From 753a750e0998ed05cb39a27a71e03848b49c3a55 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Sat, 24 Aug 2024 12:05:44 -0700 Subject: [PATCH 01/17] Move simple_dragonbox to own subproject folder --- CMakeLists.txt | 1 + subproject/simple/CMakeLists.txt | 9 + subproject/simple/README.md | 117 ++ subproject/simple/simple_dragonbox.h | 1996 +++++++++++++++++++ subproject/simple/simple_dragonbox_test.cpp | 85 + 5 files changed, 2208 insertions(+) create mode 100644 subproject/simple/CMakeLists.txt create mode 100644 subproject/simple/README.md create mode 100644 subproject/simple/simple_dragonbox.h create mode 100644 subproject/simple/simple_dragonbox_test.cpp diff --git a/CMakeLists.txt b/CMakeLists.txt index a9d80b9..3fa2456 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -106,6 +106,7 @@ if (DRAGONBOX_ENABLE_SUBPROJECT) add_subdirectory("subproject/benchmark") add_subdirectory("subproject/meta") add_subdirectory("subproject/test") + add_subdirectory("subproject/simple") endif() # ---- MSVC Specifics ---- diff --git a/subproject/simple/CMakeLists.txt b/subproject/simple/CMakeLists.txt new file mode 100644 index 0000000..9a2cb9f --- /dev/null +++ b/subproject/simple/CMakeLists.txt @@ -0,0 +1,9 @@ +add_library(simple_dragonbox INTERFACE simple_dragonbox.h) +target_compile_features(simple_dragonbox INTERFACE cxx_std_17) + +add_executable(simple_dragonbox_test simple_dragonbox_test.cpp) +target_link_libraries(simple_dragonbox_test PRIVATE + simple_dragonbox + dragonbox::common + ryu::ryu +) diff --git a/subproject/simple/README.md b/subproject/simple/README.md new file mode 100644 index 0000000..c6c6638 --- /dev/null +++ b/subproject/simple/README.md @@ -0,0 +1,117 @@ +# Simple Dragonbox + +This is a simplified implementation of the algorithm, that closely follows the +one in `include/dragonbox/dragonbox.h`, but aims to be shorter overall, use less +C++ template indirection, and offer slightly less flexibility for the benefit of +simpliciy. + +Primary sacrifices over the implementation in `include/dragonbox/dragonbox.h`: + +- No support for `sign` policies (always uses `return_sign`) +- No support for `trailing_zeros` policies (always uses `remove`) +- No support for 128-bit compiler intrinsics (always uses portable + implementation) +- No support for fast digit-generation policy (always uses `compact`) +- Assumes the existence of `if constexpr` (C++17) +- Assumes `float` and `double` types are available and use IEEE-754 +- Generally assumes a modern standard compiler environment and C standard + library + +Note the `cache`, `binary_to_decimal_rounding`, and `decimal_to_binary_rounding` +policies are still supported. + +## API + +### Basic use + +To convert to decimal (analog to `jkj::dragonbox::to_decimal`), + +```cpp +float x; +auto d = simple_dragonbox::to_decimal(x); +(void) d.significand; +(void) d.exponent; +(void) d.sign; +``` + +To convert to string (analog to `jkj::dragonbox::to_chars`), + +```cpp +float x; +char buf[simple_dragonbox::max_output_string_length + 1]; +simple_dragonbox::to_chars(x, buf); +std::cout << buf << std::endl; +``` + +In the examples above, `x` can be either a `float` or a `double`. + +### Policies + +`simple_dragonbox` supports the same style of policy interface as +`jkj::dragonbox`. For example, + +```cpp +simple_dragonbox::to_decimal(3.14, + simple_dragonbox::policy::cache::compact, + simple_dragonbox::policy::binary_to_decimal_rounding::to_odd); +``` + +Supported policies include: + +`simple_dragonbox::policy::decimal_to_binary_rounding` + +- `::nearest_to_even` +- `::nearest_to_odd` +- `::nearest_toward_plus_infinity` +- `::nearest_toward_minus_infinity` +- `::nearest_toward_zero` +- `::nearest_away_from_zero` +- `::nearest_to_even_static_boundary` +- `::nearest_to_odd_static_boundary` +- `::nearest_toward_plus_infinity_static_boundary` +- `::nearest_toward_minus_infinity_static_boundary` +- `::toward_plus_infinity` +- `::toward_minus_infinity` +- `::toward_zero` +- `::away_from_zero` + +`simple_dragonbox::policy::binary_to_decimal_rounding` + +- `::to_even` +- `::to_odd` +- `::away_from_zero` +- `::toward_zero` +- `::do_not_care` + +`simple_dragonbox::policy::cache` + +- `::full` +- `::compact` + +### Internal/direct API + +Internally, `simple_dragonbox` uses a more explicit, direct interface to express +the various policies, via a class called `simple_dragonbox::impl`. The `impl` +class has four template parameters: `Float`, `BinaryRoundMode`, +`DecimalRoundMode`, and `CacheType`, which correspond to the floating point +type and three categories of policies above. These template parameters can be +specified explicitly to instantiate a particular variant of the algorithm. The +class has a single constructor that receives a value of type `Float` (e.g. +`float` or `double`), and has methods `to_decimal()` and `to_chars()` for +performing the desired conversions. + +For example, + +```cpp +using impl = simple_dragonbox::impl; + +int main() { + char buf[32]; + auto x = impl(3.14); + x.to_decimal(); // equivalent to `simple_dragonbox::to_decimal(3.14, policies...)` + x.to_chars(buf); // equivalent to `simple_dragonbox::to_chars(3.14, buf, policies...)` +} +``` diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h new file mode 100644 index 0000000..e8d8e09 --- /dev/null +++ b/subproject/simple/simple_dragonbox.h @@ -0,0 +1,1996 @@ +#pragma once + +// Copyright 2024 Junekey Jeon, Toby Bell +// TODO: License + +#include +#include +#include +#include + +namespace simple_dragonbox { + constexpr uint32_t rotr32(uint32_t n, unsigned r) { + r &= 31; + return (n >> r) | (n << ((32 - r) & 31)); + } + + constexpr uint64_t rotr64(uint64_t n, unsigned r) { + r &= 63; + return (n >> r) | (n << ((64 - r) & 63)); + } + + static_assert((int32_t(-1) >> 1) == int32_t(-1) && (int16_t(-1) >> 1) == int16_t(-1), + "right-shift for signed integers must be arithmetic"); + + // For constexpr computation. + // Returns -1 when n = 0. + constexpr int floor_log2(uint64_t n) { + int count = -1; + while (n != 0) { + ++count; + n >>= 1; + } + return count; + } + + constexpr int floor_log10_pow2(int e) { + assert(-2620 <= e && e <= 2620); + return (e * 315653) >> 20; + } + + constexpr int floor_log2_pow10(int e) { + // Formula itself holds on [-4003,4003]; [-1233,1233] is to ensure no overflow. + assert(-1233 <= e && e <= 1233); + return (e * 1741647) >> 19; + } + + constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) { + assert(-2985 <= e && e <= 2936); + return (e * 631305 - 261663) >> 21; + } + + constexpr int floor_log5_pow2(int e) { + assert(-1831 <= e && e <= 1831); + return (e * 225799) >> 19; + } + + constexpr int floor_log5_pow2_minus_log5_3(int e) { + assert(-3543 <= e && e <= 2427); + return (e * 451597 - 715764) >> 20; + } + + struct uint128 { + uint64_t high; + uint64_t low; + + void operator+=(uint64_t n) { + auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); + high += (sum < low ? 1 : 0); + low = sum; + } + }; + + constexpr uint64_t umul64(uint32_t x, uint32_t y) { return x * uint64_t(y); } + + // Get 128-bit result of multiplication of two 64-bit unsigned integers. + constexpr uint128 umul128(uint64_t x, uint64_t y) { + auto const a = uint32_t(x >> 32); + auto const b = uint32_t(x); + auto const c = uint32_t(y >> 32); + auto const d = uint32_t(y); + + auto const ac = umul64(a, c); + auto const bc = umul64(b, c); + auto const ad = umul64(a, d); + auto const bd = umul64(b, d); + + auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); + + return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), + (intermediate << 32) + uint32_t(bd)}; + } + + // Get high half of the 128-bit result of multiplication of two 64-bit unsigned + // integers. + constexpr uint64_t umul128_upper64(uint64_t x, uint64_t y) { + auto const a = uint32_t(x >> 32); + auto const b = uint32_t(x); + auto const c = uint32_t(y >> 32); + auto const d = uint32_t(y); + + auto const ac = umul64(a, c); + auto const bc = umul64(b, c); + auto const ad = umul64(a, d); + auto const bd = umul64(b, d); + + auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); + + return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); + } + + // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + constexpr uint128 umul192_upper128(uint64_t x, uint128 y) { + auto r = umul128(x, y.high); + r += umul128_upper64(x, y.low); + return r; + } + + // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + constexpr uint64_t umul96_upper64(uint32_t x, uint64_t y) { + auto const yh = uint32_t(y >> 32); + auto const yl = uint32_t(y); + + auto const xyh = umul64(x, yh); + auto const xyl = umul64(x, yl); + + return xyh + (xyl >> 32); + } + + // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + constexpr uint128 umul192_lower128(uint64_t x, uint128 y) { + auto const high = x * y.high; + auto const high_low = umul128(x, y.low); + return {(high + high_low.high) & UINT64_C(0xffffffffffffffff), high_low.low}; + } + + // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + constexpr uint64_t umul96_lower64(uint32_t x, uint64_t y) { + return (x * y) & UINT64_C(0xffffffffffffffff); + } + + template + constexpr Int compute_power(Int a) { + static_assert(k >= 0); + int e = k; + Int p = 1; + while (e) { + if (e % 2) + p *= a; + e /= 2; + a *= a; + } + return p; + } + + template + struct compute_mul_result { + Integer integer_part; + bool is_integer; + }; + + struct compute_mul_parity_result { + bool parity; + bool is_integer; + }; + + // These classes expose encoding specs of IEEE-754-like floating-point formats. + // Currently available formats are IEEE-754 binary32 & IEEE-754 binary64. + + template + struct float_format; + + template <> + struct float_format { + using carrier_uint = uint32_t; + enum { + total_bits = 32, + significand_bits = 23, + exponent_bits = 8, + min_exponent = -126, + max_exponent = 127, + exponent_bias = -127, + decimal_significand_digits = 9, + decimal_exponent_digits = 2, + cache_bits = 64, + min_k = -31, + max_k = 46, + }; + + static void remove_trailing_zeros(uint32_t& significand, int& exponent) { + // See https://github.com/jk-jeon/rtz_benchmark. + // The idea of branchless search below is by reddit users r/pigeon768 and + // r/TheoreticalDumbass. + + auto r = rotr32(uint32_t(significand * UINT32_C(184254097)), 4); + auto b = r < UINT32_C(429497); + auto s = size_t(b); + significand = b ? r : significand; + + r = rotr32(uint32_t(significand * UINT32_C(42949673)), 2); + b = r < UINT32_C(42949673); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr32(uint32_t(significand * UINT32_C(1288490189)), 1); + b = r < UINT32_C(429496730); + s = s * 2 + b; + significand = b ? r : significand; + + exponent += s; + } + + static compute_mul_result compute_mul(uint32_t u, uint64_t cache) { + auto const r = umul96_upper64(u, cache); + return {uint32_t(r >> 32), uint32_t(r) == 0}; + } + + static uint32_t compute_delta(uint64_t cache, int beta) { + return uint32_t(cache >> (cache_bits - 1 - beta)); + } + + static compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, int beta) { + assert(beta >= 1); + assert(beta <= 32); + auto const r = umul96_lower64(two_f, cache); + return {((r >> (64 - beta)) & 1) != 0, (UINT32_C(0xffffffff) & (r >> (32 - beta))) == 0}; + } + + static uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + return (cache - (cache >> (significand_bits + 2))) >> + (cache_bits - significand_bits - 1 - beta); + } + + static uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + return (cache + (cache >> (significand_bits + 1))) >> + (cache_bits - significand_bits - 1 - beta); + } + + static uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { + return (uint32_t(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; + } + + template + static uint32_t divide_by_pow10(uint32_t n) { + static_assert(N >= 0, ""); + + // Specialize for 32-bit division by 10. + // Without the bound on n_max (which compilers these days never leverage), the + // minimum needed amount of shift is larger than 32. Hence, this may generate better + // code for 32-bit or smaller architectures. Even for 64-bit architectures, it seems + // compilers tend to generate mov + mul instead of a single imul for an unknown + // reason if we just write n / 10. + if constexpr (N == 1 && n_max <= UINT32_C(1073741828)) { + return uint32_t(umul64(n, UINT32_C(429496730)) >> 32); + } + // Specialize for 32-bit division by 100. + // It seems compilers tend to generate mov + mul instead of a single imul for an + // unknown reason if we just write n / 100. + else if constexpr (N == 2) { + return uint32_t(umul64(n, UINT32_C(1374389535)) >> 37); + } + else { + return n / compute_power(uint32_t(10)); + } + } + }; + + template <> + struct float_format { + using carrier_uint = uint64_t; + enum { + total_bits = 64, + significand_bits = 52, + exponent_bits = 11, + min_exponent = -1022, + max_exponent = 1023, + exponent_bias = -1023, + decimal_significand_digits = 17, + decimal_exponent_digits = 3, + cache_bits = 128, + min_k = -292, + max_k = 326, + }; + + static void remove_trailing_zeros(uint64_t& significand, int& exponent) { + // See https://github.com/jk-jeon/rtz_benchmark. + // The idea of branchless search below is by reddit users r/pigeon768 and + // r/TheoreticalDumbass. + + auto r = rotr64(uint64_t(significand * UINT64_C(28999941890838049)), 8); + auto b = r < UINT64_C(184467440738); + auto s = size_t(b); + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(182622766329724561)), 4); + b = r < UINT64_C(1844674407370956); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(10330176681277348905)), 2); + b = r < UINT64_C(184467440737095517); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(14757395258967641293)), 1); + b = r < UINT64_C(1844674407370955162); + s = s * 2 + b; + significand = b ? r : significand; + + exponent += s; + } + + static compute_mul_result compute_mul(uint64_t u, uint128 cache) { + auto const r = umul192_upper128(u, cache); + return {r.high, r.low == 0}; + } + + static uint64_t compute_delta(uint128 cache, int beta) { + return cache.high >> (total_bits - 1 - beta); + } + + static compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, int beta) { + assert(beta >= 1); + assert(beta < 64); + auto const r = umul192_lower128(two_f, cache); + return {((r.high >> (64 - beta)) & 1) != 0, + (((r.high << beta) & UINT64_C(0xffffffffffffffff)) | (r.low >> (64 - beta))) == 0}; + } + + static uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + return (cache.high - (cache.high >> (significand_bits + 2))) >> + (total_bits - significand_bits - 1 - beta); + } + + static uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + return (cache.high + (cache.high >> (significand_bits + 1))) >> + (total_bits - significand_bits - 1 - beta); + } + + static uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { + return ((cache.high >> (total_bits - significand_bits - 2 - beta)) + 1) / 2; + } + + template + static uint64_t divide_by_pow10(uint64_t n) { + static_assert(N >= 0, ""); + + // Specialize for 64-bit division by 10. + // Without the bound on n_max (which compilers these days never leverage), the + // minimum needed amount of shift is larger than 64. + if constexpr (N == 1 && n_max <= UINT64_C(4611686018427387908)) { + return umul128_upper64(n, UINT64_C(1844674407370955162)); + } + // Specialize for 64-bit division by 1000. + // Without the bound on n_max (which compilers these days never leverage), the + // smallest magic number for this computation does not fit into 64-bits. + else if constexpr (N == 3 && n_max <= UINT64_C(15534100272597517998)) { + return umul128_upper64(n, UINT64_C(4722366482869645214)) >> 8; + } + else { + return n / compute_power(uint64_t(10)); + } + } + }; + + static constexpr uint64_t cache32[78]{ + UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), + UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), + UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), + UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), + UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), + UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), + UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), + UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), + UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), + UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), + UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), + UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), + UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), + UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), + UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), + UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), + UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), + UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), + UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), + UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), + UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), + UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), + UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), + UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), + UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), + UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; + + static constexpr uint128 cache64[619] = { + {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, + {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, + {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, + {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, + {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, + {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, + {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, + {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, + {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, + {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, + {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, + {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, + {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, + {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, + {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, + {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, + {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, + {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, + {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, + {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, + {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, + {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, + {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, + {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, + {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, + {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, + {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, + {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, + {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, + {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, + {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, + {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, + {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, + {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, + {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, + {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, + {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, + {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, + {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, + {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, + {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, + {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, + {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, + {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, + {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, + {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, + {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, + {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, + {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, + {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, + {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, + {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, + {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, + {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, + {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, + {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, + {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, + {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, + {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, + {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, + {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, + {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, + {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, + {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, + {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, + {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, + {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, + {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, + {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, + {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, + {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, + {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, + {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, + {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, + {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, + {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, + {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, + {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, + {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, + {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, + {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, + {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, + {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, + {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, + {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, + {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, + {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, + {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, + {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, + {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, + {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, + {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, + {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, + {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, + {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, + {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, + {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, + {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, + {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, + {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, + {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, + {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, + {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, + {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, + {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, + {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, + {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, + {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, + {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, + {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, + {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, + {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, + {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, + {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, + {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, + {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, + {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, + {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, + {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, + {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, + {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, + {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, + {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, + {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, + {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, + {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, + {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, + {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, + {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, + {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, + {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, + {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, + {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, + {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, + {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, + {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, + {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, + {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, + {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, + {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, + {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, + {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, + {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, + {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, + {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, + {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, + {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, + {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, + {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, + {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, + {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, + {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, + {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, + {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, + {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, + {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, + {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, + {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, + {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, + {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, + {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, + {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, + {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, + {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, + {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, + {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, + {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, + {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, + {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, + {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, + {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, + {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, + {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, + {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, + {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, + {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, + {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, + {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, + {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, + {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, + {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, + {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, + {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, + {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, + {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, + {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, + {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, + {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, + {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, + {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, + {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, + {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, + {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, + {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, + {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, + {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, + {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, + {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, + {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, + {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, + {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, + {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, + {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, + {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, + {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, + {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, + {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, + {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, + {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, + {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, + {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, + {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, + {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, + {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, + {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, + {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, + {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, + {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, + {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, + {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, + {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, + {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, + {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, + {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, + {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, + {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, + {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, + {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, + {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, + {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, + {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, + {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, + {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, + {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, + {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, + {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, + {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, + {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, + {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, + {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, + {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, + {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, + {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, + {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, + {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, + {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, + {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, + {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, + {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, + {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, + {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, + {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, + {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, + {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, + {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, + {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, + {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, + {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, + {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, + {UINT64_C(0xa6274bbdd0fadd61), UINT64_C(0xecb1ad8aeacdd58f)}, + {UINT64_C(0xcfb11ead453994ba), UINT64_C(0x67de18eda5814af3)}, + {UINT64_C(0x81ceb32c4b43fcf4), UINT64_C(0x80eacf948770ced8)}, + {UINT64_C(0xa2425ff75e14fc31), UINT64_C(0xa1258379a94d028e)}, + {UINT64_C(0xcad2f7f5359a3b3e), UINT64_C(0x096ee45813a04331)}, + {UINT64_C(0xfd87b5f28300ca0d), UINT64_C(0x8bca9d6e188853fd)}, + {UINT64_C(0x9e74d1b791e07e48), UINT64_C(0x775ea264cf55347e)}, + {UINT64_C(0xc612062576589dda), UINT64_C(0x95364afe032a819e)}, + {UINT64_C(0xf79687aed3eec551), UINT64_C(0x3a83ddbd83f52205)}, + {UINT64_C(0x9abe14cd44753b52), UINT64_C(0xc4926a9672793543)}, + {UINT64_C(0xc16d9a0095928a27), UINT64_C(0x75b7053c0f178294)}, + {UINT64_C(0xf1c90080baf72cb1), UINT64_C(0x5324c68b12dd6339)}, + {UINT64_C(0x971da05074da7bee), UINT64_C(0xd3f6fc16ebca5e04)}, + {UINT64_C(0xbce5086492111aea), UINT64_C(0x88f4bb1ca6bcf585)}, + {UINT64_C(0xec1e4a7db69561a5), UINT64_C(0x2b31e9e3d06c32e6)}, + {UINT64_C(0x9392ee8e921d5d07), UINT64_C(0x3aff322e62439fd0)}, + {UINT64_C(0xb877aa3236a4b449), UINT64_C(0x09befeb9fad487c3)}, + {UINT64_C(0xe69594bec44de15b), UINT64_C(0x4c2ebe687989a9b4)}, + {UINT64_C(0x901d7cf73ab0acd9), UINT64_C(0x0f9d37014bf60a11)}, + {UINT64_C(0xb424dc35095cd80f), UINT64_C(0x538484c19ef38c95)}, + {UINT64_C(0xe12e13424bb40e13), UINT64_C(0x2865a5f206b06fba)}, + {UINT64_C(0x8cbccc096f5088cb), UINT64_C(0xf93f87b7442e45d4)}, + {UINT64_C(0xafebff0bcb24aafe), UINT64_C(0xf78f69a51539d749)}, + {UINT64_C(0xdbe6fecebdedd5be), UINT64_C(0xb573440e5a884d1c)}, + {UINT64_C(0x89705f4136b4a597), UINT64_C(0x31680a88f8953031)}, + {UINT64_C(0xabcc77118461cefc), UINT64_C(0xfdc20d2b36ba7c3e)}, + {UINT64_C(0xd6bf94d5e57a42bc), UINT64_C(0x3d32907604691b4d)}, + {UINT64_C(0x8637bd05af6c69b5), UINT64_C(0xa63f9a49c2c1b110)}, + {UINT64_C(0xa7c5ac471b478423), UINT64_C(0x0fcf80dc33721d54)}, + {UINT64_C(0xd1b71758e219652b), UINT64_C(0xd3c36113404ea4a9)}, + {UINT64_C(0x83126e978d4fdf3b), UINT64_C(0x645a1cac083126ea)}, + {UINT64_C(0xa3d70a3d70a3d70a), UINT64_C(0x3d70a3d70a3d70a4)}, + {UINT64_C(0xcccccccccccccccc), UINT64_C(0xcccccccccccccccd)}, + {UINT64_C(0x8000000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa000000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xc800000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xfa00000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9c40000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xc350000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xf424000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9896800000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xbebc200000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xee6b280000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9502f90000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xba43b74000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xe8d4a51000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9184e72a00000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, + {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, + {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, + {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, + {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, + {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, + {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, + {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, + {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, + {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, + {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, + {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, + {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, + {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, + {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, + {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, + {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, + {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, + {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, + {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, + {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, + {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, + {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, + {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, + {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, + {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, + {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, + {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, + {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, + {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, + {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, + {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, + {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, + {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, + {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, + {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, + {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, + {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, + {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, + {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, + {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, + {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, + {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, + {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, + {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, + {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, + {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, + {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, + {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, + {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, + {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, + {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, + {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, + {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, + {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, + {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, + {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, + {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, + {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, + {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, + {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, + {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, + {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, + {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, + {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, + {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, + {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, + {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, + {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, + {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, + {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, + {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, + {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, + {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, + {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, + {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, + {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, + {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, + {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, + {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, + {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, + {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, + {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, + {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, + {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, + {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, + {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, + {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, + {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, + {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, + {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, + {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, + {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, + {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, + {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, + {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, + {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, + {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, + {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, + {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, + {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, + {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, + {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, + {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, + {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, + {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, + {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, + {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, + {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, + {UINT64_C(0x899504ae72497eba), UINT64_C(0x6a06494a791c53a9)}, + {UINT64_C(0xabfa45da0edbde69), UINT64_C(0x0487db9d17636893)}, + {UINT64_C(0xd6f8d7509292d603), UINT64_C(0x45a9d2845d3c42b7)}, + {UINT64_C(0x865b86925b9bc5c2), UINT64_C(0x0b8a2392ba45a9b3)}, + {UINT64_C(0xa7f26836f282b732), UINT64_C(0x8e6cac7768d7141f)}, + {UINT64_C(0xd1ef0244af2364ff), UINT64_C(0x3207d795430cd927)}, + {UINT64_C(0x8335616aed761f1f), UINT64_C(0x7f44e6bd49e807b9)}, + {UINT64_C(0xa402b9c5a8d3a6e7), UINT64_C(0x5f16206c9c6209a7)}, + {UINT64_C(0xcd036837130890a1), UINT64_C(0x36dba887c37a8c10)}, + {UINT64_C(0x802221226be55a64), UINT64_C(0xc2494954da2c978a)}, + {UINT64_C(0xa02aa96b06deb0fd), UINT64_C(0xf2db9baa10b7bd6d)}, + {UINT64_C(0xc83553c5c8965d3d), UINT64_C(0x6f92829494e5acc8)}, + {UINT64_C(0xfa42a8b73abbf48c), UINT64_C(0xcb772339ba1f17fa)}, + {UINT64_C(0x9c69a97284b578d7), UINT64_C(0xff2a760414536efc)}, + {UINT64_C(0xc38413cf25e2d70d), UINT64_C(0xfef5138519684abb)}, + {UINT64_C(0xf46518c2ef5b8cd1), UINT64_C(0x7eb258665fc25d6a)}, + {UINT64_C(0x98bf2f79d5993802), UINT64_C(0xef2f773ffbd97a62)}, + {UINT64_C(0xbeeefb584aff8603), UINT64_C(0xaafb550ffacfd8fb)}, + {UINT64_C(0xeeaaba2e5dbf6784), UINT64_C(0x95ba2a53f983cf39)}, + {UINT64_C(0x952ab45cfa97a0b2), UINT64_C(0xdd945a747bf26184)}, + {UINT64_C(0xba756174393d88df), UINT64_C(0x94f971119aeef9e5)}, + {UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, + {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, + {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, + {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, + {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, + {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, + {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, + {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, + {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, + {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, + {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, + {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, + {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, + {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, + {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, + {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, + {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, + {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, + {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, + {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, + {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, + {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, + {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, + {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, + {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, + {