hash/crc32: improve the AMD64 implementation using SSE4.2

The algorithm is explained in the comments. The improvement in
throughput is about 1.4x for buffers between 500b-4Kb and 2.5x-2.6x
for larger buffers.

Additionally, we no longer initialize the software tables if SSE4.2 is
available.

Adding a test for the SSE implementation (restricted to amd64 and
amd64p32).

Benchmarks on a Haswell i5-4670 @ 3.4 GHz:

name                           old time/op    new time/op     delta
CastagnoliCrc15B-4               21.9ns ± 1%     22.9ns ± 0%    +4.45%
CastagnoliCrc15BMisaligned-4     22.6ns ± 0%     23.4ns ± 0%    +3.43%
CastagnoliCrc40B-4               23.3ns ± 0%     23.9ns ± 0%    +2.58%
CastagnoliCrc40BMisaligned-4     25.4ns ± 0%     26.1ns ± 0%    +2.86%
CastagnoliCrc512-4               72.6ns ± 0%     52.8ns ± 0%   -27.33%
CastagnoliCrc512Misaligned-4     76.3ns ± 1%     56.3ns ± 0%   -26.18%
CastagnoliCrc1KB-4                128ns ± 1%       89ns ± 0%   -30.04%
CastagnoliCrc1KBMisaligned-4      130ns ± 0%       88ns ± 0%   -32.65%
CastagnoliCrc4KB-4                461ns ± 0%      187ns ± 0%   -59.40%
CastagnoliCrc4KBMisaligned-4      463ns ± 0%      191ns ± 0%   -58.77%
CastagnoliCrc32KB-4              3.58µs ± 0%     1.35µs ± 0%   -62.22%
CastagnoliCrc32KBMisaligned-4    3.58µs ± 0%     1.36µs ± 0%   -61.84%

name                           old speed      new speed       delta
CastagnoliCrc15B-4              684MB/s ± 1%    655MB/s ± 0%    -4.32%
CastagnoliCrc15BMisaligned-4    663MB/s ± 0%    641MB/s ± 0%    -3.32%
CastagnoliCrc40B-4             1.72GB/s ± 0%   1.67GB/s ± 0%    -2.69%
CastagnoliCrc40BMisaligned-4   1.58GB/s ± 0%   1.53GB/s ± 0%    -2.82%
CastagnoliCrc512-4             7.05GB/s ± 0%   9.70GB/s ± 0%   +37.59%
CastagnoliCrc512Misaligned-4   6.71GB/s ± 1%   9.09GB/s ± 0%   +35.43%
CastagnoliCrc1KB-4             7.98GB/s ± 1%  11.46GB/s ± 0%   +43.55%
CastagnoliCrc1KBMisaligned-4   7.86GB/s ± 0%  11.70GB/s ± 0%   +48.75%
CastagnoliCrc4KB-4             8.87GB/s ± 0%  21.80GB/s ± 0%  +145.69%
CastagnoliCrc4KBMisaligned-4   8.83GB/s ± 0%  21.39GB/s ± 0%  +142.25%
CastagnoliCrc32KB-4            9.15GB/s ± 0%  24.22GB/s ± 0%  +164.62%
CastagnoliCrc32KBMisaligned-4  9.16GB/s ± 0%  24.00GB/s ± 0%  +161.94%

Fixes #16107.

Change-Id: Ibe50ea76574674ce0571ef31c31015e0ed66b907
Reviewed-on: https://go-review.googlesource.com/27931
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>

src/hash/crc32/crc32.go

@@ -52,8 +52,14 @@ var castagnoliTable8 *slicing8Table
 var castagnoliOnce sync.Once
 
 func castagnoliInit() {
-	castagnoliTable = makeTable(Castagnoli)
-	castagnoliTable8 = makeTable8(Castagnoli)
+	// Call the arch-specific init function and let it decide if we will need
+	// the tables for the generic implementation.
+	needGenericTables := castagnoliInitArch()
+
+	if needGenericTables {
+		castagnoliTable = makeTable(Castagnoli)
+		castagnoliTable8 = makeTable8(Castagnoli)
+	}
 }
 
 // IEEETable is the table for the IEEE polynomial.

src/hash/crc32/crc32_amd64.go

@@ -4,6 +4,8 @@
 
 package crc32
 
+import "unsafe"
+
 // This file contains the code to call the SSE 4.2 version of the Castagnoli
 // and IEEE CRC.
 
