketch.getLowerBound(3)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(3) ==
+      Approx(update_sketch.getUpperBound(3)).margin(1e-10));
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  // the sketches are ordered, so the iteration sequence must match exactly
+  auto iter = sketch.begin();
+  for (const auto& key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, DeserializeCompactV2EstimationFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_estimation_from_java_v2.sk", std::ios::binary);
+  auto sketch = compactThetaSketch::deserialize(is);
+  EXPECT_FALSE(sketch.isEmpty());
+  EXPECT_TRUE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.isOrdered());
+  EXPECT_TRUE(sketch.getNumRetained() == 4342);
+  EXPECT_TRUE(sketch.getTheta() == Approx(0.531700444213199).margin(1e-10));
+  EXPECT_TRUE(sketch.getEstimate() == Approx(8166.25234614053).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) == Approx(7996.956955317471).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) == Approx(8339.090301078124).margin(1e-10));
+
+  // the same construction process in Java must have produced exactly the same
+  // sketch
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+  EXPECT_TRUE(sketch.getNumRetained() == update_sketch.getNumRetained());
+  EXPECT_TRUE(
+      sketch.getTheta() == Approx(update_sketch.getTheta()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getEstimate() ==
+      Approx(update_sketch.getEstimate()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(1) ==
+      Approx(update_sketch.getLowerBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(1) ==
+      Approx(update_sketch.getUpperBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) ==
+      Approx(update_sketch.getLowerBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) ==
+      Approx(update_sketch.getUpperBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(3) ==
+      Approx(update_sketch.getLowerBound(3)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(3) ==
+      Approx(update_sketch.getUpperBound(3)).margin(1e-10));
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  // the sketches are ordered, so the iteration sequence must match exactly
+  auto iter = sketch.begin();
+  for (const auto& key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, DerializeDeserializeStreamAndBytesEquivalence) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+
+  std::stringstream s(std::ios::in | std::ios::out | std::ios::binary);
+  auto compact_sketch = update_sketch.compact();
+  compact_sketch.serialize(s);
+  auto bytes = compact_sketch.serialize();
+  EXPECT_TRUE(bytes.size() == static_cast<size_t>(s.tellp()));
+  EXPECT_TRUE(bytes.size() == compact_sketch.getSerializedSizeBytes());
+  for (size_t i = 0; i < bytes.size(); ++i) {
+    EXPECT_TRUE(((char*)bytes.data())[i] == (char)s.get());
+  }
+
+  s.seekg(0); // rewind
+  compactThetaSketch deserialized_sketch1 = compactThetaSketch::deserialize(s);
+  compactThetaSketch deserialized_sketch2 =
+      compactThetaSketch::deserialize(bytes.data(), bytes.size());
+  EXPECT_TRUE(bytes.size() == static_cast<size_t>(s.tellg()));
+  EXPECT_TRUE(deserialized_sketch2.isEmpty() == deserialized_sketch1.isEmpty());
+  EXPECT_TRUE(
+      deserialized_sketch2.isOrdered() == deserialized_sketch1.isOrdered());
+  EXPECT_TRUE(
+      deserialized_sketch2.getNumRetained() ==
+      deserialized_sketch1.getNumRetained());
+  EXPECT_TRUE(
+      deserialized_sketch2.getTheta() == deserialized_sketch1.getTheta());
+  EXPECT_TRUE(
+      deserialized_sketch2.getEstimate() == deserialized_sketch1.getEstimate());
+  EXPECT_TRUE(
+      deserialized_sketch2.getLowerBound(1) ==
+      deserialized_sketch1.getLowerBound(1));
+  EXPECT_TRUE(
+      deserialized_sketch2.getUpperBound(1) ==
+      deserialized_sketch1.getUpperBound(1));
+  // the sketches are ordered, so the iteration sequence must match exactly
+  auto iter = deserialized_sketch1.begin();
+  for (auto key : deserialized_sketch2) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, DeserializeEmptyBufferOverrun) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  auto bytes = update_sketch.compact().serialize();
+  EXPECT_TRUE(bytes.size() == 8);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), bytes.size() - 1),
+      VeloxUserError);
+}
+
+TEST(ThetaSketch, DeserializeSingleItemBufferOverrun) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  update_sketch.update(1);