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, + {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, + {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, + {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, + {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, + {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, + {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, + {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, + {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, + {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, + {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, + {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, + {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, + {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, + {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, + {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, + {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, + {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, + {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, + {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, + {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, + {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, + {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, + {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, + {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, + {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, + {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, + {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, + {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, + {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, + {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, + {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, + {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, + {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, + {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, + {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, + {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, + {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, + {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, + {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, + {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, + {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, + {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, + {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, + {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, + {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, + {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, + {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, + {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, + {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, + {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, + {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, + {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, + {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, + {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, + {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, + {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, + {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, + {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, + {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, + {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, + {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, + {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, + {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, + {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, + {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, + {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, + {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, + {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, + {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, + {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, + {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, + {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, + {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, + {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, + {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, + {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, + {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, + {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, + {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, + {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, + {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, + {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, + {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, + {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, + {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, + {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, + {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, + {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, + {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, + {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, + {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, + {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, + {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, + {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, + {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, + {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, + {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, + {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, + {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, + {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, + {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, + {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, + {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, + {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, + {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, + {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, + {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, + {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, + {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, + {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, + {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, + {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, + {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, + {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, + {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, + {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, + {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, + {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, + {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, + {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, + {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, + {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, + {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, + {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, + {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, + {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, + {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, + {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, + {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, + {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, + {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, + {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, + {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, + {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, + {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, + {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, + {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, + {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, + {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, + {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, + {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, + {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, + {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; + + enum class cache_type { + full, + compact, + }; + + template + struct cache_holder; + + template <> + struct cache_holder { + using format = float_format; + + uint64_t get_cache(int k) const { + assert(k >= format::min_k && k <= format::max_k); + return cache32[k - format::min_k]; + } + }; + + template <> + struct cache_holder { + using format = float_format; + enum { + cache_bits = format::cache_bits, + min_k = format::min_k, + max_k = format::max_k, + compression_ratio = 13, + compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, + pow5_table_size = (compression_ratio + 1) / 2, + }; + + uint64_t cache[compressed_table_size]{}; + uint16_t pow5_table[pow5_table_size]{}; + + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = cache32[i * compression_ratio]; + } + uint16_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } + } + + uint64_t get_cache(int k) const { + assert(k >= min_k && k <= max_k); + + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint16_t(int(k - min_k) * int16_t(79)) >> 10); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); + + // Get the base cache. + auto const base_cache = cache[cache_index]; + + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); + + // Try to recover the real cache. + auto const pow5 = offset >= 7 + ? uint32_t(uint32_t(pow5_table[6]) * pow5_table[offset - 6]) + : uint32_t(pow5_table[offset]); + auto mul_result = umul128(base_cache, pow5); + auto const recovered_cache = + uint64_t((((mul_result.high << int(64 - alpha)) | (mul_result.low >> alpha)) + 1) & + UINT64_C(0xffffffffffffffff)); + assert(recovered_cache != 0); + + return recovered_cache; + } + } + }; + + template <> + struct cache_holder { + using format = float_format; + + uint128 get_cache(int k) const { + assert(k >= format::min_k && k <= format::max_k); + return cache64[k - format::min_k]; + } + }; + + template <> + struct cache_holder { + using format = float_format; + enum { + cache_bits = format::cache_bits, + min_k = format::min_k, + max_k = format::max_k, + compression_ratio = 27, + compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, + pow5_table_size = compression_ratio, + }; + + uint128 cache[compressed_table_size]{}; + uint64_t pow5_table[pow5_table_size]{}; + + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = cache64[i * compression_ratio]; + } + uint64_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } + } + + uint128 get_cache(int k) const { + assert(k >= min_k && k <= max_k); + + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint32_t(int(k - min_k) * int32_t(607)) >> 14); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); + + // Get the base cache. + auto const base_cache = cache[cache_index]; + + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); + + // Try to recover the real cache. + auto const pow5 = pow5_table[offset]; + auto recovered_cache = umul128(base_cache.high, pow5); + auto const middle_low = umul128(base_cache.low, pow5); + + recovered_cache += middle_low.high; + + auto const high_to_middle = + uint64_t((recovered_cache.high << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); + auto const middle_to_low = + uint64_t((recovered_cache.low << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); + + recovered_cache = {(recovered_cache.low >> alpha) | high_to_middle, + ((middle_low.low >> alpha) | middle_to_low)}; + + assert(recovered_cache.low != UINT64_C(0xffffffffffffffff)); + recovered_cache = {recovered_cache.high, uint64_t(recovered_cache.low + 1)}; + + return recovered_cache; + } + } + }; + + template + constexpr int count_factors(UInt n) { + static_assert(a > 1); + int c = 0; + while (n % a == 0) { + n /= a; + ++c; + } + return c; + } + + static constexpr uint32_t divide_magic_number[2]{6554, 656}; + + struct interval { + bool include_left_endpoint; + bool include_right_endpoint; + }; + + enum class binary_round_mode { + nearest_to_even, + nearest_to_odd, + nearest_toward_plus_infinity, + nearest_toward_minus_infinity, + nearest_toward_zero, + nearest_away_from_zero, + nearest_to_even_static_boundary, + nearest_to_odd_static_boundary, + nearest_toward_plus_infinity_static_boundary, + nearest_toward_minus_infinity_static_boundary, + toward_plus_infinity, + toward_minus_infinity, + toward_zero, + away_from_zero, + }; + + enum class decimal_round_mode { + to_even, + to_odd, + away_from_zero, + toward_zero, + dont_care, + }; + + static_assert(sizeof(float) == 4); + static_assert(sizeof(double) == 8); + + constexpr void reverse(char* begin, char* end) { + while (begin < --end) { + char tmp = *begin; + *begin++ = *end; + *end = tmp; + } + } + + template + struct impl { + using format = float_format; + using carrier_uint = typename format::carrier_uint; + static_assert(sizeof(carrier_uint) == sizeof(Float)); + + static constexpr int min(int x, int y) { return x < y ? x : y; } + static constexpr int max(int x, int y) { return x > y ? x : y; } + + enum { + min_exponent = format::min_exponent, + max_exponent = format::max_exponent, + significand_bits = format::significand_bits, + carrier_bits = 8 * sizeof(carrier_uint), + kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1, + + min_k = min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), + -floor_log10_pow2(max_exponent - significand_bits) + kappa), + + // We do invoke shorter_interval_case for exponent == min_exponent case, + // so we should not add 1 here. + max_k = max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), + -floor_log10_pow2(min_exponent - significand_bits) + kappa), + + case_shorter_interval_left_endpoint_lower_threshold = 2, + + case_shorter_interval_left_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 2)) - 1) + + 1>(10) / + 3), + + case_shorter_interval_right_endpoint_lower_threshold = 0, + + case_shorter_interval_right_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 1)) + 1) + + 1>(10) / + 3), + + shorter_interval_tie_lower_threshold = + -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits, + + shorter_interval_tie_upper_threshold = + -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits, + + // sign + significand + decimal_point + exp_marker + exp_sign + exp + max_output_string_length = + 4 + format::decimal_significand_digits + format::decimal_exponent_digits, + }; + + static_assert(kappa >= 1); + static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); + static_assert(min_k >= format::min_k && max_k <= format::max_k); + + static constexpr cache_holder cache_; + + template + static bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); + assert(n <= compute_power(carrier_uint(10))); + + static constexpr auto magic_number = divide_magic_number[N - 1]; + auto const prod = uint32_t(n * magic_number); + + constexpr auto mask = uint32_t((uint32_t(1) << 16) - 1); + bool const result = ((prod & mask) < magic_number); + + n = carrier_uint(prod >> 16); + return result; + } + + // Compute floor(n / 10^N) for small n and N. + // Precondition: n <= 10^(N+1) + template + static carrier_uint small_division_by_pow10(carrier_uint n) { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); + assert(n <= compute_power(carrier_uint(10))); + return carrier_uint((n * divide_magic_number[N - 1]) >> 16); + } + + static bool prefer_round_down(carrier_uint decimal_significand) { + using e = decimal_round_mode; + switch (DecimalRoundMode) { + case e::dont_care: + return false; + case e::to_even: + return decimal_significand % 2 != 0; + case e::to_odd: + return decimal_significand % 2 == 0; + case e::away_from_zero: + return false; + case e::toward_zero: + return true; + } + } + + carrier_uint significand; + int exponent; + bool sign; + + constexpr impl(Float x) { + carrier_uint bits; + static_assert(sizeof(x) == sizeof(bits)); + ::memcpy(&bits, &x, sizeof(x)); + significand = bits & ((carrier_uint(1) << format::significand_bits) - 1); + exponent = bits >> format::significand_bits & ((1u << format::exponent_bits) - 1); + sign = bits >> (format::significand_bits + format::exponent_bits); + } + + bool is_finite() const { return exponent != (1u << format::exponent_bits) - 1; } + + struct decimal_result { + carrier_uint significand; + int exponent; + bool sign; + }; + + decimal_result to_decimal() { + assert(is_finite() && (significand || exponent)); + bool even = significand % 2 == 0; + using e = binary_round_mode; + switch (BinaryRoundMode) { + case e::nearest_to_even: + return nearest_to_even(); + case e::nearest_to_odd: + return nearest_to_odd(); + case e::nearest_toward_plus_infinity: + return nearest_toward_plus_infinity(); + case e::nearest_toward_minus_infinity: + return nearest_toward_minus_infinity(); + case e::nearest_toward_zero: + return nearest_toward_zero(); + case e::nearest_away_from_zero: + return nearest_away_from_zero(); + case e::nearest_to_even_static_boundary: + return even ? nearest_always_closed() : nearest_always_open(); + case e::nearest_to_odd_static_boundary: + return even ? nearest_always_open() : nearest_always_closed(); + case e::nearest_toward_plus_infinity_static_boundary: + return sign ? nearest_toward_zero() : nearest_away_from_zero(); + case e::nearest_toward_minus_infinity_static_boundary: + return sign ? nearest_away_from_zero() : nearest_toward_zero(); + case e::toward_plus_infinity: + return sign ? left_closed_directed() : right_closed_directed(); + case e::toward_minus_infinity: + return sign ? right_closed_directed() : left_closed_directed(); + case e::toward_zero: + return left_closed_directed(); + case e::away_from_zero: + return right_closed_directed(); + } + } + + auto nearest_to_even() { + bool even = significand % 2 == 0; + return nearest({even, even}, {true, true}); + } + + auto nearest_to_odd() { + bool even = significand % 2 == 0; + return nearest({!even, even}, {false, false}); + } + + auto nearest_toward_plus_infinity() { return nearest({!sign, sign}, {!sign, sign}); } + + auto nearest_toward_minus_infinity() { return nearest({sign, !sign}, {sign, !sign}); } + + auto nearest_toward_zero() { return nearest({false, true}, {false, true}); } + + auto nearest_away_from_zero() { return nearest({true, false}, {true, false}); } + + auto nearest_always_closed() { return nearest({true, true}, {true, true}); } + + auto nearest_always_open() { return nearest({false, false}, {false, false}); } + + decimal_result no_trailing_zeros(carrier_uint significand, int exponent) { + return {significand, exponent, sign}; + } + + decimal_result may_have_trailing_zeros(carrier_uint significand, int exponent) { + format::remove_trailing_zeros(significand, exponent); + return {significand, exponent, sign}; + } + + //// The main algorithm assumes the input is a normal/subnormal finite number. + + auto nearest(interval normal_interval, interval shorter_interval) { + + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; + + // Is the input a normal number? + if (binary_exponent != 0) { + binary_exponent += format::exponent_bias - format::significand_bits; + + // Shorter interval case; proceed like Schubfach. + // One might think this condition is wrong, since when exponent_bits == + // 1 and two_fc == 0, the interval is actually regular. However, it + // turns out that this seemingly wrong condition is actually fine, + // because the end result is anyway the same. + // + // [binary32] + // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 + // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 + // fc * 2^e = 1.175'494'35... * 10^-38 + // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 + // + // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. + // 1.175'494'3 * 10^-38 is also a correct shortest representation that + // will be rejected if we assume shorter interval, but 1.175'494'4 * + // 10^-38 is closer to the true value so it doesn't matter. + // + // [binary64] + // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 + // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 + // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 + // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 + // + // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * + // 10^-308. This is indeed of the shortest length, and it is the unique + // one closest to the true value among valid representations of the same + // length. + + // Shorter interval case. + if (two_fc == 0) { + + // Compute k and beta. + int const minus_k = floor_log10_pow2_minus_log10_4_over_3(binary_exponent); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute xi and zi. + auto const cache = cache_.get_cache(-minus_k); + + auto xi = format::compute_left_endpoint_for_shorter_interval_case(cache, beta); + auto zi = format::compute_right_endpoint_for_shorter_interval_case(cache, beta); + + // If we don't accept the right endpoint and + // if the right endpoint is an integer, decrease it. + if (!shorter_interval.include_right_endpoint && + is_right_endpoint_integer_shorter_interval(binary_exponent)) { + --zi; + } + // If we don't accept the left endpoint or + // if the left endpoint is not an integer, increase it. + if (!shorter_interval.include_left_endpoint || + !is_left_endpoint_integer_shorter_interval(binary_exponent)) { + ++xi; + } + + // Try bigger divisor. + // zi is at most floor((f_c + 1/2) * 2^e * 10^k0). + // Substituting f_c = 2^p and k0 = -floor(log10(3 * 2^(e-2))), we get + // zi <= floor((2^(p+1) + 1) * 20/3) <= ceil((2^(p+1) + 1)/3) * 20. + // This computation does not overflow for any of the formats I care about. + carrier_uint decimal_significand = format::template divide_by_pow10< + 1, (((carrier_uint(2) << significand_bits) + 1) / 3 + 1) * 20>(zi); + + // If succeed, remove trailing zeros if necessary and return. + if (decimal_significand * 10 >= xi) { + return may_have_trailing_zeros(decimal_significand, minus_k + 1); + } + + // Otherwise, compute the round-up of y. + decimal_significand = + format::compute_round_up_for_shorter_interval_case(cache, beta); + + // When tie occurs, choose one of them according to the rule. + if (prefer_round_down(decimal_significand) && + binary_exponent >= shorter_interval_tie_lower_threshold && + binary_exponent <= shorter_interval_tie_upper_threshold) { + --decimal_significand; + } + else if (decimal_significand < xi) { + ++decimal_significand; + } + return no_trailing_zeros(decimal_significand, minus_k); + } + + // Normal interval case. + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); + } + else { + // Is the input a subnormal number? + // Normal interval case. + binary_exponent = min_exponent - format::significand_bits; + } + + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = floor_log10_pow2(binary_exponent) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta); + // For the case of binary32, the result of integer check is not correct for + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, + // and they are the unique counterexamples. However, since 29711844 is even, + // this does not cause any problem for the endpoints calculations; it can only + // cause a problem when we need to perform integer check for the center. + // Fortunately, with these inputs, that branch is never executed, so we are + // fine. + auto const z_result = format::compute_mul(carrier_uint((two_fc | 1) << beta), cache); + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// + + auto const big_divisor = compute_power(carrier_uint(10)); + auto const small_divisor = compute_power(carrier_uint(10)); + + // Using an upper bound on zi, we might be able to optimize the division + // better than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( + z_result.integer_part); + auto r = carrier_uint(z_result.integer_part - big_divisor * decimal_significand); + + do { + if (r < deltai) { + // Exclude the right endpoint if necessary. + if ((r | carrier_uint(!z_result.is_integer) | + carrier_uint(normal_interval.include_right_endpoint)) == 0) { + if (DecimalRoundMode == decimal_round_mode::dont_care) { + decimal_significand *= 10; + --decimal_significand; + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } + else { + --decimal_significand; + r = big_divisor; + break; + } + } + } + else if (r > deltai) { + break; + } + else { + // r == deltai; compare fractional parts. + auto const x_result = + format::compute_mul_parity(carrier_uint(two_fc - 1), cache, beta); + + if (!(x_result.parity | + (x_result.is_integer & normal_interval.include_left_endpoint))) { + break; + } + } + + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); + + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor. + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + + if (DecimalRoundMode == decimal_round_mode::dont_care) { + // Normally, we want to compute + // significand += r / small_divisor + // and return, but we need to take care of the case that the resulting + // value is exactly the right endpoint, while that is not included in the + // interval. + if (!normal_interval.include_right_endpoint) { + // Is r divisible by 10^kappa? + if (check_divisibility_and_divide_by_pow10(r) && z_result.is_integer) { + // This should be in the interval. + decimal_significand += r - 1; + } + else { + decimal_significand += r; + } + } + else { + decimal_significand += small_division_by_pow10(r); + } + } + else { + // delta is equal to 10^(kappa + elog10(2) - floor(elog10(2))), so dist cannot + // be larger than r. + auto dist = carrier_uint(r - (deltai / 2) + (small_divisor / 2)); + bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; + + // Is dist divisible by 10^kappa? + bool const divisible_by_small_divisor = + check_divisibility_and_divide_by_pow10(dist); + + // Add dist / 10^kappa to the significand. + decimal_significand += dist; + + if (divisible_by_small_divisor) { + // Check z^(f) >= epsilon^(f). + // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, + // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). + // Since there are only 2 possibilities, we only need to care about the + // parity. Also, zi and r should have the same parity since the divisor + // is an even number. + auto const y_result = format::compute_mul_parity(two_fc, cache, beta); + if (y_result.parity != approx_y_parity) { + --decimal_significand; + } + else { + // If z^(f) >= epsilon^(f), we might have a tie + // when z^(f) == epsilon^(f), or equivalently, when y is an integer. + // For tie-to-up case, we can just choose the upper one. + if (prefer_round_down(decimal_significand) & y_result.is_integer) { + --decimal_significand; + } + } + } + } + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } + + auto left_closed_directed() { + + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; + + // Is the input a normal number? + if (binary_exponent != 0) { + binary_exponent += format::exponent_bias - format::significand_bits; + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + binary_exponent = min_exponent - format::significand_bits; + } + + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = floor_log10_pow2(binary_exponent) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute xi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta); + auto x_result = format::compute_mul(carrier_uint(two_fc << beta), cache); + + // Deal with the unique exceptional cases + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17 + // for binary32. + if constexpr (carrier_bits == 32) { + if (binary_exponent <= -80) { + x_result.is_integer = false; + } + } + + if (!x_result.is_integer) { + ++x_result.integer_part; + } + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// + + auto const big_divisor = compute_power(carrier_uint(10)); + + // Using an upper bound on xi, we might be able to optimize the division + // better than the compiler; we are computing xi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( + x_result.integer_part); + auto r = carrier_uint(x_result.integer_part - big_divisor * decimal_significand); + + if (r != 0) { + ++decimal_significand; + r = carrier_uint(big_divisor - r); + } + + do { + if (r > deltai) { + break; + } + else if (r == deltai) { + // Compare the fractional parts. + // This branch is never taken for the exceptional cases + // 2f_c = 29711482, e = -81 + // (6.1442649164096937243516663440523473127541365101933479309082... * + // 10^-18) and 2f_c = 29711482, e = -80 + // (1.2288529832819387448703332688104694625508273020386695861816... * + // 10^-17). + // For the case of compressed cache for binary32, there is another + // exceptional case 2f_c = 33554430, e = -10 (16383.9990234375). In this + // case, the recovered cache is two large to make compute_mul_parity + // mistakenly conclude that z is not an integer, but actually z = 16384 is + // an integer. + if constexpr (carrier_bits == 32 && CacheType == cache_type::compact) { + if (two_fc == 33554430 && binary_exponent == -10) { + break; + } + } + auto const z_result = + format::compute_mul_parity(carrier_uint(two_fc + 2), cache, beta); + if (z_result.parity || z_result.is_integer) { + break; + } + } + + // The ceiling is inside, so we are done. + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); + + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor. + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + decimal_significand -= small_division_by_pow10(r); + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } + + auto right_closed_directed() { + + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; + bool shorter_interval = false; + + // Is the input a normal number? + if (binary_exponent != 0) { + if (two_fc == 0 && binary_exponent != 1) { + shorter_interval = true; + } + binary_exponent += format::exponent_bias - format::significand_bits; + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + binary_exponent = min_exponent - format::significand_bits; + } + + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = floor_log10_pow2(binary_exponent - (shorter_interval ? 1 : 0)) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta - (shorter_interval ? 1 : 0)); + carrier_uint const zi = + format::compute_mul(carrier_uint(two_fc << beta), cache).integer_part; + + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// + + auto const big_divisor = compute_power(carrier_uint(10)); + + // Using an upper bound on zi, we might be able to optimize the division better + // than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>(zi); + auto const r = carrier_uint(zi - big_divisor * decimal_significand); + + do { + if (r > deltai) { + break; + } + else if (r == deltai) { + // Compare the fractional parts. + if (!format::compute_mul_parity(carrier_uint(two_fc - (shorter_interval ? 1 : 2)), + cache, beta) + .parity) { + break; + } + } + + // The floor is inside, so we are done. + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); + + + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the small divisor. + ////////////////////////////////////////////////////////////////////// + + decimal_significand *= 10; + decimal_significand += small_division_by_pow10(r); + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } + + static bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { + return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && + binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; + } + + static bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { + return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && + binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; + } + + char* to_chars(char* buffer) { + if (!is_finite()) { + if (!significand) { + if (sign) { + *buffer++ = '-'; + } + ::memcpy(buffer, "Infinity", 8); + return buffer + 8; + } + else { + buffer[0] = 'N'; + buffer[1] = 'a'; + buffer[2] = 'N'; + return buffer + 3; + } + } + + if (sign) { + *buffer++ = '-'; + } + + if (!significand && !exponent) { + buffer[0] = '0'; + buffer[1] = 'E'; + buffer[2] = '0'; + return buffer + 3; + } + + auto [dec_sig, dec_exp, dec_sign] = to_decimal(); + + if (dec_sig < 10) { + *buffer++ = char('0' + dec_sig); + } + else { + auto begin = buffer; + do { + *buffer++ = char('0' + dec_sig % 10); + dec_sig /= 10; + ++dec_exp; + } while (dec_sig >= 10); + *buffer++ = '.'; + *buffer++ = char('0' + dec_sig); + reverse(begin, buffer); + } + + *buffer++ = 'E'; + if (dec_exp < 0) { + *buffer++ = '-'; + dec_exp = -dec_exp; + } + + auto begin = buffer; + do { + *buffer++ = char('0' + dec_exp % 10); + dec_exp /= 10; + } while (dec_exp); + reverse(begin, buffer); + return buffer; + } + }; + + //////////////////////////////////////////////////////////////////////////////////////// + // The interface function. + //////////////////////////////////////////////////////////////////////////////////////// + + template + struct policy_ {}; + + namespace policy { + namespace decimal_to_binary_rounding { + using type = binary_round_mode; + constexpr policy_ nearest_to_even; + constexpr policy_ nearest_to_odd; + constexpr policy_ nearest_toward_plus_infinity; + constexpr policy_ nearest_toward_minus_infinity; + constexpr policy_ nearest_toward_zero; + constexpr policy_ nearest_away_from_zero; + constexpr policy_ + nearest_to_even_static_boundary; + constexpr policy_ + nearest_to_odd_static_boundary; + constexpr policy_ + nearest_toward_plus_infinity_static_boundary; + constexpr policy_ + nearest_toward_minus_infinity_static_boundary; + constexpr policy_ toward_plus_infinity; + constexpr policy_ toward_minus_infinity; + constexpr policy_ toward_zero; + constexpr policy_ away_from_zero; + } + namespace binary_to_decimal_rounding { + using type = decimal_round_mode; + constexpr policy_ to_even; + constexpr policy_ to_odd; + constexpr policy_ away_from_zero; + constexpr policy_ toward_zero; + constexpr policy_ do_not_care; + } + namespace cache { + using type = cache_type; + constexpr policy_ full; + constexpr policy_ compact; + } + } + + template + struct get_policy; + + template + struct get_policy { + static constexpr T value{}; + }; + + template + struct get_policy, Rest...> { + static constexpr T value = x; + }; + + template + struct get_policy : get_policy {}; + + template + using make_impl = impl::value, + get_policy::value, + get_policy::value>; + + template + constexpr auto to_decimal(Float x, Policies...) { + return make_impl(x).to_decimal(); + } + + // Null-terminate and bypass the return value of fp_to_chars_n + template + constexpr char* to_chars(Float x, char* buffer, Policies... policies) { + auto ptr = make_impl(x).to_chars(buffer); + *ptr = '\0'; + return ptr; + } + + // Maximum required buffer size (excluding null-terminator) + template + constexpr size_t max_output_string_length = impl::max_output_string_length; +} diff --git a/subproject/simple/simple_dragonbox_test.cpp b/subproject/simple/simple_dragonbox_test.cpp new file mode 100644 index 0000000..5445dd0 --- /dev/null +++ b/subproject/simple/simple_dragonbox_test.cpp @@ -0,0 +1,85 @@ +// Copyright 2024 Junekey Jeon, Toby Bell +// TODO: License + +#include "simple_dragonbox.h" +#include "random_float.h" +#include "ryu/ryu.h" + +#include +#include +#include + +static void reference_implementation(float x, char* buffer) { f2s_buffered(x, buffer); } +static void reference_implementation(double x, char* buffer) { d2s_buffered(x, buffer); } + +template +static bool test_simple_dragonbox(bool& success, Arg... arg) { + static constexpr char const* type_name = sizeof(Float) == 4 ? "float" : "double"; + static constexpr char const* compact = sizeof...(arg) ? "yes" : "no"; + static constexpr unsigned test_count = 10000000; + + std::cout << "uniform random test, type=" << type_name << " test_count=" << test_count << + " compact_cache=" << compact << " ...\n"; + + char buffer1[64]; + char buffer2[64]; + auto rg = generate_correctly_seeded_mt19937_64(); + for (std::size_t test_idx = 0; test_idx < test_count; ++test_idx) { + auto x = uniformly_randomly_generate_general_float(rg); + + // Check if the output is identical to the reference implementation (Ryu). + simple_dragonbox::to_chars(x, buffer1, arg...); + reference_implementation(x, buffer2); + + std::string_view view1(buffer1); + std::string_view view2(buffer2); + + if (view1 != view2) { + std::cout << "error detected, reference=" << buffer2 << " dragonbox=" << buffer1 << "\n"; + success = false; + } + } + + std::cout << "done.\n"; + + std::cout << "test all shorter interval cases, type=" << type_name << " compact_cache=" << compact << " ... \n"; + + using format = simple_dragonbox::float_format; + using carrier_uint = typename format::carrier_uint; + + for (int e = format::min_exponent; e <= format::max_exponent; ++e) { + // Compose a floating-point number + carrier_uint br = carrier_uint(e - format::exponent_bias) + << format::significand_bits; + + Float x; + static_assert(sizeof(br) == sizeof(x)); + ::memcpy(&x, &br, sizeof(br)); + + simple_dragonbox::to_chars(x, buffer1, arg...); + reference_implementation(x, buffer2); + + std::string_view view1(buffer1); + std::string_view view2(buffer2); + + if (view1 != view2) { + std::cout << "error detected, reference=" << buffer2 << " dragonbox=" << buffer1 << "\n"; + success = false; + } + } + + std::cout << "done.\n"; + + return success; +} + +int main() { + bool success = true; + test_simple_dragonbox(success); + test_simple_dragonbox(success, simple_dragonbox::policy::cache::compact); + test_simple_dragonbox(success); + test_simple_dragonbox(success, simple_dragonbox::policy::cache::compact); + if (!success) + return -1; +} + From a6b4fdc79cbe4dd6bb6cb15bf3be2be818094188 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 21:55:52 -0700 Subject: [PATCH 02/17] Clarify reduced performance --- subproject/simple/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index c6c6638..4155f77 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -2,8 +2,8 @@ This is a simplified implementation of the algorithm, that closely follows the one in `include/dragonbox/dragonbox.h`, but aims to be shorter overall, use less -C++ template indirection, and offer slightly less flexibility for the benefit of -simpliciy. +C++ template indirection, and offer less flexibility and performance for the +sake of simpliciy. Primary sacrifices over the implementation in `include/dragonbox/dragonbox.h`: From d4183bbae2b4029943608d661a9ece8b95dbb3b4 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:12:31 -0700 Subject: [PATCH 03/17] Specify assumption about `float` and `double` representation size --- subproject/simple/README.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index 4155f77..49235dd 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -13,7 +13,8 @@ Primary sacrifices over the implementation in `include/dragonbox/dragonbox.h`: implementation) - No support for fast digit-generation policy (always uses `compact`) - Assumes the existence of `if constexpr` (C++17) -- Assumes `float` and `double` types are available and use IEEE-754 +- Assumes `float` and `double` types are available and use IEEE-754 32-bit and + 64-bit representations, respectively - Generally assumes a modern standard compiler environment and C standard library From 2729e3bc0ecf82699e998b07c855c938413049f2 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:10:53 -0700 Subject: [PATCH 04/17] Use sentences instead of phrases in simplifying assumptions list --- subproject/simple/README.md | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index 49235dd..3c93dec 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -5,18 +5,18 @@ one in `include/dragonbox/dragonbox.h`, but aims to be shorter overall, use less C++ template indirection, and offer less flexibility and performance for the sake of simpliciy. -Primary sacrifices over the implementation in `include/dragonbox/dragonbox.h`: - -- No support for `sign` policies (always uses `return_sign`) -- No support for `trailing_zeros` policies (always uses `remove`) -- No support for 128-bit compiler intrinsics (always uses portable - implementation) -- No support for fast digit-generation policy (always uses `compact`) -- Assumes the existence of `if constexpr` (C++17) -- Assumes `float` and `double` types are available and use IEEE-754 32-bit and - 64-bit representations, respectively -- Generally assumes a modern standard compiler environment and C standard - library +Simplifications over the implementation in `include/dragonbox/dragonbox.h` are +made based primarily on the following assumptions: + +- No need to support `sign` policies (always uses `return_sign`). +- No need to support `trailing_zeros` policies (always uses `remove`). +- No need to support 128-bit compiler intrinsics (always uses portable + implementation). +- No need to support the `fast` digit-generation policy (always uses `compact`). +- `if constexpr` is available (C++17). +- `float` and `double` use IEEE-754 32-bit and 64-bit representations, + respectively. +- A modern compiler and standard library are available. Note the `cache`, `binary_to_decimal_rounding`, and `decimal_to_binary_rounding` policies are still supported. From a1ebcdde282edd8ae264b5956bf836858510cc83 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:37:36 -0700 Subject: [PATCH 05/17] Make usage examples more closely match those in the primary README --- subproject/simple/README.md | 122 +++++++++++++++++++----------------- 1 file changed, 66 insertions(+), 56 deletions(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index 3c93dec..1151194 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -21,35 +21,50 @@ made based primarily on the following assumptions: Note the `cache`, `binary_to_decimal_rounding`, and `decimal_to_binary_rounding` policies are still supported. -## API +# Usage Examples -### Basic use - -To convert to decimal (analog to `jkj::dragonbox::to_decimal`), +Simple string generation from `float`/`double` (mirrors the interface and +behavior of `jkj::dragonbox::to_chars`; see the [primary README](/README.md)): ```cpp -float x; -auto d = simple_dragonbox::to_decimal(x); -(void) d.significand; -(void) d.exponent; -(void) d.sign; +#include "simple_dragonbox.h" + +constexpr int buffer_length = 1 + // for '\0' + simple_dragonbox::max_output_string_length; +double x = 1.234; // Also works for float +char buffer[buffer_length]; + +// Null-terminate the buffer and return the pointer to the null character. +// Hence, the length of the string is `end - buffer`. +// `buffer` is now { '1', '.', '2', '3', '4', 'E', '0', '\0', (garbage) }. +char* end = simple_dragonbox::to_chars(x, buffer); ``` -To convert to string (analog to `jkj::dragonbox::to_chars`), +Direct use of `simple_dragonbox::to_decimal` (mirrors the interface and +behavior of `jkj::dragonbox::to_decimal`; see the [primary README](/README.md)): ```cpp -float x; -char buf[simple_dragonbox::max_output_string_length + 1]; -simple_dragonbox::to_chars(x, buf); -std::cout << buf << std::endl; +#include "simple_dragonbox.h" +double x = 1.234; // Also works for float + +// `x` must be a nonzero finite number. +// `v` is a struct with three members: +// significand : decimal significand (1234 in this case); +// it is of type std::uint64_t for double, std::uint32_t for float +// exponent : decimal exponent (-3 in this case); it is of type int +// sign : as the name suggests; it is of type bool +auto v = jkj::dragonbox::to_decimal(x); ``` -In the examples above, `x` can be either a `float` or a `double`. +Like `jkj::dragonbox::to_decimal`, `simple_dragonbox::to_decimal` only works +with finite nonzero inputs. Its behavior when given infinities, NaNs, and ±0 is +undefined. `simple_dragonbox::to_chars` works fine for any inputs. -### Policies +# Policies `simple_dragonbox` supports the same style of policy interface as -`jkj::dragonbox`. For example, +`jkj::dragonbox`. For an introduction to `jkj::dragonbox`'s policy interface, +see the [primary README](/README.md). For example, ```cpp simple_dragonbox::to_decimal(3.14, @@ -57,39 +72,36 @@ simple_dragonbox::to_decimal(3.14, simple_dragonbox::policy::binary_to_decimal_rounding::to_odd); ``` -Supported policies include: - -`simple_dragonbox::policy::decimal_to_binary_rounding` - -- `::nearest_to_even` -- `::nearest_to_odd` -- `::nearest_toward_plus_infinity` -- `::nearest_toward_minus_infinity` -- `::nearest_toward_zero` -- `::nearest_away_from_zero` -- `::nearest_to_even_static_boundary` -- `::nearest_to_odd_static_boundary` -- `::nearest_toward_plus_infinity_static_boundary` -- `::nearest_toward_minus_infinity_static_boundary` -- `::toward_plus_infinity` -- `::toward_minus_infinity` -- `::toward_zero` -- `::away_from_zero` - -`simple_dragonbox::policy::binary_to_decimal_rounding` - -- `::to_even` -- `::to_odd` -- `::away_from_zero` -- `::toward_zero` -- `::do_not_care` - -`simple_dragonbox::policy::cache` - -- `::full` -- `::compact` - -### Internal/direct API +`simple_dragonbox` supports a subset of the policies that `jkj::dragonbox` does. +When supported, policies have the same meaning as the matching policy in +`jkj::dragonbox` (see the [primary README](/README.md)). Supported policies +include: + +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_to_even` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_to_odd` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_toward_plus_infinity` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_toward_minus_infinity` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_toward_zero` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_away_from_zero` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_to_even_static_boundary` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_to_odd_static_boundary` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_toward_plus_infinity_static_boundary` +- `simple_dragonbox::policy::decimal_to_binary_rounding::nearest_toward_minus_infinity_static_boundary` +- `simple_dragonbox::policy::decimal_to_binary_rounding::toward_plus_infinity` +- `simple_dragonbox::policy::decimal_to_binary_rounding::toward_minus_infinity` +- `simple_dragonbox::policy::decimal_to_binary_rounding::toward_zero` +- `simple_dragonbox::policy::decimal_to_binary_rounding::away_from_zero` + +- `simple_dragonbox::policy::binary_to_decimal_rounding::to_even` +- `simple_dragonbox::policy::binary_to_decimal_rounding::to_odd` +- `simple_dragonbox::policy::binary_to_decimal_rounding::away_from_zero` +- `simple_dragonbox::policy::binary_to_decimal_rounding::toward_zero` +- `simple_dragonbox::policy::binary_to_decimal_rounding::do_not_care` + +- `simple_dragonbox::policy::cache::full` +- `simple_dragonbox::policy::cache::compact` + +# Internal direct API Internally, `simple_dragonbox` uses a more explicit, direct interface to express the various policies, via a class called `simple_dragonbox::impl`. The `impl` @@ -109,10 +121,8 @@ using impl = simple_dragonbox::impl; -int main() { - char buf[32]; - auto x = impl(3.14); - x.to_decimal(); // equivalent to `simple_dragonbox::to_decimal(3.14, policies...)