From 9d98cb66307efd37f028e50ab57c2182874a5bfc Mon Sep 17 00:00:00 2001
From: Daniel Lemire <lemire@gmail.com>
Date: Wed, 7 May 2014 14:40:40 -0400
Subject: [PATCH] Using faster popcnt function in pure Go

---
 popcnt.go | 41 +++++++++++++++--------------------------
 1 file changed, 15 insertions(+), 26 deletions(-)

diff --git a/popcnt.go b/popcnt.go
index 36be0d1..76577a8 100644
--- a/popcnt.go
+++ b/popcnt.go
@@ -1,32 +1,21 @@
 package bitset
 
-// From Wikipedia: http://en.wikipedia.org/wiki/Hamming_weight
-const m1 uint64 = 0x5555555555555555  //binary: 0101...
-const m2 uint64 = 0x3333333333333333  //binary: 00110011..
-const m4 uint64 = 0x0f0f0f0f0f0f0f0f  //binary:  4 zeros,  4 ones ...
-const m8 uint64 = 0x00ff00ff00ff00ff  //binary:  8 zeros,  8 ones ...
-const m16 uint64 = 0x0000ffff0000ffff //binary: 16 zeros, 16 ones ...
-const m32 uint64 = 0x00000000ffffffff //binary: 32 zeros, 32 ones
-const hff uint64 = 0xffffffffffffffff //binary: all ones
-const h01 uint64 = 0x0101010101010101 //the sum of 256 to the power of 0,1,2,3...
-
-// From Wikipedia: count number of set bits.
-// This is algorithm popcount_2 in the article retrieved May 9, 2011
-
-func popcount_2(x uint64) uint64 {
-	x -= (x >> 1) & m1             //put count of each 2 bits into those 2 bits
-	x = (x & m2) + ((x >> 2) & m2) //put count of each 4 bits into those 4 bits
-	x = (x + (x >> 4)) & m4        //put count of each 8 bits into those 8 bits
-	x += x >> 8                    //put count of each 16 bits into their lowest 8 bits
-	x += x >> 16                   //put count of each 32 bits into their lowest 8 bits
-	x += x >> 32                   //put count of each 64 bits into their lowest 8 bits
-	return x & 0x7f
+// bit population count, take from
+// https://code.google.com/p/go/issues/detail?id=4988#c11
+// credit: https://code.google.com/u/arnehormann/
+func popcount(x uint64) (n uint64) {
+	x -= (x >> 1) & 0x5555555555555555
+	x = (x>>2)&0x3333333333333333 + x&0x3333333333333333
+	x += x >> 4
+	x &= 0x0f0f0f0f0f0f0f0f
+	x *= 0x0101010101010101
+	return x >> 56
 }
 
 func popcntSliceGo(s []uint64) uint64 {
 	cnt := uint64(0)
 	for _, x := range s {
-		cnt += popcount_2(x)
+		cnt += popcount(x)
 	}
 	return cnt
 }
@@ -34,7 +23,7 @@ func popcntSliceGo(s []uint64) uint64 {
 func popcntMaskSliceGo(s, m []uint64) uint64 {
 	cnt := uint64(0)
 	for i := range s {
-		cnt += popcount_2(s[i] &^ m[i])
+		cnt += popcount(s[i] &^ m[i])
 	}
 	return cnt
 }
@@ -42,7 +31,7 @@ func popcntMaskSliceGo(s, m []uint64) uint64 {
 func popcntAndSliceGo(s, m []uint64) uint64 {
 	cnt := uint64(0)
 	for i := range s {
-		cnt += popcount_2(s[i] & m[i])
+		cnt += popcount(s[i] & m[i])
 	}
 	return cnt
 }
@@ -50,7 +39,7 @@ func popcntAndSliceGo(s, m []uint64) uint64 {
 func popcntOrSliceGo(s, m []uint64) uint64 {
 	cnt := uint64(0)
 	for i := range s {
-		cnt += popcount_2(s[i] | m[i])
+		cnt += popcount(s[i] | m[i])
 	}
 	return cnt
 }
@@ -58,7 +47,7 @@ func popcntOrSliceGo(s, m []uint64) uint64 {
 func popcntXorSliceGo(s, m []uint64) uint64 {
 	cnt := uint64(0)
 	for i := range s {
-		cnt += popcount_2(s[i] ^ m[i])
+		cnt += popcount(s[i] ^ m[i])
 	}
 	return cnt
 }