+  auto bytes = update_sketch.compact().serialize();
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 7), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), bytes.size() - 1),
+      VeloxUserError);
+}
+
+TEST(ThetaSketch, DeserializeExactModeBufferOverrun) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  for (int i = 0; i < 1000; ++i)
+    update_sketch.update(i);
+  auto bytes = update_sketch.compact().serialize();
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 7), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 8), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 16), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), bytes.size() - 1),
+      VeloxUserError);
+}
+
+TEST(ThetaSketch, DeserializeEstimationModeBufferOverrun) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  for (int i = 0; i < 10000; ++i)
+    update_sketch.update(i);
+  auto bytes = update_sketch.compact().serialize();
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 7), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 8), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 16), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), 24), VeloxUserError);
+  EXPECT_THROW(
+      compactThetaSketch::deserialize(bytes.data(), bytes.size() - 1),
+      VeloxUserError);
+}
+
+TEST(ThetaSketch, ConversionConstructorAndWrappedCompact) {
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+
+  // unordered
+  auto unordered_compact1 = update_sketch.compact(false);
+  compactThetaSketch unordered_compact2(update_sketch, false);
+  auto it = unordered_compact1.begin();
+  for (auto entry : unordered_compact2) {
+    EXPECT_TRUE(*it == entry);
+    ++it;
+  }
+
+  // ordered
+  auto ordered_compact1 = update_sketch.compact();
+  compactThetaSketch ordered_compact2(update_sketch, true);
+  it = ordered_compact1.begin();
+  for (auto entry : ordered_compact2) {
+    EXPECT_TRUE(*it == entry);
+    ++it;
+  }
+
+  // wrapped compact
+  auto bytes = ordered_compact1.serialize();
+  auto ordered_compact3 =
+      wrappedCompactThetaSketch::wrap(bytes.data(), bytes.size());
+  it = ordered_compact1.begin();
+  for (auto entry : ordered_compact3) {
+    EXPECT_TRUE(*it == entry);
+    ++it;
+  }
+  EXPECT_TRUE(ordered_compact3.getEstimate() == ordered_compact1.getEstimate());
+  EXPECT_TRUE(
+      ordered_compact3.getLowerBound(1) == ordered_compact1.getLowerBound(1));
+  EXPECT_TRUE(
+      ordered_compact3.getUpperBound(1) == ordered_compact1.getUpperBound(1));
+  EXPECT_TRUE(
+      ordered_compact3.isEstimationMode() ==
+      ordered_compact1.isEstimationMode());
+  EXPECT_TRUE(ordered_compact3.getTheta() == ordered_compact1.getTheta());
+
+  // seed mismatch
+  EXPECT_THROW(
+      wrappedCompactThetaSketch::wrap(bytes.data(), bytes.size(), 0),
+      VeloxUserError);
+}
+
+TEST(ThetaSketch, WrapCompactV1EmptyFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_empty_from_java_v1.sk",
+      std::ios::binary | std::ios::ate);
+
+  std::vector<uint8_t> buf;
+  if (is) {
+    auto size = is.tellg();
+    buf.reserve(size);
+    buf.assign(size, 0);
+    is.seekg(0, std::ios_base::beg);
+    is.read((char*)(buf.data()), buf.size());
+  }
+
+  auto sketch = wrappedCompactThetaSketch::wrap(buf.data(), buf.size());
+  EXPECT_TRUE(sketch.isEmpty());
+  EXPECT_FALSE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.getNumRetained() == 0);
+  EXPECT_TRUE(sketch.getTheta() == 1.0);
+  EXPECT_TRUE(sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(sketch.getUpperBound(1) == 0.0);
+}
+
+TEST(ThetaSketch, WrapCompactV2EmptyFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_empty_from_java_v2.sk",
+      std::ios::binary | std::ios::ate);
+
+  std::vector<uint8_t> buf;
+  if (is) {
+    auto size = is.tellg();
+    buf.reserve(size);
+    buf.assign(size, 0);
+    is.seekg(0, std::ios_base::beg);
+    is.read((char*)(buf.data()), buf.size());
+  }
+
+  auto sketch = wrappedCompactThetaSketch::wrap(buf.data(), buf.size());
+  EXPECT_TRUE(sketch.isEmpty());
+  EXPECT_FALSE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.getNumRetained() == 0);
+  EXPECT_TRUE(sketch.getTheta() == 1.0);
+  EXPECT_TRUE(sketch.getEstimate() == 0.0);
+  EXPECT_TRUE(sketch.getLowerBound(1) == 0.0);
+  EXPECT_TRUE(sketch.getUpperBound(1) == 0.0);
+}
+
+TEST(ThetaSketch, WrapCompactV1EstimationFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_estimation_from_java_v1.sk",