` - x.to_chars(buf); // equivalent to `simple_dragonbox::to_chars(3.14, buf, policies...)` -} +char buffer[32]; +auto x = impl(3.14); +x.to_decimal(); // equivalent to `simple_dragonbox::to_decimal(3.14, policies...)` +x.to_chars(buffer); // equivalent to `simple_dragonbox::to_chars(3.14, buf, policies...)` ``` From e29f2dd60b5419447331d3550e13bdc45d9a343f Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:41:05 -0700 Subject: [PATCH 06/17] Use macro-based include guard --- subproject/simple/simple_dragonbox.h | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index e8d8e09..da4f1cc 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -1,4 +1,5 @@ -#pragma once +#ifndef JKJ_HEADER_SIMPLE_DRAGONBOX +#define JKJ_HEADER_SIMPLE_DRAGONBOX // Copyright 2024 Junekey Jeon, Toby Bell // TODO: License @@ -1994,3 +1995,5 @@ namespace simple_dragonbox { template constexpr size_t max_output_string_length = impl::max_output_string_length; } + +#endif From 3b0628496da7bc9aa47062415fcc9fc2a5838437 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:44:43 -0700 Subject: [PATCH 07/17] Include C++ headers instead of C ones --- subproject/simple/simple_dragonbox.h | 19 +++++++++++++------ 1 file changed, 13 insertions(+), 6 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index da4f1cc..99a7316 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -4,12 +4,19 @@ // Copyright 2024 Junekey Jeon, Toby Bell // TODO: License -#include -#include -#include -#include +#include +#include +#include +#include namespace simple_dragonbox { + using std::int16_t; + using std::int32_t; + using std::size_t; + using std::uint16_t; + using std::uint32_t; + using std::uint64_t; + constexpr uint32_t rotr32(uint32_t n, unsigned r) { r &= 31; return (n >> r) | (n << ((32 - r) & 31)); @@ -1342,7 +1349,7 @@ namespace simple_dragonbox { constexpr impl(Float x) { carrier_uint bits; static_assert(sizeof(x) == sizeof(bits)); - ::memcpy(&bits, &x, sizeof(x)); + std::memcpy(&bits, &x, sizeof(x)); significand = bits & ((carrier_uint(1) << format::significand_bits) - 1); exponent = bits >> format::significand_bits & ((1u << format::exponent_bits) - 1); sign = bits >> (format::significand_bits + format::exponent_bits); @@ -1858,7 +1865,7 @@ namespace simple_dragonbox { if (sign) { *buffer++ = '-'; } - ::memcpy(buffer, "Infinity", 8); + std::memcpy(buffer, "Infinity", 8); return buffer + 8; } else { From 1e0111c68a0a23091d33d8c48b6ab9f96972314a Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:45:38 -0700 Subject: [PATCH 08/17] Return self from `uint128::operator+=` --- subproject/simple/simple_dragonbox.h | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 99a7316..2e65b35 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -71,10 +71,11 @@ namespace simple_dragonbox { uint64_t high; uint64_t low; - void operator+=(uint64_t n) { + uint128& operator+=(uint64_t n) { auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); high += (sum < low ? 1 : 0); low = sum; + return *this; } }; From e2f3058517602c55f30fd202683ce996b2cf8eb9 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:46:24 -0700 Subject: [PATCH 09/17] Make `uint128::operator+=` constexpr --- subproject/simple/simple_dragonbox.h | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 2e65b35..221401e 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -71,7 +71,7 @@ namespace simple_dragonbox { uint64_t high; uint64_t low; - uint128& operator+=(uint64_t n) { + constexpr uint128& operator+=(uint64_t n) { auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); high += (sum < low ? 1 : 0); low = sum; From d3591c45c7f79e5d6d6f21f1eef266ca418b9ee2 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 22:53:11 -0700 Subject: [PATCH 10/17] Put everything but the external API into a `detail` namespace --- subproject/simple/README.md | 13 +- subproject/simple/simple_dragonbox.h | 3534 ++++++++++--------- subproject/simple/simple_dragonbox_test.cpp | 2 +- 3 files changed, 1779 insertions(+), 1770 deletions(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index 1151194..07c524e 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -104,8 +104,8 @@ include: # Internal direct API Internally, `simple_dragonbox` uses a more explicit, direct interface to express -the various policies, via a class called `simple_dragonbox::impl`. The `impl` -class has four template parameters: `Float`, `BinaryRoundMode`, +the various policies, via a class called `simple_dragonbox::detail::impl`. The +`impl` class has four template parameters: `Float`, `BinaryRoundMode`, `DecimalRoundMode`, and `CacheType`, which correspond to the floating point type and three categories of policies above. These template parameters can be specified explicitly to instantiate a particular variant of the algorithm. The @@ -116,10 +116,11 @@ performing the desired conversions. For example, ```cpp -using impl = simple_dragonbox::impl; +namespace detail = simple_dragonbox::detail; +using impl = detail::impl; char buffer[32]; auto x = impl(3.14); diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 221401e..0379e45 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -10,1998 +10,2006 @@ #include namespace simple_dragonbox { - using std::int16_t; - using std::int32_t; - using std::size_t; - using std::uint16_t; - using std::uint32_t; - using std::uint64_t; - - constexpr uint32_t rotr32(uint32_t n, unsigned r) { - r &= 31; - return (n >> r) | (n << ((32 - r) & 31)); - } - - constexpr uint64_t rotr64(uint64_t n, unsigned r) { - r &= 63; - return (n >> r) | (n << ((64 - r) & 63)); - } - - static_assert((int32_t(-1) >> 1) == int32_t(-1) && (int16_t(-1) >> 1) == int16_t(-1), - "right-shift for signed integers must be arithmetic"); - - // For constexpr computation. - // Returns -1 when n = 0. - constexpr int floor_log2(uint64_t n) { - int count = -1; - while (n != 0) { - ++count; - n >>= 1; + namespace detail { + using std::int16_t; + using std::int32_t; + using std::size_t; + using std::uint16_t; + using std::uint32_t; + using std::uint64_t; + + constexpr uint32_t rotr32(uint32_t n, unsigned r) { + r &= 31; + return (n >> r) | (n << ((32 - r) & 31)); } - return count; - } - - constexpr int floor_log10_pow2(int e) { - assert(-2620 <= e && e <= 2620); - return (e * 315653) >> 20; - } - - constexpr int floor_log2_pow10(int e) { - // Formula itself holds on [-4003,4003]; [-1233,1233] is to ensure no overflow. - assert(-1233 <= e && e <= 1233); - return (e * 1741647) >> 19; - } - - constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) { - assert(-2985 <= e && e <= 2936); - return (e * 631305 - 261663) >> 21; - } - - constexpr int floor_log5_pow2(int e) { - assert(-1831 <= e && e <= 1831); - return (e * 225799) >> 19; - } - - constexpr int floor_log5_pow2_minus_log5_3(int e) { - assert(-3543 <= e && e <= 2427); - return (e * 451597 - 715764) >> 20; - } - struct uint128 { - uint64_t high; - uint64_t low; - - constexpr uint128& operator+=(uint64_t n) { - auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); - high += (sum < low ? 1 : 0); - low = sum; - return *this; + constexpr uint64_t rotr64(uint64_t n, unsigned r) { + r &= 63; + return (n >> r) | (n << ((64 - r) & 63)); } - }; - - constexpr uint64_t umul64(uint32_t x, uint32_t y) { return x * uint64_t(y); } - // Get 128-bit result of multiplication of two 64-bit unsigned integers. - constexpr uint128 umul128(uint64_t x, uint64_t y) { - auto const a = uint32_t(x >> 32); - auto const b = uint32_t(x); - auto const c = uint32_t(y >> 32); - auto const d = uint32_t(y); + static_assert((int32_t(-1) >> 1) == int32_t(-1) && (int16_t(-1) >> 1) == int16_t(-1), + "right-shift for signed integers must be arithmetic"); - auto const ac = umul64(a, c); - auto const bc = umul64(b, c); - auto const ad = umul64(a, d); - auto const bd = umul64(b, d); - - auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); + // For constexpr computation. + // Returns -1 when n = 0. + constexpr int floor_log2(uint64_t n) { + int count = -1; + while (n != 0) { + ++count; + n >>= 1; + } + return count; + } - return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), - (intermediate << 32) + uint32_t(bd)}; - } + constexpr int floor_log10_pow2(int e) { + assert(-2620 <= e && e <= 2620); + return (e * 315653) >> 20; + } - // Get high half of the 128-bit result of multiplication of two 64-bit unsigned - // integers. - constexpr uint64_t umul128_upper64(uint64_t x, uint64_t y) { - auto const a = uint32_t(x >> 32); - auto const b = uint32_t(x); - auto const c = uint32_t(y >> 32); - auto const d = uint32_t(y); + constexpr int floor_log2_pow10(int e) { + // Formula itself holds on [-4003,4003]; [-1233,1233] is to ensure no overflow. + assert(-1233 <= e && e <= 1233); + return (e * 1741647) >> 19; + } - auto const ac = umul64(a, c); - auto const bc = umul64(b, c); - auto const ad = umul64(a, d); - auto const bd = umul64(b, d); + constexpr int floor_log10_pow2_minus_log10_4_over_3(int e) { + assert(-2985 <= e && e <= 2936); + return (e * 631305 - 261663) >> 21; + } - auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); + constexpr int floor_log5_pow2(int e) { + assert(-1831 <= e && e <= 1831); + return (e * 225799) >> 19; + } - return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); - } + constexpr int floor_log5_pow2_minus_log5_3(int e) { + assert(-3543 <= e && e <= 2427); + return (e * 451597 - 715764) >> 20; + } - // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit - // unsigned integer. - constexpr uint128 umul192_upper128(uint64_t x, uint128 y) { - auto r = umul128(x, y.high); - r += umul128_upper64(x, y.low); - return r; - } + struct uint128 { + uint64_t high; + uint64_t low; - // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit - // unsigned integer. - constexpr uint64_t umul96_upper64(uint32_t x, uint64_t y) { - auto const yh = uint32_t(y >> 32); - auto const yl = uint32_t(y); + constexpr uint128& operator+=(uint64_t n) { + auto const sum = (low + n) & UINT64_C(0xffffffffffffffff); + high += (sum < low ? 1 : 0); + low = sum; + return *this; + } + }; - auto const xyh = umul64(x, yh); - auto const xyl = umul64(x, yl); + constexpr uint64_t umul64(uint32_t x, uint32_t y) { return x * uint64_t(y); } - return xyh + (xyl >> 32); - } + // Get 128-bit result of multiplication of two 64-bit unsigned integers. + constexpr uint128 umul128(uint64_t x, uint64_t y) { + auto const a = uint32_t(x >> 32); + auto const b = uint32_t(x); + auto const c = uint32_t(y >> 32); + auto const d = uint32_t(y); - // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit - // unsigned integer. - constexpr uint128 umul192_lower128(uint64_t x, uint128 y) { - auto const high = x * y.high; - auto const high_low = umul128(x, y.low); - return {(high + high_low.high) & UINT64_C(0xffffffffffffffff), high_low.low}; - } + auto const ac = umul64(a, c); + auto const bc = umul64(b, c); + auto const ad = umul64(a, d); + auto const bd = umul64(b, d); - // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit - // unsigned integer. - constexpr uint64_t umul96_lower64(uint32_t x, uint64_t y) { - return (x * y) & UINT64_C(0xffffffffffffffff); - } + auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); - template - constexpr Int compute_power(Int a) { - static_assert(k >= 0); - int e = k; - Int p = 1; - while (e) { - if (e % 2) - p *= a; - e /= 2; - a *= a; + return {ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32), + (intermediate << 32) + uint32_t(bd)}; } - return p; - } - template - struct compute_mul_result { - Integer integer_part; - bool is_integer; - }; - - struct compute_mul_parity_result { - bool parity; - bool is_integer; - }; - - // These classes expose encoding specs of IEEE-754-like floating-point formats. - // Currently available formats are IEEE-754 binary32 & IEEE-754 binary64. - - template - struct float_format; - - template <> - struct float_format { - using carrier_uint = uint32_t; - enum { - total_bits = 32, - significand_bits = 23, - exponent_bits = 8, - min_exponent = -126, - max_exponent = 127, - exponent_bias = -127, - decimal_significand_digits = 9, - decimal_exponent_digits = 2, - cache_bits = 64, - min_k = -31, - max_k = 46, - }; - - static void remove_trailing_zeros(uint32_t& significand, int& exponent) { - // See https://github.com/jk-jeon/rtz_benchmark. - // The idea of branchless search below is by reddit users r/pigeon768 and - // r/TheoreticalDumbass. + // Get high half of the 128-bit result of multiplication of two 64-bit unsigned + // integers. + constexpr uint64_t umul128_upper64(uint64_t x, uint64_t y) { + auto const a = uint32_t(x >> 32); + auto const b = uint32_t(x); + auto const c = uint32_t(y >> 32); + auto const d = uint32_t(y); - auto r = rotr32(uint32_t(significand * UINT32_C(184254097)), 4); - auto b = r < UINT32_C(429497); - auto s = size_t(b); - significand = b ? r : significand; + auto const ac = umul64(a, c); + auto const bc = umul64(b, c); + auto const ad = umul64(a, d); + auto const bd = umul64(b, d); - r = rotr32(uint32_t(significand * UINT32_C(42949673)), 2); - b = r < UINT32_C(42949673); - s = s * 2 + b; - significand = b ? r : significand; + auto const intermediate = (bd >> 32) + uint32_t(ad) + uint32_t(bc); - r = rotr32(uint32_t(significand * UINT32_C(1288490189)), 1); - b = r < UINT32_C(429496730); - s = s * 2 + b; - significand = b ? r : significand; - - exponent += s; + return ac + (intermediate >> 32) + (ad >> 32) + (bc >> 32); } - static compute_mul_result compute_mul(uint32_t u, uint64_t cache) { - auto const r = umul96_upper64(u, cache); - return {uint32_t(r >> 32), uint32_t(r) == 0}; + // Get upper 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + constexpr uint128 umul192_upper128(uint64_t x, uint128 y) { + auto r = umul128(x, y.high); + r += umul128_upper64(x, y.low); + return r; } - static uint32_t compute_delta(uint64_t cache, int beta) { - return uint32_t(cache >> (cache_bits - 1 - beta)); - } + // Get upper 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + constexpr uint64_t umul96_upper64(uint32_t x, uint64_t y) { + auto const yh = uint32_t(y >> 32); + auto const yl = uint32_t(y); - static compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, int beta) { - assert(beta >= 1); - assert(beta <= 32); - auto const r = umul96_lower64(two_f, cache); - return {((r >> (64 - beta)) & 1) != 0, (UINT32_C(0xffffffff) & (r >> (32 - beta))) == 0}; - } + auto const xyh = umul64(x, yh); + auto const xyl = umul64(x, yl); - static uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { - return (cache - (cache >> (significand_bits + 2))) >> - (cache_bits - significand_bits - 1 - beta); + return xyh + (xyl >> 32); } - static uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { - return (cache + (cache >> (significand_bits + 1))) >> - (cache_bits - significand_bits - 1 - beta); + // Get lower 128-bits of multiplication of a 64-bit unsigned integer and a 128-bit + // unsigned integer. + constexpr uint128 umul192_lower128(uint64_t x, uint128 y) { + auto const high = x * y.high; + auto const high_low = umul128(x, y.low); + return {(high + high_low.high) & UINT64_C(0xffffffffffffffff), high_low.low}; } - static uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { - return (uint32_t(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; + // Get lower 64-bits of multiplication of a 32-bit unsigned integer and a 64-bit + // unsigned integer. + constexpr uint64_t umul96_lower64(uint32_t x, uint64_t y) { + return (x * y) & UINT64_C(0xffffffffffffffff); } - template - static uint32_t divide_by_pow10(uint32_t n) { - static_assert(N >= 0, ""); - - // Specialize for 32-bit division by 10. - // Without the bound on n_max (which compilers these days never leverage), the - // minimum needed amount of shift is larger than 32. Hence, this may generate better - // code for 32-bit or smaller architectures. Even for 64-bit architectures, it seems - // compilers tend to generate mov + mul instead of a single imul for an unknown - // reason if we just write n / 10. - if constexpr (N == 1 && n_max <= UINT32_C(1073741828)) { - return uint32_t(umul64(n, UINT32_C(429496730)) >> 32); - } - // Specialize for 32-bit division by 100. - // It seems compilers tend to generate mov + mul instead of a single imul for an - // unknown reason if we just write n / 100. - else if constexpr (N == 2) { - return uint32_t(umul64(n, UINT32_C(1374389535)) >> 37); - } - else { - return n / compute_power(uint32_t(10)); + template + constexpr Int compute_power(Int a) { + static_assert(k >= 0); + int e = k; + Int p = 1; + while (e) { + if (e % 2) + p *= a; + e /= 2; + a *= a; } + return p; } - }; - - template <> - struct float_format { - using carrier_uint = uint64_t; - enum { - total_bits = 64, - significand_bits = 52, - exponent_bits = 11, - min_exponent = -1022, - max_exponent = 1023, - exponent_bias = -1023, - decimal_significand_digits = 17, - decimal_exponent_digits = 3, - cache_bits = 128, - min_k = -292, - max_k = 326, + + template + struct compute_mul_result { + Integer integer_part; + bool is_integer; }; - static void remove_trailing_zeros(uint64_t& significand, int& exponent) { - // See https://github.com/jk-jeon/rtz_benchmark. - // The idea of branchless search below is by reddit users r/pigeon768 and - // r/TheoreticalDumbass. + struct compute_mul_parity_result { + bool parity; + bool is_integer; + }; - auto r = rotr64(uint64_t(significand * UINT64_C(28999941890838049)), 8); - auto b = r < UINT64_C(184467440738); - auto s = size_t(b); - significand = b ? r : significand; + // These classes expose encoding specs of IEEE-754-like floating-point formats. + // Currently available formats are IEEE-754 binary32 & IEEE-754 binary64. + + template + struct float_format; + + template <> + struct float_format { + using carrier_uint = uint32_t; + enum { + total_bits = 32, + significand_bits = 23, + exponent_bits = 8, + min_exponent = -126, + max_exponent = 127, + exponent_bias = -127, + decimal_significand_digits = 9, + decimal_exponent_digits = 2, + cache_bits = 64, + min_k = -31, + max_k = 46, + }; + + static void remove_trailing_zeros(uint32_t& significand, int& exponent) { + // See https://github.com/jk-jeon/rtz_benchmark. + // The idea of branchless search below is by reddit users r/pigeon768 and + // r/TheoreticalDumbass. + + auto r = rotr32(uint32_t(significand * UINT32_C(184254097)), 4); + auto b = r < UINT32_C(429497); + auto s = size_t(b); + significand = b ? r : significand; + + r = rotr32(uint32_t(significand * UINT32_C(42949673)), 2); + b = r < UINT32_C(42949673); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr32(uint32_t(significand * UINT32_C(1288490189)), 1); + b = r < UINT32_C(429496730); + s = s * 2 + b; + significand = b ? r : significand; + + exponent += s; + } - r = rotr64(uint64_t(significand * UINT64_C(182622766329724561)), 4); - b = r < UINT64_C(1844674407370956); - s = s * 2 + b; - significand = b ? r : significand; + static compute_mul_result compute_mul(uint32_t u, uint64_t cache) { + auto const r = umul96_upper64(u, cache); + return {uint32_t(r >> 32), uint32_t(r) == 0}; + } - r = rotr64(uint64_t(significand * UINT64_C(10330176681277348905)), 2); - b = r < UINT64_C(184467440737095517); - s = s * 2 + b; - significand = b ? r : significand; + static uint32_t compute_delta(uint64_t cache, int beta) { + return uint32_t(cache >> (cache_bits - 1 - beta)); + } - r = rotr64(uint64_t(significand * UINT64_C(14757395258967641293)), 1); - b = r < UINT64_C(1844674407370955162); - s = s * 2 + b; - significand = b ? r : significand; + static compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, + int beta) { + assert(beta >= 1); + assert(beta <= 32); + auto const r = umul96_lower64(two_f, cache); + return {((r >> (64 - beta)) & 1) != 0, + (UINT32_C(0xffffffff) & (r >> (32 - beta))) == 0}; + } - exponent += s; - } + static uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + return (cache - (cache >> (significand_bits + 2))) >> + (cache_bits - significand_bits - 1 - beta); + } - static compute_mul_result compute_mul(uint64_t u, uint128 cache) { - auto const r = umul192_upper128(u, cache); - return {r.high, r.low == 0}; - } + static uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + return (cache + (cache >> (significand_bits + 1))) >> + (cache_bits - significand_bits - 1 - beta); + } - static uint64_t compute_delta(uint128 cache, int beta) { - return cache.high >> (total_bits - 1 - beta); - } + static uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { + return (uint32_t(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; + } - static compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, int beta) { - assert(beta >= 1); - assert(beta < 64); - auto const r = umul192_lower128(two_f, cache); - return {((r.high >> (64 - beta)) & 1) != 0, - (((r.high << beta) & UINT64_C(0xffffffffffffffff)) | (r.low >> (64 - beta))) == 0}; - } + template + static uint32_t divide_by_pow10(uint32_t n) { + static_assert(N >= 0, ""); + + // Specialize for 32-bit division by 10. + // Without the bound on n_max (which compilers these days never leverage), the + // minimum needed amount of shift is larger than 32. Hence, this may generate better + // code for 32-bit or smaller architectures. Even for 64-bit architectures, it seems + // compilers tend to generate mov + mul instead of a single imul for an unknown + // reason if we just write n / 10. + if constexpr (N == 1 && n_max <= UINT32_C(1073741828)) { + return uint32_t(umul64(n, UINT32_C(429496730)) >> 32); + } + // Specialize for 32-bit division by 100. + // It seems compilers tend to generate mov + mul instead of a single imul for an + // unknown reason if we just write n / 100. + else if constexpr (N == 2) { + return uint32_t(umul64(n, UINT32_C(1374389535)) >> 37); + } + else { + return n / compute_power(uint32_t(10)); + } + } + }; - static uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { - return (cache.high - (cache.high >> (significand_bits + 2))) >> - (total_bits - significand_bits - 1 - beta); - } + template <> + struct float_format { + using carrier_uint = uint64_t; + enum { + total_bits = 64, + significand_bits = 52, + exponent_bits = 11, + min_exponent = -1022, + max_exponent = 1023, + exponent_bias = -1023, + decimal_significand_digits = 17, + decimal_exponent_digits = 3, + cache_bits = 128, + min_k = -292, + max_k = 326, + }; + + static void remove_trailing_zeros(uint64_t& significand, int& exponent) { + // See https://github.com/jk-jeon/rtz_benchmark. + // The idea of branchless search below is by reddit users r/pigeon768 and + // r/TheoreticalDumbass. + + auto r = rotr64(uint64_t(significand * UINT64_C(28999941890838049)), 8); + auto b = r < UINT64_C(184467440738); + auto s = size_t(b); + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(182622766329724561)), 4); + b = r < UINT64_C(1844674407370956); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(10330176681277348905)), 2); + b = r < UINT64_C(184467440737095517); + s = s * 2 + b; + significand = b ? r : significand; + + r = rotr64(uint64_t(significand * UINT64_C(14757395258967641293)), 1); + b = r < UINT64_C(1844674407370955162); + s = s * 2 + b; + significand = b ? r : significand; + + exponent += s; + } - static uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { - return (cache.high + (cache.high >> (significand_bits + 1))) >> - (total_bits - significand_bits - 1 - beta); - } + static compute_mul_result compute_mul(uint64_t u, uint128 cache) { + auto const r = umul192_upper128(u, cache); + return {r.high, r.low == 0}; + } - static uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { - return ((cache.high >> (total_bits - significand_bits - 2 - beta)) + 1) / 2; - } + static uint64_t compute_delta(uint128 cache, int beta) { + return cache.high >> (total_bits - 1 - beta); + } - template - static uint64_t divide_by_pow10(uint64_t n) { - static_assert(N >= 0, ""); + static compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, + int beta) { + assert(beta >= 1); + assert(beta < 64); + auto const r = umul192_lower128(two_f, cache); + return {((r.high >> (64 - beta)) & 1) != 0, + (((r.high << beta) & UINT64_C(0xffffffffffffffff)) | (r.low >> (64 - beta))) == + 0}; + } - // Specialize for 64-bit division by 10. - // Without the bound on n_max (which compilers these days never leverage), the - // minimum needed amount of shift is larger than 64. - if constexpr (N == 1 && n_max <= UINT64_C(4611686018427387908)) { - return umul128_upper64(n, UINT64_C(1844674407370955162)); + static uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + return (cache.high - (cache.high >> (significand_bits + 2))) >> + (total_bits - significand_bits - 1 - beta); } - // Specialize for 64-bit division by 1000. - // Without the bound on n_max (which compilers these days never leverage), the - // smallest magic number for this computation does not fit into 64-bits. - else if constexpr (N == 3 && n_max <= UINT64_C(15534100272597517998)) { - return umul128_upper64(n, UINT64_C(4722366482869645214)) >> 8; + + static uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + return (cache.high + (cache.high >> (significand_bits + 1))) >> + (total_bits - significand_bits - 1 - beta); } - else { - return n / compute_power(uint64_t(10)); + + static uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { + return ((cache.high >> (total_bits - significand_bits - 2 - beta)) + 1) / 2; } - } - }; - - static constexpr uint64_t cache32[78]{ - UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), - UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), - UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), - UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), - UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), - UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), - UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), - UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), - UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), - UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), - UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), - UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), - UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), - UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), - UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), - UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), - UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), - UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), - UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), - UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), - UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), - UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), - UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), - UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), - UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), - UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; - - static constexpr uint128 cache64[619] = { - {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, - {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, - {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, - {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, - {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, - {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, - {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, - {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, - {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, - {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, - {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, - {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, - {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, - {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, - {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, - {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, - {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, - {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, - {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, - {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, - {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, - {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, - {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, - {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, - {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, - {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, - {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, - {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, - {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, - {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, - {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, - {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, - {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, - {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, - {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, - {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, - {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, - {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, - {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, - {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, - {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, - {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, - {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, - {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, - {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, - {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, - {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, - {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, - {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, - {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, - {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, - {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, - {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, - {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, - {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, - {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, - {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, - {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, - {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, - {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, - {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, - {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, - {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, - {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, - {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, - {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, - {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, - {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, - {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, - {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, - {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, - {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, - {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, - {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, - {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, - {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, - {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, - {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, - {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, - {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, - {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, - {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, - {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, - {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, - {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, - {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, - {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, - {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, - {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, - {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, - {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, - {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, - {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, - {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, - {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, - {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, - {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, - {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, - {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, - {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, - {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, - {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, - {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, - {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, - {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, - {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, - {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, - {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, - {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, - {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, - {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, - {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, - {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, - {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, - {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, - {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, - {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, - {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, - {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, - {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, - {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, - {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, - {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, - {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, - {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, - {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, - {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, - {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, - {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, - {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, - {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, - {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, - {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, - {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, - {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, - {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, - {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, - {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, - {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, - {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, - {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, - {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, - {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, - {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, - {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, - {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, - {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, - {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, - {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, - {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, - {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, - {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, - {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, - {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, - {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, - {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, - {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, - {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, - {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, - {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, - {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, - {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, - {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, - {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, - {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, - {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, - {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, - {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, - {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, - {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, - {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, - {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, - {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, - {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, - {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, - {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, - {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, - {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, - {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, - {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, - {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, - {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, - {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, - {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, - {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, - {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, - {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, - {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, - {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, - {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, - {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, - {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, - {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, - {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, - {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, - {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, - {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, - {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, - {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, - {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, - {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, - {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, - {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, - {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, - {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, - {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, - {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, - {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, - {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, - {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, - {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, - {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, - {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, - {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, - {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, - {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, - {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, - {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, - {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, - {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, - {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, - {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, - {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, - {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, - {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, - {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, - {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, - {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, - {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, - {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, - {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, - {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, - {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, - {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, - {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, - {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, - {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, - {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, - {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, - {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, - {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, - {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, - {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, - {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, - {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, - {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, - {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, - {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, - {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, - {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, - {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, - {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, - {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, - {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, - {