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Copyright (c) 2012 The Go Authors. All rights reserved.
Copyright (c) 2015 Klaus Post
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are
met:
* Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above
copyright notice, this list of conditions and the following disclaimer
in the documentation and/or other materials provided with the
distribution.
* Neither the name of Google Inc. nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

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# crc32
CRC32 hash with x64 optimizations
This package is a drop-in replacement for the standard library `hash/crc32` package, that features SSE 4.2 optimizations on x64 platforms, for a 10x speedup.
[![Build Status](https://travis-ci.org/klauspost/crc32.svg?branch=master)](https://travis-ci.org/klauspost/crc32)
# usage
Install using `go get github.com/klauspost/crc32`. This library is based on Go 1.5 code and requires Go 1.3 or newer.
Replace `import "hash/crc32"` with `import "github.com/klauspost/crc32"` and you are good to go.
# changes
* Oct 20, 2016: Changes have been merged to upstream Go. Package updated to match.
* Dec 4, 2015: Uses the "slice-by-8" trick more extensively, which gives a 1.5 to 2.5x speedup if assembler is unavailable.
# performance
For *Go 1.7* performance is equivalent to the standard library. So if you use this package for Go 1.7 you can switch back.
For IEEE tables (the most common), there is approximately a factor 10 speedup with "CLMUL" (Carryless multiplication) instruction:
```
benchmark old ns/op new ns/op delta
BenchmarkCrc32KB 99955 10258 -89.74%
benchmark old MB/s new MB/s speedup
BenchmarkCrc32KB 327.83 3194.20 9.74x
```
For other tables and "CLMUL" capable machines the performance is the same as the standard library.
Here are some detailed benchmarks, comparing to go 1.5 standard library with and without assembler enabled.
```
Std: Standard Go 1.5 library
Crc: Indicates IEEE type CRC.
40B: Size of each slice encoded.
NoAsm: Assembler was disabled (ie. not an AMD64 or SSE 4.2+ capable machine).
Castagnoli: Castagnoli CRC type.
BenchmarkStdCrc40B-4 10000000 158 ns/op 252.88 MB/s
BenchmarkCrc40BNoAsm-4 20000000 105 ns/op 377.38 MB/s (slice8)
BenchmarkCrc40B-4 20000000 105 ns/op 378.77 MB/s (slice8)
BenchmarkStdCrc1KB-4 500000 3604 ns/op 284.10 MB/s
BenchmarkCrc1KBNoAsm-4 1000000 1463 ns/op 699.79 MB/s (slice8)
BenchmarkCrc1KB-4 3000000 396 ns/op 2583.69 MB/s (asm)
BenchmarkStdCrc8KB-4 200000 11417 ns/op 717.48 MB/s (slice8)
BenchmarkCrc8KBNoAsm-4 200000 11317 ns/op 723.85 MB/s (slice8)
BenchmarkCrc8KB-4 500000 2919 ns/op 2805.73 MB/s (asm)
BenchmarkStdCrc32KB-4 30000 45749 ns/op 716.24 MB/s (slice8)
BenchmarkCrc32KBNoAsm-4 30000 45109 ns/op 726.42 MB/s (slice8)
BenchmarkCrc32KB-4 100000 11497 ns/op 2850.09 MB/s (asm)
BenchmarkStdNoAsmCastagnol40B-4 10000000 161 ns/op 246.94 MB/s
BenchmarkStdCastagnoli40B-4 50000000 28.4 ns/op 1410.69 MB/s (asm)
BenchmarkCastagnoli40BNoAsm-4 20000000 100 ns/op 398.01 MB/s (slice8)
BenchmarkCastagnoli40B-4 50000000 28.2 ns/op 1419.54 MB/s (asm)
BenchmarkStdNoAsmCastagnoli1KB-4 500000 3622 ns/op 282.67 MB/s
BenchmarkStdCastagnoli1KB-4 10000000 144 ns/op 7099.78 MB/s (asm)
BenchmarkCastagnoli1KBNoAsm-4 1000000 1475 ns/op 694.14 MB/s (slice8)
BenchmarkCastagnoli1KB-4 10000000 146 ns/op 6993.35 MB/s (asm)
BenchmarkStdNoAsmCastagnoli8KB-4 50000 28781 ns/op 284.63 MB/s
BenchmarkStdCastagnoli8KB-4 1000000 1029 ns/op 7957.89 MB/s (asm)
BenchmarkCastagnoli8KBNoAsm-4 200000 11410 ns/op 717.94 MB/s (slice8)
BenchmarkCastagnoli8KB-4 1000000 1000 ns/op 8188.71 MB/s (asm)
BenchmarkStdNoAsmCastagnoli32KB-4 10000 115426 ns/op 283.89 MB/s
BenchmarkStdCastagnoli32KB-4 300000 4065 ns/op 8059.13 MB/s (asm)
BenchmarkCastagnoli32KBNoAsm-4 30000 45171 ns/op 725.41 MB/s (slice8)
BenchmarkCastagnoli32KB-4 500000 4077 ns/op 8035.89 MB/s (asm)
```
The IEEE assembler optimizations has been submitted and will be part of the Go 1.6 standard library.