@@ -13,11 +15,20 @@ func haveSSE41() bool
 func haveSSE42() bool
 func haveCLMUL() bool
 
-// castagnoliSSE42 is defined in crc_amd64.s and uses the SSE4.2 CRC32
+// castagnoliSSE42 is defined in crc32_amd64.s and uses the SSE4.2 CRC32
 // instruction.
 //go:noescape
 func castagnoliSSE42(crc uint32, p []byte) uint32
 
+// castagnoliSSE42Triple is defined in crc32_amd64.s and uses the SSE4.2 CRC32
+// instruction.
+//go:noescape
+func castagnoliSSE42Triple(
+	crcA, crcB, crcC uint32,
+	a, b, c []byte,
+	rounds uint32,
+) (retA uint32, retB uint32, retC uint32)
+
 // ieeeCLMUL is defined in crc_amd64.s and uses the PCLMULQDQ
 // instruction as well as SSE 4.1.
 //go:noescape
@@ -26,15 +37,160 @@ func ieeeCLMUL(crc uint32, p []byte) uint32
 var sse42 = haveSSE42()
 var useFastIEEE = haveCLMUL() && haveSSE41()
 
+const castagnoliK1 = 168
+const castagnoliK2 = 1344
+
+type sse42Table [4]Table
+
+var castagnoliSSE42TableK1 *sse42Table
+var castagnoliSSE42TableK2 *sse42Table
+
+func castagnoliInitArch() (needGenericTables bool) {
+	if !sse42 {
+		return true
+	}
+	castagnoliSSE42TableK1 = new(sse42Table)
+	castagnoliSSE42TableK2 = new(sse42Table)
+	// See description in updateCastagnoli.
+	//    t[0][i] = CRC(i000, O)
+	//    t[1][i] = CRC(0i00, O)
+	//    t[2][i] = CRC(00i0, O)
+	//    t[3][i] = CRC(000i, O)
+	// where O is a sequence of K zeros.
+	var tmp [castagnoliK2]byte
+	for b := 0; b < 4; b++ {
+		for i := 0; i < 256; i++ {
+			val := uint32(i) << uint32(b*8)
+			castagnoliSSE42TableK1[b][i] = castagnoliSSE42(val, tmp[:castagnoliK1])
+			castagnoliSSE42TableK2[b][i] = castagnoliSSE42(val, tmp[:])
+		}
+	}
+	return false
+}
+
+// castagnoliShift computes the CRC32-C of K1 or K2 zeroes (depending on the
+// table given) with the given initial crc value. This corresponds to
+// CRC(crc, O) in the description in updateCastagnoli.
+func castagnoliShift(table *sse42Table, crc uint32) uint32 {
+	return table[3][crc>>24] ^
+		table[2][(crc>>16)&0xFF] ^
+		table[1][(crc>>8)&0xFF] ^
+		table[0][crc&0xFF]
+}
+
 func updateCastagnoli(crc uint32, p []byte) uint32 {
-	if sse42 {
-		return castagnoliSSE42(crc, p)
+	if !sse42 {
+		// Use slicing-by-8 on larger inputs.
+		if len(p) >= sliceBy8Cutoff {
+			return updateSlicingBy8(crc, castagnoliTable8, p)
+		}
+		return update(crc, castagnoliTable, p)
 	}
-	// Use slicing-by-8 on larger inputs.
-	if len(p) >= sliceBy8Cutoff {
-		return updateSlicingBy8(crc, castagnoliTable8, p)
+
+	// This method is inspired from the algorithm in Intel's white paper:
+	//    "Fast CRC Computation for iSCSI Polynomial Using CRC32 Instruction"
+	// The same strategy of splitting the buffer in three is used but the
+	// combining calculation is different; the complete derivation is explained
+	// below.
+	//
+	// -- The basic idea --
+	//
+	// The CRC32 instruction (available in SSE4.2) can process 8 bytes at a
+	// time. In recent Intel architectures the instruction takes 3 cycles;
+	// however the processor can pipeline up to three instructions if they
+	// don't depend on each other.
+	//
+	// Roughly this means that we can process three buffers in about the same
+	// time we can process one buffer.
+	//
+	// The idea is then to split the buffer in three, CRC the three pieces