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, - {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, - {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, - {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, - {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, - {UINT64_C(0xa6274bbdd0fadd61), UINT64_C(0xecb1ad8aeacdd58f)}, - {UINT64_C(0xcfb11ead453994ba), UINT64_C(0x67de18eda5814af3)}, - {UINT64_C(0x81ceb32c4b43fcf4), UINT64_C(0x80eacf948770ced8)}, - {UINT64_C(0xa2425ff75e14fc31), UINT64_C(0xa1258379a94d028e)}, - {UINT64_C(0xcad2f7f5359a3b3e), UINT64_C(0x096ee45813a04331)}, - {UINT64_C(0xfd87b5f28300ca0d), UINT64_C(0x8bca9d6e188853fd)}, - {UINT64_C(0x9e74d1b791e07e48), UINT64_C(0x775ea264cf55347e)}, - {UINT64_C(0xc612062576589dda), UINT64_C(0x95364afe032a819e)}, - {UINT64_C(0xf79687aed3eec551), UINT64_C(0x3a83ddbd83f52205)}, - {UINT64_C(0x9abe14cd44753b52), UINT64_C(0xc4926a9672793543)}, - {UINT64_C(0xc16d9a0095928a27), UINT64_C(0x75b7053c0f178294)}, - {UINT64_C(0xf1c90080baf72cb1), UINT64_C(0x5324c68b12dd6339)}, - {UINT64_C(0x971da05074da7bee), UINT64_C(0xd3f6fc16ebca5e04)}, - {UINT64_C(0xbce5086492111aea), UINT64_C(0x88f4bb1ca6bcf585)}, - {UINT64_C(0xec1e4a7db69561a5), UINT64_C(0x2b31e9e3d06c32e6)}, - {UINT64_C(0x9392ee8e921d5d07), UINT64_C(0x3aff322e62439fd0)}, - {UINT64_C(0xb877aa3236a4b449), UINT64_C(0x09befeb9fad487c3)}, - {UINT64_C(0xe69594bec44de15b), UINT64_C(0x4c2ebe687989a9b4)}, - {UINT64_C(0x901d7cf73ab0acd9), UINT64_C(0x0f9d37014bf60a11)}, - {UINT64_C(0xb424dc35095cd80f), UINT64_C(0x538484c19ef38c95)}, - {UINT64_C(0xe12e13424bb40e13), UINT64_C(0x2865a5f206b06fba)}, - {UINT64_C(0x8cbccc096f5088cb), UINT64_C(0xf93f87b7442e45d4)}, - {UINT64_C(0xafebff0bcb24aafe), UINT64_C(0xf78f69a51539d749)}, - {UINT64_C(0xdbe6fecebdedd5be), UINT64_C(0xb573440e5a884d1c)}, - {UINT64_C(0x89705f4136b4a597), UINT64_C(0x31680a88f8953031)}, - {UINT64_C(0xabcc77118461cefc), UINT64_C(0xfdc20d2b36ba7c3e)}, - {UINT64_C(0xd6bf94d5e57a42bc), UINT64_C(0x3d32907604691b4d)}, - {UINT64_C(0x8637bd05af6c69b5), UINT64_C(0xa63f9a49c2c1b110)}, - {UINT64_C(0xa7c5ac471b478423), UINT64_C(0x0fcf80dc33721d54)}, - {UINT64_C(0xd1b71758e219652b), UINT64_C(0xd3c36113404ea4a9)}, - {UINT64_C(0x83126e978d4fdf3b), UINT64_C(0x645a1cac083126ea)}, - {UINT64_C(0xa3d70a3d70a3d70a), UINT64_C(0x3d70a3d70a3d70a4)}, - {UINT64_C(0xcccccccccccccccc), UINT64_C(0xcccccccccccccccd)}, - {UINT64_C(0x8000000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa000000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xc800000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xfa00000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9c40000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xc350000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xf424000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9896800000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xbebc200000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xee6b280000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9502f90000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xba43b74000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xe8d4a51000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9184e72a00000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, - {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, - {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, - {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, - {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, - {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, - {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, - {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, - {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, - {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, - {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, - {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, - {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, - {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, - {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, - {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, - {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, - {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, - {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, - {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, - {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, - {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, - {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, - {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, - {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, - {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, - {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, - {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, - {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, - {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, - {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, - {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, - {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, - {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, - {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, - {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, - {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, - {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, - {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, - {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, - {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, - {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, - {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, - {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, - {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, - {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, - {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, - {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, - {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, - {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, - {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, - {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, - {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, - {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, - {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, - {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, - {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, - {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, - {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, - {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, - {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, - {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, - {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, - {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, - {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, - {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, - {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, - {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, - {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, - {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, - {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, - {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, - {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, - {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, - {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, - {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, - {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, - {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, - {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, - {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, - {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, - {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, - {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, - {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, - {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, - {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, - {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, - {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, - {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, - {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, - {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, - {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, - {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, - {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, - {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, - {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, - {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, - {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, - {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, - {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, - {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, - {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, - {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, - {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, - {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, - {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, - {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, - {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, - {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, - {UINT64_C(0x899504ae72497eba), UINT64_C(0x6a06494a791c53a9)}, - {UINT64_C(0xabfa45da0edbde69), UINT64_C(0x0487db9d17636893)}, - {UINT64_C(0xd6f8d7509292d603), UINT64_C(0x45a9d2845d3c42b7)}, - {UINT64_C(0x865b86925b9bc5c2), UINT64_C(0x0b8a2392ba45a9b3)}, - {UINT64_C(0xa7f26836f282b732), UINT64_C(0x8e6cac7768d7141f)}, - {UINT64_C(0xd1ef0244af2364ff), UINT64_C(0x3207d795430cd927)}, - {UINT64_C(0x8335616aed761f1f), UINT64_C(0x7f44e6bd49e807b9)}, - {UINT64_C(0xa402b9c5a8d3a6e7), UINT64_C(0x5f16206c9c6209a7)}, - {UINT64_C(0xcd036837130890a1), UINT64_C(0x36dba887c37a8c10)}, - {UINT64_C(0x802221226be55a64), UINT64_C(0xc2494954da2c978a)}, - {UINT64_C(0xa02aa96b06deb0fd), UINT64_C(0xf2db9baa10b7bd6d)}, - {UINT64_C(0xc83553c5c8965d3d), UINT64_C(0x6f92829494e5acc8)}, - {UINT64_C(0xfa42a8b73abbf48c), UINT64_C(0xcb772339ba1f17fa)}, - {UINT64_C(0x9c69a97284b578d7), UINT64_C(0xff2a760414536efc)}, - {UINT64_C(0xc38413cf25e2d70d), UINT64_C(0xfef5138519684abb)}, - {UINT64_C(0xf46518c2ef5b8cd1), UINT64_C(0x7eb258665fc25d6a)}, - {UINT64_C(0x98bf2f79d5993802), UINT64_C(0xef2f773ffbd97a62)}, - {UINT64_C(0xbeeefb584aff8603), UINT64_C(0xaafb550ffacfd8fb)}, - {UINT64_C(0xeeaaba2e5dbf6784), UINT64_C(0x95ba2a53f983cf39)}, - {UINT64_C(0x952ab45cfa97a0b2), UINT64_C(0xdd945a747bf26184)}, - {UINT64_C(0xba756174393d88df), UINT64_C(0x94f971119aeef9e5)}, - {UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, - {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, - {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, - {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, - {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, - {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, - {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, - {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, - {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, - {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, - {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, - {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, - {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, - {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, - {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, - {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, - {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, - {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, - {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, - {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, - {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, - {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, - {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, - {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, - {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, - {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, - {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, - {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, - {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, - {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, - {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, - {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, - {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, - {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, - {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, - {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, - {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, - {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, - {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, - {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, - {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, - {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, - {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, - {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, - {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, - {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, - {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, - {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, - {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, - {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, - {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, - {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, - {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, - {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, - {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, - {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, - {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, - {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, - {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, - {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, - {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, - {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, - {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, - {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, - {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, - {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, - {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, - {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, - {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, - {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, - {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, - {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, - {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, - {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, - {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, - {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, - {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, - {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, - {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, - {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, - {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, - {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, - {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, - {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, - {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, - {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, - {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, - {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, - {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, - {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, - {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, - {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, - {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, - {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, - {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, - {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, - {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, - {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, - {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, - {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, - {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, - {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, - {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, - {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, - {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, - {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, - {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, - {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, - {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, - {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, - {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, - {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, - {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, - {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, - {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, - {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, - {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, - {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, - {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, - {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, - {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, - {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, - {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, - {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, - {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, - {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, - {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, - {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, - {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, - {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, - {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, - {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, - {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, - {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, - {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, - {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, - {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, - {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, - {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, - {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, - {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, - {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, - {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, - {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, - {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, - {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, - {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, - {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, - {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, - {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, - {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, - {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, - {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, - {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, - {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, - {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, - {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, - {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, - {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, - {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, - {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, - {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, - {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, - {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, - {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, - {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, - {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, - {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, - {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; - - enum class cache_type { - full, - compact, - }; - - template - struct cache_holder; - - template <> - struct cache_holder { - using format = float_format; - - uint64_t get_cache(int k) const { - assert(k >= format::min_k && k <= format::max_k); - return cache32[k - format::min_k]; - } - }; - - template <> - struct cache_holder { - using format = float_format; - enum { - cache_bits = format::cache_bits, - min_k = format::min_k, - max_k = format::max_k, - compression_ratio = 13, - compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, - pow5_table_size = (compression_ratio + 1) / 2, - }; - uint64_t cache[compressed_table_size]{}; - uint16_t pow5_table[pow5_table_size]{}; + template + static uint64_t divide_by_pow10(uint64_t n) { + static_assert(N >= 0, ""); - constexpr cache_holder() { - for (size_t i = 0; i < compressed_table_size; ++i) { - cache[i] = cache32[i * compression_ratio]; - } - uint16_t p = 1; - for (size_t i = 0; i < pow5_table_size; ++i) { - pow5_table[i] = p; - p *= 5; + // Specialize for 64-bit division by 10. + // Without the bound on n_max (which compilers these days never leverage), the + // minimum needed amount of shift is larger than 64. + if constexpr (N == 1 && n_max <= UINT64_C(4611686018427387908)) { + return umul128_upper64(n, UINT64_C(1844674407370955162)); + } + // Specialize for 64-bit division by 1000. + // Without the bound on n_max (which compilers these days never leverage), the + // smallest magic number for this computation does not fit into 64-bits. + else if constexpr (N == 3 && n_max <= UINT64_C(15534100272597517998)) { + return umul128_upper64(n, UINT64_C(4722366482869645214)) >> 8; + } + else { + return n / compute_power(uint64_t(10)); + } } - } + }; - uint64_t get_cache(int k) const { - assert(k >= min_k && k <= max_k); + static constexpr uint64_t cache32[78]{ + UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), + UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), + UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), + UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), + UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), + UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), + UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), + UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), + UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), + UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), + UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), + UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), + UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), + UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), + UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), + UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), + UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), + UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), + UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), + UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), + UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), + UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), + UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), + UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), + UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), + UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; + + static constexpr uint128 cache64[619] = { + {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, + {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, + {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, + {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, + {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, + {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, + {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, + {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, + {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, + {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, + {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, + {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, + {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, + {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, + {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, + {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, + {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, + {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, + {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, + {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, + {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, + {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, + {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, + {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, + {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, + {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, + {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, + {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, + {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, + {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, + {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, + {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, + {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, + {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, + {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, + {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, + {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, + {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, + {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, + {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, + {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, + {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, + {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, + {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, + {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, + {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, + {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, + {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, + {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, + {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, + {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, + {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, + {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, + {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, + {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, + {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, + {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, + {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, + {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, + {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, + {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, + {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, + {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, + {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, + {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, + {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, + {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, + {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, + {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, + {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, + {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, + {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, + {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, + {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, + {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, + {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, + {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, + {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, + {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, + {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, + {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, + {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, + {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, + {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, + {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, + {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, + {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, + {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, + {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, + {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, + {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, + {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, + {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, + {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, + {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, + {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, + {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, + {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, + {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, + {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, + {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, + {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, + {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, + {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, + {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, + {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, + {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, + {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, + {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, + {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, + {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, + {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, + {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, + {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, + {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, + {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, + {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, + {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, + {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, + {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, + {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, + {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, + {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, + {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, + {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, + {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, + {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, + {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, + {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, + {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, + {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, + {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, + {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, + {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, + {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, + {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, + {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, + {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, + {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, + {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, + {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, + {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, + {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, + {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, + {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, + {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, + {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, + {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, + {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, + {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, + {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, + {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, + {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, + {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, + {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, + {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, + {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, + {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, + {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, + {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, + {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, + {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, + {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, + {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, + {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, + {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, + {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, + {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, + {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, + {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, + {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, + {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, + {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, + {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, + {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, + {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, + {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, + {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, + {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, + {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, + {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, + {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, + {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, + {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, + {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, + {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, + {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, + {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, + {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, + {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, + {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, + {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, + {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, + {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, + {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, + {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, + {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, + {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, + {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, + {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, + {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, + {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, + {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, + {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, + {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, + {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, + {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, + {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, + {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, + {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, + {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, + {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, + {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, + {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, + {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, + {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, + {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, + {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, + {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, + {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, + {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, + {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, + {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, + {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, + {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, + {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, + {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, + {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, + {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, + {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, + {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, + {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, + {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, + {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, + {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, + {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, + {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, + {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, + {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, + {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, + {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, + {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, + {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, + {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, + {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, + {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, + {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, + {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, + {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, + {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, + {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, + {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, + {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, + {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, + {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, + {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, + {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, + {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, + {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, + 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UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, + {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, + {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, + {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, + {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, + {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, + {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, + {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, + {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, + {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, + {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, + {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, + {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, + {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, + {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, + {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, + {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, + {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, + {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, + {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, + {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, + {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, + {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, + {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, + {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, + {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, + {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, + {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, + {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, + {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, + {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, + {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, + {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, + {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, + {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, + {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, + {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, + {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, + {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, + {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, + {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, + {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, + {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, + {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, + {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, + {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, + {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, + {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, + {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, + {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, + {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, + {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, + {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, + {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, + {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, + {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, + {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, + {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, + {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, + {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, + {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, + {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, + {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, + {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, + {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, + {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, + {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, + {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, + {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, + {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, + {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, + {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, + {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, + {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, + {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, + {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, + {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, + {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, + {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, + {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, + {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, + {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, + {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, + {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, + {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, + {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, + {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, + {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, + {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, + {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, + {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, + {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, + {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, + {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, + {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, + {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, + {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, + {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, + {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, + {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, + {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, + {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, + {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, + {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, + {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, + {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, + {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, + {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, + {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, + {UINT64_C(0x899504ae72497eba), 