+      std::ios::binary | std::ios::ate);
+  std::vector<uint8_t> buf;
+  if (is) {
+    auto size = is.tellg();
+    buf.reserve(size);
+    buf.assign(size, 0);
+    is.seekg(0, std::ios_base::beg);
+    is.read((char*)(buf.data()), buf.size());
+  }
+
+  auto sketch = wrappedCompactThetaSketch::wrap(buf.data(), buf.size());
+  EXPECT_FALSE(sketch.isEmpty());
+  EXPECT_TRUE(sketch.isEstimationMode());
+  //  EXPECT_TRUE(sketch.isOrdered());       // v1 may not be ordered
+  EXPECT_TRUE(sketch.getNumRetained() == 4342);
+  EXPECT_TRUE(sketch.getTheta() == Approx(0.531700444213199).margin(1e-10));
+  EXPECT_TRUE(sketch.getEstimate() == Approx(8166.25234614053).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) == Approx(7996.956955317471).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) == Approx(8339.090301078124).margin(1e-10));
+
+  // the same construction process in Java must have produced exactly the same
+  // sketch
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+  EXPECT_TRUE(sketch.getNumRetained() == update_sketch.getNumRetained());
+  EXPECT_TRUE(
+      sketch.getTheta() == Approx(update_sketch.getTheta()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getEstimate() ==
+      Approx(update_sketch.getEstimate()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(1) ==
+      Approx(update_sketch.getLowerBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(1) ==
+      Approx(update_sketch.getUpperBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) ==
+      Approx(update_sketch.getLowerBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) ==
+      Approx(update_sketch.getUpperBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(3) ==
+      Approx(update_sketch.getLowerBound(3)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(3) ==
+      Approx(update_sketch.getUpperBound(3)).margin(1e-10));
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  // the sketches are ordered, so the iteration sequence must match exactly
+  auto iter = sketch.begin();
+  for (const auto key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, WrapCompactV2EstimationFromJava) {
+  std::ifstream is;
+  is.exceptions(std::ios::failbit | std::ios::badbit);
+  is.open(
+      inputPath + "theta_compact_estimation_from_java_v2.sk",
+      std::ios::binary | std::ios::ate);
+  std::vector<uint8_t> buf;
+  if (is) {
+    auto size = is.tellg();
+    buf.reserve(size);
+    buf.assign(size, 0);
+    is.seekg(0, std::ios_base::beg);
+    is.read((char*)(buf.data()), buf.size());
+  }
+
+  auto sketch = wrappedCompactThetaSketch::wrap(buf.data(), buf.size());
+  EXPECT_FALSE(sketch.isEmpty());
+  EXPECT_TRUE(sketch.isEstimationMode());
+  //  EXPECT_TRUE(sketch.isOrdered());       // v1 may not be ordered
+  EXPECT_TRUE(sketch.getNumRetained() == 4342);
+  EXPECT_TRUE(sketch.getTheta() == Approx(0.531700444213199).margin(1e-10));
+  EXPECT_TRUE(sketch.getEstimate() == Approx(8166.25234614053).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) == Approx(7996.956955317471).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) == Approx(8339.090301078124).margin(1e-10));
+
+  // the same construction process in Java must have produced exactly the same
+  // sketch
+  updateThetaSketch update_sketch = updateThetaSketch::builder().build();
+  const int n = 8192;
+  for (int i = 0; i < n; i++)
+    update_sketch.update(i);
+  EXPECT_TRUE(sketch.getNumRetained() == update_sketch.getNumRetained());
+  EXPECT_TRUE(
+      sketch.getTheta() == Approx(update_sketch.getTheta()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getEstimate() ==
+      Approx(update_sketch.getEstimate()).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(1) ==
+      Approx(update_sketch.getLowerBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(1) ==
+      Approx(update_sketch.getUpperBound(1)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(2) ==
+      Approx(update_sketch.getLowerBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(2) ==
+      Approx(update_sketch.getUpperBound(2)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getLowerBound(3) ==
+      Approx(update_sketch.getLowerBound(3)).margin(1e-10));
+  EXPECT_TRUE(
+      sketch.getUpperBound(3) ==
+      Approx(update_sketch.getUpperBound(3)).margin(1e-10));
+  compactThetaSketch compact_sketch = update_sketch.compact();
+  // the sketches are ordered, so the iteration sequence must match exactly
+  auto iter = sketch.begin();