+	// separately and then combine the results.
+	//
+	// Combining the results requires precomputed tables, so we must choose a
+	// fixed buffer length to optimize. The longer the length, the faster; but
+	// only buffers longer than this length will use the optimization. We choose
+	// two cutoffs and compute tables for both:
+	//  - one around 512: 168*3=504
+	//  - one around 4KB: 1344*3=4032
+	//
+	// -- The nitty gritty --
+	//
+	// Let CRC(I, X) be the non-inverted CRC32-C of the sequence X (with
+	// initial non-inverted CRC I). This function has the following properties:
+	//   (a) CRC(I, AB) = CRC(CRC(I, A), B)
+	//   (b) CRC(I, A xor B) = CRC(I, A) xor CRC(0, B)
+	//
+	// Say we want to compute CRC(I, ABC) where A, B, C are three sequences of
+	// K bytes each, where K is a fixed constant. Let O be the sequence of K zero
+	// bytes.
+	//
+	// CRC(I, ABC) = CRC(I, ABO xor C)
+	//             = CRC(I, ABO) xor CRC(0, C)
+	//             = CRC(CRC(I, AB), O) xor CRC(0, C)
+	//             = CRC(CRC(I, AO xor B), O) xor CRC(0, C)
+	//             = CRC(CRC(I, AO) xor CRC(0, B), O) xor CRC(0, C)
+	//             = CRC(CRC(CRC(I, A), O) xor CRC(0, B), O) xor CRC(0, C)
+	//
+	// The castagnoliSSE42Triple function can compute CRC(I, A), CRC(0, B),
+	// and CRC(0, C) efficiently.  We just need to find a way to quickly compute
+	// CRC(uvwx, O) given a 4-byte initial value uvwx. We can precompute these
+	// values; since we can't have a 32-bit table, we break it up into four
+	// 8-bit tables:
+	//
+	//    CRC(uvwx, O) = CRC(u000, O) xor
+	//                   CRC(0v00, O) xor
+	//                   CRC(00w0, O) xor
+	//                   CRC(000x, O)
+	//
+	// We can compute tables corresponding to the four terms for all 8-bit
+	// values.
+
+	crc = ^crc
+
+	// If a buffer is long enough to use the optimization, process the first few
+	// bytes to align the buffer to an 8 byte boundary (if necessary).
+	if len(p) >= castagnoliK1*3 {
+		delta := int(uintptr(unsafe.Pointer(&p[0])) & 7)
+		if delta != 0 {
+			delta = 8 - delta
+			crc = castagnoliSSE42(crc, p[:delta])
+			p = p[delta:]
+		}
 	}
-	return update(crc, castagnoliTable, p)
+
+	// Process 3*K2 at a time.
+	for len(p) >= castagnoliK2*3 {
+		// Compute CRC(I, A), CRC(0, B), and CRC(0, C).
+		crcA, crcB, crcC := castagnoliSSE42Triple(
+			crc, 0, 0,
+			p, p[castagnoliK2:], p[castagnoliK2*2:],
+			castagnoliK2/24)
+
+		// CRC(I, AB) = CRC(CRC(I, A), O) xor CRC(0, B)
+		crcAB := castagnoliShift(castagnoliSSE42TableK2, crcA) ^ crcB
+		// CRC(I, ABC) = CRC(CRC(I, AB), O) xor CRC(0, C)
+		crc = castagnoliShift(castagnoliSSE42TableK2, crcAB) ^ crcC
+		p = p[castagnoliK2*3:]
+	}
+
+	// Process 3*K1 at a time.
+	for len(p) >= castagnoliK1*3 {
+		// Compute CRC(I, A), CRC(0, B), and CRC(0, C).
+		crcA, crcB, crcC := castagnoliSSE42Triple(
+			crc, 0, 0,
+			p, p[castagnoliK1:], p[castagnoliK1*2:],
+			castagnoliK1/24)
+
+		// CRC(I, AB) = CRC(CRC(I, A), O) xor CRC(0, B)
+		crcAB := castagnoliShift(castagnoliSSE42TableK1, crcA) ^ crcB
+		// CRC(I, ABC) = CRC(CRC(I, AB), O) xor CRC(0, C)
+		crc = castagnoliShift(castagnoliSSE42TableK1, crcAB) ^ crcC
+		p = p[castagnoliK1*3:]
+	}
+
+	// Use the simple implementation for what's left.
+	crc = castagnoliSSE42(crc, p)
+	return ^crc
 }
 