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{UINT64_C(0x98bf2f79d5993802), UINT64_C(0xef2f773ffbd97a62)}, + {UINT64_C(0xbeeefb584aff8603), UINT64_C(0xaafb550ffacfd8fb)}, + {UINT64_C(0xeeaaba2e5dbf6784), UINT64_C(0x95ba2a53f983cf39)}, + {UINT64_C(0x952ab45cfa97a0b2), UINT64_C(0xdd945a747bf26184)}, + {UINT64_C(0xba756174393d88df), UINT64_C(0x94f971119aeef9e5)}, + {UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, + {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, + {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, + {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, + {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, + {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, + {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, + {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, + {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, + {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, + {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, + {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, + {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, + {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, + {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, + {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, + {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, + {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, + {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, + {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, + {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, + {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, + {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, + {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, + {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, + {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, + {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, + {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, + {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, + {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, + {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, + {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, + {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, + {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, + {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, + {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, + {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, + {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, + {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, + {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, + {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, + {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, + {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, + {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, + {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, + {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, + {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, + {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, + {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, + {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, + {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, + {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, + {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, + {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, + {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, + {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, + {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, + {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, + {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, + {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, + {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, + {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, + {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, + {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, + {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, + {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, + {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, + {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, + {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, + {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, + {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, + {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, + {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, + {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, + {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, + {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, + {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, + {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, + {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, + {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, + {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, + {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, + {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, + {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, + {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, + {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, + {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, + {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, + {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, + {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, + {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, + {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, + {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, + {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, + {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, + {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, + {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, + {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, + {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, + {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, + {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, + {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, + {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, + {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, + {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, + {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, + {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, + {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, + {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, + {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, + {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, + {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, + {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, + {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, + {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, + {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, + {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, + {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, + {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, + {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, + {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, + {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, + {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, + {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, + {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, + {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, + {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, + {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, + {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, + {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, + {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, + {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, + {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, + {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, + {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, + {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, + {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, + {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, + {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, + {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, + {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, + {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, + {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, + {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, + {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, + {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, + {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, + {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, + {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, + {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, + {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, + {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, + {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, + {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, + {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, + {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, + {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, + {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, + {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, + {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, + {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, + {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, + {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, + {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, + {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, + {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, + {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, + {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, + {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; + + enum class cache_type { + full, + compact, + }; - // Compute the base index. - // Supposed to compute (k - min_k) / compression_ratio. - static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); - static_assert(max_k - min_k <= INT_MAX, ""); - auto const cache_index = int(uint16_t(int(k - min_k) * int16_t(79)) >> 10); - auto const kb = int(cache_index * compression_ratio + min_k); - auto const offset = int(k - kb); + template + struct cache_holder; - // Get the base cache. - auto const base_cache = cache[cache_index]; + template <> + struct cache_holder { + using format = float_format; - if (offset == 0) { - return base_cache; + uint64_t get_cache(int k) const { + assert(k >= format::min_k && k <= format::max_k); + return cache32[k - format::min_k]; } - else { - // Compute the required amount of bit-shift. - auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); - assert(alpha > 0 && alpha < 64); - - // Try to recover the real cache. - auto const pow5 = offset >= 7 - ? uint32_t(uint32_t(pow5_table[6]) * pow5_table[offset - 6]) - : uint32_t(pow5_table[offset]); - auto mul_result = umul128(base_cache, pow5); - auto const recovered_cache = - uint64_t((((mul_result.high << int(64 - alpha)) | (mul_result.low >> alpha)) + 1) & - UINT64_C(0xffffffffffffffff)); - assert(recovered_cache != 0); - - return recovered_cache; + }; + + template <> + struct cache_holder { + using format = float_format; + enum { + cache_bits = format::cache_bits, + min_k = format::min_k, + max_k = format::max_k, + compression_ratio = 13, + compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, + pow5_table_size = (compression_ratio + 1) / 2, + }; + + uint64_t cache[compressed_table_size]{}; + uint16_t pow5_table[pow5_table_size]{}; + + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = cache32[i * compression_ratio]; + } + uint16_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } } - } - }; - template <> - struct cache_holder { - using format = float_format; + uint64_t get_cache(int k) const { + assert(k >= min_k && k <= max_k); - uint128 get_cache(int k) const { - assert(k >= format::min_k && k <= format::max_k); - return cache64[k - format::min_k]; - } - }; - - template <> - struct cache_holder { - using format = float_format; - enum { - cache_bits = format::cache_bits, - min_k = format::min_k, - max_k = format::max_k, - compression_ratio = 27, - compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, - pow5_table_size = compression_ratio, + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint16_t(int(k - min_k) * int16_t(79)) >> 10); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); + + // Get the base cache. + auto const base_cache = cache[cache_index]; + + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); + + // Try to recover the real cache. + auto const pow5 = offset >= 7 + ? uint32_t(uint32_t(pow5_table[6]) * pow5_table[offset - 6]) + : uint32_t(pow5_table[offset]); + auto mul_result = umul128(base_cache, pow5); + auto const recovered_cache = uint64_t( + (((mul_result.high << int(64 - alpha)) | (mul_result.low >> alpha)) + 1) & + UINT64_C(0xffffffffffffffff)); + assert(recovered_cache != 0); + + return recovered_cache; + } + } }; - uint128 cache[compressed_table_size]{}; - uint64_t pow5_table[pow5_table_size]{}; + template <> + struct cache_holder { + using format = float_format; - constexpr cache_holder() { - for (size_t i = 0; i < compressed_table_size; ++i) { - cache[i] = cache64[i * compression_ratio]; + uint128 get_cache(int k) const { + assert(k >= format::min_k && k <= format::max_k); + return cache64[k - format::min_k]; } - uint64_t p = 1; - for (size_t i = 0; i < pow5_table_size; ++i) { - pow5_table[i] = p; - p *= 5; + }; + + template <> + struct cache_holder { + using format = float_format; + enum { + cache_bits = format::cache_bits, + min_k = format::min_k, + max_k = format::max_k, + compression_ratio = 27, + compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, + pow5_table_size = compression_ratio, + }; + + uint128 cache[compressed_table_size]{}; + uint64_t pow5_table[pow5_table_size]{}; + + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = cache64[i * compression_ratio]; + } + uint64_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } } - } - uint128 get_cache(int k) const { - assert(k >= min_k && k <= max_k); + uint128 get_cache(int k) const { + assert(k >= min_k && k <= max_k); - // Compute the base index. - // Supposed to compute (k - min_k) / compression_ratio. - static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); - static_assert(max_k - min_k <= INT_MAX, ""); - auto const cache_index = int(uint32_t(int(k - min_k) * int32_t(607)) >> 14); - auto const kb = int(cache_index * compression_ratio + min_k); - auto const offset = int(k - kb); + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint32_t(int(k - min_k) * int32_t(607)) >> 14); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); - // Get the base cache. - auto const base_cache = cache[cache_index]; + // Get the base cache. + auto const base_cache = cache[cache_index]; - if (offset == 0) { - return base_cache; - } - else { - // Compute the required amount of bit-shift. - auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); - assert(alpha > 0 && alpha < 64); + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); - // Try to recover the real cache. - auto const pow5 = pow5_table[offset]; - auto recovered_cache = umul128(base_cache.high, pow5); - auto const middle_low = umul128(base_cache.low, pow5); + // Try to recover the real cache. + auto const pow5 = pow5_table[offset]; + auto recovered_cache = umul128(base_cache.high, pow5); + auto const middle_low = umul128(base_cache.low, pow5); - recovered_cache += middle_low.high; + recovered_cache += middle_low.high; - auto const high_to_middle = - uint64_t((recovered_cache.high << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); - auto const middle_to_low = - uint64_t((recovered_cache.low << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); + auto const high_to_middle = + uint64_t((recovered_cache.high << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); + auto const middle_to_low = + uint64_t((recovered_cache.low << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); - recovered_cache = {(recovered_cache.low >> alpha) | high_to_middle, - ((middle_low.low >> alpha) | middle_to_low)}; + recovered_cache = {(recovered_cache.low >> alpha) | high_to_middle, + ((middle_low.low >> alpha) | middle_to_low)}; - assert(recovered_cache.low != UINT64_C(0xffffffffffffffff)); - recovered_cache = {recovered_cache.high, uint64_t(recovered_cache.low + 1)}; + assert(recovered_cache.low != UINT64_C(0xffffffffffffffff)); + recovered_cache = {recovered_cache.high, uint64_t(recovered_cache.low + 1)}; - return recovered_cache; + return recovered_cache; + } } - } - }; - - template - constexpr int count_factors(UInt n) { - static_assert(a > 1); - int c = 0; - while (n % a == 0) { - n /= a; - ++c; - } - return c; - } + }; - static constexpr uint32_t divide_magic_number[2]{6554, 656}; - - struct interval { - bool include_left_endpoint; - bool include_right_endpoint; - }; - - enum class binary_round_mode { - nearest_to_even, - nearest_to_odd, - nearest_toward_plus_infinity, - nearest_toward_minus_infinity, - nearest_toward_zero, - nearest_away_from_zero, - nearest_to_even_static_boundary, - nearest_to_odd_static_boundary, - nearest_toward_plus_infinity_static_boundary, - nearest_toward_minus_infinity_static_boundary, - toward_plus_infinity, - toward_minus_infinity, - toward_zero, - away_from_zero, - }; - - enum class decimal_round_mode { - to_even, - to_odd, - away_from_zero, - toward_zero, - dont_care, - }; - - static_assert(sizeof(float) == 4); - static_assert(sizeof(double) == 8); - - constexpr void reverse(char* begin, char* end) { - while (begin < --end) { - char tmp = *begin; - *begin++ = *end; - *end = tmp; + template + constexpr int count_factors(UInt n) { + static_assert(a > 1); + int c = 0; + while (n % a == 0) { + n /= a; + ++c; + } + return c; } - } - template - struct impl { - using format = float_format; - using carrier_uint = typename format::carrier_uint; - static_assert(sizeof(carrier_uint) == sizeof(Float)); - - static constexpr int min(int x, int y) { return x < y ? x : y; } - static constexpr int max(int x, int y) { return x > y ? x : y; } - - enum { - min_exponent = format::min_exponent, - max_exponent = format::max_exponent, - significand_bits = format::significand_bits, - carrier_bits = 8 * sizeof(carrier_uint), - kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1, - - min_k = min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), - -floor_log10_pow2(max_exponent - significand_bits) + kappa), - - // We do invoke shorter_interval_case for exponent == min_exponent case, - // so we should not add 1 here. - max_k = max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), - -floor_log10_pow2(min_exponent - significand_bits) + kappa), + static constexpr uint32_t divide_magic_number[2]{6554, 656}; - case_shorter_interval_left_endpoint_lower_threshold = 2, + struct interval { + bool include_left_endpoint; + bool include_right_endpoint; + }; - case_shorter_interval_left_endpoint_upper_threshold = - 2 + - floor_log2( - compute_power((carrier_uint(1) << (significand_bits + 2)) - 1) + - 1>(10) / - 3), + enum class binary_round_mode { + nearest_to_even, + nearest_to_odd, + nearest_toward_plus_infinity, + nearest_toward_minus_infinity, + nearest_toward_zero, + nearest_away_from_zero, + nearest_to_even_static_boundary, + nearest_to_odd_static_boundary, + nearest_toward_plus_infinity_static_boundary, + nearest_toward_minus_infinity_static_boundary, + toward_plus_infinity, + toward_minus_infinity, + toward_zero, + away_from_zero, + }; - case_shorter_interval_right_endpoint_lower_threshold = 0, + enum class decimal_round_mode { + to_even, + to_odd, + away_from_zero, + toward_zero, + dont_care, + }; - case_shorter_interval_right_endpoint_upper_threshold = - 2 + - floor_log2( - compute_power((carrier_uint(1) << (significand_bits + 1)) + 1) + - 1>(10) / - 3), + static_assert(sizeof(float) == 4); + static_assert(sizeof(double) == 8); - shorter_interval_tie_lower_threshold = - -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits, + constexpr void reverse(char* begin, char* end) { + while (begin < --end) { + char tmp = *begin; + *begin++ = *end; + *end = tmp; + } + } - shorter_interval_tie_upper_threshold = - -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits, + template + struct impl { + using format = float_format; + using carrier_uint = typename format::carrier_uint; + static_assert(sizeof(carrier_uint) == sizeof(Float)); + + static constexpr int min(int x, int y) { return x < y ? x : y; } + static constexpr int max(int x, int y) { return x > y ? x : y; } + + enum { + min_exponent = format::min_exponent, + max_exponent = format::max_exponent, + significand_bits = format::significand_bits, + carrier_bits = 8 * sizeof(carrier_uint), + kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1, + + min_k = min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), + -floor_log10_pow2(max_exponent - significand_bits) + kappa), + + // We do invoke shorter_interval_case for exponent == min_exponent case, + // so we should not add 1 here. + max_k = + max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), + -floor_log10_pow2(min_exponent - significand_bits) + kappa), - // sign + significand + decimal_point + exp_marker + exp_sign + exp - max_output_string_length = - 4 + format::decimal_significand_digits + format::decimal_exponent_digits, - }; + case_shorter_interval_left_endpoint_lower_threshold = 2, - static_assert(kappa >= 1); - static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); - static_assert(min_k >= format::min_k && max_k <= format::max_k); + case_shorter_interval_left_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power< + count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) / + 3), - static constexpr cache_holder cache_; + case_shorter_interval_right_endpoint_lower_threshold = 0, - template - static bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { - // Make sure the computation for max_n does not overflow. - static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); - assert(n <= compute_power(carrier_uint(10))); + case_shorter_interval_right_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power< + count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) / + 3), - static constexpr auto magic_number = divide_magic_number[N - 1]; - auto const prod = uint32_t(n * magic_number); + shorter_interval_tie_lower_threshold = + -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits, - constexpr auto mask = uint32_t((uint32_t(1) << 16) - 1); - bool const result = ((prod & mask) < magic_number); + shorter_interval_tie_upper_threshold = + -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits, - n = carrier_uint(prod >> 16); - return result; - } + // sign + significand + decimal_point + exp_marker + exp_sign + exp + max_output_string_length = + 4 + format::decimal_significand_digits + format::decimal_exponent_digits, + }; - // Compute floor(n / 10^N) for small n and N. - // Precondition: n <= 10^(N+1) - template - static carrier_uint small_division_by_pow10(carrier_uint n) { - // Make sure the computation for max_n does not overflow. - static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); - assert(n <= compute_power(carrier_uint(10))); - return carrier_uint((n * divide_magic_number[N - 1]) >> 16); - } + static_assert(kappa >= 1); + static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); + static_assert(min_k >= format::min_k && max_k <= format::max_k); + + static constexpr cache_holder cache_; + + template + static bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); + assert(n <= compute_power(carrier_uint(10))); - static bool prefer_round_down(carrier_uint decimal_significand) { - using e = decimal_round_mode; - switch (DecimalRoundMode) { - case e::dont_care: - return false; - case e::to_even: - return decimal_significand % 2 != 0; - case e::to_odd: - return decimal_significand % 2 == 0; - case e::away_from_zero: - return false; - case e::toward_zero: - return true; + static constexpr auto magic_number = divide_magic_number[N - 1]; + auto const prod = uint32_t(n * magic_number); + + constexpr auto mask = uint32_t((uint32_t(1) << 16) - 1); + bool const result = ((prod & mask) < magic_number); + + n = carrier_uint(prod >> 16); + return result; } - } - carrier_uint significand; - int exponent; - bool sign; - - constexpr impl(Float x) { - carrier_uint bits; - static_assert(sizeof(x) == sizeof(bits)); - std::memcpy(&bits, &x, sizeof(x)); - significand = bits & ((carrier_uint(1) << format::significand_bits) - 1); - exponent = bits >> format::significand_bits & ((1u << format::exponent_bits) - 1); - sign = bits >> (format::significand_bits + format::exponent_bits); - } + // Compute floor(n / 10^N) for small n and N. + // Precondition: n <= 10^(N+1) + template + static carrier_uint small_division_by_pow10(carrier_uint n) { + // Make sure the computation for max_n does not overflow. + static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); + assert(n <= compute_power(carrier_uint(10))); + return carrier_uint((n * divide_magic_number[N - 1]) >> 16); + } - bool is_finite() const { return exponent != (1u << format::exponent_bits) - 1; } + static bool prefer_round_down(carrier_uint decimal_significand) { + using e = decimal_round_mode; + switch (DecimalRoundMode) { + case e::dont_care: + return false; + case e::to_even: + return decimal_significand % 2 != 0; + case e::to_odd: + return decimal_significand % 2 == 0; + case e::away_from_zero: + return false; + case e::toward_zero: + return true; + } + } - struct decimal_result { carrier_uint significand; int exponent; bool sign; - }; - decimal_result to_decimal() { - assert(is_finite() && (significand || exponent)); - bool even = significand % 2 == 0; - using e = binary_round_mode; - switch (BinaryRoundMode) { - case e::nearest_to_even: - return nearest_to_even(); - case e::nearest_to_odd: - return nearest_to_odd(); - case e::nearest_toward_plus_infinity: - return nearest_toward_plus_infinity(); - case e::nearest_toward_minus_infinity: - return nearest_toward_minus_infinity(); - case e::nearest_toward_zero: - return nearest_toward_zero(); - case e::nearest_away_from_zero: - return nearest_away_from_zero(); - case e::nearest_to_even_static_boundary: - return even ? nearest_always_closed() : nearest_always_open(); - case e::nearest_to_odd_static_boundary: - return even ? nearest_always_open() : nearest_always_closed(); - case e::nearest_toward_plus_infinity_static_boundary: - return sign ? nearest_toward_zero() : nearest_away_from_zero(); - case e::nearest_toward_minus_infinity_static_boundary: - return sign ? nearest_away_from_zero() : nearest_toward_zero(); - case e::toward_plus_infinity: - return sign ? left_closed_directed() : right_closed_directed(); - case e::toward_minus_infinity: - return sign ? right_closed_directed() : left_closed_directed(); - case e::toward_zero: - return left_closed_directed(); - case e::away_from_zero: - return right_closed_directed(); + constexpr impl(Float x) { + carrier_uint bits; + static_assert(sizeof(x) == sizeof(bits)); + std::memcpy(&bits, &x, sizeof(x)); + significand = bits & ((carrier_uint(1) << format::significand_bits) - 1); + exponent = bits >> format::significand_bits & ((1u << format::exponent_bits) - 1); + sign = bits >> (format::significand_bits + format::exponent_bits); } - } - - auto nearest_to_even() { - bool even = significand % 2 == 0; - return nearest({even, even}, {true, true}); - } - auto nearest_to_odd() { - bool even = significand % 2 == 0; - return nearest({!even, even}, {false, false}); - } + bool is_finite() const { return exponent != (1u << format::exponent_bits) - 1; } + + struct decimal_result { + carrier_uint significand; + int exponent; + bool sign; + }; + + decimal_result to_decimal() { + assert(is_finite() && (significand || exponent)); + bool even = significand % 2 == 0; + using e = binary_round_mode; + switch (BinaryRoundMode) { + case e::nearest_to_even: + return nearest_to_even(); + case e::nearest_to_odd: + return nearest_to_odd(); + case e::nearest_toward_plus_infinity: + return nearest_toward_plus_infinity(); + case e::nearest_toward_minus_infinity: + return nearest_toward_minus_infinity(); + case e::nearest_toward_zero: + return nearest_toward_zero(); + case e::nearest_away_from_zero: + return nearest_away_from_zero(); + case e::nearest_to_even_static_boundary: + return even ? nearest_always_closed() : nearest_always_open(); + case e::nearest_to_odd_static_boundary: + return even ? nearest_always_open() : nearest_always_closed(); + case e::nearest_toward_plus_infinity_static_boundary: + return sign ? nearest_toward_zero() : nearest_away_from_zero(); + case e::nearest_toward_minus_infinity_static_boundary: + return sign ? nearest_away_from_zero() : nearest_toward_zero(); + case e::toward_plus_infinity: + return sign ? left_closed_directed() : right_closed_directed(); + case e::toward_minus_infinity: + return sign ? right_closed_directed() : left_closed_directed(); + case e::toward_zero: + return left_closed_directed(); + case e::away_from_zero: + return right_closed_directed(); + } + } - auto nearest_toward_plus_infinity() { return nearest({!sign, sign}, {!sign, sign}); } + auto nearest_to_even() { + bool even = significand % 2 == 0; + return nearest({even, even}, {true, true}); + } - auto nearest_toward_minus_infinity() { return nearest({sign, !sign}, {sign, !sign}); } + auto nearest_to_odd() { + bool even = significand % 2 == 0; + return nearest({!even, even}, {false, false}); + } - auto nearest_toward_zero() { return nearest({false, true}, {false, true}); } + auto nearest_toward_plus_infinity() { return nearest({!sign, sign}, {!sign, sign}); } - auto nearest_away_from_zero() { return nearest({true, false}, {true, false}); } + auto nearest_toward_minus_infinity() { return nearest({sign, !sign}, {sign, !sign}); } - auto nearest_always_closed() { return nearest({true, true}, {true, true}); } + auto nearest_toward_zero() { return nearest({false, true}, {false, true}); } - auto nearest_always_open() { return nearest({false, false}, {false, false}); } + auto nearest_away_from_zero() { return nearest({true, false}, {true, false}); } - decimal_result no_trailing_zeros(carrier_uint significand, int exponent) { - return {significand, exponent, sign}; - } + auto nearest_always_closed() { return nearest({true, true}, {true, true}); } - decimal_result may_have_trailing_zeros(carrier_uint significand, int exponent) { - format::remove_trailing_zeros(significand, exponent); - return {significand, exponent, sign}; - } + auto nearest_always_open() { return nearest({false, false}, {false, false}); } - //// The main algorithm assumes the input is a normal/subnormal finite number. - - auto nearest(interval normal_interval, interval shorter_interval) { - - carrier_uint two_fc = significand * 2; - auto binary_exponent = exponent; - - // Is the input a normal number? - if (binary_exponent != 0) { - binary_exponent += format::exponent_bias - format::significand_bits; - - // Shorter interval case; proceed like Schubfach. - // One might think this condition is wrong, since when exponent_bits == - // 1 and two_fc == 0, the interval is actually regular. However, it - // turns out that this seemingly wrong condition is actually fine, - // because the end result is anyway the same. - // - // [binary32] - // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 - // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 - // fc * 2^e = 1.175'494'35... * 10^-38 - // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 - // - // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. - // 1.175'494'3 * 10^-38 is also a correct shortest representation that - // will be rejected if we assume shorter interval, but 1.175'494'4 * - // 10^-38 is closer to the true value so it doesn't matter. - // - // [binary64] - // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 - // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 - // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 - // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 - // - // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * - // 10^-308. This is indeed of the shortest length, and it is the unique - // one closest to the true value among valid representations of the same - // length. - - // Shorter interval case. - if (two_fc == 0) { - - // Compute k and beta. - int const minus_k = floor_log10_pow2_minus_log10_4_over_3(binary_exponent); - int const beta = binary_exponent + floor_log2_pow10(-minus_k); - - // Compute xi and zi. - auto const cache = cache_.get_cache(-minus_k); - - auto xi = format::compute_left_endpoint_for_shorter_interval_case(cache, beta); - auto zi = format::compute_right_endpoint_for_shorter_interval_case(cache, beta); - - // If we don't accept the right endpoint and - // if the right endpoint is an integer, decrease it. - if (!shorter_interval.include_right_endpoint && - is_right_endpoint_integer_shorter_interval(binary_exponent)) { - --zi; - } - // If we don't accept the left endpoint or - // if the left endpoint is not an integer, increase it. - if (!shorter_interval.include_left_endpoint || - !is_left_endpoint_integer_shorter_interval(binary_exponent)) { - ++xi; - } + decimal_result no_trailing_zeros(carrier_uint significand, int exponent) { + return {significand, exponent, sign}; + } - // Try bigger divisor. - // zi is at most floor((f_c + 1/2) * 2^e * 10^k0). - // Substituting f_c = 2^p and k0 = -floor(log10(3 * 2^(e-2))), we get - // zi <= floor((2^(p+1) + 1) * 20/3) <= ceil((2^(p+1) + 1)/3) * 20. - // This computation does not overflow for any of the formats I care about. - carrier_uint decimal_significand = format::template divide_by_pow10< - 1, (((carrier_uint(2) << significand_bits) + 1) / 3 + 1) * 20>(zi); - - // If succeed, remove trailing zeros if necessary and return. - if (decimal_significand * 10 >= xi) { - return may_have_trailing_zeros(decimal_significand, minus_k + 1); - } + decimal_result may_have_trailing_zeros(carrier_uint significand, int exponent) { + format::remove_trailing_zeros(significand, exponent); + return {significand, exponent, sign}; + } - // Otherwise, compute the round-up of y. - decimal_significand = - format::compute_round_up_for_shorter_interval_case(cache, beta); + //// The main algorithm assumes the input is a normal/subnormal finite number. + + auto nearest(interval normal_interval, interval shorter_interval) { + + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; + + // Is the input a normal number? + if (binary_exponent != 0) { + binary_exponent += format::exponent_bias - format::significand_bits; + + // Shorter interval case; proceed like Schubfach. + // One might think this condition is wrong, since when exponent_bits == + // 1 and two_fc == 0, the interval is actually regular. However, it + // turns out that this seemingly wrong condition is actually fine, + // because the end result is anyway the same. + // + // [binary32] + // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38 + // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38 + // fc * 2^e = 1.175'494'35... * 10^-38 + // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38 + // + // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38. + // 1.175'494'3 * 10^-38 is also a correct shortest representation that + // will be rejected if we assume shorter interval, but 1.175'494'4 * + // 10^-38 is closer to the true value so it doesn't matter. + // + // [binary64] + // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308 + // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308 + // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308 + // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308 + // + // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 * + // 10^-308. This is indeed of the shortest length, and it is the unique + // one closest to the true value among valid representations of the same + // length. + + // Shorter interval case. + if (two_fc == 0) { + + // Compute k and beta. + int const minus_k = floor_log10_pow2_minus_log10_4_over_3(binary_exponent); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute xi and zi. + auto const cache = cache_.get_cache(-minus_k); + + auto xi = format::compute_left_endpoint_for_shorter_interval_case(cache, beta); + auto zi = format::compute_right_endpoint_for_shorter_interval_case(cache, beta); + + // If we don't accept the right endpoint and + // if the right endpoint is an integer, decrease it. + if (!shorter_interval.include_right_endpoint && + is_right_endpoint_integer_shorter_interval(binary_exponent)) { + --zi; + } + // If we don't accept the left endpoint or + // if the left endpoint is not an integer, increase it. + if (!shorter_interval.include_left_endpoint || + !is_left_endpoint_integer_shorter_interval(binary_exponent)) { + ++xi; + } - // When tie occurs, choose one of them according to the rule. - if (prefer_round_down(decimal_significand) && - binary_exponent >= shorter_interval_tie_lower_threshold && - binary_exponent <= shorter_interval_tie_upper_threshold) { - --decimal_significand; - } - else if (decimal_significand < xi) { - ++decimal_significand; - } - return no_trailing_zeros(decimal_significand, minus_k); - } + // Try bigger divisor. + // zi is at most floor((f_c + 1/2) * 2^e * 10^k0). + // Substituting f_c = 2^p and k0 = -floor(log10(3 * 2^(e-2))), we get + // zi <= floor((2^(p+1) + 1) * 20/3) <= ceil((2^(p+1) + 1)/3) * 20. + // This computation does not overflow for any of the formats I care about. + carrier_uint decimal_significand = format::template divide_by_pow10< + 1, (((carrier_uint(2) << significand_bits) + 1) / 3 + 1) * 20>(zi); + + // If succeed, remove trailing zeros if necessary and return. + if (decimal_significand * 10 >= xi) { + return may_have_trailing_zeros(decimal_significand, minus_k + 1); + } - // Normal interval case. - two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); - } - else { - // Is the input a subnormal number? - // Normal interval case. - binary_exponent = min_exponent - format::significand_bits; - } + // Otherwise, compute the round-up of y. + decimal_significand = + format::compute_round_up_for_shorter_interval_case(cache, beta); - ////////////////////////////////////////////////////////////////////// - // Step 1: Schubfach multiplier calculation. - ////////////////////////////////////////////////////////////////////// - - // Compute k and beta. - int const minus_k = floor_log10_pow2(binary_exponent) - kappa; - auto const cache = cache_.get_cache(-minus_k); - int const beta = binary_exponent + floor_log2_pow10(-minus_k); - - // Compute zi and deltai. - // 10^kappa <= deltai < 10^(kappa + 1) - auto const deltai = format::compute_delta(cache, beta); - // For the case of binary32, the result of integer check is not correct for - // 29711844 * 2^-82 - // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 - // and 29711844 * 2^-81 - // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, - // and they are the unique counterexamples. However, since 29711844 is even, - // this does not cause any problem for the endpoints calculations; it can only - // cause a problem when we need to perform integer check for the center. - // Fortunately, with these inputs, that branch is never executed, so we are - // fine. - auto const z_result = format::compute_mul(carrier_uint((two_fc | 1) << beta), cache); - - ////////////////////////////////////////////////////////////////////// - // Step 2: Try larger divisor; remove trailing zeros if necessary. - ////////////////////////////////////////////////////////////////////// - - auto const big_divisor = compute_power(carrier_uint(10)); - auto const small_divisor = compute_power(carrier_uint(10)); - - // Using an upper bound on zi, we might be able to optimize the division - // better than the compiler; we are computing zi / big_divisor here. - carrier_uint decimal_significand = format::template divide_by_pow10< - kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( - z_result.integer_part); - auto r = carrier_uint(z_result.integer_part - big_divisor * decimal_significand); - - do { - if (r < deltai) { - // Exclude the right endpoint if necessary. - if ((r | carrier_uint(!z_result.is_integer) | - carrier_uint(normal_interval.include_right_endpoint)) == 0) { - if (DecimalRoundMode == decimal_round_mode::dont_care) { - decimal_significand *= 10; + // When tie occurs, choose one of them according to the rule. + if (prefer_round_down(decimal_significand) && + binary_exponent >= shorter_interval_tie_lower_threshold && + binary_exponent <= shorter_interval_tie_upper_threshold) { --decimal_significand; - return no_trailing_zeros(decimal_significand, minus_k + kappa); } - else { - --decimal_significand; - r = big_divisor; - break; + else if (decimal_significand < xi) { + ++decimal_significand; } + return no_trailing_zeros(decimal_significand, minus_k); } - } - else if (r > deltai) { - break; + + // Normal interval case. + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); } else { - // r == deltai; compare fractional parts. - auto const x_result = - format::compute_mul_parity(carrier_uint(two_fc - 1), cache, beta); + // Is the input a subnormal number? + // Normal interval case. + binary_exponent = min_exponent - format::significand_bits; + } - if (!(x_result.parity | - (x_result.is_integer & normal_interval.include_left_endpoint))) { + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = floor_log10_pow2(binary_exponent) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta); + // For the case of binary32, the result of integer check is not correct for + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17, + // and they are the unique counterexamples. However, since 29711844 is even, + // this does not cause any problem for the endpoints calculations; it can only + // cause a problem when we need to perform integer check for the center. + // Fortunately, with these inputs, that branch is never executed, so we are + // fine. + auto const z_result = format::compute_mul(carrier_uint((two_fc | 1) << beta), cache); + + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// + + auto const big_divisor = compute_power(carrier_uint(10)); + auto const small_divisor = compute_power(carrier_uint(10)); + + // Using an upper bound on zi, we might be able to optimize the division + // better than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( + z_result.integer_part); + auto r = carrier_uint(z_result.integer_part - big_divisor * decimal_significand); + + do { + if (r < deltai) { + // Exclude the right endpoint if necessary. + if ((r | carrier_uint(!z_result.is_integer) | + carrier_uint(normal_interval.include_right_endpoint)) == 0) { + if (DecimalRoundMode == decimal_round_mode::dont_care) { + decimal_significand *= 10; + --decimal_significand; + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } + else { + --decimal_significand; + r = big_divisor; + break; + } + } + } + else if (r > deltai) { break; } - } + else { + // r == deltai; compare fractional parts. + auto const x_result = + format::compute_mul_parity(carrier_uint(two_fc - 1), cache, beta); + + if (!