+  for (const auto key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, SerializeDeserializeSmallCompressed) {
+  auto update_sketch = updateThetaSketch::builder().build();
+  for (int i = 0; i < 10; i++)
+    update_sketch.update(i);
+  auto compact_sketch = update_sketch.compact();
+
+  auto bytes = compact_sketch.serializeCompressed();
+  EXPECT_TRUE(bytes.size() == compact_sketch.getSerializedSizeBytes(true));
+  { // deserialize bytes
+    auto deserialized_sketch =
+        compactThetaSketch::deserialize(bytes.data(), bytes.size());
+    EXPECT_TRUE(
+        deserialized_sketch.getNumRetained() ==
+        compact_sketch.getNumRetained());
+    EXPECT_TRUE(deserialized_sketch.getTheta() == compact_sketch.getTheta());
+    auto iter = deserialized_sketch.begin();
+    for (const auto key : compact_sketch) {
+      EXPECT_TRUE(*iter == key);
+      ++iter;
+    }
+  }
+  { // wrap bytes
+    auto wrapped_sketch =
+        wrappedCompactThetaSketch::wrap(bytes.data(), bytes.size());
+    EXPECT_TRUE(
+        wrapped_sketch.getNumRetained() == compact_sketch.getNumRetained());
+    EXPECT_TRUE(wrapped_sketch.getTheta() == compact_sketch.getTheta());
+    auto iter = wrapped_sketch.begin();
+    for (const auto key : compact_sketch) {
+      EXPECT_TRUE(*iter == key);
+      ++iter;
+    }
+  }
+
+  std::stringstream s(std::ios::in | std::ios::out | std::ios::binary);
+  compact_sketch.serializeCompressed(s);
+  EXPECT_TRUE(
+      static_cast<size_t>(s.tellp()) ==
+      compact_sketch.getSerializedSizeBytes(true));
+  auto deserialized_sketch = compactThetaSketch::deserialize(s);
+  EXPECT_TRUE(
+      deserialized_sketch.getNumRetained() == compact_sketch.getNumRetained());
+  EXPECT_TRUE(deserialized_sketch.getTheta() == compact_sketch.getTheta());
+  auto iter = deserialized_sketch.begin();
+  for (const auto key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+TEST(ThetaSketch, SerializeDeserializeCompressed) {
+  auto update_sketch = updateThetaSketch::builder().build();
+  for (int i = 0; i < 10000; i++)
+    update_sketch.update(i);
+  auto compact_sketch = update_sketch.compact();
+
+  auto bytes = compact_sketch.serializeCompressed();
+  EXPECT_TRUE(bytes.size() == compact_sketch.getSerializedSizeBytes(true));
+  { // deserialize bytes
+    auto deserialized_sketch =
+        compactThetaSketch::deserialize(bytes.data(), bytes.size());
+    EXPECT_TRUE(
+        deserialized_sketch.getNumRetained() ==
+        compact_sketch.getNumRetained());
+    EXPECT_TRUE(deserialized_sketch.getTheta() == compact_sketch.getTheta());
+    auto iter = deserialized_sketch.begin();
+    for (const auto key : compact_sketch) {
+      EXPECT_TRUE(*iter == key);
+      ++iter;
+    }
+  }
+  { // wrap bytes
+    auto wrapped_sketch =
+        wrappedCompactThetaSketch::wrap(bytes.data(), bytes.size());
+    EXPECT_TRUE(
+        wrapped_sketch.getNumRetained() == compact_sketch.getNumRetained());
+    EXPECT_TRUE(wrapped_sketch.getTheta() == compact_sketch.getTheta());
+    auto iter = wrapped_sketch.begin();
+    for (const auto key : compact_sketch) {
+      EXPECT_TRUE(*iter == key);
+      ++iter;
+    }
+  }
+
+  std::stringstream s(std::ios::in | std::ios::out | std::ios::binary);
+  compact_sketch.serializeCompressed(s);
+  EXPECT_TRUE(
+      static_cast<size_t>(s.tellp()) ==
+      compact_sketch.getSerializedSizeBytes(true));
+  auto deserialized_sketch = compactThetaSketch::deserialize(s);
+  EXPECT_TRUE(
+      deserialized_sketch.getNumRetained() == compact_sketch.getNumRetained());
+  EXPECT_TRUE(deserialized_sketch.getTheta() == compact_sketch.getTheta());
+  auto iter = deserialized_sketch.begin();
+  for (const auto key : compact_sketch) {
+    EXPECT_TRUE(*iter == key);
+    ++iter;
+  }
+}
+
+// The sketch reaches capacity for the first time at 2 * K * 15/16,
+// but at that point it is still in exact mode, so the serialized size is not
+// the maximum (theta in not serialized in the exact mode). So we need to catch
+// the second time, but some updates will be ignored in the estimation mode, so
+// we update more than enough times keeping track of the maximum. Potentially
+// the exact number of updates to reach the peak can be figured out given this
+// particular sequence, but not assuming that might be even better (say, in case
+// we change the load factor or hash function or just out of principle not to
+// rely on implementation details too much).
