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| author | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-16 19:23:18 +0000 |
|---|---|---|
| committer | Daniel Baumann <daniel.baumann@progress-linux.org> | 2024-04-16 19:23:18 +0000 |
| commit | 43a123c1ae6613b3efeed291fa552ecd909d3acf (patch) | |
| tree | fd92518b7024bc74031f78a1cf9e454b65e73665 /src/hash | |
| parent | Initial commit. (diff) | |
| download | golang-1.20-upstream.tar.xz golang-1.20-upstream.zip | |
Adding upstream version 1.20.14.upstream/1.20.14upstream
Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>
Diffstat (limited to '')
30 files changed, 8595 insertions, 0 deletions
diff --git a/src/hash/adler32/adler32.go b/src/hash/adler32/adler32.go new file mode 100644 index 0000000..38d644d --- /dev/null +++ b/src/hash/adler32/adler32.go @@ -0,0 +1,135 @@ +// 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 adler32 implements the Adler-32 checksum. +// +// It is defined in RFC 1950: +// +// Adler-32 is composed of two sums accumulated per byte: s1 is +// the sum of all bytes, s2 is the sum of all s1 values. Both sums +// are done modulo 65521. s1 is initialized to 1, s2 to zero. The +// Adler-32 checksum is stored as s2*65536 + s1 in most- +// significant-byte first (network) order. +package adler32 + +import ( + "errors" + "hash" +) + +const ( + // mod is the largest prime that is less than 65536. + mod = 65521 + // nmax is the largest n such that + // 255 * n * (n+1) / 2 + (n+1) * (mod-1) <= 2^32-1. + // It is mentioned in RFC 1950 (search for "5552"). + nmax = 5552 +) + +// The size of an Adler-32 checksum in bytes. +const Size = 4 + +// digest represents the partial evaluation of a checksum. +// The low 16 bits are s1, the high 16 bits are s2. +type digest uint32 + +func (d *digest) Reset() { *d = 1 } + +// New returns a new hash.Hash32 computing the Adler-32 checksum. Its +// Sum method will lay the value out in big-endian byte order. The +// returned Hash32 also implements encoding.BinaryMarshaler and +// encoding.BinaryUnmarshaler to marshal and unmarshal the internal +// state of the hash. +func New() hash.Hash32 { + d := new(digest) + d.Reset() + return d +} + +func (d *digest) Size() int { return Size } + +func (d *digest) BlockSize() int { return 4 } + +const ( + magic = "adl\x01" + marshaledSize = len(magic) + 4 +) + +func (d *digest) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize) + b = append(b, magic...) + b = appendUint32(b, uint32(*d)) + return b, nil +} + +func (d *digest) UnmarshalBinary(b []byte) error { + if len(b) < len(magic) || string(b[:len(magic)]) != magic { + return errors.New("hash/adler32: invalid hash state identifier") + } + if len(b) != marshaledSize { + return errors.New("hash/adler32: invalid hash state size") + } + *d = digest(readUint32(b[len(magic):])) + return nil +} + +func appendUint32(b []byte, x uint32) []byte { + a := [4]byte{ + byte(x >> 24), + byte(x >> 16), + byte(x >> 8), + byte(x), + } + return append(b, a[:]...) +} + +func readUint32(b []byte) uint32 { + _ = b[3] + return uint32(b[3]) | uint32(b[2])<<8 | uint32(b[1])<<16 | uint32(b[0])<<24 +} + +// Add p to the running checksum d. +func update(d digest, p []byte) digest { + s1, s2 := uint32(d&0xffff), uint32(d>>16) + for len(p) > 0 { + var q []byte + if len(p) > nmax { + p, q = p[:nmax], p[nmax:] + } + for len(p) >= 4 { + s1 += uint32(p[0]) + s2 += s1 + s1 += uint32(p[1]) + s2 += s1 + s1 += uint32(p[2]) + s2 += s1 + s1 += uint32(p[3]) + s2 += s1 + p = p[4:] + } + for _, x := range p { + s1 += uint32(x) + s2 += s1 + } + s1 %= mod + s2 %= mod + p = q + } + return digest(s2<<16 | s1) +} + +func (d *digest) Write(p []byte) (nn int, err error) { + *d = update(*d, p) + return len(p), nil +} + +func (d *digest) Sum32() uint32 { return uint32(*d) } + +func (d *digest) Sum(in []byte) []byte { + s := uint32(*d) + return append(in, byte(s>>24), byte(s>>16), byte(s>>8), byte(s)) +} + +// Checksum returns the Adler-32 checksum of data. +func Checksum(data []byte) uint32 { return uint32(update(1, data)) } diff --git a/src/hash/adler32/adler32_test.go b/src/hash/adler32/adler32_test.go new file mode 100644 index 0000000..6bac802 --- /dev/null +++ b/src/hash/adler32/adler32_test.go @@ -0,0 +1,140 @@ +// 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 adler32 + +import ( + "encoding" + "io" + "strings" + "testing" +) + +var golden = []struct { + out uint32 + in string + halfState string // marshaled hash state after first half of in written, used by TestGoldenMarshal +}{ + {0x00000001, "", "adl\x01\x00\x00\x00\x01"}, + {0x00620062, "a", "adl\x01\x00\x00\x00\x01"}, + {0x012600c4, "ab", "adl\x01\x00b\x00b"}, + {0x024d0127, "abc", "adl\x01\x00b\x00b"}, + {0x03d8018b, "abcd", "adl\x01\x01&\x00\xc4"}, + {0x05c801f0, "abcde", "adl\x01\x01&\x00\xc4"}, + {0x081e0256, "abcdef", "adl\x01\x02M\x01'"}, + {0x0adb02bd, "abcdefg", "adl\x01\x02M\x01'"}, + {0x0e000325, "abcdefgh", "adl\x01\x03\xd8\x01\x8b"}, + {0x118e038e, "abcdefghi", "adl\x01\x03\xd8\x01\x8b"}, + {0x158603f8, "abcdefghij", "adl\x01\x05\xc8\x01\xf0"}, + {0x3f090f02, "Discard medicine more than two years old.", "adl\x01NU\a\x87"}, + {0x46d81477, "He who has a shady past knows that nice guys finish last.", "adl\x01\x89\x8e\t\xe9"}, + {0x40ee0ee1, "I wouldn't marry him with a ten foot pole.", "adl\x01R\t\ag"}, + {0x16661315, "Free! Free!/A trip/to Mars/for 900/empty jars/Burma Shave", "adl\x01\u007f\xbb\t\x10"}, + {0x5b2e1480, "The days of the digital watch are numbered. -Tom Stoppard", "adl\x01\x99:\n~"}, + {0x8c3c09ea, "Nepal premier won't resign.", "adl\x01\"\x05\x05\x05"}, + {0x45ac18fd, "For every action there is an equal and opposite government program.", "adl\x01\xcc\xfa\f\x00"}, + {0x53c61462, "His money is twice tainted: 'taint yours and 'taint mine.", "adl\x01\x93\xa9\n\b"}, + {0x7e511e63, "There is no reason for any individual to have a computer in their home. -Ken Olsen, 1977", "adl\x01e\xf5\x10\x14"}, + {0xe4801a6a, "It's a tiny change to the code and not completely disgusting. - Bob Manchek", "adl\x01\xee\x00\f\xb2"}, + {0x61b507df, "size: a.out: bad magic", "adl\x01\x1a\xfc\x04\x1d"}, + {0xb8631171, "The major problem is with sendmail. -Mark Horton", "adl\x01mi\b\xdc"}, + {0x8b5e1904, "Give me a rock, paper and scissors and I will move the world. CCFestoon", "adl\x01\xe3\n\f\x9f"}, + {0x7cc6102b, "If the enemy is within range, then so are you.", "adl\x01_\xe0\b\x1e"}, + {0x700318e7, "It's well we cannot hear the screams/That we create in others' dreams.", "adl\x01ۘ\f\x87"}, + {0x1e601747, "You remind me of a TV show, but that's all right: I watch it anyway.", "adl\x01\xcc}\v\x83"}, + {0xb55b0b09, "C is as portable as Stonehedge!!", "adl\x01,^\x05\xad"}, + {0x39111dd0, "Even if I could be Shakespeare, I think I should still choose to be Faraday. - A. Huxley", "adl\x01M\xd1\x0e\xc8"}, + {0x91dd304f, "The fugacity of a constituent in a mixture of gases at a given temperature is proportional to its mole fraction. Lewis-Randall Rule", "adl\x01#\xd8\x17\xd7"}, + {0x2e5d1316, "How can you write a big system without C++? -Paul Glick", "adl\x01\x8fU\n\x0f"}, + {0xd0201df6, "'Invariant assertions' is the most elegant programming technique! -Tom Szymanski", "adl\x01/\x98\x0e\xc4"}, + {0x211297c8, strings.Repeat("\xff", 5548) + "8", "adl\x01\x9a\xa6\xcb\xc1"}, + {0xbaa198c8, strings.Repeat("\xff", 5549) + "9", "adl\x01gu\xcc\xc0"}, + {0x553499be, strings.Repeat("\xff", 5550) + "0", "adl\x01gu\xcc\xc0"}, + {0xf0c19abe, strings.Repeat("\xff", 5551) + "1", "adl\x015CͿ"}, + {0x8d5c9bbe, strings.Repeat("\xff", 5552) + "2", "adl\x015CͿ"}, + {0x2af69cbe, strings.Repeat("\xff", 5553) + "3", "adl\x01\x04\x10ξ"}, + {0xc9809dbe, strings.Repeat("\xff", 5554) + "4", "adl\x01\x04\x10ξ"}, + {0x69189ebe, strings.Repeat("\xff", 5555) + "5", "adl\x01\xd3\xcdϽ"}, + {0x86af0001, strings.Repeat("\x00", 1e5), "adl\x01\xc3P\x00\x01"}, + {0x79660b4d, strings.Repeat("a", 1e5), "adl\x01\x81k\x05\xa7"}, + {0x110588ee, strings.Repeat("ABCDEFGHIJKLMNOPQRSTUVWXYZ", 1e4), "adl\x01e\xd2\xc4p"}, +} + +// checksum is a slow but simple implementation of the Adler-32 checksum. +// It is a straight port of the sample code in RFC 1950 section 9. +func checksum(p []byte) uint32 { + s1, s2 := uint32(1), uint32(0) + for _, x := range p { + s1 = (s1 + uint32(x)) % mod + s2 = (s2 + s1) % mod + } + return s2<<16 | s1 +} + +func TestGolden(t *testing.T) { + for _, g := range golden { + in := g.in + if len(in) > 220 { + in = in[:100] + "..." + in[len(in)-100:] + } + p := []byte(g.in) + if got := checksum(p); got != g.out { + t.Errorf("simple implementation: checksum(%q) = 0x%x want 0x%x", in, got, g.out) + continue + } + if got := Checksum(p); got != g.out { + t.Errorf("optimized implementation: Checksum(%q) = 0x%x want 0x%x", in, got, g.out) + continue + } + } +} + +func TestGoldenMarshal(t *testing.T) { + for _, g := range golden { + h := New() + h2 := New() + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfState { + t.Errorf("checksum(%q) state = %q, want %q", g.in, state, g.halfState) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if h.Sum32() != h2.Sum32() { + t.Errorf("checksum(%q) = 0x%x != marshaled (0x%x)", g.in, h.Sum32(), h2.Sum32()) + } + } +} + +func BenchmarkAdler32KB(b *testing.B) { + b.SetBytes(1024) + data := make([]byte, 1024) + for i := range data { + data[i] = byte(i) + } + h := New() + in := make([]byte, 0, h.Size()) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + h.Reset() + h.Write(data) + h.Sum(in) + } +} diff --git a/src/hash/crc32/crc32.go b/src/hash/crc32/crc32.go new file mode 100644 index 0000000..e828089 --- /dev/null +++ b/src/hash/crc32/crc32.go @@ -0,0 +1,265 @@ +// 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 https://en.wikipedia.org/wiki/Cyclic_redundancy_check for +// information. +// +// Polynomials are represented in LSB-first form also known as reversed representation. +// +// See https://en.wikipedia.org/wiki/Mathematics_of_cyclic_redundancy_checks#Reversed_representations_and_reciprocal_polynomials +// for information. +package crc32 + +import ( + "errors" + "hash" + "sync" + "sync/atomic" +) + +// 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. + // https://dx.doi.org/10.1109/26.231911 + Castagnoli = 0x82f63b78 + + // Koopman's polynomial. + // Also has better error detection characteristics than IEEE. + // https://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 updateCastagnoli func(crc uint32, p []byte) uint32 +var castagnoliOnce sync.Once +var haveCastagnoli atomic.Bool + +func castagnoliInit() { + castagnoliTable = simpleMakeTable(Castagnoli) + + if archAvailableCastagnoli() { + 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) + } + } + + haveCastagnoli.Store(true) +} + +// IEEETable is the table for the IEEE polynomial. +var IEEETable = simpleMakeTable(IEEE) + +// ieeeTable8 is the slicing8Table for IEEE +var ieeeTable8 *slicing8Table +var updateIEEE func(crc uint32, p []byte) uint32 +var ieeeOnce sync.Once + +func ieeeInit() { + if archAvailableIEEE() { + 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 + default: + 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. The returned Hash32 also +// implements encoding.BinaryMarshaler and encoding.BinaryUnmarshaler to +// marshal and unmarshal the internal state of the hash. +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. The returned Hash32 also implements +// encoding.BinaryMarshaler and encoding.BinaryUnmarshaler to marshal +// and unmarshal the internal state of the hash. +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 } + +const ( + magic = "crc\x01" + marshaledSize = len(magic) + 4 + 4 +) + +func (d *digest) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize) + b = append(b, magic...) + b = appendUint32(b, tableSum(d.tab)) + b = appendUint32(b, d.crc) + return b, nil +} + +func (d *digest) UnmarshalBinary(b []byte) error { + if len(b) < len(magic) || string(b[:len(magic)]) != magic { + return errors.New("hash/crc32: invalid hash state identifier") + } + if len(b) != marshaledSize { + return errors.New("hash/crc32: invalid hash state size") + } + if tableSum(d.tab) != readUint32(b[4:]) { + return errors.New("hash/crc32: tables do not match") + } + d.crc = readUint32(b[8:]) + return nil +} + +func appendUint32(b []byte, x uint32) []byte { + a := [4]byte{ + byte(x >> 24), + byte(x >> 16), + byte(x >> 8), + byte(x), + } + return append(b, a[:]...) +} + +func readUint32(b []byte) uint32 { + _ = b[3] + return uint32(b[3]) | uint32(b[2])<<8 | uint32(b[1])<<16 | uint32(b[0])<<24 +} + +func update(crc uint32, tab *Table, p []byte, checkInitIEEE bool) uint32 { + switch { + case haveCastagnoli.Load() && tab == castagnoliTable: + return updateCastagnoli(crc, p) + case tab == IEEETable: + if checkInitIEEE { + ieeeOnce.Do(ieeeInit) + } + return updateIEEE(crc, p) + default: + return simpleUpdate(crc, tab, p) + } +} + +// Update returns the result of adding the bytes in p to the crc. +func Update(crc uint32, tab *Table, p []byte) uint32 { + // 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. + return update(crc, tab, p, true) +} + +func (d *digest) Write(p []byte) (n int, err error) { + // We only create digest objects through New() which takes care of + // initialization in this case. + d.crc = update(d.crc, d.tab, p, false) + 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) +} + +// tableSum returns the IEEE checksum of table t. +func tableSum(t *Table) uint32 { + var a [1024]byte + b := a[:0] + if t != nil { + for _, x := range t { + b = appendUint32(b, x) + } + } + return ChecksumIEEE(b) +} diff --git a/src/hash/crc32/crc32_amd64.go b/src/hash/crc32/crc32_amd64.go new file mode 100644 index 0000000..6be129f --- /dev/null +++ b/src/hash/crc32/crc32_amd64.go @@ -0,0 +1,225 @@ +// 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. + +// AMD64-specific hardware-assisted CRC32 algorithms. See crc32.go for a +// description of the interface that each architecture-specific file +// implements. + +package crc32 + +import ( + "internal/cpu" + "unsafe" +) + +// This file contains the code to call the SSE 4.2 version of the Castagnoli +// and IEEE CRC. + +// castagnoliSSE42 is defined in crc32_amd64.s and uses the SSE 4.2 CRC32 +// instruction. +// +//go:noescape +func castagnoliSSE42(crc uint32, p []byte) uint32 + +// castagnoliSSE42Triple is defined in crc32_amd64.s and uses the SSE 4.2 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 + +const castagnoliK1 = 168 +const castagnoliK2 = 1344 + +type sse42Table [4]Table + +var castagnoliSSE42TableK1 *sse42Table +var castagnoliSSE42TableK2 *sse42Table + +func archAvailableCastagnoli() bool { + return cpu.X86.HasSSE42 +} + +func archInitCastagnoli() { + if !cpu.X86.HasSSE42 { + 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 !cpu.X86.HasSSE42 { + 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 cpu.X86.HasPCLMULQDQ && cpu.X86.HasSSE41 +} + +var archIeeeTable8 *slicing8Table + +func archInitIEEE() { + if !cpu.X86.HasPCLMULQDQ || !cpu.X86.HasSSE41 { + panic("not available") + } + // We still use slicing-by-8 for small buffers. + archIeeeTable8 = slicingMakeTable(IEEE) +} + +func archUpdateIEEE(crc uint32, p []byte) uint32 { + if !cpu.X86.HasPCLMULQDQ || !cpu.X86.HasSSE41 { + 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) +} diff --git a/src/hash/crc32/crc32_amd64.s b/src/hash/crc32/crc32_amd64.s new file mode 100644 index 0000000..6af6c25 --- /dev/null +++ b/src/hash/crc32/crc32_amd64.s @@ -0,0 +1,279 @@ +// 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. + +#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) + + // 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 + + SUBQ $2, CX + ADDQ $2, SI + +align_4: + BTQ $2, BX + JNC aligned + + CRC32L (SI), AX + + 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 + ADDQ $4, SI + +less_than_4: + BTQ $1, CX + JNC less_than_2 + + CRC32W (SI), AX + 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 + +// 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 r2r1<>+0(SB)/8, $0x154442bd4 +DATA r2r1<>+8(SB)/8, $0x1c6e41596 +DATA r4r3<>+0(SB)/8, $0x1751997d0 +DATA r4r3<>+8(SB)/8, $0x0ccaa009e +DATA rupoly<>+0(SB)/8, $0x1db710641 +DATA rupoly<>+8(SB)/8, $0x1f7011641 +DATA r5<>+0(SB)/8, $0x163cd6124 + +GLOBL r2r1<>(SB),RODATA,$16 +GLOBL r4r3<>(SB),RODATA,$16 +GLOBL rupoly<>(SB),RODATA,$16 +GLOBL r5<>(SB),RODATA,$8 + +// Based on https://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 r2r1<>+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 r4r3<>+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 r5<>+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 rupoly<>+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 + MOVL AX, ret+32(FP) + + RET diff --git a/src/hash/crc32/crc32_arm64.go b/src/hash/crc32/crc32_arm64.go new file mode 100644 index 0000000..9674b76 --- /dev/null +++ b/src/hash/crc32/crc32_arm64.go @@ -0,0 +1,50 @@ +// Copyright 2017 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. + +// ARM64-specific hardware-assisted CRC32 algorithms. See crc32.go for a +// description of the interface that each architecture-specific file +// implements. + +package crc32 + +import "internal/cpu" + +func castagnoliUpdate(crc uint32, p []byte) uint32 +func ieeeUpdate(crc uint32, p []byte) uint32 + +func archAvailableCastagnoli() bool { + return cpu.ARM64.HasCRC32 +} + +func archInitCastagnoli() { + if !cpu.ARM64.HasCRC32 { + panic("arch-specific crc32 instruction for Castagnoli not available") + } +} + +func archUpdateCastagnoli(crc uint32, p []byte) uint32 { + if !cpu.ARM64.HasCRC32 { + panic("arch-specific crc32 instruction for Castagnoli not available") + } + + return ^castagnoliUpdate(^crc, p) +} + +func archAvailableIEEE() bool { + return cpu.ARM64.HasCRC32 +} + +func archInitIEEE() { + if !cpu.ARM64.HasCRC32 { + panic("arch-specific crc32 instruction for IEEE not available") + } +} + +func archUpdateIEEE(crc uint32, p []byte) uint32 { + if !cpu.ARM64.HasCRC32 { + panic("arch-specific crc32 instruction for IEEE not available") + } + + return ^ieeeUpdate(^crc, p) +} diff --git a/src/hash/crc32/crc32_arm64.s b/src/hash/crc32/crc32_arm64.s new file mode 100644 index 0000000..85a113f --- /dev/null +++ b/src/hash/crc32/crc32_arm64.s @@ -0,0 +1,97 @@ +// Copyright 2017 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. + +#include "textflag.h" + +// castagnoliUpdate updates the non-inverted crc with the given data. + +// func castagnoliUpdate(crc uint32, p []byte) uint32 +TEXT ·castagnoliUpdate(SB),NOSPLIT,$0-36 + MOVWU crc+0(FP), R9 // CRC value + MOVD p+8(FP), R13 // data pointer + MOVD p_len+16(FP), R11 // len(p) + +update: + CMP $16, R11 + BLT less_than_16 + LDP.P 16(R13), (R8, R10) + CRC32CX R8, R9 + CRC32CX R10, R9 + SUB $16, R11 + + JMP update + +less_than_16: + TBZ $3, R11, less_than_8 + + MOVD.P 8(R13), R10 + CRC32CX R10, R9 + +less_than_8: + TBZ $2, R11, less_than_4 + + MOVWU.P 4(R13), R10 + CRC32CW R10, R9 + +less_than_4: + TBZ $1, R11, less_than_2 + + MOVHU.P 2(R13), R10 + CRC32CH R10, R9 + +less_than_2: + TBZ $0, R11, done + + MOVBU (R13), R10 + CRC32CB R10, R9 + +done: + MOVWU R9, ret+32(FP) + RET + +// ieeeUpdate updates the non-inverted crc with the given data. + +// func ieeeUpdate(crc uint32, p []byte) uint32 +TEXT ·ieeeUpdate(SB),NOSPLIT,$0-36 + MOVWU crc+0(FP), R9 // CRC value + MOVD p+8(FP), R13 // data pointer + MOVD p_len+16(FP), R11 // len(p) + +update: + CMP $16, R11 + BLT less_than_16 + LDP.P 16(R13), (R8, R10) + CRC32X R8, R9 + CRC32X R10, R9 + SUB $16, R11 + + JMP update + +less_than_16: + TBZ $3, R11, less_than_8 + + MOVD.P 8(R13), R10 + CRC32X R10, R9 + +less_than_8: + TBZ $2, R11, less_than_4 + + MOVWU.P 4(R13), R10 + CRC32W R10, R9 + +less_than_4: + TBZ $1, R11, less_than_2 + + MOVHU.P 2(R13), R10 + CRC32H R10, R9 + +less_than_2: + TBZ $0, R11, done + + MOVBU (R13), R10 + CRC32B R10, R9 + +done: + MOVWU R9, ret+32(FP) + RET diff --git a/src/hash/crc32/crc32_generic.go b/src/hash/crc32/crc32_generic.go new file mode 100644 index 0000000..abacbb6 --- /dev/null +++ b/src/hash/crc32/crc32_generic.go @@ -0,0 +1,89 @@ +// 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) +} diff --git a/src/hash/crc32/crc32_otherarch.go b/src/hash/crc32/crc32_otherarch.go new file mode 100644 index 0000000..7625152 --- /dev/null +++ b/src/hash/crc32/crc32_otherarch.go @@ -0,0 +1,15 @@ +// 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. + +//go:build !amd64 && !s390x && !ppc64le && !arm64 + +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") } diff --git a/src/hash/crc32/crc32_ppc64le.go b/src/hash/crc32/crc32_ppc64le.go new file mode 100644 index 0000000..c22e38e --- /dev/null +++ b/src/hash/crc32/crc32_ppc64le.go @@ -0,0 +1,88 @@ +// Copyright 2017 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 ( + "unsafe" +) + +const ( + vecMinLen = 16 + vecAlignMask = 15 // align to 16 bytes + crcIEEE = 1 + crcCast = 2 +) + +//go:noescape +func ppc64SlicingUpdateBy8(crc uint32, table8 *slicing8Table, p []byte) uint32 + +// this function requires the buffer to be 16 byte aligned and > 16 bytes long. +// +//go:noescape +func vectorCrc32(crc uint32, poly uint32, p []byte) uint32 + +var archCastagnoliTable8 *slicing8Table + +func archInitCastagnoli() { + archCastagnoliTable8 = slicingMakeTable(Castagnoli) +} + +func archUpdateCastagnoli(crc uint32, p []byte) uint32 { + if len(p) >= 4*vecMinLen { + // If not aligned then process the initial unaligned bytes + + if uint64(uintptr(unsafe.Pointer(&p[0])))&uint64(vecAlignMask) != 0 { + align := uint64(uintptr(unsafe.Pointer(&p[0]))) & uint64(vecAlignMask) + newlen := vecMinLen - align + crc = ppc64SlicingUpdateBy8(crc, archCastagnoliTable8, p[:newlen]) + p = p[newlen:] + } + // p should be aligned now + aligned := len(p) & ^vecAlignMask + crc = vectorCrc32(crc, crcCast, p[:aligned]) + p = p[aligned:] + } + if len(p) == 0 { + return crc + } + return ppc64SlicingUpdateBy8(crc, archCastagnoliTable8, p) +} + +func archAvailableIEEE() bool { + return true +} +func archAvailableCastagnoli() bool { + return true +} + +var archIeeeTable8 *slicing8Table + +func archInitIEEE() { + // 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 { + + // Check if vector code should be used. If not aligned, then handle those + // first up to the aligned bytes. + + if len(p) >= 4*vecMinLen { + if uint64(uintptr(unsafe.Pointer(&p[0])))&uint64(vecAlignMask) != 0 { + align := uint64(uintptr(unsafe.Pointer(&p[0]))) & uint64(vecAlignMask) + newlen := vecMinLen - align + crc = ppc64SlicingUpdateBy8(crc, archIeeeTable8, p[:newlen]) + p = p[newlen:] + } + aligned := len(p) & ^vecAlignMask + crc = vectorCrc32(crc, crcIEEE, p[:aligned]) + p = p[aligned:] + } + if len(p) == 0 { + return crc + } + return ppc64SlicingUpdateBy8(crc, archIeeeTable8, p) +} diff --git a/src/hash/crc32/crc32_ppc64le.s b/src/hash/crc32/crc32_ppc64le.s new file mode 100644 index 0000000..763d327 --- /dev/null +++ b/src/hash/crc32/crc32_ppc64le.s @@ -0,0 +1,705 @@ +// Copyright 2017 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. + +// The vectorized implementation found below is a derived work +// from code written by Anton Blanchard <anton@au.ibm.com> found +// at https://github.com/antonblanchard/crc32-vpmsum. The original +// is dual licensed under GPL and Apache 2. As the copyright holder +// for the work, IBM has contributed this new work under +// the golang license. + +// Changes include porting to Go assembler with modifications for +// the Go ABI for ppc64le. + +#include "textflag.h" + +#define POWER8_OFFSET 132 + +#define off16 R16 +#define off32 R17 +#define off48 R18 +#define off64 R19 +#define off80 R20 +#define off96 R21 +#define off112 R22 + +#define const1 V24 +#define const2 V25 + +#define byteswap V26 +#define mask_32bit V27 +#define mask_64bit V28 +#define zeroes V29 + +#define MAX_SIZE 32*1024 +#define REFLECT + +TEXT ·ppc64SlicingUpdateBy8(SB), NOSPLIT|NOFRAME, $0-44 + MOVWZ crc+0(FP), R3 // incoming crc + MOVD table8+8(FP), R4 // *Table + MOVD p+16(FP), R5 + MOVD p_len+24(FP), R6 // p len + + CMP $0,R6 // len == 0? + BNE start + MOVW R3,ret+40(FP) // return crc + RET + +start: + NOR R3,R3,R7 // ^crc + MOVWZ R7,R7 // 32 bits + CMP R6,$16 + MOVD R6,CTR + BLT short + SRAD $3,R6,R8 // 8 byte chunks + MOVD R8,CTR + +loop: + MOVWZ 0(R5),R8 // 0-3 bytes of p ?Endian? + MOVWZ 4(R5),R9 // 4-7 bytes of p + MOVD R4,R10 // &tab[0] + XOR R7,R8,R7 // crc ^= byte[0:3] + RLDICL $40,R9,$56,R17 // p[7] + SLD $2,R17,R17 // p[7]*4 + RLDICL $40,R7,$56,R8 // crc>>24 + ADD R17,R10,R17 // &tab[0][p[7]] + SLD $2,R8,R8 // crc>>24*4 + RLDICL $48,R9,$56,R18 // p[6] + SLD $2,R18,R18 // p[6]*4 + ADD $1024,R10,R10 // tab[1] + MOVWZ 0(R17),R21 // tab[0][p[7]] + RLDICL $56,R9,$56,R19 // p[5] + ADD R10,R18,R18 // &tab[1][p[6]] + SLD $2,R19,R19 // p[5]*4:1 + MOVWZ 0(R18),R22 // tab[1][p[6]] + ADD $1024,R10,R10 // tab[2] + XOR R21,R22,R21 // xor done R22 + ADD R19,R10,R19 // &tab[2][p[5]] + ANDCC $255,R9,R20 // p[4] ?? + SLD $2,R20,R20 // p[4]*4 + MOVWZ 0(R19),R23 // tab[2][p[5]] + ADD $1024,R10,R10 // &tab[3] + ADD R20,R10,R20 // tab[3][p[4]] + XOR R21,R23,R21 // xor done R23 + ADD $1024,R10,R10 // &tab[4] + MOVWZ 0(R20),R24 // tab[3][p[4]] + ADD R10,R8,R23 // &tab[4][crc>>24] + XOR R21,R24,R21 // xor done R24 + MOVWZ 0(R23),R25 // tab[4][crc>>24] + RLDICL $48,R7,$56,R24 // crc>>16&0xFF + XOR R21,R25,R21 // xor done R25 + ADD $1024,R10,R10 // &tab[5] + SLD $2,R24,R24 // crc>>16&0xFF*4 + ADD R24,R10,R24 // &tab[5][crc>>16&0xFF] + MOVWZ 0(R24),R26 // tab[5][crc>>16&0xFF] + XOR R21,R26,R21 // xor done R26 + RLDICL $56,R7,$56,R25 // crc>>8 + ADD $1024,R10,R10 // &tab[6] + SLD $2,R25,R25 // crc>>8&FF*2 + ADD R25,R10,R25 // &tab[6][crc>>8&0xFF] + MOVBZ R7,R26 // crc&0xFF + ADD $1024,R10,R10 // &tab[7] + MOVWZ 0(R25),R27 // tab[6][crc>>8&0xFF] + SLD $2,R26,R26 // crc&0xFF*2 + XOR R21,R27,R21 // xor done R27 + ADD R26,R10,R26 // &tab[7][crc&0xFF] + ADD $8,R5 // p = p[8:] + MOVWZ 0(R26),R28 // tab[7][crc&0xFF] + XOR R21,R28,R21 // xor done R28 + MOVWZ R21,R7 // crc for next round + BC 16,0,loop // next 8 bytes + ANDCC $7,R6,R8 // any leftover bytes + BEQ done // none --> done + MOVD R8,CTR // byte count + PCALIGN $16 // align short loop +short: + MOVBZ 0(R5),R8 // get v + MOVBZ R7,R9 // byte(crc) -> R8 BE vs LE? + SRD $8,R7,R14 // crc>>8 + XOR R8,R9,R8 // byte(crc)^v -> R8 + ADD $1,R5 // ptr to next v + SLD $2,R8 // convert index-> bytes + ADD R8,R4,R9 // &tab[byte(crc)^v] + MOVWZ 0(R9),R10 // tab[byte(crc)^v] + XOR R10,R14,R7 // loop crc in R7 + BC 16,0,short +done: + NOR R7,R7,R7 // ^crc + MOVW R7,ret+40(FP) // return crc + RET + +#ifdef BYTESWAP_DATA +DATA ·byteswapcons+0(SB)/8,$0x0706050403020100 +DATA ·byteswapcons+8(SB)/8,$0x0f0e0d0c0b0a0908 + +GLOBL ·byteswapcons+0(SB),RODATA,$16 +#endif + +TEXT ·vectorCrc32(SB), NOSPLIT|NOFRAME, $0-36 + MOVWZ crc+0(FP), R3 // incoming crc + MOVWZ ctab+4(FP), R14 // crc poly id + MOVD p+8(FP), R4 + MOVD p_len+16(FP), R5 // p len + + // R3 = incoming crc + // R14 = constant table identifier + // R5 = address of bytes + // R6 = length of bytes + + // defines for index loads + + MOVD $16,off16 + MOVD $32,off32 + MOVD $48,off48 + MOVD $64,off64 + MOVD $80,off80 + MOVD $96,off96 + MOVD $112,off112 + MOVD $0,R15 + + MOVD R3,R10 // save initial crc + + NOR R3,R3,R3 // ^crc + MOVWZ R3,R3 // 32 bits + VXOR zeroes,zeroes,zeroes // clear the V reg + VSPLTISW $-1,V0 + VSLDOI $4,V29,V0,mask_32bit + VSLDOI $8,V29,V0,mask_64bit + + VXOR V8,V8,V8 + MTVSRD R3,VS40 // crc initial value VS40 = V8 + +#ifdef REFLECT + VSLDOI $8,zeroes,V8,V8 // or: VSLDOI V29,V8,V27,4 for top 32 bits? +#else + VSLDOI $4,V8,zeroes,V8 +#endif + +#ifdef BYTESWAP_DATA + MOVD $·byteswapcons(SB),R3 + LVX (R3),byteswap +#endif + + CMPU R5,$256 // length of bytes + BLT short + + RLDICR $0,R5,$56,R6 // chunk to process + + // First step for larger sizes +l1: MOVD $32768,R7 + MOVD R7,R9 + CMP R6,R7 // compare R6, R7 (MAX SIZE) + BGT top // less than MAX, just do remainder + MOVD R6,R7 +top: + SUB R7,R6,R6 + + // mainloop does 128 bytes at a time + SRD $7,R7 + + // determine the offset into the constants table to start with. + // Each constant is 128 bytes, used against 16 bytes of data. + SLD $4,R7,R8 + SRD $3,R9,R9 + SUB R8,R9,R8 + + // The last iteration is reduced in a separate step + ADD $-1,R7 + MOVD R7,CTR + + // Determine which constant table (depends on poly) + CMP R14,$1 + BNE castTable + MOVD $·IEEEConst(SB),R3 + BR startConst +castTable: + MOVD $·CastConst(SB),R3 + +startConst: + ADD R3,R8,R3 // starting point in constants table + + VXOR V0,V0,V0 // clear the V regs + VXOR V1,V1,V1 + VXOR V2,V2,V2 + VXOR V3,V3,V3 + VXOR V4,V4,V4 + VXOR V5,V5,V5 + VXOR V6,V6,V6 + VXOR V7,V7,V7 + + LVX (R3),const1 // loading constant values + + CMP R15,$1 // Identify warm up pass + BEQ next + + // First warm up pass: load the bytes to process + LVX (R4),V16 + LVX (R4+off16),V17 + LVX (R4+off32),V18 + LVX (R4+off48),V19 + LVX (R4+off64),V20 + LVX (R4+off80),V21 + LVX (R4+off96),V22 + LVX (R4+off112),V23 + ADD $128,R4 // bump up to next 128 bytes in buffer + + VXOR V16,V8,V16 // xor in initial CRC in V8 + +next: + BC 18,0,first_warm_up_done + + ADD $16,R3 // bump up to next constants + LVX (R3),const2 // table values + + VPMSUMD V16,const1,V8 // second warm up pass + LVX (R4),V16 // load from buffer + OR $0,R2,R2 + + VPMSUMD V17,const1,V9 // vpmsumd with constants + LVX (R4+off16),V17 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V18,const1,V10 // vpmsumd with constants + LVX (R4+off32),V18 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V19,const1,V11 // vpmsumd with constants + LVX (R4+off48),V19 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V20,const1,V12 // vpmsumd with constants + LVX (R4+off64),V20 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V21,const1,V13 // vpmsumd with constants + LVX (R4+off80),V21 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V22,const1,V14 // vpmsumd with constants + LVX (R4+off96),V22 // load next from buffer + OR $0,R2,R2 + + VPMSUMD V23,const1,V15 // vpmsumd with constants + LVX (R4+off112),V23 // load next from buffer + + ADD $128,R4 // bump up to next 128 bytes in buffer + + BC 18,0,first_cool_down + +cool_top: + LVX (R3),const1 // constants + ADD $16,R3 // inc to next constants + OR $0,R2,R2 + + VXOR V0,V8,V0 // xor in previous vpmsumd + VPMSUMD V16,const2,V8 // vpmsumd with constants + LVX (R4),V16 // buffer + OR $0,R2,R2 + + VXOR V1,V9,V1 // xor in previous + VPMSUMD V17,const2,V9 // vpmsumd with constants + LVX (R4+off16),V17 // next in buffer + OR $0,R2,R2 + + VXOR V2,V10,V2 // xor in previous + VPMSUMD V18,const2,V10 // vpmsumd with constants + LVX (R4+off32),V18 // next in buffer + OR $0,R2,R2 + + VXOR V3,V11,V3 // xor in previous + VPMSUMD V19,const2,V11 // vpmsumd with constants + LVX (R4+off48),V19 // next in buffer + LVX (R3),const2 // get next constant + OR $0,R2,R2 + + VXOR V4,V12,V4 // xor in previous + VPMSUMD V20,const1,V12 // vpmsumd with constants + LVX (R4+off64),V20 // next in buffer + OR $0,R2,R2 + + VXOR V5,V13,V5 // xor in previous + VPMSUMD V21,const1,V13 // vpmsumd with constants + LVX (R4+off80),V21 // next in buffer + OR $0,R2,R2 + + VXOR V6,V14,V6 // xor in previous + VPMSUMD V22,const1,V14 // vpmsumd with constants + LVX (R4+off96),V22 // next in buffer + OR $0,R2,R2 + + VXOR V7,V15,V7 // xor in previous + VPMSUMD V23,const1,V15 // vpmsumd with constants + LVX (R4+off112),V23 // next in buffer + + ADD $128,R4 // bump up buffer pointer + BC 16,0,cool_top // are we done? + +first_cool_down: + + // load the constants + // xor in the previous value + // vpmsumd the result with constants + + LVX (R3),const1 + ADD $16,R3 + + VXOR V0,V8,V0 + VPMSUMD V16,const1,V8 + OR $0,R2,R2 + + VXOR V1,V9,V1 + VPMSUMD V17,const1,V9 + OR $0,R2,R2 + + VXOR V2,V10,V2 + VPMSUMD V18,const1,V10 + OR $0,R2,R2 + + VXOR V3,V11,V3 + VPMSUMD V19,const1,V11 + OR $0,R2,R2 + + VXOR V4,V12,V4 + VPMSUMD V20,const1,V12 + OR $0,R2,R2 + + VXOR V5,V13,V5 + VPMSUMD V21,const1,V13 + OR $0,R2,R2 + + VXOR V6,V14,V6 + VPMSUMD V22,const1,V14 + OR $0,R2,R2 + + VXOR V7,V15,V7 + VPMSUMD V23,const1,V15 + OR $0,R2,R2 + +second_cool_down: + + VXOR V0,V8,V0 + VXOR V1,V9,V1 + VXOR V2,V10,V2 + VXOR V3,V11,V3 + VXOR V4,V12,V4 + VXOR V5,V13,V5 + VXOR V6,V14,V6 + VXOR V7,V15,V7 + +#ifdef REFLECT + VSLDOI $4,V0,zeroes,V0 + VSLDOI $4,V1,zeroes,V1 + VSLDOI $4,V2,zeroes,V2 + VSLDOI $4,V3,zeroes,V3 + VSLDOI $4,V4,zeroes,V4 + VSLDOI $4,V5,zeroes,V5 + VSLDOI $4,V6,zeroes,V6 + VSLDOI $4,V7,zeroes,V7 +#endif + + LVX (R4),V8 + LVX (R4+off16),V9 + LVX (R4+off32),V10 + LVX (R4+off48),V11 + LVX (R4+off64),V12 + LVX (R4+off80),V13 + LVX (R4+off96),V14 + LVX (R4+off112),V15 + + ADD $128,R4 + + VXOR V0,V8,V16 + VXOR V1,V9,V17 + VXOR V2,V10,V18 + VXOR