(x_result.parity | + (x_result.is_integer & normal_interval.include_left_endpoint))) { + break; + } + } - return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); - } while (false); + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); - ////////////////////////////////////////////////////////////////////// - // Step 3: Find the significand with the smaller divisor. - ////////////////////////////////////////////////////////////////////// + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor. + ////////////////////////////////////////////////////////////////////// - decimal_significand *= 10; + decimal_significand *= 10; - if (DecimalRoundMode == decimal_round_mode::dont_care) { - // Normally, we want to compute - // significand += r / small_divisor - // and return, but we need to take care of the case that the resulting - // value is exactly the right endpoint, while that is not included in the - // interval. - if (!normal_interval.include_right_endpoint) { - // Is r divisible by 10^kappa? - if (check_divisibility_and_divide_by_pow10(r) && z_result.is_integer) { - // This should be in the interval. - decimal_significand += r - 1; + if (DecimalRoundMode == decimal_round_mode::dont_care) { + // Normally, we want to compute + // significand += r / small_divisor + // and return, but we need to take care of the case that the resulting + // value is exactly the right endpoint, while that is not included in the + // interval. + if (!normal_interval.include_right_endpoint) { + // Is r divisible by 10^kappa? + if (check_divisibility_and_divide_by_pow10(r) && z_result.is_integer) { + // This should be in the interval. + decimal_significand += r - 1; + } + else { + decimal_significand += r; + } } else { - decimal_significand += r; + decimal_significand += small_division_by_pow10(r); } } else { - decimal_significand += small_division_by_pow10(r); - } - } - else { - // delta is equal to 10^(kappa + elog10(2) - floor(elog10(2))), so dist cannot - // be larger than r. - auto dist = carrier_uint(r - (deltai / 2) + (small_divisor / 2)); - bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; - - // Is dist divisible by 10^kappa? - bool const divisible_by_small_divisor = - check_divisibility_and_divide_by_pow10(dist); - - // Add dist / 10^kappa to the significand. - decimal_significand += dist; - - if (divisible_by_small_divisor) { - // Check z^(f) >= epsilon^(f). - // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, - // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). - // Since there are only 2 possibilities, we only need to care about the - // parity. Also, zi and r should have the same parity since the divisor - // is an even number. - auto const y_result = format::compute_mul_parity(two_fc, cache, beta); - if (y_result.parity != approx_y_parity) { - --decimal_significand; - } - else { - // If z^(f) >= epsilon^(f), we might have a tie - // when z^(f) == epsilon^(f), or equivalently, when y is an integer. - // For tie-to-up case, we can just choose the upper one. - if (prefer_round_down(decimal_significand) & y_result.is_integer) { + // delta is equal to 10^(kappa + elog10(2) - floor(elog10(2))), so dist cannot + // be larger than r. + auto dist = carrier_uint(r - (deltai / 2) + (small_divisor / 2)); + bool const approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0; + + // Is dist divisible by 10^kappa? + bool const divisible_by_small_divisor = + check_divisibility_and_divide_by_pow10(dist); + + // Add dist / 10^kappa to the significand. + decimal_significand += dist; + + if (divisible_by_small_divisor) { + // Check z^(f) >= epsilon^(f). + // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1, + // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f). + // Since there are only 2 possibilities, we only need to care about the + // parity. Also, zi and r should have the same parity since the divisor + // is an even number. + auto const y_result = format::compute_mul_parity(two_fc, cache, beta); + if (y_result.parity != approx_y_parity) { --decimal_significand; } + else { + // If z^(f) >= epsilon^(f), we might have a tie + // when z^(f) == epsilon^(f), or equivalently, when y is an integer. + // For tie-to-up case, we can just choose the upper one. + if (prefer_round_down(decimal_significand) & y_result.is_integer) { + --decimal_significand; + } + } } } + return no_trailing_zeros(decimal_significand, minus_k + kappa); } - return no_trailing_zeros(decimal_significand, minus_k + kappa); - } - auto left_closed_directed() { + auto left_closed_directed() { - carrier_uint two_fc = significand * 2; - auto binary_exponent = exponent; + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; - // Is the input a normal number? - if (binary_exponent != 0) { - binary_exponent += format::exponent_bias - format::significand_bits; - two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); - } - // Is the input a subnormal number? - else { - binary_exponent = min_exponent - format::significand_bits; - } - - ////////////////////////////////////////////////////////////////////// - // Step 1: Schubfach multiplier calculation. - ////////////////////////////////////////////////////////////////////// - - // Compute k and beta. - int const minus_k = floor_log10_pow2(binary_exponent) - kappa; - auto const cache = cache_.get_cache(-minus_k); - int const beta = binary_exponent + floor_log2_pow10(-minus_k); - - // Compute xi and deltai. - // 10^kappa <= deltai < 10^(kappa + 1) - auto const deltai = format::compute_delta(cache, beta); - auto x_result = format::compute_mul(carrier_uint(two_fc << beta), cache); - - // Deal with the unique exceptional cases - // 29711844 * 2^-82 - // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 - // and 29711844 * 2^-81 - // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17 - // for binary32. - if constexpr (carrier_bits == 32) { - if (binary_exponent <= -80) { - x_result.is_integer = false; + // Is the input a normal number? + if (binary_exponent != 0) { + binary_exponent += format::exponent_bias - format::significand_bits; + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + binary_exponent = min_exponent - format::significand_bits; } - } - if (!x_result.is_integer) { - ++x_result.integer_part; - } + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// + + // Compute k and beta. + int const minus_k = floor_log10_pow2(binary_exponent) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); + + // Compute xi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta); + auto x_result = format::compute_mul(carrier_uint(two_fc << beta), cache); + + // Deal with the unique exceptional cases + // 29711844 * 2^-82 + // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18 + // and 29711844 * 2^-81 + // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17 + // for binary32. + if constexpr (carrier_bits == 32) { + if (binary_exponent <= -80) { + x_result.is_integer = false; + } + } - ////////////////////////////////////////////////////////////////////// - // Step 2: Try larger divisor; remove trailing zeros if necessary. - ////////////////////////////////////////////////////////////////////// + if (!x_result.is_integer) { + ++x_result.integer_part; + } - auto const big_divisor = compute_power(carrier_uint(10)); + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// - // Using an upper bound on xi, we might be able to optimize the division - // better than the compiler; we are computing xi / big_divisor here. - carrier_uint decimal_significand = format::template divide_by_pow10< - kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( - x_result.integer_part); - auto r = carrier_uint(x_result.integer_part - big_divisor * decimal_significand); + auto const big_divisor = compute_power(carrier_uint(10)); - if (r != 0) { - ++decimal_significand; - r = carrier_uint(big_divisor - r); - } + // Using an upper bound on xi, we might be able to optimize the division + // better than the compiler; we are computing xi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>( + x_result.integer_part); + auto r = carrier_uint(x_result.integer_part - big_divisor * decimal_significand); - do { - if (r > deltai) { - break; + if (r != 0) { + ++decimal_significand; + r = carrier_uint(big_divisor - r); } - else if (r == deltai) { - // Compare the fractional parts. - // This branch is never taken for the exceptional cases - // 2f_c = 29711482, e = -81 - // (6.1442649164096937243516663440523473127541365101933479309082... * - // 10^-18) and 2f_c = 29711482, e = -80 - // (1.2288529832819387448703332688104694625508273020386695861816... * - // 10^-17). - // For the case of compressed cache for binary32, there is another - // exceptional case 2f_c = 33554430, e = -10 (16383.9990234375). In this - // case, the recovered cache is two large to make compute_mul_parity - // mistakenly conclude that z is not an integer, but actually z = 16384 is - // an integer. - if constexpr (carrier_bits == 32 && CacheType == cache_type::compact) { - if (two_fc == 33554430 && binary_exponent == -10) { + + do { + if (r > deltai) { + break; + } + else if (r == deltai) { + // Compare the fractional parts. + // This branch is never taken for the exceptional cases + // 2f_c = 29711482, e = -81 + // (6.1442649164096937243516663440523473127541365101933479309082... * + // 10^-18) and 2f_c = 29711482, e = -80 + // (1.2288529832819387448703332688104694625508273020386695861816... * + // 10^-17). + // For the case of compressed cache for binary32, there is another + // exceptional case 2f_c = 33554430, e = -10 (16383.9990234375). In this + // case, the recovered cache is two large to make compute_mul_parity + // mistakenly conclude that z is not an integer, but actually z = 16384 is + // an integer. + if constexpr (carrier_bits == 32 && CacheType == cache_type::compact) { + if (two_fc == 33554430 && binary_exponent == -10) { + break; + } + } + auto const z_result = + format::compute_mul_parity(carrier_uint(two_fc + 2), cache, beta); + if (z_result.parity || z_result.is_integer) { break; } } - auto const z_result = - format::compute_mul_parity(carrier_uint(two_fc + 2), cache, beta); - if (z_result.parity || z_result.is_integer) { - break; - } - } - // The ceiling is inside, so we are done. - return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); - } while (false); + // The ceiling is inside, so we are done. + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); - ////////////////////////////////////////////////////////////////////// - // Step 3: Find the significand with the smaller divisor. - ////////////////////////////////////////////////////////////////////// + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the smaller divisor. + ////////////////////////////////////////////////////////////////////// - decimal_significand *= 10; - decimal_significand -= small_division_by_pow10(r); - return no_trailing_zeros(decimal_significand, minus_k + kappa); - } + decimal_significand *= 10; + decimal_significand -= small_division_by_pow10(r); + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } - auto right_closed_directed() { + auto right_closed_directed() { - carrier_uint two_fc = significand * 2; - auto binary_exponent = exponent; - bool shorter_interval = false; + carrier_uint two_fc = significand * 2; + auto binary_exponent = exponent; + bool shorter_interval = false; - // Is the input a normal number? - if (binary_exponent != 0) { - if (two_fc == 0 && binary_exponent != 1) { - shorter_interval = true; + // Is the input a normal number? + if (binary_exponent != 0) { + if (two_fc == 0 && binary_exponent != 1) { + shorter_interval = true; + } + binary_exponent += format::exponent_bias - format::significand_bits; + two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); + } + // Is the input a subnormal number? + else { + binary_exponent = min_exponent - format::significand_bits; } - binary_exponent += format::exponent_bias - format::significand_bits; - two_fc |= (carrier_uint(1) << (format::significand_bits + 1)); - } - // Is the input a subnormal number? - else { - binary_exponent = min_exponent - format::significand_bits; - } - ////////////////////////////////////////////////////////////////////// - // Step 1: Schubfach multiplier calculation. - ////////////////////////////////////////////////////////////////////// + ////////////////////////////////////////////////////////////////////// + // Step 1: Schubfach multiplier calculation. + ////////////////////////////////////////////////////////////////////// - // Compute k and beta. - int const minus_k = floor_log10_pow2(binary_exponent - (shorter_interval ? 1 : 0)) - kappa; - auto const cache = cache_.get_cache(-minus_k); - int const beta = binary_exponent + floor_log2_pow10(-minus_k); + // Compute k and beta. + int const minus_k = + floor_log10_pow2(binary_exponent - (shorter_interval ? 1 : 0)) - kappa; + auto const cache = cache_.get_cache(-minus_k); + int const beta = binary_exponent + floor_log2_pow10(-minus_k); - // Compute zi and deltai. - // 10^kappa <= deltai < 10^(kappa + 1) - auto const deltai = format::compute_delta(cache, beta - (shorter_interval ? 1 : 0)); - carrier_uint const zi = - format::compute_mul(carrier_uint(two_fc << beta), cache).integer_part; + // Compute zi and deltai. + // 10^kappa <= deltai < 10^(kappa + 1) + auto const deltai = format::compute_delta(cache, beta - (shorter_interval ? 1 : 0)); + carrier_uint const zi = + format::compute_mul(carrier_uint(two_fc << beta), cache).integer_part; - ////////////////////////////////////////////////////////////////////// - // Step 2: Try larger divisor; remove trailing zeros if necessary. - ////////////////////////////////////////////////////////////////////// + ////////////////////////////////////////////////////////////////////// + // Step 2: Try larger divisor; remove trailing zeros if necessary. + ////////////////////////////////////////////////////////////////////// - auto const big_divisor = compute_power(carrier_uint(10)); + auto const big_divisor = compute_power(carrier_uint(10)); - // Using an upper bound on zi, we might be able to optimize the division better - // than the compiler; we are computing zi / big_divisor here. - carrier_uint decimal_significand = format::template divide_by_pow10< - kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>(zi); - auto const r = carrier_uint(zi - big_divisor * decimal_significand); + // Using an upper bound on zi, we might be able to optimize the division better + // than the compiler; we are computing zi / big_divisor here. + carrier_uint decimal_significand = format::template divide_by_pow10< + kappa + 1, (carrier_uint(2) << significand_bits) * big_divisor - 1>(zi); + auto const r = carrier_uint(zi - big_divisor * decimal_significand); - do { - if (r > deltai) { - break; - } - else if (r == deltai) { - // Compare the fractional parts. - if (!format::compute_mul_parity(carrier_uint(two_fc - (shorter_interval ? 1 : 2)), - cache, beta) - .parity) { + do { + if (r > deltai) { break; } - } + else if (r == deltai) { + // Compare the fractional parts. + if (!format::compute_mul_parity( + carrier_uint(two_fc - (shorter_interval ? 1 : 2)), cache, beta) + .parity) { + break; + } + } - // The floor is inside, so we are done. - return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); - } while (false); + // The floor is inside, so we are done. + return may_have_trailing_zeros(decimal_significand, minus_k + kappa + 1); + } while (false); - ////////////////////////////////////////////////////////////////////// - // Step 3: Find the significand with the small divisor. - ////////////////////////////////////////////////////////////////////// + ////////////////////////////////////////////////////////////////////// + // Step 3: Find the significand with the small divisor. + ////////////////////////////////////////////////////////////////////// - decimal_significand *= 10; - decimal_significand += small_division_by_pow10(r); - return no_trailing_zeros(decimal_significand, minus_k + kappa); - } + decimal_significand *= 10; + decimal_significand += small_division_by_pow10(r); + return no_trailing_zeros(decimal_significand, minus_k + kappa); + } - static bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { - return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && - binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; - } + static bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { + return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && + binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; + } - static bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { - return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && - binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; - } + static bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { + return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && + binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; + } - char* to_chars(char* buffer) { - if (!is_finite()) { - if (!significand) { - if (sign) { - *buffer++ = '-'; + char* to_chars(char* buffer) { + if (!is_finite()) { + if (!significand) { + if (sign) { + *buffer++ = '-'; + } + std::memcpy(buffer, "Infinity", 8); + return buffer + 8; + } + else { + buffer[0] = 'N'; + buffer[1] = 'a'; + buffer[2] = 'N'; + return buffer + 3; } - std::memcpy(buffer, "Infinity", 8); - return buffer + 8; } - else { - buffer[0] = 'N'; - buffer[1] = 'a'; - buffer[2] = 'N'; + + if (sign) { + *buffer++ = '-'; + } + + if (!significand && !exponent) { + buffer[0] = '0'; + buffer[1] = 'E'; + buffer[2] = '0'; return buffer + 3; } - } - if (sign) { - *buffer++ = '-'; - } + auto [dec_sig, dec_exp, dec_sign] = to_decimal(); - if (!significand && !exponent) { - buffer[0] = '0'; - buffer[1] = 'E'; - buffer[2] = '0'; - return buffer + 3; - } + if (dec_sig < 10) { + *buffer++ = char('0' + dec_sig); + } + else { + auto begin = buffer; + do { + *buffer++ = char('0' + dec_sig % 10); + dec_sig /= 10; + ++dec_exp; + } while (dec_sig >= 10); + *buffer++ = '.'; + *buffer++ = char('0' + dec_sig); + reverse(begin, buffer); + } - auto [dec_sig, dec_exp, dec_sign] = to_decimal(); + *buffer++ = 'E'; + if (dec_exp < 0) { + *buffer++ = '-'; + dec_exp = -dec_exp; + } - if (dec_sig < 10) { - *buffer++ = char('0' + dec_sig); - } - else { auto begin = buffer; do { - *buffer++ = char('0' + dec_sig % 10); - dec_sig /= 10; - ++dec_exp; - } while (dec_sig >= 10); - *buffer++ = '.'; - *buffer++ = char('0' + dec_sig); + *buffer++ = char('0' + dec_exp % 10); + dec_exp /= 10; + } while (dec_exp); reverse(begin, buffer); + return buffer; } + }; - *buffer++ = 'E'; - if (dec_exp < 0) { - *buffer++ = '-'; - dec_exp = -dec_exp; - } + template + struct policy_ {}; - auto begin = buffer; - do { - *buffer++ = char('0' + dec_exp % 10); - dec_exp /= 10; - } while (dec_exp); - reverse(begin, buffer); - return buffer; - } - }; + template + struct get_policy; + + template + struct get_policy { + static constexpr T value{}; + }; - //////////////////////////////////////////////////////////////////////////////////////// - // The interface function. - //////////////////////////////////////////////////////////////////////////////////////// + template + struct get_policy, Rest...> { + static constexpr T value = x; + }; - template - struct policy_ {}; + template + struct get_policy : get_policy {}; + + template + using make_impl = impl::value, + get_policy::value, + get_policy::value>; + + } // namespace detail namespace policy { namespace decimal_to_binary_rounding { - using type = binary_round_mode; - constexpr policy_ nearest_to_even; - constexpr policy_ nearest_to_odd; - constexpr policy_ nearest_toward_plus_infinity; - constexpr policy_ nearest_toward_minus_infinity; - constexpr policy_ nearest_toward_zero; - constexpr policy_ nearest_away_from_zero; - constexpr policy_ + using type = detail::binary_round_mode; + constexpr detail::policy_ nearest_to_even; + constexpr detail::policy_ nearest_to_odd; + constexpr detail::policy_ + nearest_toward_plus_infinity; + constexpr detail::policy_ + nearest_toward_minus_infinity; + constexpr detail::policy_ nearest_toward_zero; + constexpr detail::policy_ nearest_away_from_zero; + constexpr detail::policy_ nearest_to_even_static_boundary; - constexpr policy_ + constexpr detail::policy_ nearest_to_odd_static_boundary; - constexpr policy_ + constexpr detail::policy_ nearest_toward_plus_infinity_static_boundary; - constexpr policy_ + constexpr detail::policy_ nearest_toward_minus_infinity_static_boundary; - constexpr policy_ toward_plus_infinity; - constexpr policy_ toward_minus_infinity; - constexpr policy_ toward_zero; - constexpr policy_ away_from_zero; + constexpr detail::policy_ toward_plus_infinity; + constexpr detail::policy_ toward_minus_infinity; + constexpr detail::policy_ toward_zero; + constexpr detail::policy_ away_from_zero; } namespace binary_to_decimal_rounding { - using type = decimal_round_mode; - constexpr policy_ to_even; - constexpr policy_ to_odd; - constexpr policy_ away_from_zero; - constexpr policy_ toward_zero; - constexpr policy_ do_not_care; + using type = detail::decimal_round_mode; + constexpr detail::policy_ to_even; + constexpr detail::policy_ to_odd; + constexpr detail::policy_ away_from_zero; + constexpr detail::policy_ toward_zero; + constexpr detail::policy_ do_not_care; } namespace cache { - using type = cache_type; - constexpr policy_ full; - constexpr policy_ compact; + using type = detail::cache_type; + constexpr detail::policy_ full; + constexpr detail::policy_ compact; } } - template - struct get_policy; - - template - struct get_policy { - static constexpr T value{}; - }; - - template - struct get_policy, Rest...> { - static constexpr T value = x; - }; - - template - struct get_policy : get_policy {}; - - template - using make_impl = impl::value, - get_policy::value, - get_policy::value>; template constexpr auto to_decimal(Float x, Policies...) { - return make_impl(x).to_decimal(); + return detail::make_impl(x).to_decimal(); } // Null-terminate and bypass the return value of fp_to_chars_n template constexpr char* to_chars(Float x, char* buffer, Policies... policies) { - auto ptr = make_impl(x).to_chars(buffer); + auto ptr = detail::make_impl(x).to_chars(buffer); *ptr = '\0'; return ptr; } // Maximum required buffer size (excluding null-terminator) template - constexpr size_t max_output_string_length = impl::max_output_string_length; -} + constexpr size_t max_output_string_length = detail::impl::max_output_string_length; +} // namespace simple_dragonbox #endif diff --git a/subproject/simple/simple_dragonbox_test.cpp b/subproject/simple/simple_dragonbox_test.cpp index 5445dd0..f5e633e 100644 --- a/subproject/simple/simple_dragonbox_test.cpp +++ b/subproject/simple/simple_dragonbox_test.cpp @@ -44,7 +44,7 @@ static bool test_simple_dragonbox(bool& success, Arg... arg) { std::cout << "test all shorter interval cases, type=" << type_name << " compact_cache=" << compact << " ... \n"; - using format = simple_dragonbox::float_format; + using format = simple_dragonbox::detail::float_format; using carrier_uint = typename format::carrier_uint; for (int e = format::min_exponent; e <= format::max_exponent; ++e) { From 29383b0d51cfe8a5b1715245903f73683d698b95 Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 23:02:14 -0700 Subject: [PATCH 11/17] Use `static constexpr int` instead of `enum {` --- subproject/simple/simple_dragonbox.h | 165 +++++++++++++-------------- 1 file changed, 79 insertions(+), 86 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 0379e45..a8455db 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -186,19 +186,17 @@ namespace simple_dragonbox { template <> struct float_format { using carrier_uint = uint32_t; - enum { - total_bits = 32, - significand_bits = 23, - exponent_bits = 8, - min_exponent = -126, - max_exponent = 127, - exponent_bias = -127, - decimal_significand_digits = 9, - decimal_exponent_digits = 2, - cache_bits = 64, - min_k = -31, - max_k = 46, - }; + static constexpr int total_bits = 32; + static constexpr int significand_bits = 23; + static constexpr int exponent_bits = 8; + static constexpr int min_exponent = -126; + static constexpr int max_exponent = 127; + static constexpr int exponent_bias = -127; + static constexpr int decimal_significand_digits = 9; + static constexpr int decimal_exponent_digits = 2; + static constexpr int cache_bits = 64; + static constexpr int min_k = -31; + static constexpr int max_k = 46; static void remove_trailing_zeros(uint32_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. @@ -283,19 +281,17 @@ namespace simple_dragonbox { template <> struct float_format { using carrier_uint = uint64_t; - enum { - total_bits = 64, - significand_bits = 52, - exponent_bits = 11, - min_exponent = -1022, - max_exponent = 1023, - exponent_bias = -1023, - decimal_significand_digits = 17, - decimal_exponent_digits = 3, - cache_bits = 128, - min_k = -292, - max_k = 326, - }; + static constexpr int total_bits = 64; + static constexpr int significand_bits = 52; + static constexpr int exponent_bits = 11; + static constexpr int min_exponent = -1022; + static constexpr int max_exponent = 1023; + static constexpr int exponent_bias = -1023; + static constexpr int decimal_significand_digits = 17; + static constexpr int decimal_exponent_digits = 3; + static constexpr int cache_bits = 128; + static constexpr int min_k = -292; + static constexpr int max_k = 326; static void remove_trailing_zeros(uint64_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. @@ -1050,14 +1046,13 @@ namespace simple_dragonbox { template <> struct cache_holder { using format = float_format; - enum { - cache_bits = format::cache_bits, - min_k = format::min_k, - max_k = format::max_k, - compression_ratio = 13, - compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, - pow5_table_size = (compression_ratio + 1) / 2, - }; + static constexpr int cache_bits = format::cache_bits; + static constexpr int min_k = format::min_k; + static constexpr int max_k = format::max_k; + static constexpr int compression_ratio = 13; + static constexpr int compressed_table_size = + (max_k - min_k + compression_ratio) / compression_ratio; + static constexpr int pow5_table_size = (compression_ratio + 1) / 2; uint64_t cache[compressed_table_size]{}; uint16_t pow5_table[pow5_table_size]{}; @@ -1123,14 +1118,13 @@ namespace simple_dragonbox { template <> struct cache_holder { using format = float_format; - enum { - cache_bits = format::cache_bits, - min_k = format::min_k, - max_k = format::max_k, - compression_ratio = 27, - compressed_table_size = (max_k - min_k + compression_ratio) / compression_ratio, - pow5_table_size = compression_ratio, - }; + static constexpr int cache_bits = format::cache_bits; + static constexpr int min_k = format::min_k; + static constexpr int max_k = format::max_k; + static constexpr int compression_ratio = 27; + static constexpr int compressed_table_size = + (max_k - min_k + compression_ratio) / compression_ratio; + static constexpr int pow5_table_size = compression_ratio; uint128 cache[compressed_table_size]{}; uint64_t pow5_table[pow5_table_size]{}; @@ -1256,50 +1250,49 @@ namespace simple_dragonbox { static constexpr int min(int x, int y) { return x < y ? x : y; } static constexpr int max(int x, int y) { return x > y ? x : y; } - enum { - min_exponent = format::min_exponent, - max_exponent = format::max_exponent, - significand_bits = format::significand_bits, - carrier_bits = 8 * sizeof(carrier_uint), - kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1, - - min_k = min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), - -floor_log10_pow2(max_exponent - significand_bits) + kappa), - - // We do invoke shorter_interval_case for exponent == min_exponent case, - // so we should not add 1 here. - max_k = - max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), - -floor_log10_pow2(min_exponent - significand_bits) + kappa), - - case_shorter_interval_left_endpoint_lower_threshold = 2, - - case_shorter_interval_left_endpoint_upper_threshold = - 2 + - floor_log2( - compute_power< - count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1>(10) / - 3), - - case_shorter_interval_right_endpoint_lower_threshold = 0, - - case_shorter_interval_right_endpoint_upper_threshold = - 2 + - floor_log2( - compute_power< - count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1>(10) / - 3), - - shorter_interval_tie_lower_threshold = - -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits, - - shorter_interval_tie_upper_threshold = - -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits, - - // sign + significand + decimal_point + exp_marker + exp_sign + exp - max_output_string_length = - 4 + format::decimal_significand_digits + format::decimal_exponent_digits, - }; + static constexpr int min_exponent = format::min_exponent; + static constexpr int max_exponent = format::max_exponent; + static constexpr int significand_bits = format::significand_bits; + static constexpr int carrier_bits = 8 * sizeof(carrier_uint); + static constexpr int kappa = floor_log10_pow2(carrier_bits - significand_bits - 2) - 1; + + static constexpr int min_k = + min(-floor_log10_pow2_minus_log10_4_over_3(max_exponent - significand_bits), + -floor_log10_pow2(max_exponent - significand_bits) + kappa); + + // We do invoke shorter_interval_case for exponent == min_exponent case; + // so we should not add 1 here. + static constexpr int max_k = + max(-floor_log10_pow2_minus_log10_4_over_3(min_exponent - significand_bits /*+ 1*/), + -floor_log10_pow2(min_exponent - significand_bits) + kappa); + + static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2; + + static constexpr int case_shorter_interval_left_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 2)) - 1) + + 1>(10) / + 3); + + static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0; + + static constexpr int case_shorter_interval_right_endpoint_upper_threshold = + 2 + + floor_log2( + compute_power((carrier_uint(1) << (significand_bits + 1)) + 1) + + 1>(10) / + 3); + + static constexpr int shorter_interval_tie_lower_threshold = + -floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits; + + static constexpr int shorter_interval_tie_upper_threshold = + -floor_log5_pow2(significand_bits + 2) - 2 - significand_bits; + + // sign + significand + decimal_point + exp_marker + exp_sign + exp + static constexpr int max_output_string_length = + 4 + format::decimal_significand_digits + format::decimal_exponent_digits; static_assert(kappa >= 1); static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); From b1b42f188358337da5146d3ddc4f7298331b70da Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 23:14:31 -0700 Subject: [PATCH 12/17] Move cache data and types into `float_format` specializations --- subproject/simple/simple_dragonbox.h | 1591 +++++++++++++------------- 1 file changed, 796 insertions(+), 795 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index a8455db..036fd3d 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -177,8 +177,10 @@ namespace simple_dragonbox { bool is_integer; }; - // These classes expose encoding specs of IEEE-754-like floating-point formats. - // Currently available formats are IEEE-754 binary32 & IEEE-754 binary64. + enum class cache_type { + full, + compact, + }; template struct float_format; @@ -276,6 +278,116 @@ namespace simple_dragonbox { return n / compute_power(uint32_t(10)); } } + + static constexpr uint64_t cache[78]{ + UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), + UINT64_C(0xcad2f7f5359a3b3f), UINT64_C(0xfd87b5f28300ca0e), + UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), + UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), + UINT64_C(0xc16d9a0095928a28), UINT64_C(0xf1c90080baf72cb2), + UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), + UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), + UINT64_C(0xb877aa3236a4b44a), UINT64_C(0xe69594bec44de15c), + UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), + UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), + UINT64_C(0xafebff0bcb24aaff), UINT64_C(0xdbe6fecebdedd5bf), + UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), + UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), + UINT64_C(0xa7c5ac471b478424), UINT64_C(0xd1b71758e219652c), + UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), + UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), + UINT64_C(0xa000000000000000), UINT64_C(0xc800000000000000), + UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), + UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), + UINT64_C(0x9896800000000000), UINT64_C(0xbebc200000000000), + UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), + UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), + UINT64_C(0x9184e72a00000000), UINT64_C(0xb5e620f480000000), + UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), + UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), + UINT64_C(0x8ac7230489e80000), UINT64_C(0xad78ebc5ac620000), + UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), + UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), + UINT64_C(0x84595161401484a0), UINT64_C(0xa56fa5b99019a5c8), + UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), + UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), + UINT64_C(0xfc6f7c4045812297), UINT64_C(0x9dc5ada82b70b59e), + UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), + UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), + UINT64_C(0xf0bdc21abb48db21), UINT64_C(0x96769950b50d88f5), + UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), + UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), + UINT64_C(0xe596b7b0c643c71a), UINT64_C(0x8f7e32ce7bea5c70), + UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; + + template + struct cache_holder; + + template <> + struct cache_holder { + uint64_t get_cache(int k) const { + assert(k >= min_k && k <= max_k); + return cache[k - min_k]; + } + }; + + template <> + struct cache_holder { + static constexpr int compression_ratio = 13; + static constexpr int compressed_table_size = + (max_k - min_k + compression_ratio) / compression_ratio; + static constexpr int pow5_table_size = (compression_ratio + 1) / 2; + + uint64_t cache[compressed_table_size]{}; + uint16_t pow5_table[pow5_table_size]{}; + + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = float_format::cache[i * compression_ratio]; + } + uint16_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } + } + + uint64_t get_cache(int k) const { + assert(k >= min_k && k <= max_k); + + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint16_t(int(k - min_k) * int16_t(79)) >> 10); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); + + // Get the base cache. + auto const base_cache = cache[cache_index]; + + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); + + // Try to recover the real cache. + auto const pow5 = + offset >= 7 ? uint32_t(uint32_t(pow5_table[6]) * pow5_table[offset - 6]) + : uint32_t(pow5_table[offset]); + auto mul_result = umul128(base_cache, pow5); + auto const recovered_cache = uint64_t( + (((mul_result.high << int(64 - alpha)) | (mul_result.low >> alpha)) + 1) & + UINT64_C(0xffffffffffffffff)); + assert(recovered_cache != 0); + + return recovered_cache; + } + } + }; }; template <> @@ -374,815 +486,704 @@ namespace simple_dragonbox { return n / compute_power(uint64_t(10)); } } - }; - - static constexpr uint64_t cache32[78]{ - UINT64_C(0x81ceb32c4b43fcf5), UINT64_C(0xa2425ff75e14fc32), UINT64_C(0xcad2f7f5359a3b3f), - UINT64_C(0xfd87b5f28300ca0e), UINT64_C(0x9e74d1b791e07e49), UINT64_C(0xc612062576589ddb), - UINT64_C(0xf79687aed3eec552), UINT64_C(0x9abe14cd44753b53), UINT64_C(0xc16d9a0095928a28), - UINT64_C(0xf1c90080baf72cb2), UINT64_C(0x971da05074da7bef), UINT64_C(0xbce5086492111aeb), - UINT64_C(0xec1e4a7db69561a6), UINT64_C(0x9392ee8e921d5d08), UINT64_C(0xb877aa3236a4b44a), - UINT64_C(0xe69594bec44de15c), UINT64_C(0x901d7cf73ab0acda), UINT64_C(0xb424dc35095cd810), - UINT64_C(0xe12e13424bb40e14), UINT64_C(0x8cbccc096f5088cc), UINT64_C(0xafebff0bcb24aaff), - UINT64_C(0xdbe6fecebdedd5bf), UINT64_C(0x89705f4136b4a598), UINT64_C(0xabcc77118461cefd), - UINT64_C(0xd6bf94d5e57a42bd), UINT64_C(0x8637bd05af6c69b6), UINT64_C(0xa7c5ac471b478424), - UINT64_C(0xd1b71758e219652c), UINT64_C(0x83126e978d4fdf3c), UINT64_C(0xa3d70a3d70a3d70b), - UINT64_C(0xcccccccccccccccd), UINT64_C(0x8000000000000000), UINT64_C(0xa000000000000000), - UINT64_C(0xc800000000000000), UINT64_C(0xfa00000000000000), UINT64_C(0x9c40000000000000), - UINT64_C(0xc350000000000000), UINT64_C(0xf424000000000000), UINT64_C(0x9896800000000000), - UINT64_C(0xbebc200000000000), UINT64_C(0xee6b280000000000), UINT64_C(0x9502f90000000000), - UINT64_C(0xba43b74000000000), UINT64_C(0xe8d4a51000000000), UINT64_C(0x9184e72a00000000), - UINT64_C(0xb5e620f480000000), UINT64_C(0xe35fa931a0000000), UINT64_C(0x8e1bc9bf04000000), - UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0xde0b6b3a76400000), UINT64_C(0x8ac7230489e80000), - UINT64_C(0xad78ebc5ac620000), UINT64_C(0xd8d726b7177a8000), UINT64_C(0x878678326eac9000), - UINT64_C(0xa968163f0a57b400), UINT64_C(0xd3c21bcecceda100), UINT64_C(0x84595161401484a0), - UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x813f3978f8940985), - UINT64_C(0xa18f07d736b90be6), UINT64_C(0xc9f2c9cd04674edf), UINT64_C(0xfc6f7c4045812297), - UINT64_C(0x9dc5ada82b70b59e), UINT64_C(0xc5371912364ce306), UINT64_C(0xf684df56c3e01bc7), - UINT64_C(0x9a130b963a6c115d), UINT64_C(0xc097ce7bc90715b4), UINT64_C(0xf0bdc21abb48db21), - UINT64_C(0x96769950b50d88f5), UINT64_C(0xbc143fa4e250eb32), UINT64_C(0xeb194f8e1ae525fe), - UINT64_C(0x92efd1b8d0cf37bf), UINT64_C(0xb7abc627050305ae), UINT64_C(0xe596b7b0c643c71a), - UINT64_C(0x8f7e32ce7bea5c70), UINT64_C(0xb35dbf821ae4f38c), UINT64_C(0xe0352f62a19e306f)}; - - static constexpr uint128 