+TEST(ThetaSketch, maxSerializedSize) {
+  const uint8_t lg_k = 10;
+  auto sketch = updateThetaSketch::builder().set_lg_k(lg_k).build();
+  int value = 0;
+
+  // this will go over the first peak, which is not the highest
+  for (int i = 0; i < (1 << lg_k) * 2; ++i)
+    sketch.update(value++);
+
+  // this will to over the second peak keeping track of the max size
+  size_t max_size_bytes = 0;
+  for (int i = 0; i < (1 << lg_k) * 2; ++i) {
+    sketch.update(value++);
+    auto bytes = sketch.compact().serialize();
+    max_size_bytes = std::max(max_size_bytes, bytes.size());
+  }
+  EXPECT_TRUE(
+      max_size_bytes == compactThetaSketch::getMaxSerializedSizeBytes(lg_k));
+}
+
+} // namespace facebook::velox::common::theta
diff --git a/velox/external/theta/tests/ThetaUnionTest.cpp b/velox/external/theta/tests/ThetaUnionTest.cpp
new file mode 100644
index 00000000000..5740f33abc4
--- /dev/null
+++ b/velox/external/theta/tests/ThetaUnionTest.cpp
@@ -0,0 +1,164 @@
+/*
+* Copyright (c) Facebook, Inc. and its affiliates.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*     http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+ */
+
+// Adapted from Apache DataSketches
+
+#include "velox/external/theta/ThetaUnion.h"
+#include "TestUtils.h"
+
+#include <gtest/gtest.h>
+#include <stdexcept>
+
+namespace facebook::velox::common::theta {
+
+TEST(ThetaUnion, empty) {
+  updateThetaSketch sketch1 = updateThetaSketch::builder().build();
+  ThetaUnion u = ThetaUnion::builder().build();
+  compactThetaSketch sketch2 = u.getResult();
+  EXPECT_TRUE(sketch2.getNumRetained() == 0);
+  EXPECT_TRUE(sketch2.isEmpty());
+  EXPECT_FALSE(sketch2.isEstimationMode());
+
+  u.update(sketch1);
+  sketch2 = u.getResult();
+  EXPECT_TRUE(sketch2.getNumRetained() == 0);
+  EXPECT_TRUE(sketch2.isEmpty());
+  EXPECT_FALSE(sketch2.isEstimationMode());
+}
+
+TEST(ThetaUnion, nonEmptyNoRetainedKeys) {
+  updateThetaSketch update_sketch =
+      updateThetaSketch::builder().setP(0.001f).build();
+  update_sketch.update(1);
+  ThetaUnion u = ThetaUnion::builder().build();
+  u.update(update_sketch);
+  compactThetaSketch sketch = u.getResult();
+  EXPECT_TRUE(sketch.getNumRetained() == 0);
+  EXPECT_FALSE(sketch.isEmpty());
+  EXPECT_TRUE(sketch.isEstimationMode());
+  EXPECT_TRUE(sketch.getTheta() == Approx(0.001).margin(1e-10));
+}
+
+TEST(ThetaUnion, exactModeHalfOverlap) {
+  auto sketch1 = updateThetaSketch::builder().build();
+  int value = 0;
+  for (int i = 0; i < 1000; i++)
+    sketch1.update(value++);
+
+  auto sketch2 = updateThetaSketch::builder().build();
+  value = 500;
+  for (int i = 0; i < 1000; i++)
+    sketch2.update(value++);
+
+  auto u = ThetaUnion::builder().build();
+  u.update(sketch1);
+  u.update(sketch2);
+  auto sketch3 = u.getResult();
+  EXPECT_FALSE(sketch3.isEmpty());
+  EXPECT_FALSE(sketch3.isEstimationMode());
+  EXPECT_TRUE(sketch3.getEstimate() == 1500.0);
+
+  u.reset();
+  sketch3 = u.getResult();
+  EXPECT_TRUE(sketch3.getNumRetained() == 0);
+  EXPECT_TRUE(sketch3.isEmpty());