V3,V11,V19 + VXOR V4,V12,V20 + VXOR V5,V13,V21 + VXOR V6,V14,V22 + VXOR V7,V15,V23 + + MOVD $1,R15 + CMP $0,R6 + ADD $128,R6 + + BNE l1 + ANDCC $127,R5 + SUBC R5,$128,R6 + ADD R3,R6,R3 + + SRD $4,R5,R7 + MOVD R7,CTR + LVX (R3),V0 + LVX (R3+off16),V1 + LVX (R3+off32),V2 + LVX (R3+off48),V3 + LVX (R3+off64),V4 + LVX (R3+off80),V5 + LVX (R3+off96),V6 + LVX (R3+off112),V7 + + ADD $128,R3 + + VPMSUMW V16,V0,V0 + VPMSUMW V17,V1,V1 + VPMSUMW V18,V2,V2 + VPMSUMW V19,V3,V3 + VPMSUMW V20,V4,V4 + VPMSUMW V21,V5,V5 + VPMSUMW V22,V6,V6 + VPMSUMW V23,V7,V7 + + // now reduce the tail + + CMP $0,R7 + BEQ next1 + + LVX (R4),V16 + LVX (R3),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off16),V16 + LVX (R3+off16),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off32),V16 + LVX (R3+off32),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off48),V16 + LVX (R3+off48),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off64),V16 + LVX (R3+off64),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off80),V16 + LVX (R3+off80),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + BC 18,0,next1 + + LVX (R4+off96),V16 + LVX (R3+off96),V17 + VPMSUMW V16,V17,V16 + VXOR V0,V16,V0 + +next1: + VXOR V0,V1,V0 + VXOR V2,V3,V2 + VXOR V4,V5,V4 + VXOR V6,V7,V6 + VXOR V0,V2,V0 + VXOR V4,V6,V4 + VXOR V0,V4,V0 + +barrett_reduction: + + CMP R14,$1 + BNE barcstTable + MOVD $·IEEEBarConst(SB),R3 + BR startbarConst +barcstTable: + MOVD $·CastBarConst(SB),R3 + +startbarConst: + LVX (R3),const1 + LVX (R3+off16),const2 + + VSLDOI $8,V0,V0,V1 + VXOR V0,V1,V0 + +#ifdef REFLECT + VSPLTISB $1,V1 + VSL V0,V1,V0 +#endif + + VAND V0,mask_64bit,V0 + +#ifndef REFLECT + + VPMSUMD V0,const1,V1 + VSLDOI $8,zeroes,V1,V1 + VPMSUMD V1,const2,V1 + VXOR V0,V1,V0 + VSLDOI $8,V0,zeroes,V0 + +#else + + VAND V0,mask_32bit,V1 + VPMSUMD V1,const1,V1 + VAND V1,mask_32bit,V1 + VPMSUMD V1,const2,V1 + VXOR V0,V1,V0 + VSLDOI $4,V0,zeroes,V0 + +#endif + + MFVSRD VS32,R3 // VS32 = V0 + + NOR R3,R3,R3 // return ^crc + MOVW R3,ret+32(FP) + RET + +first_warm_up_done: + + LVX (R3),const1 + ADD $16,R3 + + VPMSUMD V16,const1,V8 + VPMSUMD V17,const1,V9 + VPMSUMD V18,const1,V10 + VPMSUMD V19,const1,V11 + VPMSUMD V20,const1,V12 + VPMSUMD V21,const1,V13 + VPMSUMD V22,const1,V14 + VPMSUMD V23,const1,V15 + + BR second_cool_down + +short: + CMP $0,R5 + BEQ zero + + // compute short constants + + CMP R14,$1 + BNE castshTable + MOVD $·IEEEConst(SB),R3 + ADD $4080,R3 + BR startshConst +castshTable: + MOVD $·CastConst(SB),R3 + ADD $4080,R3 + +startshConst: + SUBC R5,$256,R6 // sub from 256 + ADD R3,R6,R3 + + // calculate where to start + + SRD $4,R5,R7 + MOVD R7,CTR + + VXOR V19,V19,V19 + VXOR V20,V20,V20 + + LVX (R4),V0 + LVX (R3),V16 + VXOR V0,V8,V0 + VPMSUMW V0,V16,V0 + BC 18,0,v0 + + LVX (R4+off16),V1 + LVX (R3+off16),V17 + VPMSUMW V1,V17,V1 + BC 18,0,v1 + + LVX (R4+off32),V2 + LVX (R3+off32),V16 + VPMSUMW V2,V16,V2 + BC 18,0,v2 + + LVX (R4+off48),V3 + LVX (R3+off48),V17 + VPMSUMW V3,V17,V3 + BC 18,0,v3 + + LVX (R4+off64),V4 + LVX (R3+off64),V16 + VPMSUMW V4,V16,V4 + BC 18,0,v4 + + LVX (R4+off80),V5 + LVX (R3+off80),V17 + VPMSUMW V5,V17,V5 + BC 18,0,v5 + + LVX (R4+off96),V6 + LVX (R3+off96),V16 + VPMSUMW V6,V16,V6 + BC 18,0,v6 + + LVX (R4+off112),V7 + LVX (R3+off112),V17 + VPMSUMW V7,V17,V7 + BC 18,0,v7 + + ADD $128,R3 + ADD $128,R4 + + LVX (R4),V8 + LVX (R3),V16 + VPMSUMW V8,V16,V8 + BC 18,0,v8 + + LVX (R4+off16),V9 + LVX (R3+off16),V17 + VPMSUMW V9,V17,V9 + BC 18,0,v9 + + LVX (R4+off32),V10 + LVX (R3+off32),V16 + VPMSUMW V10,V16,V10 + BC 18,0,v10 + + LVX (R4+off48),V11 + LVX (R3+off48),V17 + VPMSUMW V11,V17,V11 + BC 18,0,v11 + + LVX (R4+off64),V12 + LVX (R3+off64),V16 + VPMSUMW V12,V16,V12 + BC 18,0,v12 + + LVX (R4+off80),V13 + LVX (R3+off80),V17 + VPMSUMW V13,V17,V13 + BC 18,0,v13 + + LVX (R4+off96),V14 + LVX (R3+off96),V16 + VPMSUMW V14,V16,V14 + BC 18,0,v14 + + LVX (R4+off112),V15 + LVX (R3+off112),V17 + VPMSUMW V15,V17,V15 + + VXOR V19,V15,V19 +v14: VXOR V20,V14,V20 +v13: VXOR V19,V13,V19 +v12: VXOR V20,V12,V20 +v11: VXOR V19,V11,V19 +v10: VXOR V20,V10,V20 +v9: VXOR V19,V9,V19 +v8: VXOR V20,V8,V20 +v7: VXOR V19,V7,V19 +v6: VXOR V20,V6,V20 +v5: VXOR V19,V5,V19 +v4: VXOR V20,V4,V20 +v3: VXOR V19,V3,V19 +v2: VXOR V20,V2,V20 +v1: VXOR V19,V1,V19 +v0: VXOR V20,V0,V20 + + VXOR V19,V20,V0 + + BR barrett_reduction + +zero: + // This case is the original crc, so just return it + MOVW R10,ret+32(FP) + RET diff --git a/src/hash/crc32/crc32_s390x.go b/src/hash/crc32/crc32_s390x.go new file mode 100644 index 0000000..4e50b56 --- /dev/null +++ b/src/hash/crc32/crc32_s390x.go @@ -0,0 +1,91 @@ +// 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. + +package crc32 + +import "internal/cpu" + +const ( + vxMinLen = 64 + vxAlignMask = 15 // align to 16 bytes +) + +// hasVX reports whether the machine has the z/Architecture +// vector facility installed and enabled. +var hasVX = cpu.S390X.HasVX + +// 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) +} diff --git a/src/hash/crc32/crc32_s390x.s b/src/hash/crc32/crc32_s390x.s new file mode 100644 index 0000000..8aabc60 --- /dev/null +++ b/src/hash/crc32/crc32_s390x.s @@ -0,0 +1,230 @@ +// 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. + +#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 ·crclecons+0(SB)/8, $0x0F0E0D0C0B0A0908 // LE-to-BE mask +DATA ·crclecons+8(SB)/8, $0x0706050403020100 +DATA ·crclecons+16(SB)/8, $0x00000001c6e41596 // R2 +DATA ·crclecons+24(SB)/8, $0x0000000154442bd4 // R1 +DATA ·crclecons+32(SB)/8, $0x00000000ccaa009e // R4 +DATA ·crclecons+40(SB)/8, $0x00000001751997d0 // R3 +DATA ·crclecons+48(SB)/8, $0x0000000000000000 +DATA ·crclecons+56(SB)/8, $0x0000000163cd6124 // R5 +DATA ·crclecons+64(SB)/8, $0x0000000000000000 +DATA ·crclecons+72(SB)/8, $0x00000001F7011641 // u' +DATA ·crclecons+80(SB)/8, $0x0000000000000000 +DATA ·crclecons+88(SB)/8, $0x00000001DB710641 // P'(x) << 1 + +GLOBL ·crclecons(SB),RODATA, $144 + +// Castagonli Polynomial constants +DATA ·crcclecons+0(SB)/8, $0x0F0E0D0C0B0A0908 // LE-to-BE mask +DATA ·crcclecons+8(SB)/8, $0x0706050403020100 +DATA ·crcclecons+16(SB)/8, $0x000000009e4addf8 // R2 +DATA ·crcclecons+24(SB)/8, $0x00000000740eef02 // R1 +DATA ·crcclecons+32(SB)/8, $0x000000014cd00bd6 // R4 +DATA ·crcclecons+40(SB)/8, $0x00000000f20c0dfe // R3 +DATA ·crcclecons+48(SB)/8, $0x0000000000000000 +DATA ·crcclecons+56(SB)/8, $0x00000000dd45aab8 // R5 +DATA ·crcclecons+64(SB)/8, $0x0000000000000000 +DATA ·crcclecons+72(SB)/8, $0x00000000dea713f1 // u' +DATA ·crcclecons+80(SB)/8, $0x0000000000000000 +DATA ·crcclecons+88(SB)/8, $0x0000000105ec76f0 // P'(x) << 1 + +GLOBL ·crcclecons(SB),RODATA, $144 + +// 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 $·crclecons(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 $·crcclecons(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 intermediate 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 diff --git a/src/hash/crc32/crc32_table_ppc64le.s b/src/hash/crc32/crc32_table_ppc64le.s new file mode 100644 index 0000000..191810f --- /dev/null +++ b/src/hash/crc32/crc32_table_ppc64le.s @@ -0,0 +1,3286 @@ +// autogenerated: do not edit! +// generated from crc32/gen_const_ppc64le.go + +#include "textflag.h" + + /* Reduce 262144 kbits to 1024 bits */ + /* x^261184 mod p(x), x^261120 mod p(x) */ +DATA ·IEEEConst+0(SB)/8,$0x0000000099ea94a8 +DATA ·IEEEConst+8(SB)/8,$0x00000001651797d2 + + /* x^260160 mod p(x), x^260096 mod p(x) */ +DATA ·IEEEConst+16(SB)/8,$0x00000000945a8420 +DATA ·IEEEConst+24(SB)/8,$0x0000000021e0d56c + + /* x^259136 mod p(x), x^259072 mod p(x) */ +DATA ·IEEEConst+32(SB)/8,$0x0000000030762706 +DATA ·IEEEConst+40(SB)/8,$0x000000000f95ecaa + + /* x^258112 mod p(x), x^258048 mod p(x) */ +DATA ·IEEEConst+48(SB)/8,$0x00000001a52fc582 +DATA ·IEEEConst+56(SB)/8,$0x00000001ebd224ac + + /* x^257088 mod p(x), x^257024 mod p(x) */ +DATA ·IEEEConst+64(SB)/8,$0x00000001a4a7167a +DATA ·IEEEConst+72(SB)/8,$0x000000000ccb97ca + + /* x^256064 mod p(x), x^256000 mod p(x) */ +DATA ·IEEEConst+80(SB)/8,$0x000000000c18249a +DATA ·IEEEConst+88(SB)/8,$0x00000001006ec8a8 + + /* x^255040 mod p(x), x^254976 mod p(x) */ +DATA ·IEEEConst+96(SB)/8,$0x00000000a924ae7c +DATA ·IEEEConst+104(SB)/8,$0x000000014f58f196 + + /* x^254016 mod p(x), x^253952 mod p(x) */ +DATA ·IEEEConst+112(SB)/8,$0x00000001e12ccc12 +DATA ·IEEEConst+120(SB)/8,$0x00000001a7192ca6 + + /* x^252992 mod p(x), x^252928 mod p(x) */ +DATA ·IEEEConst+128(SB)/8,$0x00000000a0b9d4ac +DATA ·IEEEConst+136(SB)/8,$0x000000019a64bab2 + + /* x^251968 mod p(x), x^251904 mod p(x) */ +DATA ·IEEEConst+144(SB)/8,$0x0000000095e8ddfe +DATA ·IEEEConst+152(SB)/8,$0x0000000014f4ed2e + + /* x^250944 mod p(x), x^250880 mod p(x) */ +DATA ·IEEEConst+160(SB)/8,$0x00000000233fddc4 +DATA ·IEEEConst+168(SB)/8,$0x000000011092b6a2 + + /* x^249920 mod p(x), x^249856 mod p(x) */ +DATA ·IEEEConst+176(SB)/8,$0x00000001b4529b62 +DATA ·IEEEConst+184(SB)/8,$0x00000000c8a1629c + + /* x^248896 mod p(x), x^248832 mod p(x) */ +DATA ·IEEEConst+192(SB)/8,$0x00000001a7fa0e64 +DATA ·IEEEConst+200(SB)/8,$0x000000017bf32e8e + + /* x^247872 mod p(x), x^247808 mod p(x) */ +DATA ·IEEEConst+208(SB)/8,$0x00000001b5334592 +DATA ·IEEEConst+216(SB)/8,$0x00000001f8cc6582 + + /* x^246848 mod p(x), x^246784 mod p(x) */ +DATA ·IEEEConst+224(SB)/8,$0x000000011f8ee1b4 +DATA ·IEEEConst+232(SB)/8,$0x000000008631ddf0 + + /* x^245824 mod p(x), x^245760 mod p(x) */ +DATA ·IEEEConst+240(SB)/8,$0x000000006252e632 +DATA ·IEEEConst+248(SB)/8,$0x000000007e5a76d0 + + /* x^244800 mod p(x), x^244736 mod p(x) */ +DATA ·IEEEConst+256(SB)/8,$0x00000000ab973e84 +DATA ·IEEEConst+264(SB)/8,$0x000000002b09b31c + + /* x^243776 mod p(x), x^243712 mod p(x) */ +DATA ·IEEEConst+272(SB)/8,$0x000000007734f5ec +DATA ·IEEEConst+280(SB)/8,$0x00000001b2df1f84 + + /* x^242752 mod p(x), x^242688 mod p(x) */ +DATA ·IEEEConst+288(SB)/8,$0x000000007c547798 +DATA ·IEEEConst+296(SB)/8,$0x00000001d6f56afc + + /* x^241728 mod p(x), x^241664 mod p(x) */ +DATA ·IEEEConst+304(SB)/8,$0x000000007ec40210 +DATA ·IEEEConst+312(SB)/8,$0x00000001b9b5e70c + + /* x^240704 mod p(x), x^240640 mod p(x) */ +DATA ·IEEEConst+320(SB)/8,$0x00000001ab1695a8 +DATA ·IEEEConst+328(SB)/8,$0x0000000034b626d2 + + /* x^239680 mod p(x), x^239616 mod p(x) */ +DATA ·IEEEConst+336(SB)/8,$0x0000000090494bba +DATA ·IEEEConst+344(SB)/8,$0x000000014c53479a + + /* x^238656 mod p(x), x^238592 mod p(x) */ +DATA ·IEEEConst+352(SB)/8,$0x00000001123fb816 +DATA ·IEEEConst+360(SB)/8,$0x00000001a6d179a4 + + /* x^237632 mod p(x), x^237568 mod p(x) */ +DATA ·IEEEConst+368(SB)/8,$0x00000001e188c74c +DATA ·IEEEConst+376(SB)/8,$0x000000015abd16b4 + + /* x^236608 mod p(x), x^236544 mod p(x) */ +DATA ·IEEEConst+384(SB)/8,$0x00000001c2d3451c +DATA ·IEEEConst+392(SB)/8,$0x00000000018f9852 + + /* x^235584 mod p(x), x^235520 mod p(x) */ +DATA ·IEEEConst+400(SB)/8,$0x00000000f55cf1ca +DATA ·IEEEConst+408(SB)/8,$0x000000001fb3084a + + /* x^234560 