However, the improved use of slice-by-8 has not, but will probably be submitted for Go 1.7.
# license
Standard Go license. Changes are Copyright (c) 2015 Klaus Post under same conditions.

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// 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 implements the 32-bit cyclic redundancy check, or CRC-32,
// checksum. See http://en.wikipedia.org/wiki/Cyclic_redundancy_check for
// information.
//
// Polynomials are represented in LSB-first form also known as reversed representation.
//
// See http://en.wikipedia.org/wiki/Mathematics_of_cyclic_redundancy_checks#Reversed_representations_and_reciprocal_polynomials
// for information.
package crc32
import (
"hash"
"sync"
)
// The size of a CRC-32 checksum in bytes.
const Size = 4
// Predefined polynomials.
const (
// IEEE is by far and away the most common CRC-32 polynomial.
// Used by ethernet (IEEE 802.3), v.42, fddi, gzip, zip, png, ...
IEEE = 0xedb88320
// Castagnoli's polynomial, used in iSCSI.
// Has better error detection characteristics than IEEE.
// http://dx.doi.org/10.1109/26.231911
Castagnoli = 0x82f63b78
// Koopman's polynomial.
// Also has better error detection characteristics than IEEE.
// http://dx.doi.org/10.1109/DSN.2002.1028931
Koopman = 0xeb31d82e
)
// Table is a 256-word table representing the polynomial for efficient processing.
type Table [256]uint32
// This file makes use of functions implemented in architecture-specific files.
// The interface that they implement is as follows:
//
// // archAvailableIEEE reports whether an architecture-specific CRC32-IEEE
// // algorithm is available.
// archAvailableIEEE() bool
//
// // archInitIEEE initializes the architecture-specific CRC3-IEEE algorithm.
// // It can only be called if archAvailableIEEE() returns true.
// archInitIEEE()
//
// // archUpdateIEEE updates the given CRC32-IEEE. It can only be called if
// // archInitIEEE() was previously called.
// archUpdateIEEE(crc uint32, p []byte) uint32
//
// // archAvailableCastagnoli reports whether an architecture-specific
// // CRC32-C algorithm is available.
// archAvailableCastagnoli() bool
//
// // archInitCastagnoli initializes the architecture-specific CRC32-C
// // algorithm. It can only be called if archAvailableCastagnoli() returns
// // true.
// archInitCastagnoli()
//
// // archUpdateCastagnoli updates the given CRC32-C. It can only be called
// // if archInitCastagnoli() was previously called.
// archUpdateCastagnoli(crc uint32, p []byte) uint32
// castagnoliTable points to a lazily initialized Table for the Castagnoli
// polynomial. MakeTable will always return this value when asked to make a
// Castagnoli table so we can compare against it to find when the caller is
// using this polynomial.
var castagnoliTable *Table
var castagnoliTable8 *slicing8Table
var castagnoliArchImpl bool
var updateCastagnoli func(crc uint32, p []byte) uint32
var castagnoliOnce sync.Once
func castagnoliInit() {
castagnoliTable = simpleMakeTable(Castagnoli)
castagnoliArchImpl = archAvailableCastagnoli()
if castagnoliArchImpl {
archInitCastagnoli()
updateCastagnoli = archUpdateCastagnoli
} else {
// Initialize the slicing-by-8 table.
castagnoliTable8 = slicingMakeTable(Castagnoli)
updateCastagnoli = func(crc uint32, p []byte) uint32 {
return slicingUpdate(crc, castagnoliTable8, p)
}
}
}
// IEEETable is the table for the IEEE polynomial.
var IEEETable = simpleMakeTable(IEEE)
// ieeeTable8 is the slicing8Table for IEEE
var ieeeTable8 *slicing8Table
var ieeeArchImpl bool
var updateIEEE func(crc uint32, p []byte) uint32
var ieeeOnce sync.Once
func ieeeInit() {
ieeeArchImpl = archAvailableIEEE()
if ieeeArchImpl {
archInitIEEE()
updateIEEE = archUpdateIEEE
} else {
// Initialize the slicing-by-8 table.
ieeeTable8 = slicingMakeTable(IEEE)
updateIEEE = func(crc uint32, p []byte) uint32 {
return slicingUpdate(crc, ieeeTable8, p)
}
}
}
// MakeTable returns a Table constructed from the specified polynomial.
// The contents of this Table must not be modified.
func MakeTable(poly uint32) *Table {
switch poly {
case IEEE:
ieeeOnce.Do(ieeeInit)
return IEEETable
case Castagnoli:
castagnoliOnce.Do(castagnoliInit)
return castagnoliTable
}
return simpleMakeTable(poly)
}
// digest represents the partial evaluation of a checksum.
type digest struct {
crc uint32
tab *Table
}
// New creates a new hash.Hash32 computing the CRC-32 checksum
// using the polynomial represented by the Table.