 func updateIEEE(crc uint32, p []byte) uint32 {

src/hash/crc32/crc32_amd64.s

@@ -4,14 +4,14 @@
 
 #include "textflag.h"
 
+// castagnoliSSE42 updates the (non-inverted) crc with the given buffer.
+//
 // func castagnoliSSE42(crc uint32, p []byte) uint32
 TEXT ·castagnoliSSE42(SB),NOSPLIT,$0
 	MOVL crc+0(FP), AX  // CRC value
 	MOVQ p+8(FP), SI  // data pointer
 	MOVQ p_len+16(FP), CX  // len(p)
 
-	NOTL AX
-
 	// If there are fewer than 8 bytes to process, skip alignment.
 	CMPQ CX, $8
 	JL less_than_8
@@ -87,10 +87,53 @@ less_than_2:
 	CRC32B (SI), AX
 
 done:
-	NOTL AX
 	MOVL AX, ret+32(FP)
 	RET
 
+// castagnoliSSE42Triple updates three (non-inverted) crcs with (24*rounds)
+// bytes from each buffer.
+//
+// func castagnoliSSE42Triple(
+//     crc1, crc2, crc3 uint32,
+//     a, b, c []byte,
+//     rounds uint32,
+// ) (retA uint32, retB uint32, retC uint32)
+TEXT ·castagnoliSSE42Triple(SB),NOSPLIT,$0
+	MOVL crcA+0(FP), AX
+	MOVL crcB+4(FP), CX
+	MOVL crcC+8(FP), DX
+
+	MOVQ a+16(FP), R8   // data pointer
+	MOVQ b+40(FP), R9   // data pointer
+	MOVQ c+64(FP), R10  // data pointer
+
+	MOVL rounds+88(FP), R11
+
+loop:
+	CRC32Q (R8), AX
+	CRC32Q (R9), CX
+	CRC32Q (R10), DX
+
+	CRC32Q 8(R8), AX
+	CRC32Q 8(R9), CX
+	CRC32Q 8(R10), DX
+
+	CRC32Q 16(R8), AX
+	CRC32Q 16(R9), CX
+	CRC32Q 16(R10), DX
+
+	ADDQ $24, R8
+	ADDQ $24, R9
+	ADDQ $24, R10
+
+	DECQ R11
+	JNZ loop
+
+	MOVL AX, retA+96(FP)
+	MOVL CX, retB+100(FP)
+	MOVL DX, retC+104(FP)
+	RET
+
 // func haveSSE42() bool
 TEXT ·haveSSE42(SB),NOSPLIT,$0
 	XORQ AX, AX