+  EXPECT_FALSE(sketch3.isEstimationMode());
+}
+
+TEST(ThetaUnion, exactModeHalfOverlapWrappedCompact) {
+  auto sketch1 = updateThetaSketch::builder().build();
+  int value = 0;
+  for (int i = 0; i < 1000; i++)
+    sketch1.update(value++);
+  auto bytes1 = sketch1.compact().serialize();
+
+  auto sketch2 = updateThetaSketch::builder().build();
+  value = 500;
+  for (int i = 0; i < 1000; i++)
+    sketch2.update(value++);
+  auto bytes2 = sketch2.compact().serialize();
+
+  auto u = ThetaUnion::builder().build();
+  u.update(wrappedCompactThetaSketch::wrap(bytes1.data(), bytes1.size()));
+  u.update(wrappedCompactThetaSketch::wrap(bytes2.data(), bytes2.size()));
+  compactThetaSketch sketch3 = u.getResult();
+  EXPECT_FALSE(sketch3.isEmpty());
+  EXPECT_FALSE(sketch3.isEstimationMode());
+  EXPECT_TRUE(sketch3.getEstimate() == 1500.0);
+}
+
+TEST(ThetaUnion, estimationModeHalfOverlap) {
+  auto sketch1 = updateThetaSketch::builder().build();
+  int value = 0;
+  for (int i = 0; i < 10000; i++)
+    sketch1.update(value++);
+
+  auto sketch2 = updateThetaSketch::builder().build();
+  value = 5000;
+  for (int i = 0; i < 10000; i++)
+    sketch2.update(value++);
+
+  auto u = ThetaUnion::builder().build();
+  u.update(sketch1);
+  u.update(sketch2);
+  auto sketch3 = u.getResult();
+  EXPECT_FALSE(sketch3.isEmpty());
+  EXPECT_TRUE(sketch3.isEstimationMode());
+  EXPECT_TRUE(sketch3.getEstimate() == Approx(15000).margin(15000 * 0.01));
+
+  u.reset();
+  sketch3 = u.getResult();
+  EXPECT_TRUE(sketch3.getNumRetained() == 0);
+  EXPECT_TRUE(sketch3.isEmpty());
+  EXPECT_FALSE(sketch3.isEstimationMode());
+}
+
+TEST(ThetaUnion, seedMismatch) {
+  updateThetaSketch sketch = updateThetaSketch::builder().build();
+  sketch.update(1); // non-empty should not be ignored
+  ThetaUnion u = ThetaUnion::builder().setSeed(123).build();
+  EXPECT_THROW(u.update(sketch), VeloxRuntimeError);
+}
+
+TEST(ThetaUnion, largerK) {
+  auto update_sketch1 = updateThetaSketch::builder().set_lg_k(14).build();
+  for (int i = 0; i < 16384; ++i)
+    update_sketch1.update(i);
+
+  auto update_sketch2 = updateThetaSketch::builder().set_lg_k(14).build();
+  for (int i = 0; i < 26384; ++i)
+    update_sketch2.update(i);
+
+  auto update_sketch3 = updateThetaSketch::builder().set_lg_k(14).build();
+  for (int i = 0; i < 86384; ++i)
+    update_sketch3.update(i);
+
+  auto union1 = ThetaUnion::builder().set_lg_k(16).build();
+  union1.update(update_sketch2);
+  union1.update(update_sketch1);
+  union1.update(update_sketch3);
+  auto result1 = union1.getResult();
+  EXPECT_TRUE(result1.getEstimate() == update_sketch3.getEstimate());
+
+  auto union2 = ThetaUnion::builder().set_lg_k(16).build();
+  union2.update(update_sketch1);
+  union2.update(update_sketch3);
+  union2.update(update_sketch2);
+  auto result2 = union2.getResult();
+  EXPECT_TRUE(result2.getEstimate() == update_sketch3.getEstimate());
+}
+
+} // namespace facebook::velox::common::theta
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