// Its Sum method will lay the value out in big-endian byte order.
func New(tab *Table) hash.Hash32 {
if tab == IEEETable {
ieeeOnce.Do(ieeeInit)
}
return &digest{0, tab}
}
// NewIEEE creates a new hash.Hash32 computing the CRC-32 checksum
// using the IEEE polynomial.
// Its Sum method will lay the value out in big-endian byte order.
func NewIEEE() hash.Hash32 { return New(IEEETable) }
func (d *digest) Size() int { return Size }
func (d *digest) BlockSize() int { return 1 }
func (d *digest) Reset() { d.crc = 0 }
// Update returns the result of adding the bytes in p to the crc.
func Update(crc uint32, tab *Table, p []byte) uint32 {
switch tab {
case castagnoliTable:
return updateCastagnoli(crc, p)
case IEEETable:
// Unfortunately, because IEEETable is exported, IEEE may be used without a
// call to MakeTable. We have to make sure it gets initialized in that case.
ieeeOnce.Do(ieeeInit)
return updateIEEE(crc, p)
default:
return simpleUpdate(crc, tab, p)
}
}
func (d *digest) Write(p []byte) (n int, err error) {
switch d.tab {
case castagnoliTable:
d.crc = updateCastagnoli(d.crc, p)
case IEEETable:
// We only create digest objects through New() which takes care of
// initialization in this case.
d.crc = updateIEEE(d.crc, p)
default:
d.crc = simpleUpdate(d.crc, d.tab, p)
}
return len(p), nil
}
func (d *digest) Sum32() uint32 { return d.crc }
func (d *digest) Sum(in []byte) []byte {
s := d.Sum32()
return append(in, byte(s>>24), byte(s>>16), byte(s>>8), byte(s))
}
// Checksum returns the CRC-32 checksum of data
// using the polynomial represented by the Table.
func Checksum(data []byte, tab *Table) uint32 { return Update(0, tab, data) }
// ChecksumIEEE returns the CRC-32 checksum of data
// using the IEEE polynomial.
func ChecksumIEEE(data []byte) uint32 {
ieeeOnce.Do(ieeeInit)
return updateIEEE(0, data)
}

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// Copyright 2011 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.
// +build !appengine,!gccgo
// AMD64-specific hardware-assisted CRC32 algorithms. See crc32.go for a
// description of the interface that each architecture-specific file
// implements.
package crc32
import "unsafe"
// This file contains the code to call the SSE 4.2 version of the Castagnoli
// and IEEE CRC.
// haveSSE41/haveSSE42/haveCLMUL are defined in crc_amd64.s and use
// CPUID to test for SSE 4.1, 4.2 and CLMUL support.
func haveSSE41() bool
func haveSSE42() bool
func haveCLMUL() bool
// 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
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 archAvailableCastagnoli() bool {
return sse42
}
func archInitCastagnoli() {
if !sse42 {
panic("arch-specific Castagnoli not available")
}
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[:])
}
}
}
// 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 archUpdateCastagnoli(crc uint32, p []byte) uint32 {
if !sse42 {
panic("not available")
}
// 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:]
}
}
// 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 archAvailableIEEE() bool {
return useFastIEEE
}
var archIeeeTable8 *slicing8Table
func archInitIEEE() {
if !useFastIEEE {
panic("not available")
}
// We still use slicing-by-8 for small buffers.
archIeeeTable8 = slicingMakeTable(IEEE)
}
func archUpdateIEEE(crc uint32, p []byte) uint32 {
if !useFastIEEE {
panic("not available")
}
if len(p) >= 64 {
left := len(p) & 15
do := len(p) - left
crc = ^ieeeCLMUL(^crc, p[:do])
p = p[do:]
}
if len(p) == 0 {
return crc
}
return slicingUpdate(crc, archIeeeTable8, p)
}

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// Copyright 2011 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.
// +build gc
#define NOSPLIT 4
#define RODATA 8
// 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)
// If there are fewer than 8 bytes to process, skip alignment.
CMPQ CX, $8
JL less_than_8
MOVQ SI, BX
ANDQ $7, BX
JZ aligned
// Process the first few bytes to 8-byte align the input.
// BX = 8 - BX. We need to process this many bytes to align.
SUBQ $1, BX
XORQ $7, BX
BTQ $0, BX
JNC align_2
CRC32B (SI), AX
DECQ CX
INCQ SI
align_2:
BTQ $1, BX
JNC align_4
// CRC32W (SI), AX
BYTE $0x66; BYTE $0xf2; BYTE $0x0f; BYTE $0x38; BYTE $0xf1; BYTE $0x06
SUBQ $2, CX
ADDQ $2, SI
align_4:
BTQ $2, BX
JNC aligned
// CRC32L (SI), AX
BYTE $0xf2; BYTE $0x0f; BYTE $0x38; BYTE $0xf1; BYTE $0x06
SUBQ $4, CX
ADDQ $4, SI
aligned:
// The input is now 8-byte aligned and we can process 8-byte chunks.