src/hash/crc32/crc32_amd64_test.go

@@ -0,0 +1,45 @@
+// Copyright 2009 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package crc32
+
+import (
+	"math/rand"
+	"testing"
+)
+
+func TestCastagnoliSSE42(t *testing.T) {
+	if !sse42 {
+		t.Skip("SSE42 not supported")
+	}
+
+	// Init the SSE42 tables.
+	MakeTable(Castagnoli)
+
+	// Manually init the software implementation to compare against.
+	castagnoliTable = makeTable(Castagnoli)
+	castagnoliTable8 = makeTable8(Castagnoli)
+
+	// The optimized SSE4.2 implementation behaves differently for different
+	// lengths (especially around multiples of K*3). Crosscheck against the
+	// software implementation for various lengths.
+	for _, base := range []int{castagnoliK1, castagnoliK2, castagnoliK1 + castagnoliK2} {
+		for _, baseMult := range []int{2, 3, 5, 6, 9, 30} {
+			for _, variation := range []int{0, 1, 2, 3, 4, 7, 10, 16, 32, 50, 128} {
+				for _, varMult := range []int{-2, -1, +1, +2} {
+					length := base*baseMult + variation*varMult
+					p := make([]byte, length)
+					_, _ = rand.Read(p)
+					crcInit := uint32(rand.Int63())
+					correct := updateSlicingBy8(crcInit, castagnoliTable8, p)
+					result := updateCastagnoli(crcInit, p)
+					if result != correct {
+						t.Errorf("SSE42 implementation = 0x%x want 0x%x (buffer length %d)",
+							result, correct, len(p))
+					}
+				}
+			}
+		}
+	}
+}

src/hash/crc32/crc32_amd64p32.go

@@ -7,17 +7,22 @@ package crc32
 // This file contains the code to call the SSE 4.2 version of the Castagnoli
 // CRC.
 
-// haveSSE42 is defined in crc_amd64p32.s and uses CPUID to test for SSE 4.2
+// haveSSE42 is defined in crc32_amd64p32.s and uses CPUID to test for SSE 4.2
 // support.
 func haveSSE42() bool
 
-// castagnoliSSE42 is defined in crc_amd64.s and uses the SSE4.2 CRC32
+// castagnoliSSE42 is defined in crc32_amd64.s and uses the SSE4.2 CRC32
 // instruction.
 //go:noescape
 func castagnoliSSE42(crc uint32, p []byte) uint32
 
 var sse42 = haveSSE42()
 
+func castagnoliInitArch() (needGenericTables bool) {
+	// We only need the generic implementation tables if we don't have SSE4.2.
+	return !sse42
+}
+
 func updateCastagnoli(crc uint32, p []byte) uint32 {
 	if sse42 {
 		return castagnoliSSE42(crc, p)

src/hash/crc32/crc32_generic.go

@@ -9,6 +9,10 @@ package crc32
 // This file contains the generic version of updateCastagnoli which does
 // slicing-by-8, or uses the fallback for very small sizes.
 
+func castagnoliInitArch() (needGenericTables bool) {
+	return true
+}
+
 func updateCastagnoli(crc uint32, p []byte) uint32 {
 	// Use slicing-by-8 on larger inputs.
 	if len(p) >= sliceBy8Cutoff {

src/hash/crc32/crc32_s390x.go

@@ -25,6 +25,10 @@ func vectorizedCastagnoli(crc uint32, p []byte) uint32
 //go:noescape
 func vectorizedIEEE(crc uint32, p []byte) uint32
 
+func castagnoliInitArch() (needGenericTables bool) {
+	return true
+}
+
 func genericCastagnoli(crc uint32, p []byte) uint32 {
 	// Use slicing-by-8 on larger inputs.
 	if len(p) >= sliceBy8Cutoff {