cache64[619] = { - {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, - {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, - {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, - {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, - {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, - {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, - {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, - {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, - {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, - {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, - {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, - {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, - {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, - {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, - {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, - {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, - {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, - {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, - {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, - {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, - {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, - {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, - {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, - {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, - {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, - {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, - {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, - {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, - {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, - {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, - {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, - {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, - {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, - {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, - {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, - {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, - {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, - {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, - {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, - {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, - {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, - {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, - {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, - {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, - {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, - {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, - {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, - {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, - {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, - {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, - {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, - {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, - {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, - {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, - {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, - {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, - {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, - {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, - {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, - {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, - {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, - {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, - {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, - {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, - {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, - {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, - {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, - {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, - {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, - {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, - {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, - {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, - {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, - {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, - {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, - {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, - {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, - {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, - {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, - {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, - {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, - {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, - {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, - {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, - {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, - {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, - {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, - {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, - {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, - {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, - {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, - {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, - {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, - {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, - {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, - {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, - {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, - {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, - {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, - {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, - {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, - {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, - {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, - {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, - {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, - {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, - {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, - {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, - {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, - {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, - {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, - {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, - {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, - {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, - {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, - {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, - {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, - {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, - {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, - {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, - {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, - {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, - {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, - {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, - {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, - {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, - {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, - {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, - {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, - {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, - {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, - {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, - {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, - {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, - {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, - {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, - {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, - {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, - {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, - {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, - {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, - {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, - {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, - {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, - {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, - {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, - {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, - {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, - {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, - {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, - {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, - {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, - {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, - {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, - {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, - {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, - {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, - {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, - {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, - {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, - {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, - {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, - {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, - {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, - {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, - {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, - {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, - {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, - {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, - {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, - {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, - {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, - {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, - {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, - {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, - {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, - {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, - {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, - {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, - {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, - {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, - {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, - {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, - {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, - {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, - {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, - {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, - {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, - {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, - {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, - {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, - {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, - {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, - {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, - {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, - {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, - {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, - {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, - {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, - {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, - {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, - {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, - {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, - {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, - {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, - {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, - {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, - {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, - {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, - {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, - {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, - {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, - {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, - {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, - {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, - {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, - {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, - {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, - {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, - {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, - {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, - {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, - {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, - {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, - {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, - {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, - {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, - {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, - {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, - {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, - {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, - {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, - {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, - {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, - {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, - {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, - {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, - {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, - {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, - {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, - {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, - {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, - {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, - {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, - {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, - {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, - {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, - {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, - {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, - {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, - {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, - {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, - {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, - {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, - {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, - {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, - {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, - {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, - {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, - {UINT64_C(0xa6274bbdd0fadd61), UINT64_C(0xecb1ad8aeacdd58f)}, - {UINT64_C(0xcfb11ead453994ba), UINT64_C(0x67de18eda5814af3)}, - {UINT64_C(0x81ceb32c4b43fcf4), UINT64_C(0x80eacf948770ced8)}, - {UINT64_C(0xa2425ff75e14fc31), UINT64_C(0xa1258379a94d028e)}, - {UINT64_C(0xcad2f7f5359a3b3e), UINT64_C(0x096ee45813a04331)}, - {UINT64_C(0xfd87b5f28300ca0d), UINT64_C(0x8bca9d6e188853fd)}, - {UINT64_C(0x9e74d1b791e07e48), UINT64_C(0x775ea264cf55347e)}, - {UINT64_C(0xc612062576589dda), UINT64_C(0x95364afe032a819e)}, - {UINT64_C(0xf79687aed3eec551), UINT64_C(0x3a83ddbd83f52205)}, - {UINT64_C(0x9abe14cd44753b52), UINT64_C(0xc4926a9672793543)}, - {UINT64_C(0xc16d9a0095928a27), UINT64_C(0x75b7053c0f178294)}, - {UINT64_C(0xf1c90080baf72cb1), UINT64_C(0x5324c68b12dd6339)}, - {UINT64_C(0x971da05074da7bee), UINT64_C(0xd3f6fc16ebca5e04)}, - {UINT64_C(0xbce5086492111aea), UINT64_C(0x88f4bb1ca6bcf585)}, - {UINT64_C(0xec1e4a7db69561a5), UINT64_C(0x2b31e9e3d06c32e6)}, - {UINT64_C(0x9392ee8e921d5d07), UINT64_C(0x3aff322e62439fd0)}, - {UINT64_C(0xb877aa3236a4b449), UINT64_C(0x09befeb9fad487c3)}, - {UINT64_C(0xe69594bec44de15b), UINT64_C(0x4c2ebe687989a9b4)}, - {UINT64_C(0x901d7cf73ab0acd9), UINT64_C(0x0f9d37014bf60a11)}, - {UINT64_C(0xb424dc35095cd80f), UINT64_C(0x538484c19ef38c95)}, - {UINT64_C(0xe12e13424bb40e13), UINT64_C(0x2865a5f206b06fba)}, - {UINT64_C(0x8cbccc096f5088cb), UINT64_C(0xf93f87b7442e45d4)}, - {UINT64_C(0xafebff0bcb24aafe), UINT64_C(0xf78f69a51539d749)}, - {UINT64_C(0xdbe6fecebdedd5be), UINT64_C(0xb573440e5a884d1c)}, - {UINT64_C(0x89705f4136b4a597), UINT64_C(0x31680a88f8953031)}, - {UINT64_C(0xabcc77118461cefc), UINT64_C(0xfdc20d2b36ba7c3e)}, - {UINT64_C(0xd6bf94d5e57a42bc), UINT64_C(0x3d32907604691b4d)}, - {UINT64_C(0x8637bd05af6c69b5), UINT64_C(0xa63f9a49c2c1b110)}, - {UINT64_C(0xa7c5ac471b478423), UINT64_C(0x0fcf80dc33721d54)}, - {UINT64_C(0xd1b71758e219652b), UINT64_C(0xd3c36113404ea4a9)}, - {UINT64_C(0x83126e978d4fdf3b), UINT64_C(0x645a1cac083126ea)}, - {UINT64_C(0xa3d70a3d70a3d70a), UINT64_C(0x3d70a3d70a3d70a4)}, - {UINT64_C(0xcccccccccccccccc), UINT64_C(0xcccccccccccccccd)}, - {UINT64_C(0x8000000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa000000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xc800000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xfa00000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9c40000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xc350000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xf424000000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9896800000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xbebc200000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xee6b280000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9502f90000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xba43b74000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xe8d4a51000000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x9184e72a00000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, - {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, - {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, - {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, - {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, - {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, - {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, - {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, - {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, - {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, - {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, - {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, - {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, - {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, - {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, - {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, - {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, - {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, - {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, - {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, - {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, - {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, - {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, - {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, - {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, - {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, - {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, - {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, - {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, - {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, - {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, - {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, - {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, - {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, - {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, - {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, - {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, - {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, - {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, - {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, - {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, - {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, - {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, - {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, - {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, - {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, - {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, - {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, - {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, - {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, - {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, - {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, - {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, - {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, - {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, - {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, - {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, - {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, - {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, - {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, - {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, - {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, - {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, - {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, - {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, - {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, - {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, - {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, - {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, - {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, - {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, - {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, - {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, - {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, - {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, - {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, - {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, - {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, - {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, - {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, - {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, - {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, - {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, - {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, - {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, - {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, - {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, - {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, - {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, - {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, - {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, - {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, - {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, - {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, - {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, - {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, - {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, - {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, - {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, - {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, - {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, - {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, - {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, - {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, - {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, - {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, - {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, - {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, - {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, - {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, - {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, - {UINT64_C(0x899504ae72497eba), UINT64_C(0x6a06494a791c53a9)}, - {UINT64_C(0xabfa45da0edbde69), UINT64_C(0x0487db9d17636893)}, - {UINT64_C(0xd6f8d7509292d603), UINT64_C(0x45a9d2845d3c42b7)}, - {UINT64_C(0x865b86925b9bc5c2), UINT64_C(0x0b8a2392ba45a9b3)}, - {UINT64_C(0xa7f26836f282b732), UINT64_C(0x8e6cac7768d7141f)}, - {UINT64_C(0xd1ef0244af2364ff), UINT64_C(0x3207d795430cd927)}, - {UINT64_C(0x8335616aed761f1f), UINT64_C(0x7f44e6bd49e807b9)}, - {UINT64_C(0xa402b9c5a8d3a6e7), UINT64_C(0x5f16206c9c6209a7)}, - {UINT64_C(0xcd036837130890a1), UINT64_C(0x36dba887c37a8c10)}, - {UINT64_C(0x802221226be55a64), UINT64_C(0xc2494954da2c978a)}, - {UINT64_C(0xa02aa96b06deb0fd), UINT64_C(0xf2db9baa10b7bd6d)}, - {UINT64_C(0xc83553c5c8965d3d), UINT64_C(0x6f92829494e5acc8)}, - {UINT64_C(0xfa42a8b73abbf48c), UINT64_C(0xcb772339ba1f17fa)}, - {UINT64_C(0x9c69a97284b578d7), UINT64_C(0xff2a760414536efc)}, - {UINT64_C(0xc38413cf25e2d70d), UINT64_C(0xfef5138519684abb)}, - {UINT64_C(0xf46518c2ef5b8cd1), UINT64_C(0x7eb258665fc25d6a)}, - {UINT64_C(0x98bf2f79d5993802), UINT64_C(0xef2f773ffbd97a62)}, - {UINT64_C(0xbeeefb584aff8603), UINT64_C(0xaafb550ffacfd8fb)}, - {UINT64_C(0xeeaaba2e5dbf6784), UINT64_C(0x95ba2a53f983cf39)}, - {UINT64_C(0x952ab45cfa97a0b2), UINT64_C(0xdd945a747bf26184)}, - {UINT64_C(0xba756174393d88df), UINT64_C(0x94f971119aeef9e5)}, - {UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, - {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, - {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, - {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, - {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, - {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, - {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, - {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, - {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, - {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, - {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, - {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, - {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, - {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, - {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, - {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, - {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, - {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, - {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, - {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, - {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, - {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, - {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, - {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, - {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, - {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, - {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, - {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, - {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, - {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, - {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, - {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, - {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, - {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, - {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, - {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, - {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, - {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, - {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, - {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, - {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, - {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, - {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, - {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, - {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, - {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, - {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, - {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, - {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, - {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, - {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, - {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, - {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, - {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, - {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, - {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, - {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, - {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, - {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, - {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, - {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, - {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, - {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, - {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, - {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, - {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, - {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, - {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, - {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, - {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, - {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, - {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, - {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, - {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, - {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, - {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, - {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, - {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, - {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, - {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, - {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, - {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, - {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, - {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, - {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, - {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, - {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, - {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, - {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, - {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, - {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, - {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, - {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, - {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, - {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, - {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, - {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, - {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, - {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, - {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, - {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, - {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, - {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, - {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, - {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, - {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, - {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, - {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, - {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, - {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, - {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, - {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, - {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, - {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, - {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, - {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, - {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, - {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, - {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, - {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, - {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, - {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, - {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, - {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, - {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, - {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, - {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, - {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, - {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, - {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, - {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, - {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, - {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, - {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, - {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, - {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, - {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, - {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, - {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, - {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, - {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, - {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, - {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, - {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, - {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, - {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, - {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, - {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, - {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, - {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, - {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, - {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, - {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, - {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, - {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, - {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, - {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, - {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, - {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, - {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, - {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, - {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, - {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, - {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, - {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, - {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, - {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, - {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, - {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; - - enum class cache_type { - full, - compact, - }; - - template - struct cache_holder; - - template <> - struct cache_holder { - using format = float_format; - uint64_t get_cache(int k) const { - assert(k >= format::min_k && k <= format::max_k); - return cache32[k - format::min_k]; - } - }; - - template <> - struct cache_holder { - using format = float_format; - static constexpr int cache_bits = format::cache_bits; - static constexpr int min_k = format::min_k; - static constexpr int max_k = format::max_k; - static constexpr int compression_ratio = 13; - static constexpr int compressed_table_size = - (max_k - min_k + compression_ratio) / compression_ratio; - static constexpr int pow5_table_size = (compression_ratio + 1) / 2; - - uint64_t cache[compressed_table_size]{}; - uint16_t pow5_table[pow5_table_size]{}; - - constexpr cache_holder() { - for (size_t i = 0; i < compressed_table_size; ++i) { - cache[i] = cache32[i * compression_ratio]; + static constexpr uint128 cache[619] = { + {UINT64_C(0xff77b1fcbebcdc4f), UINT64_C(0x25e8e89c13bb0f7b)}, + {UINT64_C(0x9faacf3df73609b1), UINT64_C(0x77b191618c54e9ad)}, + {UINT64_C(0xc795830d75038c1d), UINT64_C(0xd59df5b9ef6a2418)}, + {UINT64_C(0xf97ae3d0d2446f25), UINT64_C(0x4b0573286b44ad1e)}, + {UINT64_C(0x9becce62836ac577), UINT64_C(0x4ee367f9430aec33)}, + {UINT64_C(0xc2e801fb244576d5), UINT64_C(0x229c41f793cda740)}, + {UINT64_C(0xf3a20279ed56d48a), UINT64_C(0x6b43527578c11110)}, + {UINT64_C(0x9845418c345644d6), UINT64_C(0x830a13896b78aaaa)}, + {UINT64_C(0xbe5691ef416bd60c), UINT64_C(0x23cc986bc656d554)}, + {UINT64_C(0xedec366b11c6cb8f), UINT64_C(0x2cbfbe86b7ec8aa9)}, + {UINT64_C(0x94b3a202eb1c3f39), UINT64_C(0x7bf7d71432f3d6aa)}, + {UINT64_C(0xb9e08a83a5e34f07), UINT64_C(0xdaf5ccd93fb0cc54)}, + {UINT64_C(0xe858ad248f5c22c9), UINT64_C(0xd1b3400f8f9cff69)}, + {UINT64_C(0x91376c36d99995be), UINT64_C(0x23100809b9c21fa2)}, + {UINT64_C(0xb58547448ffffb2d), UINT64_C(0xabd40a0c2832a78b)}, + {UINT64_C(0xe2e69915b3fff9f9), UINT64_C(0x16c90c8f323f516d)}, + {UINT64_C(0x8dd01fad907ffc3b), UINT64_C(0xae3da7d97f6792e4)}, + {UINT64_C(0xb1442798f49ffb4a), UINT64_C(0x99cd11cfdf41779d)}, + {UINT64_C(0xdd95317f31c7fa1d), UINT64_C(0x40405643d711d584)}, + {UINT64_C(0x8a7d3eef7f1cfc52), UINT64_C(0x482835ea666b2573)}, + {UINT64_C(0xad1c8eab5ee43b66), UINT64_C(0xda3243650005eed0)}, + {UINT64_C(0xd863b256369d4a40), UINT64_C(0x90bed43e40076a83)}, + {UINT64_C(0x873e4f75e2224e68), UINT64_C(0x5a7744a6e804a292)}, + {UINT64_C(0xa90de3535aaae202), UINT64_C(0x711515d0a205cb37)}, + {UINT64_C(0xd3515c2831559a83), UINT64_C(0x0d5a5b44ca873e04)}, + {UINT64_C(0x8412d9991ed58091), UINT64_C(0xe858790afe9486c3)}, + {UINT64_C(0xa5178fff668ae0b6), UINT64_C(0x626e974dbe39a873)}, + {UINT64_C(0xce5d73ff402d98e3), UINT64_C(0xfb0a3d212dc81290)}, + {UINT64_C(0x80fa687f881c7f8e), UINT64_C(0x7ce66634bc9d0b9a)}, + {UINT64_C(0xa139029f6a239f72), UINT64_C(0x1c1fffc1ebc44e81)}, + {UINT64_C(0xc987434744ac874e), UINT64_C(0xa327ffb266b56221)}, + {UINT64_C(0xfbe9141915d7a922), UINT64_C(0x4bf1ff9f0062baa9)}, + {UINT64_C(0x9d71ac8fada6c9b5), UINT64_C(0x6f773fc3603db4aa)}, + {UINT64_C(0xc4ce17b399107c22), UINT64_C(0xcb550fb4384d21d4)}, + {UINT64_C(0xf6019da07f549b2b), UINT64_C(0x7e2a53a146606a49)}, + {UINT64_C(0x99c102844f94e0fb), UINT64_C(0x2eda7444cbfc426e)}, + {UINT64_C(0xc0314325637a1939), UINT64_C(0xfa911155fefb5309)}, + {UINT64_C(0xf03d93eebc589f88), UINT64_C(0x793555ab7eba27cb)}, + {UINT64_C(0x96267c7535b763b5), UINT64_C(0x4bc1558b2f3458df)}, + {UINT64_C(0xbbb01b9283253ca2), UINT64_C(0x9eb1aaedfb016f17)}, + {UINT64_C(0xea9c227723ee8bcb), UINT64_C(0x465e15a979c1cadd)}, + {UINT64_C(0x92a1958a7675175f), UINT64_C(0x0bfacd89ec191eca)}, + {UINT64_C(0xb749faed14125d36), UINT64_C(0xcef980ec671f667c)}, + {UINT64_C(0xe51c79a85916f484), UINT64_C(0x82b7e12780e7401b)}, + {UINT64_C(0x8f31cc0937ae58d2), UINT64_C(0xd1b2ecb8b0908811)}, + {UINT64_C(0xb2fe3f0b8599ef07), UINT64_C(0x861fa7e6dcb4aa16)}, + {UINT64_C(0xdfbdcece67006ac9), UINT64_C(0x67a791e093e1d49b)}, + {UINT64_C(0x8bd6a141006042bd), UINT64_C(0xe0c8bb2c5c6d24e1)}, + {UINT64_C(0xaecc49914078536d), UINT64_C(0x58fae9f773886e19)}, + {UINT64_C(0xda7f5bf590966848), UINT64_C(0xaf39a475506a899f)}, + {UINT64_C(0x888f99797a5e012d), UINT64_C(0x6d8406c952429604)}, + {UINT64_C(0xaab37fd7d8f58178), UINT64_C(0xc8e5087ba6d33b84)}, + {UINT64_C(0xd5605fcdcf32e1d6), UINT64_C(0xfb1e4a9a90880a65)}, + {UINT64_C(0x855c3be0a17fcd26), UINT64_C(0x5cf2eea09a550680)}, + {UINT64_C(0xa6b34ad8c9dfc06f), UINT64_C(0xf42faa48c0ea481f)}, + {UINT64_C(0xd0601d8efc57b08b), UINT64_C(0xf13b94daf124da27)}, + {UINT64_C(0x823c12795db6ce57), UINT64_C(0x76c53d08d6b70859)}, + {UINT64_C(0xa2cb1717b52481ed), UINT64_C(0x54768c4b0c64ca6f)}, + {UINT64_C(0xcb7ddcdda26da268), UINT64_C(0xa9942f5dcf7dfd0a)}, + {UINT64_C(0xfe5d54150b090b02), UINT64_C(0xd3f93b35435d7c4d)}, + {UINT64_C(0x9efa548d26e5a6e1), UINT64_C(0xc47bc5014a1a6db0)}, + {UINT64_C(0xc6b8e9b0709f109a), UINT64_C(0x359ab6419ca1091c)}, + {UINT64_C(0xf867241c8cc6d4c0), UINT64_C(0xc30163d203c94b63)}, + {UINT64_C(0x9b407691d7fc44f8), UINT64_C(0x79e0de63425dcf1e)}, + {UINT64_C(0xc21094364dfb5636), UINT64_C(0x985915fc12f542e5)}, + {UINT64_C(0xf294b943e17a2bc4), UINT64_C(0x3e6f5b7b17b2939e)}, + {UINT64_C(0x979cf3ca6cec5b5a), UINT64_C(0xa705992ceecf9c43)}, + {UINT64_C(0xbd8430bd08277231), UINT64_C(0x50c6ff782a838354)}, + {UINT64_C(0xece53cec4a314ebd), UINT64_C(0xa4f8bf5635246429)}, + {UINT64_C(0x940f4613ae5ed136), UINT64_C(0x871b7795e136be9a)}, + {UINT64_C(0xb913179899f68584), UINT64_C(0x28e2557b59846e40)}, + {UINT64_C(0xe757dd7ec07426e5), UINT64_C(0x331aeada2fe589d0)}, + {UINT64_C(0x9096ea6f3848984f), UINT64_C(0x3ff0d2c85def7622)}, + {UINT64_C(0xb4bca50b065abe63), UINT64_C(0x0fed077a756b53aa)}, + {UINT64_C(0xe1ebce4dc7f16dfb), UINT64_C(0xd3e8495912c62895)}, + {UINT64_C(0x8d3360f09cf6e4bd), UINT64_C(0x64712dd7abbbd95d)}, + {UINT64_C(0xb080392cc4349dec), UINT64_C(0xbd8d794d96aacfb4)}, + {UINT64_C(0xdca04777f541c567), UINT64_C(0xecf0d7a0fc5583a1)}, + {UINT64_C(0x89e42caaf9491b60), UINT64_C(0xf41686c49db57245)}, + {UINT64_C(0xac5d37d5b79b6239), UINT64_C(0x311c2875c522ced6)}, + {UINT64_C(0xd77485cb25823ac7), UINT64_C(0x7d633293366b828c)}, + {UINT64_C(0x86a8d39ef77164bc), UINT64_C(0xae5dff9c02033198)}, + {UINT64_C(0xa8530886b54dbdeb), UINT64_C(0xd9f57f830283fdfd)}, + {UINT64_C(0xd267caa862a12d66), UINT64_C(0xd072df63c324fd7c)}, + {UINT64_C(0x8380dea93da4bc60), UINT64_C(0x4247cb9e59f71e6e)}, + {UINT64_C(0xa46116538d0deb78), UINT64_C(0x52d9be85f074e609)}, + {UINT64_C(0xcd795be870516656), UINT64_C(0x67902e276c921f8c)}, + {UINT64_C(0x806bd9714632dff6), UINT64_C(0x00ba1cd8a3db53b7)}, + {UINT64_C(0xa086cfcd97bf97f3), UINT64_C(0x80e8a40eccd228a5)}, + {UINT64_C(0xc8a883c0fdaf7df0), UINT64_C(0x6122cd128006b2ce)}, + {UINT64_C(0xfad2a4b13d1b5d6c), UINT64_C(0x796b805720085f82)}, + {UINT64_C(0x9cc3a6eec6311a63), UINT64_C(0xcbe3303674053bb1)}, + {UINT64_C(0xc3f490aa77bd60fc), UINT64_C(0xbedbfc4411068a9d)}, + {UINT64_C(0xf4f1b4d515acb93b), UINT64_C(0xee92fb5515482d45)}, + {UINT64_C(0x991711052d8bf3c5), UINT64_C(0x751bdd152d4d1c4b)}, + {UINT64_C(0xbf5cd54678eef0b6), UINT64_C(0xd262d45a78a0635e)}, + {UINT64_C(0xef340a98172aace4), UINT64_C(0x86fb897116c87c35)}, + {UINT64_C(0x9580869f0e7aac0e), UINT64_C(0xd45d35e6ae3d4da1)}, + {UINT64_C(0xbae0a846d2195712), UINT64_C(0x8974836059cca10a)}, + {UINT64_C(0xe998d258869facd7), UINT64_C(0x2bd1a438703fc94c)}, + {UINT64_C(0x91ff83775423cc06), UINT64_C(0x7b6306a34627ddd0)}, + {UINT64_C(0xb67f6455292cbf08), UINT64_C(0x1a3bc84c17b1d543)}, + {UINT64_C(0xe41f3d6a7377eeca), UINT64_C(0x20caba5f1d9e4a94)}, + {UINT64_C(0x8e938662882af53e), UINT64_C(0x547eb47b7282ee9d)}, + {UINT64_C(0xb23867fb2a35b28d), UINT64_C(0xe99e619a4f23aa44)}, + {UINT64_C(0xdec681f9f4c31f31), UINT64_C(0x6405fa00e2ec94d5)}, + {UINT64_C(0x8b3c113c38f9f37e), UINT64_C(0xde83bc408dd3dd05)}, + {UINT64_C(0xae0b158b4738705e), UINT64_C(0x9624ab50b148d446)}, + {UINT64_C(0xd98ddaee19068c76), UINT64_C(0x3badd624dd9b0958)}, + {UINT64_C(0x87f8a8d4cfa417c9), UINT64_C(0xe54ca5d70a80e5d7)}, + {UINT64_C(0xa9f6d30a038d1dbc), UINT64_C(0x5e9fcf4ccd211f4d)}, + {UINT64_C(0xd47487cc8470652b), UINT64_C(0x7647c32000696720)}, + {UINT64_C(0x84c8d4dfd2c63f3b), UINT64_C(0x29ecd9f40041e074)}, + {UINT64_C(0xa5fb0a17c777cf09), UINT64_C(0xf468107100525891)}, + {UINT64_C(0xcf79cc9db955c2cc), UINT64_C(0x7182148d4066eeb5)}, + {UINT64_C(0x81ac1fe293d599bf), UINT64_C(0xc6f14cd848405531)}, + {UINT64_C(0xa21727db38cb002f), UINT64_C(0xb8ada00e5a506a7d)}, + {UINT64_C(0xca9cf1d206fdc03b), UINT64_C(0xa6d90811f0e4851d)}, + {UINT64_C(0xfd442e4688bd304a), UINT64_C(0x908f4a166d1da664)}, + {UINT64_C(0x9e4a9cec15763e2e), UINT64_C(0x9a598e4e043287ff)}, + {UINT64_C(0xc5dd44271ad3cdba), UINT64_C(0x40eff1e1853f29fe)}, + {UINT64_C(0xf7549530e188c128), UINT64_C(0xd12bee59e68ef47d)}, + {UINT64_C(0x9a94dd3e8cf578b9), UINT64_C(0x82bb74f8301958cf)}, + {UINT64_C(0xc13a148e3032d6e7), UINT64_C(0xe36a52363c1faf02)}, + {UINT64_C(0xf18899b1bc3f8ca1), UINT64_C(0xdc44e6c3cb279ac2)}, + {UINT64_C(0x96f5600f15a7b7e5), UINT64_C(0x29ab103a5ef8c0ba)}, + {UINT64_C(0xbcb2b812db11a5de), UINT64_C(0x7415d448f6b6f0e8)}, + {UINT64_C(0xebdf661791d60f56), UINT64_C(0x111b495b3464ad22)}, + {UINT64_C(0x936b9fcebb25c995), UINT64_C(0xcab10dd900beec35)}, + {UINT64_C(0xb84687c269ef3bfb), UINT64_C(0x3d5d514f40eea743)}, + {UINT64_C(0xe65829b3046b0afa), UINT64_C(0x0cb4a5a3112a5113)}, + {UINT64_C(0x8ff71a0fe2c2e6dc), UINT64_C(0x47f0e785eaba72ac)}, + {UINT64_C(0xb3f4e093db73a093), UINT64_C(0x59ed216765690f57)}, + {UINT64_C(0xe0f218b8d25088b8), UINT64_C(0x306869c13ec3532d)}, + {UINT64_C(0x8c974f7383725573), UINT64_C(0x1e414218c73a13fc)}, + {UINT64_C(0xafbd2350644eeacf), UINT64_C(0xe5d1929ef90898fb)}, + {UINT64_C(0xdbac6c247d62a583), UINT64_C(0xdf45f746b74abf3a)}, + {UINT64_C(0x894bc396ce5da772), UINT64_C(0x6b8bba8c328eb784)}, + {UINT64_C(0xab9eb47c81f5114f), UINT64_C(0x066ea92f3f326565)}, + {UINT64_C(0xd686619ba27255a2), UINT64_C(0xc80a537b0efefebe)}, + {UINT64_C(0x8613fd0145877585), UINT64_C(0xbd06742ce95f5f37)}, + {UINT64_C(0xa798fc4196e952e7), UINT64_C(0x2c48113823b73705)}, + {UINT64_C(0xd17f3b51fca3a7a0), UINT64_C(0xf75a15862ca504c6)}, + {UINT64_C(0x82ef85133de648c4), UINT64_C(0x9a984d73dbe722fc)}, + {UINT64_C(0xa3ab66580d5fdaf5), UINT64_C(0xc13e60d0d2e0ebbb)}, + {UINT64_C(0xcc963fee10b7d1b3), UINT64_C(0x318df905079926a9)}, + {UINT64_C(0xffbbcfe994e5c61f), UINT64_C(0xfdf17746497f7053)}, + {UINT64_C(0x9fd561f1fd0f9bd3), UINT64_C(0xfeb6ea8bedefa634)}, + {UINT64_C(0xc7caba6e7c5382c8), UINT64_C(0xfe64a52ee96b8fc1)}, + {UINT64_C(0xf9bd690a1b68637b), UINT64_C(0x3dfdce7aa3c673b1)}, + {UINT64_C(0x9c1661a651213e2d), UINT64_C(0x06bea10ca65c084f)}, + {UINT64_C(0xc31bfa0fe5698db8), UINT64_C(0x486e494fcff30a63)}, + {UINT64_C(0xf3e2f893dec3f126), UINT64_C(0x5a89dba3c3efccfb)}, + {UINT64_C(0x986ddb5c6b3a76b7), UINT64_C(0xf89629465a75e01d)}, + {UINT64_C(0xbe89523386091465), UINT64_C(0xf6bbb397f1135824)}, + {UINT64_C(0xee2ba6c0678b597f), UINT64_C(0x746aa07ded582e2d)}, + {UINT64_C(0x94db483840b717ef), UINT64_C(0xa8c2a44eb4571cdd)}, + {UINT64_C(0xba121a4650e4ddeb), UINT64_C(0x92f34d62616ce414)}, + {UINT64_C(0xe896a0d7e51e1566), UINT64_C(0x77b020baf9c81d18)}, + {UINT64_C(0x915e2486ef32cd60), UINT64_C(0x0ace1474dc1d122f)}, + {UINT64_C(0xb5b5ada8aaff80b8), UINT64_C(0x0d819992132456bb)}, + {UINT64_C(0xe3231912d5bf60e6), UINT64_C(0x10e1fff697ed6c6a)}, + {UINT64_C(0x8df5efabc5979c8f), UINT64_C(0xca8d3ffa1ef463c2)}, + {UINT64_C(0xb1736b96b6fd83b3), UINT64_C(0xbd308ff8a6b17cb3)}, + {UINT64_C(0xddd0467c64bce4a0), UINT64_C(0xac7cb3f6d05ddbdf)}, + {UINT64_C(0x8aa22c0dbef60ee4), UINT64_C(0x6bcdf07a423aa96c)}, + {UINT64_C(0xad4ab7112eb3929d), UINT64_C(0x86c16c98d2c953c7)}, + {UINT64_C(0xd89d64d57a607744), UINT64_C(0xe871c7bf077ba8b8)}, + {UINT64_C(0x87625f056c7c4a8b), UINT64_C(0x11471cd764ad4973)}, + {UINT64_C(0xa93af6c6c79b5d2d), UINT64_C(0xd598e40d3dd89bd0)}, + {UINT64_C(0xd389b47879823479), UINT64_C(0x4aff1d108d4ec2c4)}, + {UINT64_C(0x843610cb4bf160cb), UINT64_C(0xcedf722a585139bb)}, + {UINT64_C(0xa54394fe1eedb8fe), UINT64_C(0xc2974eb4ee658829)}, + {UINT64_C(0xce947a3da6a9273e), UINT64_C(0x733d226229feea33)}, + {UINT64_C(0x811ccc668829b887), UINT64_C(0x0806357d5a3f5260)}, + {UINT64_C(0xa163ff802a3426a8), UINT64_C(0xca07c2dcb0cf26f8)}, + {UINT64_C(0xc9bcff6034c13052), UINT64_C(0xfc89b393dd02f0b6)}, + {UINT64_C(0xfc2c3f3841f17c67), UINT64_C(0xbbac2078d443ace3)}, + {UINT64_C(0x9d9ba7832936edc0), UINT64_C(0xd54b944b84aa4c0e)}, + {UINT64_C(0xc5029163f384a931), UINT64_C(0x0a9e795e65d4df12)}, + {UINT64_C(0xf64335bcf065d37d), UINT64_C(0x4d4617b5ff4a16d6)}, + {UINT64_C(0x99ea0196163fa42e), UINT64_C(0x504bced1bf8e4e46)}, + {UINT64_C(0xc06481fb9bcf8d39), UINT64_C(0xe45ec2862f71e1d7)}, + {UINT64_C(0xf07da27a82c37088), UINT64_C(0x5d767327bb4e5a4d)}, + {UINT64_C(0x964e858c91ba2655), UINT64_C(0x3a6a07f8d510f870)}, + {UINT64_C(0xbbe226efb628afea), UINT64_C(0x890489f70a55368c)}, + {UINT64_C(0xeadab0aba3b2dbe5), UINT64_C(0x2b45ac74ccea842f)}, + {UINT64_C(0x92c8ae6b464fc96f), UINT64_C(0x3b0b8bc90012929e)}, + {UINT64_C(0xb77ada0617e3bbcb), UINT64_C(0x09ce6ebb40173745)}, + {UINT64_C(0xe55990879ddcaabd), UINT64_C(0xcc420a6a101d0516)}, + {UINT64_C(0x8f57fa54c2a9eab6), UINT64_C(0x9fa946824a12232e)}, + {UINT64_C(0xb32df8e9f3546564), UINT64_C(0x47939822dc96abfa)}, + {UINT64_C(0xdff9772470297ebd), UINT64_C(0x59787e2b93bc56f8)}, + {UINT64_C(0x8bfbea76c619ef36), UINT64_C(0x57eb4edb3c55b65b)}, + {UINT64_C(0xaefae51477a06b03), UINT64_C(0xede622920b6b23f2)}, + {UINT64_C(0xdab99e59958885c4), UINT64_C(0xe95fab368e45ecee)}, + {UINT64_C(0x88b402f7fd75539b), UINT64_C(0x11dbcb0218ebb415)}, + {UINT64_C(0xaae103b5fcd2a881), UINT64_C(0xd652bdc29f26a11a)}, + {UINT64_C(0xd59944a37c0752a2), UINT64_C(0x4be76d3346f04960)}, + {UINT64_C(0x857fcae62d8493a5), UINT64_C(0x6f70a4400c562ddc)}, + {UINT64_C(0xa6dfbd9fb8e5b88e), UINT64_C(0xcb4ccd500f6bb953)}, + {UINT64_C(0xd097ad07a71f26b2), UINT64_C(0x7e2000a41346a7a8)}, + {UINT64_C(0x825ecc24c873782f), UINT64_C(0x8ed400668c0c28c9)}, + {UINT64_C(0xa2f67f2dfa90563b), UINT64_C(0x728900802f0f32fb)}, + {UINT64_C(0xcbb41ef979346bca), UINT64_C(0x4f2b40a03ad2ffba)}, + {UINT64_C(0xfea126b7d78186bc), UINT64_C(0xe2f610c84987bfa9)}, + {UINT64_C(0x9f24b832e6b0f436), UINT64_C(0x0dd9ca7d2df4d7ca)}, + {UINT64_C(0xc6ede63fa05d3143), UINT64_C(0x91503d1c79720dbc)}, + {UINT64_C(0xf8a95fcf88747d94), UINT64_C(0x75a44c6397ce912b)}, + {UINT64_C(0x9b69dbe1b548ce7c), UINT64_C(0xc986afbe3ee11abb)}, + {UINT64_C(0xc24452da229b021b), UINT64_C(0xfbe85badce996169)}, + {UINT64_C(0xf2d56790ab41c2a2), UINT64_C(0xfae27299423fb9c4)}, + {UINT64_C(0x97c560ba6b0919a5), UINT64_C(0xdccd879fc967d41b)}, + {UINT64_C(0xbdb6b8e905cb600f), UINT64_C(0x5400e987bbc1c921)}, + {UINT64_C(0xed246723473e3813), UINT64_C(0x290123e9aab23b69)}, + {UINT64_C(0x9436c0760c86e30b), UINT64_C(0xf9a0b6720aaf6522)}, + {UINT64_C(0xb94470938fa89bce), UINT64_C(0xf808e40e8d5b3e6a)}, + {UINT64_C(0xe7958cb87392c2c2), UINT64_C(0xb60b1d1230b20e05)}, + {UINT64_C(0x90bd77f3483bb9b9), UINT64_C(0xb1c6f22b5e6f48c3)}, + {UINT64_C(0xb4ecd5f01a4aa828), UINT64_C(0x1e38aeb6360b1af4)}, + {UINT64_C(0xe2280b6c20dd5232), UINT64_C(0x25c6da63c38de1b1)}, + {UINT64_C(0x8d590723948a535f), UINT64_C(0x579c487e5a38ad0f)}, + {UINT64_C(0xb0af48ec79ace837), UINT64_C(0x2d835a9df0c6d852)}, + {UINT64_C(0xdcdb1b2798182244), UINT64_C(0xf8e431456cf88e66)}, + {UINT64_C(0x8a08f0f8bf0f156b), UINT64_C(0x1b8e9ecb641b5900)}, + {UINT64_C(0xac8b2d36eed2dac5), UINT64_C(0xe272467e3d222f40)}, + {UINT64_C(0xd7adf884aa879177), UINT64_C(0x5b0ed81dcc6abb10)}, + {UINT64_C(0x86ccbb52ea94baea), UINT64_C(0x98e947129fc2b4ea)}, + {UINT64_C(0xa87fea27a539e9a5), UINT64_C(0x3f2398d747b36225)}, + {UINT64_C(0xd29fe4b18e88640e), UINT64_C(0x8eec7f0d19a03aae)}, + {UINT64_C(0x83a3eeeef9153e89), UINT64_C(0x1953cf68300424ad)}, + {UINT64_C(0xa48ceaaab75a8e2b), UINT64_C(0x5fa8c3423c052dd8)}, + {UINT64_C(0xcdb02555653131b6), UINT64_C(0x3792f412cb06794e)}, + {UINT64_C(0x808e17555f3ebf11), UINT64_C(0xe2bbd88bbee40bd1)}, + {UINT64_C(0xa0b19d2ab70e6ed6), UINT64_C(0x5b6aceaeae9d0ec5)}, + {UINT64_C(0xc8de047564d20a8b), UINT64_C(0xf245825a5a445276)}, + {UINT64_C(0xfb158592be068d2e), UINT64_C(0xeed6e2f0f0d56713)}, + {UINT64_C(0x9ced737bb6c4183d), UINT64_C(0x55464dd69685606c)}, + {UINT64_C(0xc428d05aa4751e4c), UINT64_C(0xaa97e14c3c26b887)}, + {UINT64_C(0xf53304714d9265df), UINT64_C(0xd53dd99f4b3066a9)}, + {UINT64_C(0x993fe2c6d07b7fab), UINT64_C(0xe546a8038efe402a)}, + {UINT64_C(0xbf8fdb78849a5f96), UINT64_C(0xde98520472bdd034)}, + {UINT64_C(0xef73d256a5c0f77c), UINT64_C(0x963e66858f6d4441)}, + {UINT64_C(0x95a8637627989aad), UINT64_C(0xdde7001379a44aa9)}, + {UINT64_C(0xbb127c53b17ec159), UINT64_C(0x5560c018580d5d53)}, + {UINT64_C(0xe9d71b689dde71af), UINT64_C(0xaab8f01e6e10b4a7)}, + {UINT64_C(0x9226712162ab070d), UINT64_C(0xcab3961304ca70e9)}, + {UINT64_C(0xb6b00d69bb55c8d1), UINT64_C(0x3d607b97c5fd0d23)}, + {UINT64_C(0xe45c10c42a2b3b05), UINT64_C(0x8cb89a7db77c506b)}, + {UINT64_C(0x8eb98a7a9a5b04e3), UINT64_C(0x77f3608e92adb243)}, + {UINT64_C(0xb267ed1940f1c61c), UINT64_C(0x55f038b237591ed4)}, + {UINT64_C(0xdf01e85f912e37a3), UINT64_C(0x6b6c46dec52f6689)}, + {UINT64_C(0x8b61313bbabce2c6), UINT64_C(0x2323ac4b3b3da016)}, + {UINT64_C(0xae397d8aa96c1b77), UINT64_C(0xabec975e0a0d081b)}, + {UINT64_C(0xd9c7dced53c72255), UINT64_C(0x96e7bd358c904a22)}, + {UINT64_C(0x881cea14545c7575), UINT64_C(0x7e50d64177da2e55)}, + {UINT64_C(0xaa242499697392d2), UINT64_C(0xdde50bd1d5d0b9ea)}, + {UINT64_C(0xd4ad2dbfc3d07787), UINT64_C(0x955e4ec64b44e865)}, + {UINT64_C(0x84ec3c97da624ab4), UINT64_C(0xbd5af13bef0b113f)}, + {UINT64_C(0xa6274bbdd0fadd61), UINT64_C(0xecb1ad8aeacdd58f)}, + {UINT64_C(0xcfb11ead453994ba), UINT64_C(0x67de18eda5814af3)}, + {UINT64_C(0x81ceb32c4b43fcf4), UINT64_C(0x80eacf948770ced8)}, + {UINT64_C(0xa2425ff75e14fc31), UINT64_C(0xa1258379a94d028e)}, + {UINT64_C(0xcad2f7f5359a3b3e), UINT64_C(0x096ee45813a04331)}, + 