CMPQ CX, $8
JL less_than_8
CRC32Q (SI), AX
ADDQ $8, SI
SUBQ $8, CX
JMP aligned
less_than_8:
// We may have some bytes left over; process 4 bytes, then 2, then 1.
BTQ $2, CX
JNC less_than_4
// CRC32L (SI), AX
BYTE $0xf2; BYTE $0x0f; BYTE $0x38; BYTE $0xf1; BYTE $0x06
ADDQ $4, SI
less_than_4:
BTQ $1, CX
JNC less_than_2
// CRC32W (SI), AX
BYTE $0x66; BYTE $0xf2; BYTE $0x0f; BYTE $0x38; BYTE $0xf1; BYTE $0x06
ADDQ $2, SI
less_than_2:
BTQ $0, CX
JNC done
CRC32B (SI), AX
done:
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
INCL AX
CPUID
SHRQ $20, CX
ANDQ $1, CX
MOVB CX, ret+0(FP)
RET
// func haveCLMUL() bool
TEXT ·haveCLMUL(SB), NOSPLIT, $0
XORQ AX, AX
INCL AX
CPUID
SHRQ $1, CX
ANDQ $1, CX
MOVB CX, ret+0(FP)
RET
// func haveSSE41() bool
TEXT ·haveSSE41(SB), NOSPLIT, $0
XORQ AX, AX
INCL AX
CPUID
SHRQ $19, CX
ANDQ $1, CX
MOVB CX, ret+0(FP)
RET
// CRC32 polynomial data
//
// These constants are lifted from the
// Linux kernel, since they avoid the costly
// PSHUFB 16 byte reversal proposed in the
// original Intel paper.
DATA r2r1kp<>+0(SB)/8, $0x154442bd4
DATA r2r1kp<>+8(SB)/8, $0x1c6e41596
DATA r4r3kp<>+0(SB)/8, $0x1751997d0
DATA r4r3kp<>+8(SB)/8, $0x0ccaa009e
DATA rupolykp<>+0(SB)/8, $0x1db710641
DATA rupolykp<>+8(SB)/8, $0x1f7011641
DATA r5kp<>+0(SB)/8, $0x163cd6124
GLOBL r2r1kp<>(SB), RODATA, $16
GLOBL r4r3kp<>(SB), RODATA, $16
GLOBL rupolykp<>(SB), RODATA, $16
GLOBL r5kp<>(SB), RODATA, $8
// Based on http://www.intel.com/content/dam/www/public/us/en/documents/white-papers/fast-crc-computation-generic-polynomials-pclmulqdq-paper.pdf
// len(p) must be at least 64, and must be a multiple of 16.
// func ieeeCLMUL(crc uint32, p []byte) uint32
TEXT ·ieeeCLMUL(SB), NOSPLIT, $0
MOVL crc+0(FP), X0 // Initial CRC value
MOVQ p+8(FP), SI // data pointer
MOVQ p_len+16(FP), CX // len(p)
MOVOU (SI), X1
MOVOU 16(SI), X2
MOVOU 32(SI), X3
MOVOU 48(SI), X4
PXOR X0, X1
ADDQ $64, SI // buf+=64
SUBQ $64, CX // len-=64
CMPQ CX, $64 // Less than 64 bytes left
JB remain64
MOVOA r2r1kp<>+0(SB), X0
loopback64:
MOVOA X1, X5
MOVOA X2, X6
MOVOA X3, X7
MOVOA X4, X8
PCLMULQDQ $0, X0, X1
PCLMULQDQ $0, X0, X2
PCLMULQDQ $0, X0, X3
PCLMULQDQ $0, X0, X4
// Load next early
MOVOU (SI), X11
MOVOU 16(SI), X12
MOVOU 32(SI), X13
MOVOU 48(SI), X14
PCLMULQDQ $0x11, X0, X5
PCLMULQDQ $0x11, X0, X6
PCLMULQDQ $0x11, X0, X7
PCLMULQDQ $0x11, X0, X8
PXOR X5, X1
PXOR X6, X2
PXOR X7, X3
PXOR X8, X4
PXOR X11, X1
PXOR X12, X2
PXOR X13, X3
PXOR X14, X4
ADDQ $0x40, DI
ADDQ $64, SI // buf+=64
SUBQ $64, CX // len-=64
CMPQ CX, $64 // Less than 64 bytes left?
JGE loopback64
// Fold result into a single register (X1)
remain64:
MOVOA r4r3kp<>+0(SB), X0
MOVOA X1, X5
PCLMULQDQ $0, X0, X1
PCLMULQDQ $0x11, X0, X5
PXOR X5, X1
PXOR X2, X1
MOVOA X1, X5
PCLMULQDQ $0, X0, X1
PCLMULQDQ $0x11, X0, X5
PXOR X5, X1
PXOR X3, X1
MOVOA X1, X5
PCLMULQDQ $0, X0, X1
PCLMULQDQ $0x11, X0, X5
PXOR X5, X1
PXOR X4, X1
// If there is less than 16 bytes left we are done
CMPQ CX, $16
JB finish
// Encode 16 bytes
remain16:
MOVOU (SI), X10
MOVOA X1, X5
PCLMULQDQ $0, X0, X1
PCLMULQDQ $0x11, X0, X5
PXOR X5, X1
PXOR X10, X1
SUBQ $16, CX
ADDQ $16, SI
CMPQ CX, $16
JGE remain16
finish:
// Fold final result into 32 bits and return it
PCMPEQB X3, X3
PCLMULQDQ $1, X1, X0
PSRLDQ $8, X1
PXOR X0, X1
MOVOA X1, X2
MOVQ r5kp<>+0(SB), X0
// Creates 32 bit mask. Note that we don't care about upper half.
