math/bits: use Wilkes-Wheeler-Gill algorithm for OnesCount64

src/math/bits/bits.go

@@ -132,33 +132,14 @@ func OnesCount32(x uint32) int {
 
 // OnesCount64 returns the number of one bits ("population count") in x.
 func OnesCount64(x uint64) int {
-	// Implementation: Parallel summing of adjacent bits.
-	// See "Hacker's Delight", Chap. 5: Counting Bits.
-	// The following pattern shows the general approach:
-	//
-	//   x = x>>1&(m0&m) + x&(m0&m)
-	//   x = x>>2&(m1&m) + x&(m1&m)
-	//   x = x>>4&(m2&m) + x&(m2&m)
-	//   x = x>>8&(m3&m) + x&(m3&m)
-	//   x = x>>16&(m4&m) + x&(m4&m)
-	//   x = x>>32&(m5&m) + x&(m5&m)
-	//   return int(x)
-	//
-	// Masking (& operations) can be left away when there's no
-	// danger that a field's sum will carry over into the next
-	// field: Since the result cannot be > 64, 8 bits is enough
-	// and we can ignore the masks for the shifts by 8 and up.
-	// Per "Hacker's Delight", the first line can be simplified
-	// more, but it saves at best one instruction, so we leave
-	// it alone for clarity.
-	const m = 1<<64 - 1
-	x = x>>1&(m0&m) + x&(m0&m)
-	x = x>>2&(m1&m) + x&(m1&m)
-	x = (x>>4 + x) & (m2 & m)
-	x += x >> 8
-	x += x >> 16
-	x += x >> 32
-	return int(x) & (1<<7 - 1)
+	// Implementation: Wilkes-Wheeler-Gill algorithm.
+	// See "Faster Population Counts Using AVX2 Instructions", FIGURE 3.
+	// Full paper is available at https://arxiv.org/pdf/1611.07612.pdf
+	x -= (x >> 1) & m0
+	x = ((x >> 2) & m1) + (x & m1)
+	x = (x + (x >> 4)) & m2
+	x *= 0x0101010101010101
+	return int(x >> 56)
 }
 
 // --- RotateLeft ---