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{UINT64_C(0xfa00000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9c40000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xc350000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xf424000000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9896800000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xbebc200000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xee6b280000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9502f90000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xba43b74000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xe8d4a51000000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x9184e72a00000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb5e620f480000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xe35fa931a0000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8e1bc9bf04000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xb1a2bc2ec5000000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xde0b6b3a76400000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x8ac7230489e80000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xad78ebc5ac620000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd8d726b7177a8000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x878678326eac9000), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa968163f0a57b400), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xd3c21bcecceda100), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x84595161401484a0), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xa56fa5b99019a5c8), UINT64_C(0x0000000000000000)}, + {UINT64_C(0xcecb8f27f4200f3a), UINT64_C(0x0000000000000000)}, + {UINT64_C(0x813f3978f8940984), UINT64_C(0x4000000000000000)}, + {UINT64_C(0xa18f07d736b90be5), UINT64_C(0x5000000000000000)}, + {UINT64_C(0xc9f2c9cd04674ede), UINT64_C(0xa400000000000000)}, + {UINT64_C(0xfc6f7c4045812296), UINT64_C(0x4d00000000000000)}, + {UINT64_C(0x9dc5ada82b70b59d), UINT64_C(0xf020000000000000)}, + {UINT64_C(0xc5371912364ce305), UINT64_C(0x6c28000000000000)}, + {UINT64_C(0xf684df56c3e01bc6), UINT64_C(0xc732000000000000)}, + {UINT64_C(0x9a130b963a6c115c), UINT64_C(0x3c7f400000000000)}, + {UINT64_C(0xc097ce7bc90715b3), UINT64_C(0x4b9f100000000000)}, + {UINT64_C(0xf0bdc21abb48db20), UINT64_C(0x1e86d40000000000)}, + {UINT64_C(0x96769950b50d88f4), UINT64_C(0x1314448000000000)}, + {UINT64_C(0xbc143fa4e250eb31), UINT64_C(0x17d955a000000000)}, + {UINT64_C(0xeb194f8e1ae525fd), UINT64_C(0x5dcfab0800000000)}, + {UINT64_C(0x92efd1b8d0cf37be), UINT64_C(0x5aa1cae500000000)}, + {UINT64_C(0xb7abc627050305ad), UINT64_C(0xf14a3d9e40000000)}, + {UINT64_C(0xe596b7b0c643c719), UINT64_C(0x6d9ccd05d0000000)}, + {UINT64_C(0x8f7e32ce7bea5c6f), UINT64_C(0xe4820023a2000000)}, + {UINT64_C(0xb35dbf821ae4f38b), UINT64_C(0xdda2802c8a800000)}, + {UINT64_C(0xe0352f62a19e306e), UINT64_C(0xd50b2037ad200000)}, + {UINT64_C(0x8c213d9da502de45), UINT64_C(0x4526f422cc340000)}, + {UINT64_C(0xaf298d050e4395d6), UINT64_C(0x9670b12b7f410000)}, + {UINT64_C(0xdaf3f04651d47b4c), UINT64_C(0x3c0cdd765f114000)}, + {UINT64_C(0x88d8762bf324cd0f), UINT64_C(0xa5880a69fb6ac800)}, + {UINT64_C(0xab0e93b6efee0053), UINT64_C(0x8eea0d047a457a00)}, + {UINT64_C(0xd5d238a4abe98068), UINT64_C(0x72a4904598d6d880)}, + {UINT64_C(0x85a36366eb71f041), UINT64_C(0x47a6da2b7f864750)}, + {UINT64_C(0xa70c3c40a64e6c51), UINT64_C(0x999090b65f67d924)}, + {UINT64_C(0xd0cf4b50cfe20765), UINT64_C(0xfff4b4e3f741cf6d)}, + {UINT64_C(0x82818f1281ed449f), UINT64_C(0xbff8f10e7a8921a5)}, + {UINT64_C(0xa321f2d7226895c7), UINT64_C(0xaff72d52192b6a0e)}, + {UINT64_C(0xcbea6f8ceb02bb39), UINT64_C(0x9bf4f8a69f764491)}, + {UINT64_C(0xfee50b7025c36a08), UINT64_C(0x02f236d04753d5b5)}, + {UINT64_C(0x9f4f2726179a2245), UINT64_C(0x01d762422c946591)}, + {UINT64_C(0xc722f0ef9d80aad6), UINT64_C(0x424d3ad2b7b97ef6)}, + {UINT64_C(0xf8ebad2b84e0d58b), UINT64_C(0xd2e0898765a7deb3)}, + {UINT64_C(0x9b934c3b330c8577), UINT64_C(0x63cc55f49f88eb30)}, + {UINT64_C(0xc2781f49ffcfa6d5), UINT64_C(0x3cbf6b71c76b25fc)}, + {UINT64_C(0xf316271c7fc3908a), UINT64_C(0x8bef464e3945ef7b)}, + {UINT64_C(0x97edd871cfda3a56), UINT64_C(0x97758bf0e3cbb5ad)}, + {UINT64_C(0xbde94e8e43d0c8ec), UINT64_C(0x3d52eeed1cbea318)}, + {UINT64_C(0xed63a231d4c4fb27), UINT64_C(0x4ca7aaa863ee4bde)}, + {UINT64_C(0x945e455f24fb1cf8), UINT64_C(0x8fe8caa93e74ef6b)}, + {UINT64_C(0xb975d6b6ee39e436), UINT64_C(0xb3e2fd538e122b45)}, + {UINT64_C(0xe7d34c64a9c85d44), UINT64_C(0x60dbbca87196b617)}, + {UINT64_C(0x90e40fbeea1d3a4a), UINT64_C(0xbc8955e946fe31ce)}, + {UINT64_C(0xb51d13aea4a488dd), UINT64_C(0x6babab6398bdbe42)}, + {UINT64_C(0xe264589a4dcdab14), UINT64_C(0xc696963c7eed2dd2)}, + {UINT64_C(0x8d7eb76070a08aec), UINT64_C(0xfc1e1de5cf543ca3)}, + {UINT64_C(0xb0de65388cc8ada8), UINT64_C(0x3b25a55f43294bcc)}, + {UINT64_C(0xdd15fe86affad912), UINT64_C(0x49ef0eb713f39ebf)}, + {UINT64_C(0x8a2dbf142dfcc7ab), UINT64_C(0x6e3569326c784338)}, + {UINT64_C(0xacb92ed9397bf996), UINT64_C(0x49c2c37f07965405)}, + {UINT64_C(0xd7e77a8f87daf7fb), UINT64_C(0xdc33745ec97be907)}, + {UINT64_C(0x86f0ac99b4e8dafd), UINT64_C(0x69a028bb3ded71a4)}, + {UINT64_C(0xa8acd7c0222311bc), UINT64_C(0xc40832ea0d68ce0d)}, + {UINT64_C(0xd2d80db02aabd62b), UINT64_C(0xf50a3fa490c30191)}, + {UINT64_C(0x83c7088e1aab65db), UINT64_C(0x792667c6da79e0fb)}, + {UINT64_C(0xa4b8cab1a1563f52), UINT64_C(0x577001b891185939)}, + {UINT64_C(0xcde6fd5e09abcf26), UINT64_C(0xed4c0226b55e6f87)}, + {UINT64_C(0x80b05e5ac60b6178), UINT64_C(0x544f8158315b05b5)}, + {UINT64_C(0xa0dc75f1778e39d6), UINT64_C(0x696361ae3db1c722)}, + {UINT64_C(0xc913936dd571c84c), UINT64_C(0x03bc3a19cd1e38ea)}, + {UINT64_C(0xfb5878494ace3a5f), UINT64_C(0x04ab48a04065c724)}, + {UINT64_C(0x9d174b2dcec0e47b), UINT64_C(0x62eb0d64283f9c77)}, + {UINT64_C(0xc45d1df942711d9a), UINT64_C(0x3ba5d0bd324f8395)}, + {UINT64_C(0xf5746577930d6500), UINT64_C(0xca8f44ec7ee3647a)}, + {UINT64_C(0x9968bf6abbe85f20), UINT64_C(0x7e998b13cf4e1ecc)}, + {UINT64_C(0xbfc2ef456ae276e8), UINT64_C(0x9e3fedd8c321a67f)}, + {UINT64_C(0xefb3ab16c59b14a2), UINT64_C(0xc5cfe94ef3ea101f)}, + {UINT64_C(0x95d04aee3b80ece5), UINT64_C(0xbba1f1d158724a13)}, + {UINT64_C(0xbb445da9ca61281f), UINT64_C(0x2a8a6e45ae8edc98)}, + {UINT64_C(0xea1575143cf97226), UINT64_C(0xf52d09d71a3293be)}, + {UINT64_C(0x924d692ca61be758), UINT64_C(0x593c2626705f9c57)}, + {UINT64_C(0xb6e0c377cfa2e12e), UINT64_C(0x6f8b2fb00c77836d)}, + {UINT64_C(0xe498f455c38b997a), UINT64_C(0x0b6dfb9c0f956448)}, + {UINT64_C(0x8edf98b59a373fec), UINT64_C(0x4724bd4189bd5ead)}, + {UINT64_C(0xb2977ee300c50fe7), UINT64_C(0x58edec91ec2cb658)}, + {UINT64_C(0xdf3d5e9bc0f653e1), UINT64_C(0x2f2967b66737e3ee)}, + {UINT64_C(0x8b865b215899f46c), UINT64_C(0xbd79e0d20082ee75)}, + {UINT64_C(0xae67f1e9aec07187), UINT64_C(0xecd8590680a3aa12)}, + {UINT64_C(0xda01ee641a708de9), UINT64_C(0xe80e6f4820cc9496)}, + {UINT64_C(0x884134fe908658b2), UINT64_C(0x3109058d147fdcde)}, + {UINT64_C(0xaa51823e34a7eede), UINT64_C(0xbd4b46f0599fd416)}, + {UINT64_C(0xd4e5e2cdc1d1ea96), UINT64_C(0x6c9e18ac7007c91b)}, + {UINT64_C(0x850fadc09923329e), UINT64_C(0x03e2cf6bc604ddb1)}, + {UINT64_C(0xa6539930bf6bff45), UINT64_C(0x84db8346b786151d)}, + {UINT64_C(0xcfe87f7cef46ff16), UINT64_C(0xe612641865679a64)}, + {UINT64_C(0x81f14fae158c5f6e), UINT64_C(0x4fcb7e8f3f60c07f)}, + {UINT64_C(0xa26da3999aef7749), UINT64_C(0xe3be5e330f38f09e)}, + {UINT64_C(0xcb090c8001ab551c), UINT64_C(0x5cadf5bfd3072cc6)}, + {UINT64_C(0xfdcb4fa002162a63), UINT64_C(0x73d9732fc7c8f7f7)}, + {UINT64_C(0x9e9f11c4014dda7e), UINT64_C(0x2867e7fddcdd9afb)}, + {UINT64_C(0xc646d63501a1511d), UINT64_C(0xb281e1fd541501b9)}, + {UINT64_C(0xf7d88bc24209a565), UINT64_C(0x1f225a7ca91a4227)}, + {UINT64_C(0x9ae757596946075f), UINT64_C(0x3375788de9b06959)}, + {UINT64_C(0xc1a12d2fc3978937), UINT64_C(0x0052d6b1641c83af)}, + {UINT64_C(0xf209787bb47d6b84), UINT64_C(0xc0678c5dbd23a49b)}, + {UINT64_C(0x9745eb4d50ce6332), UINT64_C(0xf840b7ba963646e1)}, + {UINT64_C(0xbd176620a501fbff), UINT64_C(0xb650e5a93bc3d899)}, + {UINT64_C(0xec5d3fa8ce427aff), UINT64_C(0xa3e51f138ab4cebf)}, + {UINT64_C(0x93ba47c980e98cdf), UINT64_C(0xc66f336c36b10138)}, + {UINT64_C(0xb8a8d9bbe123f017), UINT64_C(0xb80b0047445d4185)}, + {UINT64_C(0xe6d3102ad96cec1d), UINT64_C(0xa60dc059157491e6)}, + {UINT64_C(0x9043ea1ac7e41392), UINT64_C(0x87c89837ad68db30)}, + {UINT64_C(0xb454e4a179dd1877), UINT64_C(0x29babe4598c311fc)}, + {UINT64_C(0xe16a1dc9d8545e94), UINT64_C(0xf4296dd6fef3d67b)}, + {UINT64_C(0x8ce2529e2734bb1d), UINT64_C(0x1899e4a65f58660d)}, + {UINT64_C(0xb01ae745b101e9e4), UINT64_C(0x5ec05dcff72e7f90)}, + {UINT64_C(0xdc21a1171d42645d), UINT64_C(0x76707543f4fa1f74)}, + {UINT64_C(0x899504ae72497eba), UINT64_C(0x6a06494a791c53a9)}, + {UINT64_C(0xabfa45da0edbde69), UINT64_C(0x0487db9d17636893)}, + {UINT64_C(0xd6f8d7509292d603), UINT64_C(0x45a9d2845d3c42b7)}, + {UINT64_C(0x865b86925b9bc5c2), UINT64_C(0x0b8a2392ba45a9b3)}, + {UINT64_C(0xa7f26836f282b732), UINT64_C(0x8e6cac7768d7141f)}, + {UINT64_C(0xd1ef0244af2364ff), 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{UINT64_C(0xe912b9d1478ceb17), UINT64_C(0x7a37cd5601aab85e)}, + {UINT64_C(0x91abb422ccb812ee), UINT64_C(0xac62e055c10ab33b)}, + {UINT64_C(0xb616a12b7fe617aa), UINT64_C(0x577b986b314d600a)}, + {UINT64_C(0xe39c49765fdf9d94), UINT64_C(0xed5a7e85fda0b80c)}, + {UINT64_C(0x8e41ade9fbebc27d), UINT64_C(0x14588f13be847308)}, + {UINT64_C(0xb1d219647ae6b31c), UINT64_C(0x596eb2d8ae258fc9)}, + {UINT64_C(0xde469fbd99a05fe3), UINT64_C(0x6fca5f8ed9aef3bc)}, + {UINT64_C(0x8aec23d680043bee), UINT64_C(0x25de7bb9480d5855)}, + {UINT64_C(0xada72ccc20054ae9), UINT64_C(0xaf561aa79a10ae6b)}, + {UINT64_C(0xd910f7ff28069da4), UINT64_C(0x1b2ba1518094da05)}, + {UINT64_C(0x87aa9aff79042286), UINT64_C(0x90fb44d2f05d0843)}, + {UINT64_C(0xa99541bf57452b28), UINT64_C(0x353a1607ac744a54)}, + {UINT64_C(0xd3fa922f2d1675f2), UINT64_C(0x42889b8997915ce9)}, + {UINT64_C(0x847c9b5d7c2e09b7), UINT64_C(0x69956135febada12)}, + {UINT64_C(0xa59bc234db398c25), UINT64_C(0x43fab9837e699096)}, + {UINT64_C(0xcf02b2c21207ef2e), UINT64_C(0x94f967e45e03f4bc)}, + {UINT64_C(0x8161afb94b44f57d), UINT64_C(0x1d1be0eebac278f6)}, + {UINT64_C(0xa1ba1ba79e1632dc), UINT64_C(0x6462d92a69731733)}, + {UINT64_C(0xca28a291859bbf93), UINT64_C(0x7d7b8f7503cfdcff)}, + {UINT64_C(0xfcb2cb35e702af78), UINT64_C(0x5cda735244c3d43f)}, + {UINT64_C(0x9defbf01b061adab), UINT64_C(0x3a0888136afa64a8)}, + {UINT64_C(0xc56baec21c7a1916), UINT64_C(0x088aaa1845b8fdd1)}, + {UINT64_C(0xf6c69a72a3989f5b), UINT64_C(0x8aad549e57273d46)}, + {UINT64_C(0x9a3c2087a63f6399), UINT64_C(0x36ac54e2f678864c)}, + {UINT64_C(0xc0cb28a98fcf3c7f), UINT64_C(0x84576a1bb416a7de)}, + {UINT64_C(0xf0fdf2d3f3c30b9f), UINT64_C(0x656d44a2a11c51d6)}, + {UINT64_C(0x969eb7c47859e743), UINT64_C(0x9f644ae5a4b1b326)}, + {UINT64_C(0xbc4665b596706114), UINT64_C(0x873d5d9f0dde1fef)}, + {UINT64_C(0xeb57ff22fc0c7959), UINT64_C(0xa90cb506d155a7eb)}, + {UINT64_C(0x9316ff75dd87cbd8), UINT64_C(0x09a7f12442d588f3)}, + {UINT64_C(0xb7dcbf5354e9bece), UINT64_C(0x0c11ed6d538aeb30)}, + {UINT64_C(0xe5d3ef282a242e81), UINT64_C(0x8f1668c8a86da5fb)}, + {UINT64_C(0x8fa475791a569d10), UINT64_C(0xf96e017d694487bd)}, + {UINT64_C(0xb38d92d760ec4455), UINT64_C(0x37c981dcc395a9ad)}, + {UINT64_C(0xe070f78d3927556a), UINT64_C(0x85bbe253f47b1418)}, + {UINT64_C(0x8c469ab843b89562), UINT64_C(0x93956d7478ccec8f)}, + {UINT64_C(0xaf58416654a6babb), UINT64_C(0x387ac8d1970027b3)}, + {UINT64_C(0xdb2e51bfe9d0696a), UINT64_C(0x06997b05fcc0319f)}, + {UINT64_C(0x88fcf317f22241e2), UINT64_C(0x441fece3bdf81f04)}, + {UINT64_C(0xab3c2fddeeaad25a), UINT64_C(0xd527e81cad7626c4)}, + {UINT64_C(0xd60b3bd56a5586f1), UINT64_C(0x8a71e223d8d3b075)}, + {UINT64_C(0x85c7056562757456), UINT64_C(0xf6872d5667844e4a)}, + {UINT64_C(0xa738c6bebb12d16c), UINT64_C(0xb428f8ac016561dc)}, + {UINT64_C(0xd106f86e69d785c7), UINT64_C(0xe13336d701beba53)}, + {UINT64_C(0x82a45b450226b39c), UINT64_C(0xecc0024661173474)}, + {UINT64_C(0xa34d721642b06084), UINT64_C(0x27f002d7f95d0191)}, + {UINT64_C(0xcc20ce9bd35c78a5), UINT64_C(0x31ec038df7b441f5)}, + {UINT64_C(0xff290242c83396ce), UINT64_C(0x7e67047175a15272)}, + {UINT64_C(0x9f79a169bd203e41), UINT64_C(0x0f0062c6e984d387)}, + {UINT64_C(0xc75809c42c684dd1), UINT64_C(0x52c07b78a3e60869)}, + {UINT64_C(0xf92e0c3537826145), UINT64_C(0xa7709a56ccdf8a83)}, + {UINT64_C(0x9bbcc7a142b17ccb), UINT64_C(0x88a66076400bb692)}, + {UINT64_C(0xc2abf989935ddbfe), UINT64_C(0x6acff893d00ea436)}, + {UINT64_C(0xf356f7ebf83552fe), UINT64_C(0x0583f6b8c4124d44)}, + {UINT64_C(0x98165af37b2153de), UINT64_C(0xc3727a337a8b704b)}, + {UINT64_C(0xbe1bf1b059e9a8d6), UINT64_C(0x744f18c0592e4c5d)}, + {UINT64_C(0xeda2ee1c7064130c), UINT64_C(0x1162def06f79df74)}, + {UINT64_C(0x9485d4d1c63e8be7), UINT64_C(0x8addcb5645ac2ba9)}, + {UINT64_C(0xb9a74a0637ce2ee1), UINT64_C(0x6d953e2bd7173693)}, + {UINT64_C(0xe8111c87c5c1ba99), UINT64_C(0xc8fa8db6ccdd0438)}, + {UINT64_C(0x910ab1d4db9914a0), UINT64_C(0x1d9c9892400a22a3)}, + {UINT64_C(0xb54d5e4a127f59c8), UINT64_C(0x2503beb6d00cab4c)}, + {UINT64_C(0xe2a0b5dc971f303a), UINT64_C(0x2e44ae64840fd61e)}, + {UINT64_C(0x8da471a9de737e24), UINT64_C(0x5ceaecfed289e5d3)}, + {UINT64_C(0xb10d8e1456105dad), UINT64_C(0x7425a83e872c5f48)}, + {UINT64_C(0xdd50f1996b947518), UINT64_C(0xd12f124e28f7771a)}, + {UINT64_C(0x8a5296ffe33cc92f), UINT64_C(0x82bd6b70d99aaa70)}, + {UINT64_C(0xace73cbfdc0bfb7b), UINT64_C(0x636cc64d1001550c)}, + {UINT64_C(0xd8210befd30efa5a), UINT64_C(0x3c47f7e05401aa4f)}, + {UINT64_C(0x8714a775e3e95c78), UINT64_C(0x65acfaec34810a72)}, + {UINT64_C(0xa8d9d1535ce3b396), UINT64_C(0x7f1839a741a14d0e)}, + {UINT64_C(0xd31045a8341ca07c), UINT64_C(0x1ede48111209a051)}, + {UINT64_C(0x83ea2b892091e44d), UINT64_C(0x934aed0aab460433)}, + {UINT64_C(0xa4e4b66b68b65d60), UINT64_C(0xf81da84d56178540)}, + {UINT64_C(0xce1de40642e3f4b9), UINT64_C(0x36251260ab9d668f)}, + {UINT64_C(0x80d2ae83e9ce78f3), UINT64_C(0xc1d72b7c6b42601a)}, + {UINT64_C(0xa1075a24e4421730), UINT64_C(0xb24cf65b8612f820)}, + {UINT64_C(0xc94930ae1d529cfc), UINT64_C(0xdee033f26797b628)}, + {UINT64_C(0xfb9b7cd9a4a7443c), UINT64_C(0x169840ef017da3b2)}, + {UINT64_C(0x9d412e0806e88aa5), UINT64_C(0x8e1f289560ee864f)}, + {UINT64_C(0xc491798a08a2ad4e), UINT64_C(0xf1a6f2bab92a27e3)}, + {UINT64_C(0xf5b5d7ec8acb58a2), UINT64_C(0xae10af696774b1dc)}, + {UINT64_C(0x9991a6f3d6bf1765), UINT64_C(0xacca6da1e0a8ef2a)}, + {UINT64_C(0xbff610b0cc6edd3f), UINT64_C(0x17fd090a58d32af4)}, + {UINT64_C(0xeff394dcff8a948e), UINT64_C(0xddfc4b4cef07f5b1)}, + {UINT64_C(0x95f83d0a1fb69cd9), UINT64_C(0x4abdaf101564f98f)}, + {UINT64_C(0xbb764c4ca7a4440f), UINT64_C(0x9d6d1ad41abe37f2)}, + {UINT64_C(0xea53df5fd18d5513), UINT64_C(0x84c86189216dc5ee)}, + {UINT64_C(0x92746b9be2f8552c), UINT64_C(0x32fd3cf5b4e49bb5)}, + {UINT64_C(0xb7118682dbb66a77), UINT64_C(0x3fbc8c33221dc2a2)}, + {UINT64_C(0xe4d5e82392a40515), UINT64_C(0x0fabaf3feaa5334b)}, + {UINT64_C(0x8f05b1163ba6832d), UINT64_C(0x29cb4d87f2a7400f)}, + {UINT64_C(0xb2c71d5bca9023f8), UINT64_C(0x743e20e9ef511013)}, + {UINT64_C(0xdf78e4b2bd342cf6), UINT64_C(0x914da9246b255417)}, + {UINT64_C(0x8bab8eefb6409c1a), UINT64_C(0x1ad089b6c2f7548f)}, + {UINT64_C(0xae9672aba3d0c320), UINT64_C(0xa184ac2473b529b2)}, + {UINT64_C(0xda3c0f568cc4f3e8), UINT64_C(0xc9e5d72d90a2741f)}, + {UINT64_C(0x8865899617fb1871), UINT64_C(0x7e2fa67c7a658893)}, + {UINT64_C(0xaa7eebfb9df9de8d), UINT64_C(0xddbb901b98feeab8)}, + {UINT64_C(0xd51ea6fa85785631), UINT64_C(0x552a74227f3ea566)}, + {UINT64_C(0x8533285c936b35de), UINT64_C(0xd53a88958f872760)}, + {UINT64_C(0xa67ff273b8460356), UINT64_C(0x8a892abaf368f138)}, + {UINT64_C(0xd01fef10a657842c), UINT64_C(0x2d2b7569b0432d86)}, + {UINT64_C(0x8213f56a67f6b29b), UINT64_C(0x9c3b29620e29fc74)}, + {UINT64_C(0xa298f2c501f45f42), UINT64_C(0x8349f3ba91b47b90)}, + {UINT64_C(0xcb3f2f7642717713), UINT64_C(0x241c70a936219a74)}, + {UINT64_C(0xfe0efb53d30dd4d7), UINT64_C(0xed238cd383aa0111)}, + {UINT64_C(0x9ec95d1463e8a506), UINT64_C(0xf4363804324a40ab)}, + {UINT64_C(0xc67bb4597ce2ce48), UINT64_C(0xb143c6053edcd0d6)}, + {UINT64_C(0xf81aa16fdc1b81da), UINT64_C(0xdd94b7868e94050b)}, + {UINT64_C(0x9b10a4e5e9913128), UINT64_C(0xca7cf2b4191c8327)}, + {UINT64_C(0xc1d4ce1f63f57d72), UINT64_C(0xfd1c2f611f63a3f1)}, + {UINT64_C(0xf24a01a73cf2dccf), UINT64_C(0xbc633b39673c8ced)}, + {UINT64_C(0x976e41088617ca01), UINT64_C(0xd5be0503e085d814)}, + {UINT64_C(0xbd49d14aa79dbc82), UINT64_C(0x4b2d8644d8a74e19)}, + {UINT64_C(0xec9c459d51852ba2), UINT64_C(0xddf8e7d60ed1219f)}, + {UINT64_C(0x93e1ab8252f33b45), UINT64_C(0xcabb90e5c942b504)}, + {UINT64_C(0xb8da1662e7b00a17), UINT64_C(0x3d6a751f3b936244)}, + {UINT64_C(0xe7109bfba19c0c9d), UINT64_C(0x0cc512670a783ad5)}, + {UINT64_C(0x906a617d450187e2), UINT64_C(0x27fb2b80668b24c6)}, + {UINT64_C(0xb484f9dc9641e9da), UINT64_C(0xb1f9f660802dedf7)}, + {UINT64_C(0xe1a63853bbd26451), UINT64_C(0x5e7873f8a0396974)}, + {UINT64_C(0x8d07e33455637eb2), UINT64_C(0xdb0b487b6423e1e9)}, + {UINT64_C(0xb049dc016abc5e5f), UINT64_C(0x91ce1a9a3d2cda63)}, + {UINT64_C(0xdc5c5301c56b75f7), UINT64_C(0x7641a140cc7810fc)}, + {UINT64_C(0x89b9b3e11b6329ba), UINT64_C(0xa9e904c87fcb0a9e)}, + {UINT64_C(0xac2820d9623bf429), UINT64_C(0x546345fa9fbdcd45)}, + {UINT64_C(0xd732290fbacaf133), UINT64_C(0xa97c177947ad4096)}, + {UINT64_C(0x867f59a9d4bed6c0), UINT64_C(0x49ed8eabcccc485e)}, + {UINT64_C(0xa81f301449ee8c70), UINT64_C(0x5c68f256bfff5a75)}, + {UINT64_C(0xd226fc195c6a2f8c), UINT64_C(0x73832eec6fff3112)}, + {UINT64_C(0x83585d8fd9c25db7), UINT64_C(0xc831fd53c5ff7eac)}, + {UINT64_C(0xa42e74f3d032f525), UINT64_C(0xba3e7ca8b77f5e56)}, + {UINT64_C(0xcd3a1230c43fb26f), UINT64_C(0x28ce1bd2e55f35ec)}, + {UINT64_C(0x80444b5e7aa7cf85), UINT64_C(0x7980d163cf5b81b4)}, + {UINT64_C(0xa0555e361951c366), UINT64_C(0xd7e105bcc3326220)}, + {UINT64_C(0xc86ab5c39fa63440), UINT64_C(0x8dd9472bf3fefaa8)}, + {UINT64_C(0xfa856334878fc150), UINT64_C(0xb14f98f6f0feb952)}, + {UINT64_C(0x9c935e00d4b9d8d2), UINT64_C(0x6ed1bf9a569f33d4)}, + {UINT64_C(0xc3b8358109e84f07), UINT64_C(0x0a862f80ec4700c9)}, + {UINT64_C(0xf4a642e14c6262c8), UINT64_C(0xcd27bb612758c0fb)}, + {UINT64_C(0x98e7e9cccfbd7dbd), UINT64_C(0x8038d51cb897789d)}, + {UINT64_C(0xbf21e44003acdd2c), UINT64_C(0xe0470a63e6bd56c4)}, + {UINT64_C(0xeeea5d5004981478), UINT64_C(0x1858ccfce06cac75)}, + {UINT64_C(0x95527a5202df0ccb), UINT64_C(0x0f37801e0c43ebc9)}, + {UINT64_C(0xbaa718e68396cffd), UINT64_C(0xd30560258f54e6bb)}, + {UINT64_C(0xe950df20247c83fd), UINT64_C(0x47c6b82ef32a206a)}, + {UINT64_C(0x91d28b7416cdd27e), UINT64_C(0x4cdc331d57fa5442)}, + {UINT64_C(0xb6472e511c81471d), UINT64_C(0xe0133fe4adf8e953)}, + {UINT64_C(0xe3d8f9e563a198e5), UINT64_C(0x58180fddd97723a7)}, + {UINT64_C(0x8e679c2f5e44ff8f), UINT64_C(0x570f09eaa7ea7649)}, + {UINT64_C(0xb201833b35d63f73), UINT64_C(0x2cd2cc6551e513db)}, + {UINT64_C(0xde81e40a034bcf4f), UINT64_C(0xf8077f7ea65e58d2)}, + {UINT64_C(0x8b112e86420f6191), UINT64_C(0xfb04afaf27faf783)}, + {UINT64_C(0xadd57a27d29339f6), UINT64_C(0x79c5db9af1f9b564)}, + {UINT64_C(0xd94ad8b1c7380874), UINT64_C(0x18375281ae7822bd)}, + {UINT64_C(0x87cec76f1c830548), UINT64_C(0x8f2293910d0b15b6)}, + {UINT64_C(0xa9c2794ae3a3c69a), UINT64_C(0xb2eb3875504ddb23)}, + {UINT64_C(0xd433179d9c8cb841), UINT64_C(0x5fa60692a46151ec)}, + {UINT64_C(0x849feec281d7f328), UINT64_C(0xdbc7c41ba6bcd334)}, + {UINT64_C(0xa5c7ea73224deff3), UINT64_C(0x12b9b522906c0801)}, + {UINT64_C(0xcf39e50feae16bef), UINT64_C(0xd768226b34870a01)}, + {UINT64_C(0x81842f29f2cce375), UINT64_C(0xe6a1158300d46641)}, + {UINT64_C(0xa1e53af46f801c53), UINT64_C(0x60495ae3c1097fd1)}, + {UINT64_C(0xca5e89b18b602368), UINT64_C(0x385bb19cb14bdfc5)}, + {UINT64_C(0xfcf62c1dee382c42), UINT64_C(0x46729e03dd9ed7b6)}, + {UINT64_C(0x9e19db92b4e31ba9), UINT64_C(0x6c07a2c26a8346d2)}, + {UINT64_C(0xc5a05277621be293), UINT64_C(0xc7098b7305241886)}, + {UINT64_C(0xf70867153aa2db38), UINT64_C(0xb8cbee4fc66d1ea8)}}; + + template + struct cache_holder; + + template <> + struct cache_holder { + uint128 get_cache(int k) const { + assert(k >= min_k && k <= max_k); + return cache[k - min_k]; } - uint16_t p = 1; - for (size_t i = 0; i < pow5_table_size; ++i) { - pow5_table[i] = p; - p *= 5; - } - } - - uint64_t get_cache(int k) const { - assert(k >= min_k && k <= max_k); - - // Compute the base index. - // Supposed to compute (k - min_k) / compression_ratio. - static_assert(max_k - min_k <= 89 && compression_ratio == 13, ""); - static_assert(max_k - min_k <= INT_MAX, ""); - auto const cache_index = int(uint16_t(int(k - min_k) * int16_t(79)) >> 10); - auto const kb = int(cache_index * compression_ratio + min_k); - auto const offset = int(k - kb); - - // Get the base cache. - auto const base_cache = cache[cache_index]; + }; - if (offset == 0) { - return base_cache; - } - else { - // Compute the required amount of bit-shift. - auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); - assert(alpha > 0 && alpha < 64); - - // Try to recover the real cache. - auto const pow5 = offset >= 7 - ? uint32_t(uint32_t(pow5_table[6]) * pow5_table[offset - 6]) - : uint32_t(pow5_table[offset]); - auto mul_result = umul128(base_cache, pow5); - auto const recovered_cache = uint64_t( - (((mul_result.high << int(64 - alpha)) | (mul_result.low >> alpha)) + 1) & - UINT64_C(0xffffffffffffffff)); - assert(recovered_cache != 0); - - return recovered_cache; - } - } - }; + template <> + struct cache_holder { + static constexpr int compression_ratio = 27; + static constexpr int compressed_table_size = + (max_k - min_k + compression_ratio) / compression_ratio; + static constexpr int pow5_table_size = compression_ratio; - template <> - struct cache_holder { - using format = float_format; + uint128 cache[compressed_table_size]{}; + uint64_t pow5_table[pow5_table_size]{}; - uint128 get_cache(int k) const { - assert(k >= format::min_k && k <= format::max_k); - return cache64[k - format::min_k]; - } - }; - - template <> - struct cache_holder { - using format = float_format; - static constexpr int cache_bits = format::cache_bits; - static constexpr int min_k = format::min_k; - static constexpr int max_k = format::max_k; - static constexpr int compression_ratio = 27; - static constexpr int compressed_table_size = - (max_k - min_k + compression_ratio) / compression_ratio; - static constexpr int pow5_table_size = compression_ratio; - - uint128 cache[compressed_table_size]{}; - uint64_t pow5_table[pow5_table_size]{}; - - constexpr cache_holder() { - for (size_t i = 0; i < compressed_table_size; ++i) { - cache[i] = cache64[i * compression_ratio]; - } - uint64_t p = 1; - for (size_t i = 0; i < pow5_table_size; ++i) { - pow5_table[i] = p; - p *= 5; + constexpr cache_holder() { + for (size_t i = 0; i < compressed_table_size; ++i) { + cache[i] = float_format::cache[i * compression_ratio]; + } + uint64_t p = 1; + for (size_t i = 0; i < pow5_table_size; ++i) { + pow5_table[i] = p; + p *= 5; + } } - } - uint128 get_cache(int k) const { - assert(k >= min_k && k <= max_k); + uint128 get_cache(int k) const { + assert(k >= min_k && k <= max_k); - // Compute the base index. - // Supposed to compute (k - min_k) / compression_ratio. - static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); - static_assert(max_k - min_k <= INT_MAX, ""); - auto const cache_index = int(uint32_t(int(k - min_k) * int32_t(607)) >> 14); - auto const kb = int(cache_index * compression_ratio + min_k); - auto const offset = int(k - kb); + // Compute the base index. + // Supposed to compute (k - min_k) / compression_ratio. + static_assert(max_k - min_k <= 619 && compression_ratio == 27, ""); + static_assert(max_k - min_k <= INT_MAX, ""); + auto const cache_index = int(uint32_t(int(k - min_k) * int32_t(607)) >> 14); + auto const kb = int(cache_index * compression_ratio + min_k); + auto const offset = int(k - kb); - // Get the base cache. - auto const base_cache = cache[cache_index]; + // Get the base cache. + auto const base_cache = cache[cache_index]; - if (offset == 0) { - return base_cache; - } - else { - // Compute the required amount of bit-shift. - auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); - assert(alpha > 0 && alpha < 64); + if (offset == 0) { + return base_cache; + } + else { + // Compute the required amount of bit-shift. + auto const alpha = int(floor_log2_pow10(k) - floor_log2_pow10(kb) - offset); + assert(alpha > 0 && alpha < 64); - // Try to recover the real cache. - auto const pow5 = pow5_table[offset]; - auto recovered_cache = umul128(base_cache.high, pow5); - auto const middle_low = umul128(base_cache.low, pow5); + // Try to recover the real cache. + auto const pow5 = pow5_table[offset]; + auto recovered_cache = umul128(base_cache.high, pow5); + auto const middle_low = umul128(base_cache.low, pow5); - recovered_cache += middle_low.high; + recovered_cache += middle_low.high; - auto const high_to_middle = - uint64_t((recovered_cache.high << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); - auto const middle_to_low = - uint64_t((recovered_cache.low << (64 - alpha)) & UINT64_C(0xffffffffffffffff)); + auto const high_to_middle = uint64_t((recovered_cache.high << (64 - alpha)) & + UINT64_C(0xffffffffffffffff)); + auto const middle_to_low = uint64_t((recovered_cache.low << (64 - alpha)) & + UINT64_C(0xffffffffffffffff)); - recovered_cache = {(recovered_cache.low >> alpha) | high_to_middle, - ((middle_low.low >> alpha) | middle_to_low)}; + recovered_cache = {(recovered_cache.low >> alpha) | high_to_middle, + ((middle_low.low >> alpha) | middle_to_low)}; - assert(recovered_cache.low != UINT64_C(0xffffffffffffffff)); - recovered_cache = {recovered_cache.high, uint64_t(recovered_cache.low + 1)}; + assert(recovered_cache.low != UINT64_C(0xffffffffffffffff)); + recovered_cache = {recovered_cache.high, uint64_t(recovered_cache.low + 1)}; - return recovered_cache; + return recovered_cache; + } } - } + }; }; template @@ -1298,7 +1299,7 @@ namespace simple_dragonbox { static_assert(carrier_bits >= significand_bits + 2 + floor_log2_pow10(kappa + 1)); static_assert(min_k >= format::min_k && max_k <= format::max_k); - static constexpr cache_holder cache_; + static constexpr typename format::template cache_holder cache_; template static bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { From 9f6d7684fa24a1e698b8448099cba2f6c64d173e Mon Sep 17 00:00:00 2001 From: Toby Bell Date: Mon, 26 Aug 2024 23:19:49 -0700 Subject: [PATCH 13/17] Preserve more complex static assert from original implementation --- subproject/simple/simple_dragonbox.h | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 036fd3d..5f78335 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -8,6 +8,7 @@ #include #include #include +#include namespace simple_dragonbox { namespace detail { @@ -1229,8 +1230,11 @@ namespace simple_dragonbox { dont_care, }; - static_assert(sizeof(float) == 4); - static_assert(sizeof(double) == 8); + template + static constexpr bool valid_float = std::numeric_limits::is_iec559 && + std::numeric_limits::radix == 2 && sizeof(T) == Size; + static_assert(valid_float, "simple_dragonbox: float may not be IEEE 754 binary32"); + static_assert(valid_float, "simple_dragonbox: double may not be IEEE 754 binary64"); constexpr void reverse(char* begin, char* end) { while (begin < --end) { From 3ba3d7bead751226e7076c41cb464013a3567d89 Mon Sep 17 00:00:00 2001 From: Junekey Jeon <33922675+jk-jeon@users.noreply.github.com> Date: Wed, 28 Aug 2024 13:12:03 -0700 Subject: [PATCH 14/17] Update README.md Fix a typo, some clarification, etc. --- subproject/simple/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/subproject/simple/README.md b/subproject/simple/README.md index 07c524e..b1d4f85 100644 --- a/subproject/simple/README.md +++ b/subproject/simple/README.md @@ -3,7 +3,7 @@ This is a simplified implementation of the algorithm, that closely follows the one in `include/dragonbox/dragonbox.h`, but aims to be shorter overall, use less C++ template indirection, and offer less flexibility and performance for the -sake of simpliciy. +sake of simplicity. Simplifications over the implementation in `include/dragonbox/dragonbox.h` are made based primarily on the following assumptions: @@ -14,7 +14,7 @@ made based primarily on the following assumptions: implementation). - No need to support the `fast` digit-generation policy (always uses `compact`). - `if constexpr` is available (C++17). -- `float` and `double` use IEEE-754 32-bit and 64-bit representations, +- `float` and `double` use [IEEE-754 binary32](https://en.wikipedia.org/wiki/Single-precision_floating-point_format) and [IEEE-754 binary64](https://en.wikipedia.org/wiki/Double-precision_floating-point_format) representations, respectively. - A modern compiler and standard library are available. From 1c9c8af9320b051f6f53b959122f1889146ac9ea Mon Sep 17 00:00:00 2001 From: Junekey Jeon <33922675+jk-jeon@users.noreply.github.com> Date: Wed, 28 Aug 2024 13:25:14 -0700 Subject: [PATCH 15/17] Add more constexpr into simple_dragonbox.h --- subproject/simple/simple_dragonbox.h | 89 ++++++++++++++-------------- 1 file changed, 43 insertions(+), 46 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index 5f78335..f800776 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -201,7 +201,7 @@ namespace simple_dragonbox { static constexpr int min_k = -31; static constexpr int max_k = 46; - static void remove_trailing_zeros(uint32_t& significand, int& exponent) { + static constexpr void remove_trailing_zeros(uint32_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. // The idea of branchless search below is by reddit users r/pigeon768 and // r/TheoreticalDumbass. @@ -224,17 +224,17 @@ namespace simple_dragonbox { exponent += s; } - static compute_mul_result compute_mul(uint32_t u, uint64_t cache) { + static constexpr compute_mul_result compute_mul(uint32_t u, uint64_t cache) { auto const r = umul96_upper64(u, cache); return {uint32_t(r >> 32), uint32_t(r) == 0}; } - static uint32_t compute_delta(uint64_t cache, int beta) { + static constexpr uint32_t compute_delta(uint64_t cache, int beta) { return uint32_t(cache >> (cache_bits - 1 - beta)); } - static compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, - int beta) { + static constexpr compute_mul_parity_result compute_mul_parity(uint32_t two_f, uint64_t cache, + int beta) { assert(beta >= 1); assert(beta <= 32); auto const r = umul96_lower64(two_f, cache); @@ -242,22 +242,22 @@ namespace simple_dragonbox { (UINT32_C(0xffffffff) & (r >> (32 - beta))) == 0}; } - static uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + static constexpr uint32_t compute_left_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { return (cache - (cache >> (significand_bits + 2))) >> (cache_bits - significand_bits - 1 - beta); } - static uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { + static constexpr uint32_t compute_right_endpoint_for_shorter_interval_case(uint64_t cache, int beta) { return (cache + (cache >> (significand_bits + 1))) >> (cache_bits - significand_bits - 1 - beta); } - static uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { + static constexpr uint32_t compute_round_up_for_shorter_interval_case(uint64_t cache, int beta) { return (uint32_t(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2; } template - static uint32_t divide_by_pow10(uint32_t n) { + static constexpr uint32_t divide_by_pow10(uint32_t n) { static_assert(N >= 0, ""); // Specialize for 32-bit division by 10. @@ -353,7 +353,7 @@ namespace simple_dragonbox { } } - uint64_t get_cache(int k) const { + constexpr uint64_t get_cache(int k) const { assert(k >= min_k && k <= max_k); // Compute the base index. @@ -406,7 +406,7 @@ namespace simple_dragonbox { static constexpr int min_k = -292; static constexpr int max_k = 326; - static void remove_trailing_zeros(uint64_t& significand, int& exponent) { + static constexpr void remove_trailing_zeros(uint64_t& significand, int& exponent) { // See https://github.com/jk-jeon/rtz_benchmark. // The idea of branchless search below is by reddit users r/pigeon768 and // r/TheoreticalDumbass. @@ -434,17 +434,17 @@ namespace simple_dragonbox { exponent += s; } - static compute_mul_result compute_mul(uint64_t u, uint128 cache) { + static constexpr compute_mul_result compute_mul(uint64_t u, uint128 cache) { auto const r = umul192_upper128(u, cache); return {r.high, r.low == 0}; } - static uint64_t compute_delta(uint128 cache, int beta) { + static constexpr uint64_t compute_delta(uint128 cache, int beta) { return cache.high >> (total_bits - 1 - beta); } - static compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, - int beta) { + static constexpr compute_mul_parity_result compute_mul_parity(uint64_t two_f, uint128 cache, + int beta) { assert(beta >= 1); assert(beta < 64); auto const r = umul192_lower128(two_f, cache); @@ -453,22 +453,22 @@ namespace simple_dragonbox { 0}; } - static uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + static constexpr uint64_t compute_left_endpoint_for_shorter_interval_case(uint128 cache, int beta) { return (cache.high - (cache.high >> (significand_bits + 2))) >> (total_bits - significand_bits - 1 - beta); } - static uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { + static constexpr uint64_t compute_right_endpoint_for_shorter_interval_case(uint128 cache, int beta) { return (cache.high + (cache.high >> (significand_bits + 1))) >> (total_bits - significand_bits - 1 - beta); } - static uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { + static constexpr uint64_t compute_round_up_for_shorter_interval_case(uint128 cache, int beta) { return ((cache.high >> (total_bits - significand_bits - 2 - beta)) + 1) / 2; } template - static uint64_t divide_by_pow10(uint64_t n) { + static constexpr uint64_t divide_by_pow10(uint64_t n) { static_assert(N >= 0, ""); // Specialize for 64-bit division by 10. @@ -1114,7 +1114,7 @@ namespace simple_dragonbox { template <> struct cache_holder { - uint128 get_cache(int k) const { + constexpr uint128 get_cache(int k) const { assert(k >= min_k && k <= max_k); return cache[k - min_k]; } @@ -1141,7 +1141,7 @@ namespace simple_dragonbox { } } - uint128 get_cache(int k) const { + constexpr uint128 get_cache(int k) const { assert(k >= min_k && k <= max_k); // Compute the base index. @@ -1306,7 +1306,7 @@ namespace simple_dragonbox { static constexpr typename format::template cache_holder cache_; template - static bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { + static constexpr bool check_divisibility_and_divide_by_pow10(carrier_uint& n) { // Make sure the computation for max_n does not overflow. static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); assert(n <= compute_power(carrier_uint(10))); @@ -1324,14 +1324,14 @@ namespace simple_dragonbox { // Compute floor(n / 10^N) for small n and N. // Precondition: n <= 10^(N+1) template - static carrier_uint small_division_by_pow10(carrier_uint n) { + static constexpr carrier_uint small_division_by_pow10(carrier_uint n) { // Make sure the computation for max_n does not overflow. static_assert(N + 1 <= floor_log10_pow2(carrier_bits), ""); assert(n <= compute_power(carrier_uint(10))); return carrier_uint((n * divide_magic_number[N - 1]) >> 16); } - static bool prefer_round_down(carrier_uint decimal_significand) { + static constexpr bool prefer_round_down(carrier_uint decimal_significand) { using e = decimal_round_mode; switch (DecimalRoundMode) { case e::dont_care: @@ -1351,7 +1351,7 @@ namespace simple_dragonbox { int exponent; bool sign; - constexpr impl(Float x) { + constexpr constexpr impl(Float x) { carrier_uint bits; static_assert(sizeof(x) == sizeof(bits)); std::memcpy(&bits, &x, sizeof(x)); @@ -1360,7 +1360,7 @@ namespace simple_dragonbox { sign = bits >> (format::significand_bits + format::exponent_bits); } - bool is_finite() const { return exponent != (1u << format::exponent_bits) - 1; } + constexpr bool is_finite() const { return exponent != (1u << format::exponent_bits) - 1; } struct decimal_result { carrier_uint significand; @@ -1368,7 +1368,7 @@ namespace simple_dragonbox { bool sign; }; - decimal_result to_decimal() { + constexpr decimal_result to_decimal() { assert(is_finite() && (significand || exponent)); bool even = significand % 2 == 0; using e = binary_round_mode; @@ -1404,41 +1404,40 @@ namespace simple_dragonbox { } } - auto nearest_to_even() { + constexpr auto nearest_to_even() { bool even = significand % 2 == 0; return nearest({even, even}, {true, true}); } - auto nearest_to_odd() { + constexpr auto nearest_to_odd() { bool even = significand % 2 == 0; return nearest({!even, even}, {false, false}); } - auto nearest_toward_plus_infinity() { return nearest({!sign, sign}, {!sign, sign}); } + constexpr auto nearest_toward_plus_infinity() { return nearest({!sign, sign}, {!sign, sign}); } - auto nearest_toward_minus_infinity() { return nearest({sign, !sign}, {sign, !sign}); } + constexpr auto nearest_toward_minus_infinity() { return nearest({sign, !sign}, {sign, !sign}); } - auto nearest_toward_zero() { return nearest({false, true}, {false, true}); } + constexpr auto nearest_toward_zero() { return nearest({false, true}, {false, true}); } - auto nearest_away_from_zero() { return nearest({true, false}, {true, false}); } + constexpr auto nearest_away_from_zero() { return nearest({true, false}, {true, false}); } - auto nearest_always_closed() { return nearest({true, true}, {true, true}); } + constexpr auto nearest_always_closed() { return nearest({true, true}, {true, true}); } - auto nearest_always_open() { return nearest({false, false}, {false, false}); } + constexpr auto nearest_always_open() { return nearest({false, false}, {false, false}); } - decimal_result no_trailing_zeros(carrier_uint significand, int exponent) { + constexpr decimal_result no_trailing_zeros(carrier_uint significand, int exponent) { return {significand, exponent, sign}; } - decimal_result may_have_trailing_zeros(carrier_uint significand, int exponent) { + constexpr decimal_result may_have_trailing_zeros(carrier_uint significand, int exponent) { format::remove_trailing_zeros(significand, exponent); return {significand, exponent, sign}; } //// The main algorithm assumes the input is a normal/subnormal finite number. - auto nearest(interval normal_interval, interval shorter_interval) { - + constexpr auto nearest(interval normal_interval, interval shorter_interval) { carrier_uint two_fc = significand * 2; auto binary_exponent = exponent; @@ -1674,8 +1673,7 @@ namespace simple_dragonbox { return no_trailing_zeros(decimal_significand, minus_k + kappa); } - auto left_closed_directed() { - + constexpr auto left_closed_directed() { carrier_uint two_fc = significand * 2; auto binary_exponent = exponent; @@ -1780,8 +1778,7 @@ namespace simple_dragonbox { return no_trailing_zeros(decimal_significand, minus_k + kappa); } - auto right_closed_directed() { - + constexpr auto right_closed_directed() { carrier_uint two_fc = significand * 2; auto binary_exponent = exponent; bool shorter_interval = false; @@ -1855,17 +1852,17 @@ namespace simple_dragonbox { return no_trailing_zeros(decimal_significand, minus_k + kappa); } - static bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { + static constexpr bool is_right_endpoint_integer_shorter_interval(int binary_exponent) { return binary_exponent >= case_shorter_interval_right_endpoint_lower_threshold && binary_exponent <= case_shorter_interval_right_endpoint_upper_threshold; } - static bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { + static constexpr bool is_left_endpoint_integer_shorter_interval(int binary_exponent) { return binary_exponent >= case_shorter_interval_left_endpoint_lower_threshold && binary_exponent <= case_shorter_interval_left_endpoint_upper_threshold; } - char* to_chars(char* buffer) { + constexpr char* to_chars(char* buffer) { if (!is_finite()) { if (!significand) { if (sign) { From c72f0089310958df32ce2d2420396c9bc89b6a31 Mon Sep 17 00:00:00 2001 From: Junekey Jeon <33922675+jk-jeon@users.noreply.github.com> Date: Wed, 28 Aug 2024 13:28:45 -0700 Subject: [PATCH 16/17] Minor fixup --- subproject/simple/simple_dragonbox.h | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/subproject/simple/simple_dragonbox.h b/subproject/simple/simple_dragonbox.h index f800776..4d1e634 100644 --- a/subproject/simple/simple_dragonbox.h +++ b/subproject/simple/simple_dragonbox.h @@ -1233,8 +1233,8 @@ namespace simple_dragonbox { template static constexpr bool valid_float = std::numeric_limits::is_iec559 && std::numeric_limits::radix == 2 && sizeof(T) == Size; - static_assert(valid_float, "simple_dragonbox: float may not be IEEE 754 binary32"); - static_assert(valid_float, "simple_dragonbox: double may not be IEEE 754 binary64"); + static_assert(valid_float, "simple_dragonbox: float may not be IEEE-754 binary32"); + static_assert(valid_float, "simple_dragonbox: double may not be IEEE-754 binary64"); constexpr void reverse(char* begin, char* end) { while (begin < --end) { From 23abf541cf70c1ce2c7b2a07eda21535cef923af Mon Sep 17 00:00:00 2001 From: Junekey Jeon <33922675+jk-jeon@users.noreply.github.com> Date: Wed, 28 Aug 2024 13:30:33 -0700 Subject: [PATCH 17/17] Replace ::memcpy by std::memcpy --- subproject/simple/simple_dragonbox_test.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/subproject/simple/simple_dragonbox_test.cpp b/subproject/simple/simple_dragonbox_test.cpp index f5e633e..4fea5c6 100644 --- a/subproject/simple/simple_dragonbox_test.cpp +++ b/subproject/simple/simple_dragonbox_test.cpp @@ -54,7 +54,7 @@ static bool test_simple_dragonbox(bool& success, Arg... arg) { Float x; static_assert(sizeof(br) == sizeof(x)); - ::memcpy(&x, &br, sizeof(br)); + std::memcpy(&x, &br, sizeof(br)); simple_dragonbox::to_chars(x, buffer1, arg...); reference_implementation(x, buffer2);