PSRLQ $32, X3
PSRLDQ $4, X2
PAND X3, X1
PCLMULQDQ $0, X0, X1
PXOR X2, X1
MOVOA rupolykp<>+0(SB), X0
MOVOA X1, X2
PAND X3, X1
PCLMULQDQ $0x10, X0, X1
PAND X3, X1
PCLMULQDQ $0, X0, X1
PXOR X2, X1
// PEXTRD $1, X1, AX (SSE 4.1)
BYTE $0x66; BYTE $0x0f; BYTE $0x3a
BYTE $0x16; BYTE $0xc8; BYTE $0x01
MOVL AX, ret+32(FP)
RET

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// Copyright 2011 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.
// +build !appengine,!gccgo
package crc32
// This file contains the code to call the SSE 4.2 version of the Castagnoli
// CRC.
// haveSSE42 is defined in crc32_amd64p32.s and uses CPUID to test for SSE 4.2
// support.
func haveSSE42() bool
// castagnoliSSE42 is defined in crc32_amd64p32.s and uses the SSE4.2 CRC32
// instruction.
//go:noescape
func castagnoliSSE42(crc uint32, p []byte) uint32
var sse42 = haveSSE42()
func archAvailableCastagnoli() bool {
return sse42
}
func archInitCastagnoli() {
if !sse42 {
panic("not available")
}
// No initialization necessary.
}
func archUpdateCastagnoli(crc uint32, p []byte) uint32 {
if !sse42 {
panic("not available")
}
return castagnoliSSE42(crc, p)
}
func archAvailableIEEE() bool { return false }
func archInitIEEE() { panic("not available") }
func archUpdateIEEE(crc uint32, p []byte) uint32 { panic("not available") }

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// Copyright 2011 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.
// +build gc
#define NOSPLIT 4
#define RODATA 8
// func castagnoliSSE42(crc uint32, p []byte) uint32
TEXT ·castagnoliSSE42(SB), NOSPLIT, $0
MOVL crc+0(FP), AX // CRC value
MOVL p+4(FP), SI // data pointer
MOVL p_len+8(FP), CX // len(p)
NOTL AX
// If there's less than 8 bytes to process, we do it byte-by-byte.
CMPQ CX, $8
JL cleanup
// Process individual bytes until the input is 8-byte aligned.
startup:
MOVQ SI, BX
ANDQ $7, BX
JZ aligned
CRC32B (SI), AX
DECQ CX
INCQ SI
JMP startup
aligned:
// The input is now 8-byte aligned and we can process 8-byte chunks.
CMPQ CX, $8
JL cleanup
CRC32Q (SI), AX
ADDQ $8, SI
SUBQ $8, CX
JMP aligned
cleanup:
// We may have some bytes left over that we process one at a time.
CMPQ CX, $0
JE done
CRC32B (SI), AX
INCQ SI
DECQ CX
JMP cleanup
done:
NOTL AX
MOVL AX, ret+16(FP)
RET
// func haveSSE42() bool
TEXT ·haveSSE42(SB), NOSPLIT, $0
XORQ AX, AX
INCL AX
CPUID
SHRQ $20, CX
ANDQ $1, CX
MOVB CX, ret+0(FP)
RET

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// Copyright 2011 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.
// This file contains CRC32 algorithms that are not specific to any architecture
// and don't use hardware acceleration.
//
// The simple (and slow) CRC32 implementation only uses a 256*4 bytes table.
//
// The slicing-by-8 algorithm is a faster implementation that uses a bigger
// table (8*256*4 bytes).
package crc32
// simpleMakeTable allocates and constructs a Table for the specified
// polynomial. The table is suitable for use with the simple algorithm
// (simpleUpdate).
func simpleMakeTable(poly uint32) *Table {
t := new(Table)
simplePopulateTable(poly, t)
return t
}
// simplePopulateTable constructs a Table for the specified polynomial, suitable
// for use with simpleUpdate.
func simplePopulateTable(poly uint32, t *Table) {
for i := 0; i < 256; i++ {
crc := uint32(i)
for j := 0; j < 8; j++ {
if crc&1 == 1 {
crc = (crc >> 1) ^ poly
} else {
crc >>= 1
}
}
t[i] = crc
}
}
// simpleUpdate uses the simple algorithm to update the CRC, given a table that
// was previously computed using simpleMakeTable.
func simpleUpdate(crc uint32, tab *Table, p []byte) uint32 {
crc = ^crc
for _, v := range p {
crc = tab[byte(crc)^v] ^ (crc >> 8)
}
return ^crc
}
// Use slicing-by-8 when payload >= this value.
const slicing8Cutoff = 16
// slicing8Table is array of 8 Tables, used by the slicing-by-8 algorithm.
type slicing8Table [8]Table
// slicingMakeTable constructs a slicing8Table for the specified polynomial. The
// table is suitable for use with the slicing-by-8 algorithm (slicingUpdate).
func slicingMakeTable(poly uint32) *slicing8Table {
t := new(slicing8Table)
simplePopulateTable(poly, &t[0])
for i := 0; i < 256; i++ {
crc := t[0][i]
for j := 1; j < 8; j++ {
crc = t[0][crc&0xFF] ^ (crc >> 8)
t[j][i] = crc
}
}
return t
}
// slicingUpdate uses the slicing-by-8 algorithm to update the CRC, given a
// table that was previously computed using slicingMakeTable.
func slicingUpdate(crc uint32, tab *slicing8Table, p []byte) uint32 {
if len(p) >= slicing8Cutoff {
crc = ^crc
for len(p) > 8 {
crc ^= uint32(p[0]) | uint32(p[1])<<8 | uint32(p[2])<<16 | uint32(p[3])<<24
crc = tab[0][p[7]] ^ tab[1][p[6]] ^ tab[2][p[5]] ^ tab[3][p[4]] ^
tab[4][crc>>24] ^ tab[5][(crc>>16)&0xFF] ^
tab[6][(crc>>8)&0xFF] ^ tab[7][crc&0xFF]
p = p[8:]
}
crc = ^crc
}
if len(p) == 0 {
return crc
}
return simpleUpdate(crc, &tab[0], p)
}

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// Copyright 2011 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.
// +build !amd64,!amd64p32,!s390x
package crc32
func archAvailableIEEE() bool { return false }
func archInitIEEE() { panic("not available") }
func archUpdateIEEE(crc uint32, p []byte) uint32 { panic("not available") }
func archAvailableCastagnoli() bool { return false }
func archInitCastagnoli() { panic("not available") }
func archUpdateCastagnoli(crc uint32, p []byte) uint32 { panic("not available") }

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// Copyright 2016 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.
// +build s390x
package crc32
const (
vxMinLen = 64
vxAlignMask = 15 // align to 16 bytes
)
// hasVectorFacility reports whether the machine has the z/Architecture
// vector facility installed and enabled.
func hasVectorFacility() bool
var hasVX = hasVectorFacility()
// vectorizedCastagnoli implements CRC32 using vector instructions.
// It is defined in crc32_s390x.s.
//go:noescape
func vectorizedCastagnoli(crc uint32, p []byte) uint32
// vectorizedIEEE implements CRC32 using vector instructions.
// It is defined in crc32_s390x.s.
//go:noescape
func vectorizedIEEE(crc uint32, p []byte) uint32
func archAvailableCastagnoli() bool {
return hasVX
}
var archCastagnoliTable8 *slicing8Table
func archInitCastagnoli() {
if !hasVX {
panic("not available")
}
// We still use slicing-by-8 for small buffers.
archCastagnoliTable8 = slicingMakeTable(Castagnoli)
}
// archUpdateCastagnoli calculates the checksum of p using
// vectorizedCastagnoli.
func archUpdateCastagnoli(crc uint32, p []byte) uint32 {
if !hasVX {
panic("not available")
}
// Use vectorized function if data length is above threshold.
if len(p) >= vxMinLen {
aligned := len(p) & ^vxAlignMask
crc = vectorizedCastagnoli(crc, p[:aligned])
p = p[aligned:]
}
if len(p) == 0 {
return crc
}
return slicingUpdate(crc, archCastagnoliTable8, p)
}
func archAvailableIEEE() bool {
return hasVX
}
var archIeeeTable8 *slicing8Table
func archInitIEEE() {
if !hasVX {
panic("not available")
}
// We still use slicing-by-8 for small buffers.
archIeeeTable8 = slicingMakeTable(IEEE)
}
// archUpdateIEEE calculates the checksum of p using vectorizedIEEE.
func archUpdateIEEE(crc uint32, p []byte) uint32 {
if !hasVX {
panic("not available")
}
// Use vectorized function if data length is above threshold.
if len(p) >= vxMinLen {
aligned := len(p) & ^vxAlignMask
crc = vectorizedIEEE(crc, p[:aligned])
p = p[aligned:]
}
if len(p) == 0 {
return crc
}
return slicingUpdate(crc, archIeeeTable8, p)
}

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// Copyright 2016 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.
// +build s390x
#include "textflag.h"
// Vector register range containing CRC-32 constants
#define CONST_PERM_LE2BE V9
#define CONST_R2R1 V10
#define CONST_R4R3 V11
#define CONST_R5 V12
#define CONST_RU_POLY V13
#define CONST_CRC_POLY V14
// The CRC-32 constant block contains reduction constants to fold and
// process particular chunks of the input data stream in parallel.
//
// Note that the constant definitions below are extended in order to compute
// intermediate results with a single VECTOR GALOIS FIELD MULTIPLY instruction.
// The rightmost doubleword can be 0 to prevent contribution to the result or
// can be multiplied by 1 to perform an XOR without the need for a separate
// VECTOR EXCLUSIVE OR instruction.
//
// The polynomials used are bit-reflected:
//
// IEEE: P'(x) = 0x0edb88320
// Castagnoli: P'(x) = 0x082f63b78
// IEEE polynomial constants
DATA ·crcleconskp+0(SB)/8, $0x0F0E0D0C0B0A0908 // LE-to-BE mask
DATA ·crcleconskp+8(SB)/8, $0x0706050403020100
DATA ·crcleconskp+16(SB)/8, $0x00000001c6e41596 // R2
DATA ·crcleconskp+24(SB)/8, $0x0000000154442bd4 // R1
DATA ·crcleconskp+32(SB)/8, $0x00000000ccaa009e // R4
DATA ·crcleconskp+40(SB)/8, $0x00000001751997d0 // R3
DATA ·crcleconskp+48(SB)/8, $0x0000000000000000
DATA ·crcleconskp+56(SB)/8, $0x0000000163cd6124 // R5
DATA ·crcleconskp+64(SB)/8, $0x0000000000000000
DATA ·crcleconskp+72(SB)/8, $0x00000001F7011641 // u'
DATA ·crcleconskp+80(SB)/8, $0x0000000000000000
DATA ·crcleconskp+88(SB)/8, $0x00000001DB710641 // P'(x) << 1
GLOBL ·crcleconskp(SB), RODATA, $144
// Castagonli Polynomial constants
DATA ·crccleconskp+0(SB)/8, $0x0F0E0D0C0B0A0908 // LE-to-BE mask
DATA ·crccleconskp+8(SB)/8, $0x0706050403020100
DATA ·crccleconskp+16(SB)/8, $0x000000009e4addf8 // R2
DATA ·crccleconskp+24(SB)/8, $0x00000000740eef02 // R1
DATA ·crccleconskp+32(SB)/8, $0x000000014cd00bd6 // R4
DATA ·crccleconskp+40(SB)/8, $0x00000000f20c0dfe // R3
DATA ·crccleconskp+48(SB)/8, $0x0000000000000000
DATA ·crccleconskp+56(SB)/8, $0x00000000dd45aab8 // R5
DATA ·crccleconskp+64(SB)/8, $0x0000000000000000
DATA ·crccleconskp+72(SB)/8, $0x00000000dea713f1 // u'
DATA ·crccleconskp+80(SB)/8, $0x0000000000000000
DATA ·crccleconskp+88(SB)/8, $0x0000000105ec76f0 // P'(x) << 1
GLOBL ·crccleconskp(SB), RODATA, $144
// func hasVectorFacility() bool
TEXT ·hasVectorFacility(SB), NOSPLIT, $24-1
MOVD $x-24(SP), R1
XC $24, 0(R1), 0(R1) // clear the storage
MOVD $2, R0 // R0 is the number of double words stored -1
WORD $0xB2B01000 // STFLE 0(R1)
XOR R0, R0 // reset the value of R0
MOVBZ z-8(SP), R1
AND $0x40, R1
BEQ novector
vectorinstalled:
// check if the vector instruction has been enabled
VLEIB $0, $0xF, V16
VLGVB $0, V16, R1
CMPBNE R1, $0xF, novector
MOVB $1, ret+0(FP) // have vx
RET
novector:
MOVB $0, ret+0(FP) // no vx
RET
// The CRC-32 function(s) use these calling conventions:
//
// Parameters:
//
// R2: Initial CRC value, typically ~0; and final CRC (return) value.
// R3: Input buffer pointer, performance might be improved if the
// buffer is on a doubleword boundary.
// R4: Length of the buffer, must be 64 bytes or greater.
//
// Register usage:
//
// R5: CRC-32 constant pool base pointer.
// V0: Initial CRC value and intermediate constants and results.
// V1..V4: Data for CRC computation.
// V5..V8: Next data chunks that are fetched from the input buffer.
//
// V9..V14: CRC-32 constants.
// func vectorizedIEEE(crc uint32, p []byte) uint32
TEXT ·vectorizedIEEE(SB), NOSPLIT, $0
MOVWZ crc+0(FP), R2 // R2 stores the CRC value
MOVD p+8(FP), R3 // data pointer
MOVD p_len+16(FP), R4 // len(p)
MOVD $·crcleconskp(SB), R5
BR vectorizedBody<>(SB)
// func vectorizedCastagnoli(crc uint32, p []byte) uint32
TEXT ·vectorizedCastagnoli(SB), NOSPLIT, $0
MOVWZ crc+0(FP), R2 // R2 stores the CRC value
MOVD p+8(FP), R3 // data pointer
MOVD p_len+16(FP), R4 // len(p)
// R5: crc-32 constant pool base pointer, constant is used to reduce crc
MOVD $·crccleconskp(SB), R5
BR vectorizedBody<>(SB)
TEXT vectorizedBody<>(SB), NOSPLIT, $0
XOR $0xffffffff, R2 // NOTW R2
VLM 0(R5), CONST_PERM_LE2BE, CONST_CRC_POLY
// Load the initial CRC value into the rightmost word of V0
VZERO V0
VLVGF $3, R2, V0
// Crash if the input size is less than 64-bytes.
CMP R4, $64
BLT crash
// Load a 64-byte data chunk and XOR with CRC
VLM 0(R3), V1, V4 // 64-bytes into V1..V4
// Reflect the data if the CRC operation is in the bit-reflected domain
VPERM V1, V1, CONST_PERM_LE2BE, V1
VPERM V2, V2, CONST_PERM_LE2BE, V2
VPERM V3, V3, CONST_PERM_LE2BE, V3
VPERM V4, V4, CONST_PERM_LE2BE, V4
VX V0, V1, V1 // V1 ^= CRC
ADD $64, R3 // BUF = BUF + 64
ADD $(-64), R4
// Check remaining buffer size and jump to proper folding method
CMP R4, $64
BLT less_than_64bytes
fold_64bytes_loop:
// Load the next 64-byte data chunk into V5 to V8
VLM 0(R3), V5, V8
VPERM V5, V5, CONST_PERM_LE2BE, V5
VPERM V6, V6, CONST_PERM_LE2BE, V6
VPERM V7, V7, CONST_PERM_LE2BE, V7
VPERM V8, V8, CONST_PERM_LE2BE, V8
// Perform a GF(2) multiplication of the doublewords in V1 with
// the reduction constants in V0. The intermediate result is
// then folded (accumulated) with the next data chunk in V5 and
// stored in V1. Repeat this step for the register contents
// in V2, V3, and V4 respectively.
VGFMAG CONST_R2R1, V1, V5, V1
VGFMAG CONST_R2R1, V2, V6, V2
VGFMAG CONST_R2R1, V3, V7, V3
VGFMAG CONST_R2R1, V4, V8, V4
// Adjust buffer pointer and length for next loop
ADD $64, R3 // BUF = BUF + 64
ADD $(-64), R4 // LEN = LEN - 64
CMP R4, $64
BGE fold_64bytes_loop
less_than_64bytes:
// Fold V1 to V4 into a single 128-bit value in V1
VGFMAG CONST_R4R3, V1, V2, V1
VGFMAG CONST_R4R3, V1, V3, V1
VGFMAG CONST_R4R3, V1, V4, V1
// Check whether to continue with 64-bit folding
CMP R4, $16
BLT final_fold
fold_16bytes_loop:
VL 0(R3), V2 // Load next data chunk
VPERM V2, V2, CONST_PERM_LE2BE, V2
VGFMAG CONST_R4R3, V1, V2, V1 // Fold next data chunk
// Adjust buffer pointer and size for folding next data chunk
ADD $16, R3
ADD $-16, R4
// Process remaining data chunks
CMP R4, $16
BGE fold_16bytes_loop
final_fold:
VLEIB $7, $0x40, V9
VSRLB V9, CONST_R4R3, V0
VLEIG $0, $1, V0
VGFMG V0, V1, V1
VLEIB $7, $0x20, V9 // Shift by words
VSRLB V9, V1, V2 // Store remaining bits in V2
VUPLLF V1, V1 // Split rightmost doubleword
VGFMAG CONST_R5, V1, V2, V1 // V1 = (V1 * R5) XOR V2
// The input values to the Barret reduction are the degree-63 polynomial
// in V1 (R(x)), degree-32 generator polynomial, and the reduction
// constant u. The Barret reduction result is the CRC value of R(x) mod
// P(x).
//
// The Barret reduction algorithm is defined as:
//
// 1. T1(x) = floor( R(x) / x^32 ) GF2MUL u
// 2. T2(x) = floor( T1(x) / x^32 ) GF2MUL P(x)
// 3. C(x) = R(x) XOR T2(x) mod x^32
//
// Note: To compensate the division by x^32, use the vector unpack
// instruction to move the leftmost word into the leftmost doubleword
// of the vector register. The rightmost doubleword is multiplied
// with zero to not contribute to the intermedate results.
// T1(x) = floor( R(x) / x^32 ) GF2MUL u
VUPLLF V1, V2
VGFMG CONST_RU_POLY, V2, V2
// Compute the GF(2) product of the CRC polynomial in VO with T1(x) in
// V2 and XOR the intermediate result, T2(x), with the value in V1.
// The final result is in the rightmost word of V2.
VUPLLF V2, V2
VGFMAG CONST_CRC_POLY, V2, V1, V2
done:
VLGVF $2, V2, R2
XOR $0xffffffff, R2 // NOTW R2
MOVWZ R2, ret + 32(FP)
RET
crash:
MOVD $0, (R0) // input size is less than 64-bytes