mod p(x), x^234496 mod p(x) */ +DATA ·IEEEConst+416(SB)/8,$0x00000001a0531540 +DATA ·IEEEConst+424(SB)/8,$0x00000000c53dfb04 + + /* x^233536 mod p(x), x^233472 mod p(x) */ +DATA ·IEEEConst+432(SB)/8,$0x0000000132cd7ebc +DATA ·IEEEConst+440(SB)/8,$0x00000000e10c9ad6 + + /* x^232512 mod p(x), x^232448 mod p(x) */ +DATA ·IEEEConst+448(SB)/8,$0x0000000073ab7f36 +DATA ·IEEEConst+456(SB)/8,$0x0000000025aa994a + + /* x^231488 mod p(x), x^231424 mod p(x) */ +DATA ·IEEEConst+464(SB)/8,$0x0000000041aed1c2 +DATA ·IEEEConst+472(SB)/8,$0x00000000fa3a74c4 + + /* x^230464 mod p(x), x^230400 mod p(x) */ +DATA ·IEEEConst+480(SB)/8,$0x0000000136c53800 +DATA ·IEEEConst+488(SB)/8,$0x0000000033eb3f40 + + /* x^229440 mod p(x), x^229376 mod p(x) */ +DATA ·IEEEConst+496(SB)/8,$0x0000000126835a30 +DATA ·IEEEConst+504(SB)/8,$0x000000017193f296 + + /* x^228416 mod p(x), x^228352 mod p(x) */ +DATA ·IEEEConst+512(SB)/8,$0x000000006241b502 +DATA ·IEEEConst+520(SB)/8,$0x0000000043f6c86a + + /* x^227392 mod p(x), x^227328 mod p(x) */ +DATA ·IEEEConst+528(SB)/8,$0x00000000d5196ad4 +DATA ·IEEEConst+536(SB)/8,$0x000000016b513ec6 + + /* x^226368 mod p(x), x^226304 mod p(x) */ +DATA ·IEEEConst+544(SB)/8,$0x000000009cfa769a +DATA ·IEEEConst+552(SB)/8,$0x00000000c8f25b4e + + /* x^225344 mod p(x), x^225280 mod p(x) */ +DATA ·IEEEConst+560(SB)/8,$0x00000000920e5df4 +DATA ·IEEEConst+568(SB)/8,$0x00000001a45048ec + + /* x^224320 mod p(x), x^224256 mod p(x) */ +DATA ·IEEEConst+576(SB)/8,$0x0000000169dc310e +DATA ·IEEEConst+584(SB)/8,$0x000000000c441004 + + /* x^223296 mod p(x), x^223232 mod p(x) */ +DATA ·IEEEConst+592(SB)/8,$0x0000000009fc331c +DATA ·IEEEConst+600(SB)/8,$0x000000000e17cad6 + + /* x^222272 mod p(x), x^222208 mod p(x) */ +DATA ·IEEEConst+608(SB)/8,$0x000000010d94a81e +DATA ·IEEEConst+616(SB)/8,$0x00000001253ae964 + + /* x^221248 mod p(x), x^221184 mod p(x) */ +DATA ·IEEEConst+624(SB)/8,$0x0000000027a20ab2 +DATA ·IEEEConst+632(SB)/8,$0x00000001d7c88ebc + + /* x^220224 mod p(x), x^220160 mod p(x) */ +DATA ·IEEEConst+640(SB)/8,$0x0000000114f87504 +DATA ·IEEEConst+648(SB)/8,$0x00000001e7ca913a + + /* x^219200 mod p(x), x^219136 mod p(x) */ +DATA ·IEEEConst+656(SB)/8,$0x000000004b076d96 +DATA ·IEEEConst+664(SB)/8,$0x0000000033ed078a + + /* x^218176 mod p(x), x^218112 mod p(x) */ +DATA ·IEEEConst+672(SB)/8,$0x00000000da4d1e74 +DATA ·IEEEConst+680(SB)/8,$0x00000000e1839c78 + + /* x^217152 mod p(x), x^217088 mod p(x) */ +DATA ·IEEEConst+688(SB)/8,$0x000000001b81f672 +DATA ·IEEEConst+696(SB)/8,$0x00000001322b267e + + /* x^216128 mod p(x), x^216064 mod p(x) */ +DATA ·IEEEConst+704(SB)/8,$0x000000009367c988 +DATA ·IEEEConst+712(SB)/8,$0x00000000638231b6 + + /* x^215104 mod p(x), x^215040 mod p(x) */ +DATA ·IEEEConst+720(SB)/8,$0x00000001717214ca +DATA ·IEEEConst+728(SB)/8,$0x00000001ee7f16f4 + + /* x^214080 mod p(x), x^214016 mod p(x) */ +DATA ·IEEEConst+736(SB)/8,$0x000000009f47d820 +DATA ·IEEEConst+744(SB)/8,$0x0000000117d9924a + + /* x^213056 mod p(x), x^212992 mod p(x) */ +DATA ·IEEEConst+752(SB)/8,$0x000000010d9a47d2 +DATA ·IEEEConst+760(SB)/8,$0x00000000e1a9e0c4 + + /* x^212032 mod p(x), x^211968 mod p(x) */ +DATA ·IEEEConst+768(SB)/8,$0x00000000a696c58c +DATA ·IEEEConst+776(SB)/8,$0x00000001403731dc + + /* x^211008 mod p(x), x^210944 mod p(x) */ +DATA ·IEEEConst+784(SB)/8,$0x000000002aa28ec6 +DATA ·IEEEConst+792(SB)/8,$0x00000001a5ea9682 + + /* x^209984 mod p(x), x^209920 mod p(x) */ +DATA ·IEEEConst+800(SB)/8,$0x00000001fe18fd9a +DATA ·IEEEConst+808(SB)/8,$0x0000000101c5c578 + + /* x^208960 mod p(x), x^208896 mod p(x) */ +DATA ·IEEEConst+816(SB)/8,$0x000000019d4fc1ae +DATA ·IEEEConst+824(SB)/8,$0x00000000dddf6494 + + /* x^207936 mod p(x), x^207872 mod p(x) */ +DATA ·IEEEConst+832(SB)/8,$0x00000001ba0e3dea +DATA ·IEEEConst+840(SB)/8,$0x00000000f1c3db28 + + /* x^206912 mod p(x), x^206848 mod p(x) */ +DATA ·IEEEConst+848(SB)/8,$0x0000000074b59a5e +DATA ·IEEEConst+856(SB)/8,$0x000000013112fb9c + + /* x^205888 mod p(x), x^205824 mod p(x) */ +DATA ·IEEEConst+864(SB)/8,$0x00000000f2b5ea98 +DATA ·IEEEConst+872(SB)/8,$0x00000000b680b906 + + /* x^204864 mod p(x), x^204800 mod p(x) */ +DATA ·IEEEConst+880(SB)/8,$0x0000000187132676 +DATA ·IEEEConst+888(SB)/8,$0x000000001a282932 + + /* x^203840 mod p(x), x^203776 mod p(x) */ +DATA ·IEEEConst+896(SB)/8,$0x000000010a8c6ad4 +DATA ·IEEEConst+904(SB)/8,$0x0000000089406e7e + + /* x^202816 mod p(x), x^202752 mod p(x) */ +DATA ·IEEEConst+912(SB)/8,$0x00000001e21dfe70 +DATA ·IEEEConst+920(SB)/8,$0x00000001def6be8c + + /* x^201792 mod p(x), x^201728 mod p(x) */ +DATA ·IEEEConst+928(SB)/8,$0x00000001da0050e4 +DATA ·IEEEConst+936(SB)/8,$0x0000000075258728 + + /* x^200768 mod p(x), x^200704 mod p(x) */ +DATA ·IEEEConst+944(SB)/8,$0x00000000772172ae +DATA ·IEEEConst+952(SB)/8,$0x000000019536090a + + /* x^199744 mod p(x), x^199680 mod p(x) */ +DATA ·IEEEConst+960(SB)/8,$0x00000000e47724aa +DATA ·IEEEConst+968(SB)/8,$0x00000000f2455bfc + + /* x^198720 mod p(x), x^198656 mod p(x) */ +DATA ·IEEEConst+976(SB)/8,$0x000000003cd63ac4 +DATA ·IEEEConst+984(SB)/8,$0x000000018c40baf4 + + /* x^197696 mod p(x), x^197632 mod p(x) */ +DATA ·IEEEConst+992(SB)/8,$0x00000001bf47d352 +DATA ·IEEEConst+1000(SB)/8,$0x000000004cd390d4 + + /* x^196672 mod p(x), x^196608 mod p(x) */ +DATA ·IEEEConst+1008(SB)/8,$0x000000018dc1d708 +DATA ·IEEEConst+1016(SB)/8,$0x00000001e4ece95a + + /* x^195648 mod p(x), x^195584 mod p(x) */ +DATA ·IEEEConst+1024(SB)/8,$0x000000002d4620a4 +DATA ·IEEEConst+1032(SB)/8,$0x000000001a3ee918 + + /* x^194624 mod p(x), x^194560 mod p(x) */ +DATA ·IEEEConst+1040(SB)/8,$0x0000000058fd1740 +DATA ·IEEEConst+1048(SB)/8,$0x000000007c652fb8 + + /* x^193600 mod p(x), x^193536 mod p(x) */ +DATA ·IEEEConst+1056(SB)/8,$0x00000000dadd9bfc +DATA ·IEEEConst+1064(SB)/8,$0x000000011c67842c + + /* x^192576 mod p(x), x^192512 mod p(x) */ +DATA ·IEEEConst+1072(SB)/8,$0x00000001ea2140be +DATA ·IEEEConst+1080(SB)/8,$0x00000000254f759c + + /* x^191552 mod p(x), x^191488 mod p(x) */ +DATA ·IEEEConst+1088(SB)/8,$0x000000009de128ba +DATA ·IEEEConst+1096(SB)/8,$0x000000007ece94ca + + /* x^190528 mod p(x), x^190464 mod p(x) */ +DATA ·IEEEConst+1104(SB)/8,$0x000000013ac3aa8e +DATA ·IEEEConst+1112(SB)/8,$0x0000000038f258c2 + + /* x^189504 mod p(x), x^189440 mod p(x) */ +DATA ·IEEEConst+1120(SB)/8,$0x0000000099980562 +DATA ·IEEEConst+1128(SB)/8,$0x00000001cdf17b00 + + /* x^188480 mod p(x), x^188416 mod p(x) */ +DATA ·IEEEConst+1136(SB)/8,$0x00000001c1579c86 +DATA ·IEEEConst+1144(SB)/8,$0x000000011f882c16 + + /* x^187456 mod p(x), x^187392 mod p(x) */ +DATA ·IEEEConst+1152(SB)/8,$0x0000000068dbbf94 +DATA ·IEEEConst+1160(SB)/8,$0x0000000100093fc8 + + /* x^186432 mod p(x), x^186368 mod p(x) */ +DATA ·IEEEConst+1168(SB)/8,$0x000000004509fb04 +DATA ·IEEEConst+1176(SB)/8,$0x00000001cd684f16 + + /* x^185408 mod p(x), x^185344 mod p(x) */ +DATA ·IEEEConst+1184(SB)/8,$0x00000001202f6398 +DATA ·IEEEConst+1192(SB)/8,$0x000000004bc6a70a + + /* x^184384 mod p(x), x^184320 mod p(x) */ +DATA ·IEEEConst+1200(SB)/8,$0x000000013aea243e +DATA ·IEEEConst+1208(SB)/8,$0x000000004fc7e8e4 + + /* x^183360 mod p(x), x^183296 mod p(x) */ +DATA ·IEEEConst+1216(SB)/8,$0x00000001b4052ae6 +DATA ·IEEEConst+1224(SB)/8,$0x0000000130103f1c + + /* x^182336 mod p(x), x^182272 mod p(x) */ +DATA ·IEEEConst+1232(SB)/8,$0x00000001cd2a0ae8 +DATA ·IEEEConst+1240(SB)/8,$0x0000000111b0024c + + /* x^181312 mod p(x), x^181248 mod p(x) */ +DATA ·IEEEConst+1248(SB)/8,$0x00000001fe4aa8b4 +DATA ·IEEEConst+1256(SB)/8,$0x000000010b3079da + + /* x^180288 mod p(x), x^180224 mod p(x) */ +DATA ·IEEEConst+1264(SB)/8,$0x00000001d1559a42 +DATA ·IEEEConst+1272(SB)/8,$0x000000010192bcc2 + + /* x^179264 mod p(x), x^179200 mod p(x) */ +DATA ·IEEEConst+1280(SB)/8,$0x00000001f3e05ecc +DATA ·IEEEConst+1288(SB)/8,$0x0000000074838d50 + + /* x^178240 mod p(x), x^178176 mod p(x) */ +DATA ·IEEEConst+1296(SB)/8,$0x0000000104ddd2cc +DATA ·IEEEConst+1304(SB)/8,$0x000000001b20f520 + + /* x^177216 mod p(x), x^177152 mod p(x) */ +DATA ·IEEEConst+1312(SB)/8,$0x000000015393153c +DATA ·IEEEConst+1320(SB)/8,$0x0000000050c3590a + + /* x^176192 mod p(x), x^176128 mod p(x) */ +DATA ·IEEEConst+1328(SB)/8,$0x0000000057e942c6 +DATA ·IEEEConst+1336(SB)/8,$0x00000000b41cac8e + + /* x^175168 mod p(x), x^175104 mod p(x) */ +DATA ·IEEEConst+1344(SB)/8,$0x000000012c633850 +DATA ·IEEEConst+1352(SB)/8,$0x000000000c72cc78 + + /* x^174144 mod p(x), x^174080 mod p(x) */ +DATA ·IEEEConst+1360(SB)/8,$0x00000000ebcaae4c +DATA ·IEEEConst+1368(SB)/8,$0x0000000030cdb032 + + /* x^173120 mod p(x), x^173056 mod p(x) */ +DATA ·IEEEConst+1376(SB)/8,$0x000000013ee532a6 +DATA ·IEEEConst+1384(SB)/8,$0x000000013e09fc32 + + /* x^172096 mod p(x), x^172032 mod p(x) */ +DATA ·IEEEConst+1392(SB)/8,$0x00000001bf0cbc7e +DATA ·IEEEConst+1400(SB)/8,$0x000000001ed624d2 + + /* x^171072 mod p(x), x^171008 mod p(x) */ +DATA ·IEEEConst+1408(SB)/8,$0x00000000d50b7a5a +DATA ·IEEEConst+1416(SB)/8,$0x00000000781aee1a + + /* x^170048 mod p(x), x^169984 mod p(x) */ +DATA ·IEEEConst+1424(SB)/8,$0x0000000002fca6e8 +DATA ·IEEEConst+1432(SB)/8,$0x00000001c4d8348c + + /* x^169024 mod p(x), x^168960 mod p(x) */ +DATA ·IEEEConst+1440(SB)/8,$0x000000007af40044 +DATA ·IEEEConst+1448(SB)/8,$0x0000000057a40336 + + /* x^168000 mod p(x), x^167936 mod p(x) */ +DATA ·IEEEConst+1456(SB)/8,$0x0000000016178744 +DATA ·IEEEConst+1464(SB)/8,$0x0000000085544940 + + /* x^166976 mod p(x), x^166912 mod p(x) */ +DATA ·IEEEConst+1472(SB)/8,$0x000000014c177458 +DATA ·IEEEConst+1480(SB)/8,$0x000000019cd21e80 + + /* x^165952 mod p(x), x^165888 mod p(x) */ +DATA ·IEEEConst+1488(SB)/8,$0x000000011b6ddf04 +DATA ·IEEEConst+1496(SB)/8,$0x000000013eb95bc0 + + /* x^164928 mod p(x), x^164864 mod p(x) */ +DATA ·IEEEConst+1504(SB)/8,$0x00000001f3e29ccc +DATA ·IEEEConst+1512(SB)/8,$0x00000001dfc9fdfc + + /* x^163904 mod p(x), x^163840 mod p(x) */ +DATA ·IEEEConst+1520(SB)/8,$0x0000000135ae7562 +DATA ·IEEEConst+1528(SB)/8,$0x00000000cd028bc2 + + /* x^162880 mod p(x), x^162816 mod p(x) */ +DATA ·IEEEConst+1536(SB)/8,$0x0000000190ef812c +DATA ·IEEEConst+1544(SB)/8,$0x0000000090db8c44 + + /* x^161856 mod p(x), x^161792 mod p(x) */ +DATA ·IEEEConst+1552(SB)/8,$0x0000000067a2c786 +DATA ·IEEEConst+1560(SB)/8,$0x000000010010a4ce + + /* x^160832 mod p(x), x^160768 mod p(x) */ +DATA ·IEEEConst+1568(SB)/8,$0x0000000048b9496c +DATA ·IEEEConst+1576(SB)/8,$0x00000001c8f4c72c + + /* x^159808 mod p(x), x^159744 mod p(x) */ +DATA ·IEEEConst+1584(SB)/8,$0x000000015a422de6 +DATA ·IEEEConst+1592(SB)/8,$0x000000001c26170c + + /* x^158784 mod p(x), x^158720 mod p(x) */ +DATA ·IEEEConst+1600(SB)/8,$0x00000001ef0e3640 +DATA ·IEEEConst+1608(SB)/8,$0x00000000e3fccf68 + + /* x^157760 mod p(x), x^157696 mod p(x) */ +DATA ·IEEEConst+1616(SB)/8,$0x00000001006d2d26 +DATA ·IEEEConst+1624(SB)/8,$0x00000000d513ed24 + + /* x^156736 mod p(x), x^156672 mod p(x) */ +DATA ·IEEEConst+1632(SB)/8,$0x00000001170d56d6 +DATA ·IEEEConst+1640(SB)/8,$0x00000000141beada + + /* x^155712 mod p(x), x^155648 mod p(x) */ +DATA ·IEEEConst+1648(SB)/8,$0x00000000a5fb613c +DATA ·IEEEConst+1656(SB)/8,$0x000000011071aea0 + + /* x^154688 mod p(x), x^154624 mod p(x) */ +DATA ·IEEEConst+1664(SB)/8,$0x0000000040bbf7fc +DATA ·IEEEConst+1672(SB)/8,$0x000000012e19080a + + /* x^153664 mod p(x), x^153600 mod p(x) */ +DATA ·IEEEConst+1680(SB)/8,$0x000000016ac3a5b2 +DATA ·IEEEConst+1688(SB)/8,$0x0000000100ecf826 + + /* x^152640 mod p(x), x^152576 mod p(x) */ +DATA ·IEEEConst+1696(SB)/8,$0x00000000abf16230 +DATA ·IEEEConst+1704(SB)/8,$0x0000000069b09412 + + /* x^151616 mod p(x), x^151552 mod p(x) */ +DATA ·IEEEConst+1712(SB)/8,$0x00000001ebe23fac +DATA ·IEEEConst+1720(SB)/8,$0x0000000122297bac + + /* x^150592 mod p(x), x^150528 mod p(x) */ +DATA ·IEEEConst+1728(SB)/8,$0x000000008b6a0894 +DATA ·IEEEConst+1736(SB)/8,$0x00000000e9e4b068 + + /* x^149568 mod p(x), x^149504 mod p(x) */ +DATA ·IEEEConst+1744(SB)/8,$0x00000001288ea478 +DATA ·IEEEConst+1752(SB)/8,$0x000000004b38651a + + /* x^148544 mod p(x), x^148480 mod p(x) */ +DATA ·IEEEConst+1760(SB)/8,$0x000000016619c442 +DATA ·IEEEConst+1768(SB)/8,$0x00000001468360e2 + + /* x^147520 mod p(x), x^147456 mod p(x) */ +DATA ·IEEEConst+1776(SB)/8,$0x0000000086230038 +DATA ·IEEEConst+1784(SB)/8,$0x00000000121c2408 + + /* x^146496 mod p(x), x^146432 mod p(x) */ +DATA ·IEEEConst+1792(SB)/8,$0x000000017746a756 +DATA ·IEEEConst+1800(SB)/8,$0x00000000da7e7d08 + + /* x^145472 mod p(x), x^145408 mod p(x) */ +DATA ·IEEEConst+1808(SB)/8,$0x0000000191b8f8f8 +DATA ·IEEEConst+1816(SB)/8,$0x00000001058d7652 + + /* x^144448 mod p(x), x^144384 mod p(x) */ +DATA ·IEEEConst+1824(SB)/8,$0x000000008e167708 +DATA ·IEEEConst+1832(SB)/8,$0x000000014a098a90 + + /* x^143424 mod p(x), x^143360 mod p(x) */ +DATA ·IEEEConst+1840(SB)/8,$0x0000000148b22d54 +DATA ·IEEEConst+1848(SB)/8,$0x0000000020dbe72e + + /* x^142400 mod p(x), x^142336 mod p(x) */ +DATA ·IEEEConst+1856(SB)/8,$0x0000000044ba2c3c +DATA ·IEEEConst+1864(SB)/8,$0x000000011e7323e8 + + /* x^141376 mod p(x), x^141312 mod p(x) */ +DATA ·IEEEConst+1872(SB)/8,$0x00000000b54d2b52 +DATA ·IEEEConst+1880(SB)/8,$0x00000000d5d4bf94 + + /* x^140352 mod p(x), x^140288 mod p(x) */ +DATA ·IEEEConst+1888(SB)/8,$0x0000000005a4fd8a +DATA ·IEEEConst+1896(SB)/8,$0x0000000199d8746c + + /* x^139328 mod p(x), x^139264 mod p(x) */ +DATA ·IEEEConst+1904(SB)/8,$0x0000000139f9fc46 +DATA ·IEEEConst+1912(SB)/8,$0x00000000ce9ca8a0 + + /* x^138304 mod p(x), x^138240 mod p(x) */ +DATA ·IEEEConst+1920(SB)/8,$0x000000015a1fa824 +DATA ·IEEEConst+1928(SB)/8,$0x00000000136edece + + /* x^137280 mod p(x), x^137216 mod p(x) */ +DATA ·IEEEConst+1936(SB)/8,$0x000000000a61ae4c +DATA ·IEEEConst+1944(SB)/8,$0x000000019b92a068 + + /* x^136256 mod p(x), x^136192 mod p(x) */ +DATA ·IEEEConst+1952(SB)/8,$0x0000000145e9113e +DATA ·IEEEConst+1960(SB)/8,$0x0000000071d62206 + + /* x^135232 mod p(x), x^135168 mod p(x) */ +DATA ·IEEEConst+1968(SB)/8,$0x000000006a348448 +DATA ·IEEEConst+1976(SB)/8,$0x00000000dfc50158 + + /* x^134208 mod p(x), x^134144 mod p(x) */ +DATA ·IEEEConst+1984(SB)/8,$0x000000004d80a08c +DATA ·IEEEConst+1992(SB)/8,$0x00000001517626bc + + /* x^133184 mod p(x), x^133120 mod p(x) */ +DATA ·IEEEConst+2000(SB)/8,$0x000000014b6837a0 +DATA ·IEEEConst+2008(SB)/8,$0x0000000148d1e4fa + + /* x^132160 mod p(x), x^132096 mod p(x) */ +DATA ·IEEEConst+2016(SB)/8,$0x000000016896a7fc +DATA ·IEEEConst+2024(SB)/8,$0x0000000094d8266e + + /* x^131136 mod p(x), x^131072 mod p(x) */ +DATA ·IEEEConst+2032(SB)/8,$0x000000014f187140 +DATA ·IEEEConst+2040(SB)/8,$0x00000000606c5e34 + + /* x^130112 mod p(x), x^130048 mod p(x) */ +DATA ·IEEEConst+2048(SB)/8,$0x000000019581b9da +DATA ·IEEEConst+2056(SB)/8,$0x000000019766beaa + + /* x^129088 mod p(x), x^129024 mod p(x) */ +DATA ·IEEEConst+2064(SB)/8,$0x00000001091bc984 +DATA ·IEEEConst+2072(SB)/8,$0x00000001d80c506c + + /* x^128064 mod p(x), x^128000 mod p(x) */ +DATA ·IEEEConst+2080(SB)/8,$0x000000001067223c +DATA ·IEEEConst+2088(SB)/8,$0x000000001e73837c + + /* x^127040 mod p(x), x^126976 mod p(x) */ +DATA ·IEEEConst+2096(SB)/8,$0x00000001ab16ea02 +DATA ·IEEEConst+2104(SB)/8,$0x0000000064d587de + + /* x^126016 mod p(x), x^125952 mod p(x) */ +DATA ·IEEEConst+2112(SB)/8,$0x000000013c4598a8 +DATA ·IEEEConst+2120(SB)/8,$0x00000000f4a507b0 + + /* x^124992 mod p(x), x^124928 mod p(x) */ +DATA ·IEEEConst+2128(SB)/8,$0x00000000b3735430 +DATA ·IEEEConst+2136(SB)/8,$0x0000000040e342fc + + /* x^123968 mod p(x), x^123904 mod p(x) */ +DATA ·IEEEConst+2144(SB)/8,$0x00000001bb3fc0c0 +DATA ·IEEEConst+2152(SB)/8,$0x00000001d5ad9c3a + + /* x^122944 mod p(x), x^122880 mod p(x) */ +DATA ·IEEEConst+2160(SB)/8,$0x00000001570ae19c +DATA ·IEEEConst+2168(SB)/8,$0x0000000094a691a4 + + /* x^121920 mod p(x), x^121856 mod p(x) */ +DATA ·IEEEConst+2176(SB)/8,$0x00000001ea910712 +DATA ·IEEEConst+2184(SB)/8,$0x00000001271ecdfa + + /* x^120896 mod p(x), x^120832 mod p(x) */ +DATA ·IEEEConst+2192(SB)/8,$0x0000000167127128 +DATA ·IEEEConst+2200(SB)/8,$0x000000009e54475a + + /* x^119872 mod p(x), x^119808 mod p(x) */ +DATA ·IEEEConst+2208(SB)/8,$0x0000000019e790a2 +DATA ·IEEEConst+2216(SB)/8,$0x00000000c9c099ee + + /* x^118848 mod p(x), x^118784 mod p(x) */ +DATA ·IEEEConst+2224(SB)/8,$0x000000003788f710 +DATA ·IEEEConst+2232(SB)/8,$0x000000009a2f736c + + /* x^117824 mod p(x), x^117760 mod p(x) */ +DATA ·IEEEConst+2240(SB)/8,$0x00000001682a160e +DATA ·IEEEConst+2248(SB)/8,$0x00000000bb9f4996 + + /* x^116800 mod p(x), x^116736 mod p(x) */ +DATA ·IEEEConst+2256(SB)/8,$0x000000007f0ebd2e +DATA ·IEEEConst+2264(SB)/8,$0x00000001db688050 + + /* x^115776 mod p(x), x^115712 mod p(x) */ +DATA ·IEEEConst+2272(SB)/8,$0x000000002b032080 +DATA ·IEEEConst+2280(SB)/8,$0x00000000e9b10af4 + + /* x^114752 mod p(x), x^114688 mod p(x) */ +DATA ·IEEEConst+2288(SB)/8,$0x00000000cfd1664a +DATA ·IEEEConst+2296(SB)/8,$0x000000012d4545e4 + + /* x^113728 mod p(x), x^113664 mod p(x) */ +DATA ·IEEEConst+2304(SB)/8,$0x00000000aa1181c2 +DATA ·IEEEConst+2312(SB)/8,$0x000000000361139c + + /* x^112704 mod p(x), x^112640 mod p(x) */ +DATA ·IEEEConst+2320(SB)/8,$0x00000000ddd08002 +DATA ·IEEEConst+2328(SB)/8,$0x00000001a5a1a3a8 + + /* x^111680 mod p(x), x^111616 mod p(x) */ +DATA ·IEEEConst+2336(SB)/8,$0x00000000e8dd0446 +DATA ·IEEEConst+2344(SB)/8,$0x000000006844e0b0 + + /* x^110656 mod p(x), x^110592 mod p(x) */ +DATA ·IEEEConst+2352(SB)/8,$0x00000001bbd94a00 +DATA ·IEEEConst+2360(SB)/8,$0x00000000c3762f28 + + /* x^109632 mod p(x), x^109568 mod p(x) */ +DATA ·IEEEConst+2368(SB)/8,$0x00000000ab6cd180 +DATA ·IEEEConst+2376(SB)/8,$0x00000001d26287a2 + + /* x^108608 mod p(x), x^108544 mod p(x) */ +DATA ·IEEEConst+2384(SB)/8,$0x0000000031803ce2 +DATA ·IEEEConst+2392(SB)/8,$0x00000001f6f0bba8 + + /* x^107584 mod p(x), x^107520 mod p(x) */ +DATA ·IEEEConst+2400(SB)/8,$0x0000000024f40b0c +DATA ·IEEEConst+2408(SB)/8,$0x000000002ffabd62 + + /* x^106560 mod p(x), x^106496 mod p(x) */ +DATA ·IEEEConst+2416(SB)/8,$0x00000001ba1d9834 +DATA ·IEEEConst+2424(SB)/8,$0x00000000fb4516b8 + + /* x^105536 mod p(x), x^105472 mod p(x) */ +DATA ·IEEEConst+2432(SB)/8,$0x0000000104de61aa +DATA ·IEEEConst+2440(SB)/8,$0x000000018cfa961c + + /* x^104512 mod p(x), x^104448 mod p(x) */ +DATA ·IEEEConst+2448(SB)/8,$0x0000000113e40d46 +DATA ·IEEEConst+2456(SB)/8,$0x000000019e588d52 + + /* x^103488 mod p(x), x^103424 mod p(x) */ +DATA ·IEEEConst+2464(SB)/8,$0x00000001415598a0 +DATA ·IEEEConst+2472(SB)/8,$0x00000001180f0bbc + + /* x^102464 mod p(x), x^102400 mod p(x) */ +DATA ·IEEEConst+2480(SB)/8,$0x00000000bf6c8c90 +DATA ·IEEEConst+2488(SB)/8,$0x00000000e1d9177a + + /* x^101440 mod p(x), x^101376 mod p(x) */ +DATA ·IEEEConst+2496(SB)/8,$0x00000001788b0504 +DATA ·IEEEConst+2504(SB)/8,$0x0000000105abc27c + + /* x^100416 mod p(x), x^100352 mod p(x) */ +DATA ·IEEEConst+2512(SB)/8,$0x0000000038385d02 +DATA ·IEEEConst+2520(SB)/8,$0x00000000972e4a58 + + /* x^99392 mod p(x), x^99328 mod p(x) */ +DATA ·IEEEConst+2528(SB)/8,$0x00000001b6c83844 +DATA ·IEEEConst+2536(SB)/8,$0x0000000183499a5e + + /* x^98368 mod p(x), x^98304 mod p(x) */ +DATA ·IEEEConst+2544(SB)/8,$0x0000000051061a8a +DATA ·IEEEConst+2552(SB)/8,$0x00000001c96a8cca + + /* x^97344 mod p(x), x^97280 mod p(x) */ +DATA ·IEEEConst+2560(SB)/8,$0x000000017351388a +DATA ·IEEEConst+2568(SB)/8,$0x00000001a1a5b60c + + /* x^96320 mod p(x), x^96256 mod p(x) */ +DATA ·IEEEConst+2576(SB)/8,$0x0000000132928f92 +DATA ·IEEEConst+2584(SB)/8,$0x00000000e4b6ac9c + + /* x^95296 mod p(x), x^95232 mod p(x) */ +DATA ·IEEEConst+2592(SB)/8,$0x00000000e6b4f48a +DATA ·IEEEConst+2600(SB)/8,$0x00000001807e7f5a + + /* x^94272 mod p(x), x^94208 mod p(x) */ +DATA ·IEEEConst+2608(SB)/8,$0x0000000039d15e90 +DATA ·IEEEConst+2616(SB)/8,$0x000000017a7e3bc8 + + /* x^93248 mod p(x), x^93184 mod p(x) */ +DATA ·IEEEConst+2624(SB)/8,$0x00000000312d6074 +DATA ·IEEEConst+2632(SB)/8,$0x00000000d73975da + + /* x^92224 mod p(x), x^92160 mod p(x) */ +DATA ·IEEEConst+2640(SB)/8,$0x000000017bbb2cc4 +DATA ·IEEEConst+2648(SB)/8,$0x000000017375d038 + + /* x^91200 mod p(x), x^91136 mod p(x) */ +DATA ·IEEEConst+2656(SB)/8,$0x000000016ded3e18 +DATA ·IEEEConst+2664(SB)/8,$0x00000000193680bc + + /* x^90176 mod p(x), x^90112 mod p(x) */ +DATA ·IEEEConst+2672(SB)/8,$0x00000000f1638b16 +DATA ·IEEEConst+2680(SB)/8,$0x00000000999b06f6 + + /* x^89152 mod p(x), x^89088 mod p(x) */ +DATA ·IEEEConst+2688(SB)/8,$0x00000001d38b9ecc +DATA ·IEEEConst+2696(SB)/8,$0x00000001f685d2b8 + + /* x^88128 mod p(x), x^88064 mod p(x) */ +DATA ·IEEEConst+2704(SB)/8,$0x000000018b8d09dc +DATA ·IEEEConst+2712(SB)/8,$0x00000001f4ecbed2 + + /* x^87104 mod p(x), x^87040 mod p(x) */ +DATA ·IEEEConst+2720(SB)/8,$0x00000000e7bc27d2 +DATA ·IEEEConst+2728(SB)/8,$0x00000000ba16f1a0 + + /* x^86080 mod p(x), x^86016 mod p(x) */ +DATA ·IEEEConst+2736(SB)/8,$0x00000000275e1e96 +DATA ·IEEEConst+2744(SB)/8,$0x0000000115aceac4 + + /* x^85056 mod p(x), x^84992 mod p(x) */ +DATA ·IEEEConst+2752(SB)/8,$0x00000000e2e3031e +DATA ·IEEEConst+2760(SB)/8,$0x00000001aeff6292 + + /* x^84032 mod p(x), x^83968 mod p(x) */ +DATA ·IEEEConst+2768(SB)/8,$0x00000001041c84d8 +DATA ·IEEEConst+2776(SB)/8,$0x000000009640124c + + /* x^83008 mod p(x), x^82944 mod p(x) */ +DATA ·IEEEConst+2784(SB)/8,$0x00000000706ce672 +DATA ·IEEEConst+2792(SB)/8,$0x0000000114f41f02 + + /* x^81984 mod p(x), x^81920 mod p(x) */ +DATA ·IEEEConst+2800(SB)/8,$0x000000015d5070da +DATA ·IEEEConst+2808(SB)/8,$0x000000009c5f3586 + + /* x^80960 mod p(x), x^80896 mod p(x) */ +DATA ·IEEEConst+2816(SB)/8,$0x0000000038f9493a +DATA ·IEEEConst+2824(SB)/8,$0x00000001878275fa + + /* x^79936 mod p(x), x^79872 mod p(x) */ +DATA ·IEEEConst+2832(SB)/8,$0x00000000a3348a76 +DATA ·IEEEConst+2840(SB)/8,$0x00000000ddc42ce8 + + /* x^78912 mod p(x), x^78848 mod p(x) */ +DATA ·IEEEConst+2848(SB)/8,$0x00000001ad0aab92 +DATA ·IEEEConst+2856(SB)/8,$0x0000000181d2c73a + + /* x^77888 mod p(x), x^77824 mod p(x) */ +DATA ·IEEEConst+2864(SB)/8,$0x000000019e85f712 +DATA ·IEEEConst+2872(SB)/8,$0x0000000141c9320a + + /* x^76864 mod p(x), x^76800 mod p(x) */ +DATA ·IEEEConst+2880(SB)/8,$0x000000005a871e76 +DATA ·IEEEConst+2888(SB)/8,$0x000000015235719a + + /* x^75840 mod p(x), x^75776 mod p(x) */ +DATA ·IEEEConst+2896(SB)/8,$0x000000017249c662 +DATA ·IEEEConst+2904(SB)/8,$0x00000000be27d804 + + /* x^74816 mod p(x), x^74752 mod p(x) */ +DATA ·IEEEConst+2912(SB)/8,$0x000000003a084712 +DATA ·IEEEConst+2920(SB)/8,$0x000000006242d45a + + /* x^73792 mod p(x), x^73728 mod p(x) */ +DATA ·IEEEConst+2928(SB)/8,$0x00000000ed438478 +DATA ·IEEEConst+2936(SB)/8,$0x000000009a53638e + + /* x^72768 mod p(x), x^72704 mod p(x) */ +DATA ·IEEEConst+2944(SB)/8,$0x00000000abac34cc +DATA ·IEEEConst+2952(SB)/8,$0x00000001001ecfb6 + + /* x^71744 mod p(x), x^71680 mod p(x) */ +DATA ·IEEEConst+2960(SB)/8,$0x000000005f35ef3e +DATA ·IEEEConst+2968(SB)/8,$0x000000016d7c2d64 + + /* x^70720 mod p(x), x^70656 mod p(x) */ +DATA ·IEEEConst+2976(SB)/8,$0x0000000047d6608c +DATA ·IEEEConst+2984(SB)/8,$0x00000001d0ce46c0 + + /* x^69696 mod p(x), x^69632 mod p(x) */ +DATA ·IEEEConst+2992(SB)/8,$0x000000002d01470e +DATA ·IEEEConst+3000(SB)/8,$0x0000000124c907b4 + + /* x^68672 mod p(x), x^68608 mod p(x) */ +DATA ·IEEEConst+3008(SB)/8,$0x0000000158bbc7b0 +DATA ·IEEEConst+3016(SB)/8,$0x0000000018a555ca + + /* x^67648 mod p(x), x^67584 mod p(x) */ +DATA ·IEEEConst+3024(SB)/8,$0x00000000c0a23e8e +DATA ·IEEEConst+3032(SB)/8,$0x000000006b0980bc + + /* x^66624 mod p(x), x^66560 mod p(x) */ +DATA ·IEEEConst+3040(SB)/8,$0x00000001ebd85c88 +DATA ·IEEEConst+3048(SB)/8,$0x000000008bbba964 + + /* x^65600 mod p(x), x^65536 mod p(x) */ +DATA ·IEEEConst+3056(SB)/8,$0x000000019ee20bb2 +DATA ·IEEEConst+3064(SB)/8,$0x00000001070a5a1e + + /* x^64576 mod p(x), x^64512 mod p(x) */ +DATA ·IEEEConst+3072(SB)/8,$0x00000001acabf2d6 +DATA ·IEEEConst+3080(SB)/8,$0x000000002204322a + + /* x^63552 mod p(x), x^63488 mod p(x) */ +DATA ·IEEEConst+3088(SB)/8,$0x00000001b7963d56 +DATA ·IEEEConst+3096(SB)/8,$0x00000000a27524d0 + + /* x^62528 mod p(x), x^62464 mod p(x) */ +DATA ·IEEEConst+3104(SB)/8,$0x000000017bffa1fe +DATA ·IEEEConst+3112(SB)/8,$0x0000000020b1e4ba + + /* x^61504 mod p(x), x^61440 mod p(x) */ +DATA ·IEEEConst+3120(SB)/8,$0x000000001f15333e +DATA ·IEEEConst+3128(SB)/8,$0x0000000032cc27fc + + /* x^60480 mod p(x), x^60416 mod p(x) */ +DATA ·IEEEConst+3136(SB)/8,$0x000000018593129e +DATA ·IEEEConst+3144(SB)/8,$0x0000000044dd22b8 + + /* x^59456 mod p(x), x^59392 mod p(x) */ +DATA ·IEEEConst+3152(SB)/8,$0x000000019cb32602 +DATA ·IEEEConst+3160(SB)/8,$0x00000000dffc9e0a + + /* x^58432 mod p(x), x^58368 mod p(x) */ +DATA ·IEEEConst+3168(SB)/8,$0x0000000142b05cc8 +DATA ·IEEEConst+3176(SB)/8,$0x00000001b7a0ed14 + + /* x^57408 mod p(x), x^57344 mod p(x) */ +DATA ·IEEEConst+3184(SB)/8,$0x00000001be49e7a4 +DATA ·IEEEConst+3192(SB)/8,$0x00000000c7842488 + + /* x^56384 mod p(x), x^56320 mod p(x) */ +DATA ·IEEEConst+3200(SB)/8,$0x0000000108f69d6c +DATA ·IEEEConst+3208(SB)/8,$0x00000001c02a4fee + + /* x^55360 mod p(x), x^55296 mod p(x) */ +DATA ·IEEEConst+3216(SB)/8,$0x000000006c0971f0 +DATA ·IEEEConst+3224(SB)/8,$0x000000003c273778 + + /* x^54336 mod p(x), x^54272 mod p(x) */ +DATA ·IEEEConst+3232(SB)/8,$0x000000005b16467a +DATA ·IEEEConst+3240(SB)/8,$0x00000001d63f8894 + + /* x^53312 mod p(x), x^53248 mod p(x) */ +DATA ·IEEEConst+3248(SB)/8,$0x00000001551a628e +DATA ·IEEEConst+3256(SB)/8,$0x000000006be557d6 + + /* x^52288 mod p(x), x^52224 mod p(x) */ +DATA ·IEEEConst+3264(SB)/8,$0x000000019e42ea92 +DATA ·IEEEConst+3272(SB)/8,$0x000000006a7806ea + + /* x^51264 mod p(x), x^51200 mod p(x) */ +DATA ·IEEEConst+3280(SB)/8,$0x000000012fa83ff2 +DATA ·IEEEConst+3288(SB)/8,$0x000000016155aa0c + + /* x^50240 mod p(x), x^50176 mod p(x) */ +DATA ·IEEEConst+3296(SB)/8,$0x000000011ca9cde0 +DATA ·IEEEConst+3304(SB)/8,$0x00000000908650ac + + /* x^49216 mod p(x), x^49152 mod p(x) */ +DATA ·IEEEConst+3312(SB)/8,$0x00000000c8e5cd74 +DATA ·IEEEConst+3320(SB)/8,$0x00000000aa5a8084 + + /* x^48192 mod p(x), x^48128 mod p(x) */ +DATA ·IEEEConst+3328(SB)/8,$0x0000000096c27f0c +DATA ·IEEEConst+3336(SB)/8,$0x0000000191bb500a + + /* x^47168 mod p(x), x^47104 mod p(x) */ +DATA ·IEEEConst+3344(SB)/8,$0x000000002baed926 +DATA ·IEEEConst+3352(SB)/8,$0x0000000064e9bed0 + + /* x^46144 mod p(x), x^46080 mod p(x) */ +DATA ·IEEEConst+3360(SB)/8,$0x000000017c8de8d2 +DATA ·IEEEConst+3368(SB)/8,$0x000000009444f302 + + /* x^45120 mod p(x), x^45056 mod p(x) */ +DATA ·IEEEConst+3376(SB)/8,$0x00000000d43d6068 +DATA ·IEEEConst+3384(SB)/8,$0x000000019db07d3c + + /* x^44096 mod p(x), x^44032 mod p(x) */ +DATA ·IEEEConst+3392(SB)/8,$0x00000000cb2c4b26 +DATA ·IEEEConst+3400(SB)/8,$0x00000001359e3e6e + + /* x^43072 mod p(x), x^43008 mod p(x) */ +DATA ·IEEEConst+3408(SB)/8,$0x0000000145b8da26 +DATA ·IEEEConst+3416(SB)/8,$0x00000001e4f10dd2 + + /* x^42048 mod p(x), x^41984 mod p(x) */ +DATA ·IEEEConst+3424(SB)/8,$0x000000018fff4b08 +DATA ·IEEEConst+3432(SB)/8,$0x0000000124f5735e + + /* x^41024 mod p(x), x^40960 mod p(x) */ +DATA ·IEEEConst+3440(SB)/8,$0x0000000150b58ed0 +DATA ·IEEEConst+3448(SB)/8,$0x0000000124760a4c + + /* x^40000 mod p(x), x^39936 mod p(x) */ +DATA ·IEEEConst+3456(SB)/8,$0x00000001549f39bc +DATA ·IEEEConst+3464(SB)/8,$0x000000000f1fc186 + + /* x^38976 mod p(x), x^38912 mod p(x) */ +DATA ·IEEEConst+3472(SB)/8,$0x00000000ef4d2f42 +DATA ·IEEEConst+3480(SB)/8,$0x00000000150e4cc4 + + /* x^37952 mod p(x), x^37888 mod p(x) */ +DATA ·IEEEConst+3488(SB)/8,$0x00000001b1468572 +DATA ·IEEEConst+3496(SB)/8,$0x000000002a6204e8 + + /* x^36928 mod p(x), x^36864 mod p(x) */ +DATA ·IEEEConst+3504(SB)/8,$0x000000013d7403b2 +DATA ·IEEEConst+3512(SB)/8,$0x00000000beb1d432 + + /* x^35904 mod p(x), x^35840 mod p(x) */ +DATA ·IEEEConst+3520(SB)/8,$0x00000001a4681842 +DATA ·IEEEConst+3528(SB)/8,$0x0000000135f3f1f0 + + /* x^34880 mod p(x), x^34816 mod p(x) */ +DATA ·IEEEConst+3536(SB)/8,$0x0000000167714492 +DATA ·IEEEConst+3544(SB)/8,$0x0000000074fe2232 + + /* x^33856 mod p(x), x^33792 mod p(x) */ +DATA ·IEEEConst+3552(SB)/8,$0x00000001e599099a +DATA ·IEEEConst+3560(SB)/8,$0x000000001ac6e2ba + + /* x^32832 mod p(x), x^32768 mod p(x) */ +DATA ·IEEEConst+3568(SB)/8,$0x00000000fe128194 +DATA ·IEEEConst+3576(SB)/8,$0x0000000013fca91e + + /* x^31808 mod p(x), x^31744 mod p(x) */ +DATA ·IEEEConst+3584(SB)/8,$0x0000000077e8b990 +DATA ·IEEEConst+3592(SB)/8,$0x0000000183f4931e + + /* x^30784 mod p(x), x^30720 mod p(x) */ +DATA ·IEEEConst+3600(SB)/8,$0x00000001a267f63a +DATA ·IEEEConst+3608(SB)/8,$0x00000000b6d9b4e4 + + /* x^29760 mod p(x), x^29696 mod p(x) */ +DATA ·IEEEConst+3616(SB)/8,$0x00000001945c245a +DATA ·IEEEConst+3624(SB)/8,$0x00000000b5188656 + + /* x^28736 mod p(x), x^28672 mod p(x) */ +DATA ·IEEEConst+3632(SB)/8,$0x0000000149002e76 +DATA ·IEEEConst+3640(SB)/8,$0x0000000027a81a84 + + /* x^27712 mod p(x), x^27648 mod p(x) */ +DATA ·IEEEConst+3648(SB)/8,$0x00000001bb8310a4 +DATA ·IEEEConst+3656(SB)/8,$0x0000000125699258 + + /* x^26688 mod p(x), x^26624 mod p(x) */ +DATA ·IEEEConst+3664(SB)/8,$0x000000019ec60bcc +DATA ·IEEEConst+3672(SB)/8,$0x00000001b23de796 + + /* x^25664 mod p(x), x^25600 mod p(x) */ +DATA ·IEEEConst+3680(SB)/8,$0x000000012d8590ae +DATA ·IEEEConst+3688(SB)/8,$0x00000000fe4365dc + + /* x^24640 mod p(x), x^24576 mod p(x) */ +DATA ·IEEEConst+3696(SB)/8,$0x0000000065b00684 +DATA ·IEEEConst+3704(SB)/8,$0x00000000c68f497a + + /* x^23616 mod p(x), x^23552 mod p(x) */ +DATA ·IEEEConst+3712(SB)/8,$0x000000015e5aeadc +DATA ·IEEEConst+3720(SB)/8,$0x00000000fbf521ee + + /* x^22592 mod p(x), x^22528 mod p(x) */ +DATA ·IEEEConst+3728(SB)/8,$0x00000000b77ff2b0 +DATA ·IEEEConst+3736(SB)/8,$0x000000015eac3378 + + /* x^21568 mod p(x), x^21504 mod p(x) */ +DATA ·IEEEConst+3744(SB)/8,$0x0000000188da2ff6 +DATA ·IEEEConst+3752(SB)/8,$0x0000000134914b90 + + /* x^20544 mod p(x), x^20480 mod p(x) */ +DATA ·IEEEConst+3760(SB)/8,$0x0000000063da929a +DATA ·IEEEConst+3768(SB)/8,$0x0000000016335cfe + + /* x^19520 mod p(x), x^19456 mod p(x) */ +DATA ·IEEEConst+3776(SB)/8,$0x00000001389caa80 +DATA ·IEEEConst+3784(SB)/8,$0x000000010372d10c + + /* x^18496 mod p(x), x^18432 mod p(x) */ +DATA ·IEEEConst+3792(SB)/8,$0x000000013db599d2 +DATA ·IEEEConst+3800(SB)/8,$0x000000015097b908 + + /* x^17472 mod p(x), x^17408 mod p(x) */ +DATA ·IEEEConst+3808(SB)/8,$0x0000000122505a86 +DATA ·IEEEConst+3816(SB)/8,$0x00000001227a7572 + + /* x^16448 mod p(x), x^16384 mod p(x) */ +DATA ·IEEEConst+3824(SB)/8,$0x000000016bd72746 +DATA ·IEEEConst+3832(SB)/8,$0x000000009a8f75c0 + + /* x^15424 mod p(x), x^15360 mod p(x) */ +DATA ·IEEEConst+3840(SB)/8,$0x00000001c3faf1d4 +DATA ·IEEEConst+3848(SB)/8,$0x00000000682c77a2 + + /* x^14400 mod p(x), x^14336 mod p(x) */ +DATA ·IEEEConst+3856(SB)/8,$0x00000001111c826c +DATA ·IEEEConst+3864(SB)/8,$0x00000000231f091c + + /* x^13376 mod p(x), x^13312 mod p(x) */ +DATA ·IEEEConst+3872(SB)/8,$0x00000000153e9fb2 +DATA ·IEEEConst+3880(SB)/8,$0x000000007d4439f2 + + /* x^12352 mod p(x), x^12288 mod p(x) */ +DATA ·IEEEConst+3888(SB)/8,$0x000000002b1f7b60 +DATA ·IEEEConst+3896(SB)/8,$0x000000017e221efc + + /* x^11328 mod p(x), x^11264 mod p(x) */ +DATA ·IEEEConst+3904(SB)/8,$0x00000000b1dba570 +DATA ·IEEEConst+3912(SB)/8,$0x0000000167457c38 + + /* x^10304 mod p(x), x^10240 mod p(x) */ +DATA ·IEEEConst+3920(SB)/8,$0x00000001f6397b76 +DATA ·IEEEConst+3928(SB)/8,$0x00000000bdf081c4 + + /* x^9280 mod p(x), x^9216 mod p(x) */ +DATA ·IEEEConst+3936(SB)/8,$0x0000000156335214 +DATA ·IEEEConst+3944(SB)/8,$0x000000016286d6b0 + + /* x^8256 mod p(x), x^8192 mod p(x) */ +DATA ·IEEEConst+3952(SB)/8,$0x00000001d70e3986 +DATA ·IEEEConst+3960(SB)/8,$0x00000000c84f001c + + /* x^7232 mod p(x), x^7168 mod p(x) */ +DATA ·IEEEConst+3968(SB)/8,$0x000000003701a774 +DATA ·IEEEConst+3976(SB)/8,$0x0000000064efe7c0 + + /* x^6208 mod p(x), x^6144 mod p(x) */ +DATA ·IEEEConst+3984(SB)/8,$0x00000000ac81ef72 +DATA ·IEEEConst+3992(SB)/8,$0x000000000ac2d904 + + /* x^5184 mod p(x), x^5120 mod p(x) */ +DATA ·IEEEConst+4000(SB)/8,$0x0000000133212464 +DATA ·IEEEConst+4008(SB)/8,$0x00000000fd226d14 + + /* x^4160 mod p(x), x^4096 mod p(x) */ +DATA ·IEEEConst+4016(SB)/8,$0x00000000e4e45610 +DATA ·IEEEConst+4024(SB)/8,$0x000000011cfd42e0 + + /* x^3136 mod p(x), x^3072 mod p(x) */ +DATA ·IEEEConst+4032(SB)/8,$0x000000000c1bd370 +DATA ·IEEEConst+4040(SB)/8,$0x000000016e5a5678 + + /* x^2112 mod p(x), x^2048 mod p(x) */ +DATA ·IEEEConst+4048(SB)/8,$0x00000001a7b9e7a6 +DATA ·IEEEConst+4056(SB)/8,$0x00000001d888fe22 + + /* x^1088 mod p(x), x^1024 mod p(x) */ +DATA ·IEEEConst+4064(SB)/8,$0x000000007d657a10 +DATA ·IEEEConst+4072(SB)/8,$0x00000001af77fcd4 + + /* x^2048 mod p(x), x^2016 mod p(x), x^1984 mod p(x), x^1952 mod p(x) */ +DATA ·IEEEConst+4080(SB)/8,$0x99168a18ec447f11 +DATA ·IEEEConst+4088(SB)/8,$0xed837b2613e8221e + + /* x^1920 mod p(x), x^1888 mod p(x), x^1856 mod p(x), x^1824 mod p(x) */ +DATA ·IEEEConst+4096(SB)/8,$0xe23e954e8fd2cd3c +DATA ·IEEEConst+4104(SB)/8,$0xc8acdd8147b9ce5a + + /* x^1792 mod p(x), x^1760 mod p(x), x^1728 mod p(x), x^1696 mod p(x) */ +DATA ·IEEEConst+4112(SB)/8,$0x92f8befe6b1d2b53 +DATA ·IEEEConst+4120(SB)/8,$0xd9ad6d87d4277e25 + + /* x^1664 mod p(x), x^1632 mod p(x), x^1600 mod p(x), x^1568 mod p(x) */ +DATA ·IEEEConst+4128(SB)/8,$0xf38a3556291ea462 +DATA ·IEEEConst+4136(SB)/8,$0xc10ec5e033fbca3b + + /* x^1536 mod p(x), x^1504 mod p(x), x^1472 mod p(x), x^1440 mod p(x) */ +DATA ·IEEEConst+4144(SB)/8,$0x974ac56262b6ca4b +DATA ·IEEEConst+4152(SB)/8,$0xc0b55b0e82e02e2f + + /* x^1408 mod p(x), x^1376 mod p(x), x^1344 mod p(x), x^1312 mod p(x) */ +DATA ·IEEEConst+4160(SB)/8,$0x855712b3784d2a56 +DATA ·IEEEConst+4168(SB)/8,$0x71aa1df0e172334d + + /* x^1280 mod p(x), x^1248 mod p(x), x^1216 mod p(x), x^1184 mod p(x) */ +DATA ·IEEEConst+4176(SB)/8,$0xa5abe9f80eaee722 +DATA ·IEEEConst+4184(SB)/8,$0xfee3053e3969324d + + /* x^1152 mod p(x), x^1120 mod p(x), x^1088 mod p(x), x^1056 mod p(x) */ +DATA ·IEEEConst+4192(SB)/8,$0x1fa0943ddb54814c +DATA ·IEEEConst+4200(SB)/8,$0xf44779b93eb2bd08 + + /* x^1024 mod p(x), x^992 mod p(x), x^960 mod p(x), x^928 mod p(x) */ +DATA ·IEEEConst+4208(SB)/8,$0xa53ff440d7bbfe6a +DATA ·IEEEConst+4216(SB)/8,$0xf5449b3f00cc3374 + + /* x^896 mod p(x), x^864 mod p(x), x^832 mod p(x), x^800 mod p(x) */ +DATA ·IEEEConst+4224(SB)/8,$0xebe7e3566325605c +DATA ·IEEEConst+4232(SB)/8,$0x6f8346e1d777606e + + /* x^768 mod p(x), x^736 mod p(x), x^704 mod p(x), x^672 mod p(x) */ +DATA ·IEEEConst+4240(SB)/8,$0xc65a272ce5b592b8 +DATA ·IEEEConst+4248(SB)/8,$0xe3ab4f2ac0b95347 + + /* x^640 mod p(x), x^608 mod p(x), x^576 mod p(x), x^544 mod p(x) */ +DATA ·IEEEConst+4256(SB)/8,$0x5705a9ca4721589f +DATA ·IEEEConst+4264(SB)/8,$0xaa2215ea329ecc11 + + /* x^512 mod p(x), x^480 mod p(x), x^448 mod p(x), x^416 mod p(x) */ +DATA ·IEEEConst+4272(SB)/8,$0xe3720acb88d14467 +DATA ·IEEEConst+4280(SB)/8,$0x1ed8f66ed95efd26 + + /* x^384 mod p(x), x^352 mod p(x), x^320 mod p(x), x^288 mod p(x) */ +DATA ·IEEEConst+4288(SB)/8,$0xba1aca0315141c31 +DATA ·IEEEConst+4296(SB)/8,$0x78ed02d5a700e96a + + /* x^256 mod p(x), x^224 mod p(x), x^192 mod p(x), x^160 mod p(x) */ +DATA ·IEEEConst+4304(SB)/8,$0xad2a31b3ed627dae +DATA ·IEEEConst+4312(SB)/8,$0xba8ccbe832b39da3 + + /* x^128 mod p(x), x^96 mod p(x), x^64 mod p(x), x^32 mod p(x) */ +DATA ·IEEEConst+4320(SB)/8,$0x6655004fa06a2517 +DATA ·IEEEConst+4328(SB)/8,$0xedb88320b1e6b092 + +GLOBL ·IEEEConst(SB),RODATA,$4336 + + /* Barrett constant m - (4^32)/n */ +DATA ·IEEEBarConst(SB)/8,$0x00000001f7011641 +DATA ·IEEEBarConst+8(SB)/8,$0x0000000000000000 +DATA ·IEEEBarConst+16(SB)/8,$0x00000001db710641 +DATA ·IEEEBarConst+24(SB)/8,$0x0000000000000000 +GLOBL ·IEEEBarConst(SB),RODATA,$32 + + /* Reduce 262144 kbits to 1024 bits */ + /* x^261184 mod p(x), x^261120 mod p(x) */ +DATA ·CastConst+0(SB)/8,$0x000000009c37c408 +DATA ·CastConst+8(SB)/8,$0x00000000b6ca9e20 + + /* x^260160 mod p(x), x^260096 mod p(x) */ +DATA ·CastConst+16(SB)/8,$0x00000001b51df26c +DATA ·CastConst+24(SB)/8,$0x00000000350249a8 + + /* x^259136 mod p(x), x^259072 mod p(x) */ +DATA ·CastConst+32(SB)/8,$0x000000000724b9d0 +DATA ·CastConst+40(SB)/8,$0x00000001862dac54 + + /* x^258112 mod p(x), x^258048 mod p(x) */ +DATA ·CastConst+48(SB)/8,$0x00000001c00532fe +DATA ·CastConst+56(SB)/8,$0x00000001d87fb48c + + /* x^257088 mod p(x), x^257024 mod p(x) */ +DATA ·CastConst+64(SB)/8,$0x00000000f05a9362 +DATA ·CastConst+72(SB)/8,$0x00000001f39b699e + + /* x^256064 mod p(x), x^256000 mod p(x) */ +DATA ·CastConst+80(SB)/8,$0x00000001e1007970 +DATA ·CastConst+88(SB)/8,$0x0000000101da11b4 + + /* x^255040 mod p(x), x^254976 mod p(x) */ +DATA ·CastConst+96(SB)/8,$0x00000000a57366ee +DATA ·CastConst+104(SB)/8,$0x00000001cab571e0 + + /* x^254016 mod p(x), x^253952 mod p(x) */ +DATA ·CastConst+112(SB)/8,$0x0000000192011284 +DATA ·CastConst+120(SB)/8,$0x00000000c7020cfe + + /* x^252992 mod p(x), x^252928 mod p(x) */ +DATA ·CastConst+128(SB)/8,$0x0000000162716d9a +DATA ·CastConst+136(SB)/8,$0x00000000cdaed1ae + + /* x^251968 mod p(x), x^251904 mod p(x) */ +DATA ·CastConst+144(SB)/8,$0x00000000cd97ecde +DATA ·CastConst+152(SB)/8,$0x00000001e804effc + + /* x^250944 mod p(x), x^250880 mod p(x) */ +DATA ·CastConst+160(SB)/8,$0x0000000058812bc0 +DATA ·CastConst+168(SB)/8,$0x0000000077c3ea3a + + /* x^249920 mod p(x), x^249856 mod p(x) */ +DATA ·CastConst+176(SB)/8,$0x0000000088b8c12e +DATA ·CastConst+184(SB)/8,$0x0000000068df31b4 + + /* x^248896 mod p(x), x^248832 mod p(x) */ +DATA ·CastConst+192(SB)/8,$0x00000001230b234c +DATA ·CastConst+200(SB)/8,$0x00000000b059b6c2 + + /* x^247872 mod p(x), x^247808 mod p(x) */ +DATA ·CastConst+208(SB)/8,$0x00000001120b416e +DATA ·CastConst+216(SB)/8,$0x0000000145fb8ed8 + + /* x^246848 mod p(x), x^246784 mod p(x) */ +DATA ·CastConst+224(SB)/8,$0x00000001974aecb0 +DATA ·CastConst+232(SB)/8,$0x00000000cbc09168 + + /* x^245824 mod p(x), x^245760 mod p(x) */ +DATA ·CastConst+240(SB)/8,$0x000000008ee3f226 +DATA ·CastConst+248(SB)/8,$0x000000005ceeedc2 + + /* x^244800 mod p(x), x^244736 mod p(x) */ +DATA ·CastConst+256(SB)/8,$0x00000001089aba9a +DATA ·CastConst+264(SB)/8,$0x0000000047d74e86 + + /* x^243776 mod p(x), x^243712 mod p(x) */ +DATA ·CastConst+272(SB)/8,$0x0000000065113872 +DATA ·CastConst+280(SB)/8,$0x00000001407e9e22 + + /* x^242752 mod p(x), x^242688 mod p(x) */ +DATA ·CastConst+288(SB)/8,$0x000000005c07ec10 +DATA ·CastConst+296(SB)/8,$0x00000001da967bda + + /* x^241728 mod p(x), x^241664 mod p(x) */ +DATA ·CastConst+304(SB)/8,$0x0000000187590924 +DATA ·CastConst+312(SB)/8,$0x000000006c898368 + + /* x^240704 mod p(x), x^240640 mod p(x) */ +DATA ·CastConst+320(SB)/8,$0x00000000e35da7c6 +DATA ·CastConst+328(SB)/8,$0x00000000f2d14c98 + + /* x^239680 mod p(x), x^239616 mod p(x) */ +DATA ·CastConst+336(SB)/8,$0x000000000415855a +DATA ·CastConst+344(SB)/8,$0x00000001993c6ad4 + + /* x^238656 mod p(x), x^238592 mod p(x) */ +DATA ·CastConst+352(SB)/8,$0x0000000073617758 +DATA ·CastConst+360(SB)/8,$0x000000014683d1ac + + /* x^237632 mod p(x), x^237568 mod p(x) */ +DATA ·CastConst+368(SB)/8,$0x0000000176021d28 +DATA ·CastConst+376(SB)/8,$0x00000001a7c93e6c + + /* x^236608 mod p(x), x^236544 mod p(x) */ +DATA ·CastConst+384(SB)/8,$0x00000001c358fd0a +DATA ·CastConst+392(SB)/8,$0x000000010211e90a + + /* x^235584 mod p(x), x^235520 mod p(x) */ +DATA ·CastConst+400(SB)/8,$0x00000001ff7a2c18 +DATA ·CastConst+408(SB)/8,$0x000000001119403e + + /* x^234560 mod p(x), x^234496 mod p(x) */ +DATA ·CastConst+416(SB)/8,$0x00000000f2d9f7e4 +DATA ·CastConst+424(SB)/8,$0x000000001c3261aa + + /* x^233536 mod p(x), x^233472 mod p(x) */ +DATA ·CastConst+432(SB)/8,$0x000000016cf1f9c8 +DATA ·CastConst+440(SB)/8,$0x000000014e37a634 + + /* x^232512 mod p(x), x^232448 mod p(x) */ +DATA ·CastConst+448(SB)/8,$0x000000010af9279a +DATA ·CastConst+456(SB)/8,$0x0000000073786c0c + + /* x^231488 mod p(x), x^231424 mod p(x) */ +DATA ·CastConst+464(SB)/8,$0x0000000004f101e8 +DATA ·CastConst+472(SB)/8,$0x000000011dc037f8 + + /* x^230464 mod p(x), x^230400 mod p(x) */ +DATA ·CastConst+480(SB)/8,$0x0000000070bcf184 +DATA ·CastConst+488(SB)/8,$0x0000000031433dfc + + /* x^229440 mod p(x), x^229376 mod p(x) */ +DATA ·CastConst+496(SB)/8,$0x000000000a8de642 +DATA ·CastConst+504(SB)/8,$0x000000009cde8348 + + /* x^228416 mod p(x), x^228352 mod p(x) */ +DATA ·CastConst+512(SB)/8,$0x0000000062ea130c +DATA ·CastConst+520(SB)/8,$0x0000000038d3c2a6 + + /* x^227392 mod p(x), x^227328 mod p(x) */ +DATA ·CastConst+528(SB)/8,$0x00000001eb31cbb2 +DATA ·CastConst+536(SB)/8,$0x000000011b25f260 + + /* x^226368 mod p(x), x^226304 mod p(x) */ +DATA ·CastConst+544(SB)/8,$0x0000000170783448 +DATA ·CastConst+552(SB)/8,$0x000000001629e6f0 + + /* x^225344 mod p(x), x^225280 mod p(x) */ +DATA ·CastConst+560(SB)/8,$0x00000001a684b4c6 +DATA ·CastConst+568(SB)/8,$0x0000000160838b4c + + /* x^224320 mod p(x), x^224256 mod p(x) */ +DATA ·CastConst+576(SB)/8,$0x00000000253ca5b4 +DATA ·CastConst+584(SB)/8,$0x000000007a44011c + + /* x^223296 mod p(x), x^223232 mod p(x) */ +DATA ·CastConst+592(SB)/8,$0x0000000057b4b1e2 +DATA ·CastConst+600(SB)/8,$0x00000000226f417a + + /* x^222272 mod p(x), x^222208 mod p(x) */ +DATA ·CastConst+608(SB)/8,$0x00000000b6bd084c +DATA ·CastConst+616(SB)/8,$0x0000000045eb2eb4 + + /* x^221248 mod p(x), x^221184 mod p(x) */ +DATA ·CastConst+624(SB)/8,$0x0000000123c2d592 +DATA ·CastConst+632(SB)/8,$0x000000014459d70c + + /* x^220224 mod p(x), x^220160 mod p(x) */ +DATA ·CastConst+640(SB)/8,$0x00000000159dafce +DATA ·CastConst+648(SB)/8,$0x00000001d406ed82 + + /* x^219200 mod p(x), x^219136 mod p(x) */ +DATA ·CastConst+656(SB)/8,$0x0000000127e1a64e +DATA ·CastConst+664(SB)/8,$0x0000000160c8e1a8 + + /* x^218176 mod p(x), x^218112 mod p(x) */ +DATA ·CastConst+672(SB)/8,$0x0000000056860754 +DATA ·CastConst+680(SB)/8,$0x0000000027ba8098 + + /* x^217152 mod p(x), x^217088 mod p(x) */ +DATA ·CastConst+688(SB)/8,$0x00000001e661aae8 +DATA ·CastConst+696(SB)/8,$0x000000006d92d018 + + /* x^216128 mod p(x), x^216064 mod p(x) */ +DATA ·CastConst+704(SB)/8,$0x00000000f82c6166 +DATA ·CastConst+712(SB)/8,$0x000000012ed7e3f2 + + /* x^215104 mod p(x), x^215040 mod p(x) */ +DATA ·CastConst+720(SB)/8,$0x00000000c4f9c7ae +DATA ·CastConst+728(SB)/8,$0x000000002dc87788 + + /* x^214080 mod p(x), x^214016 mod p(x) */ +DATA ·CastConst+736(SB)/8,$0x0000000074203d20 +DATA ·CastConst+744(SB)/8,$0x0000000018240bb8 + + /* x^213056 mod p(x), x^212992 mod p(x) */ +DATA ·CastConst+752(SB)/8,$0x0000000198173052 +DATA ·CastConst+760(SB)/8,$0x000000001ad38158 + + /* x^212032 mod p(x), x^211968 mod p(x) */ +DATA ·CastConst+768(SB)/8,$0x00000001ce8aba54 +DATA ·CastConst+776(SB)/8,$0x00000001396b78f2 + + /* x^211008 mod p(x), x^210944 mod p(x) */ +DATA ·CastConst+784(SB)/8,$0x00000001850d5d94 +DATA ·CastConst+792(SB)/8,$0x000000011a681334 + + /* x^209984 mod p(x), x^209920 mod p(x) */ +DATA ·CastConst+800(SB)/8,$0x00000001d609239c +DATA ·CastConst+808(SB)/8,$0x000000012104732e + + /* x^208960 mod p(x), x^208896 mod p(x) */ +DATA ·CastConst+816(SB)/8,$0x000000001595f048 +DATA ·CastConst+824(SB)/8,$0x00000000a140d90c + + /* x^207936 mod p(x), x^207872 mod p(x) */ +DATA ·CastConst+832(SB)/8,$0x0000000042ccee08 +DATA ·CastConst+840(SB)/8,$0x00000001b7215eda + + /* x^206912 mod p(x), x^206848 mod p(x) */ +DATA ·CastConst+848(SB)/8,$0x000000010a389d74 +DATA ·CastConst+856(SB)/8,$0x00000001aaf1df3c + + /* x^205888 mod p(x), x^205824 mod p(x) */ +DATA ·CastConst+864(SB)/8,$0x000000012a840da6 +DATA ·CastConst+872(SB)/8,$0x0000000029d15b8a + + /* x^204864 mod p(x), x^204800 mod p(x) */ +DATA ·CastConst+880(SB)/8,$0x000000001d181c0c +DATA ·CastConst+888(SB)/8,$0x00000000f1a96922 + + /* x^203840 mod p(x), x^203776 mod p(x) */ +DATA ·CastConst+896(SB)/8,$0x0000000068b7d1f6 +DATA ·CastConst+904(SB)/8,$0x00000001ac80d03c + + /* x^202816 mod p(x), x^202752 mod p(x) */ +DATA ·CastConst+912(SB)/8,$0x000000005b0f14fc +DATA ·CastConst+920(SB)/8,$0x000000000f11d56a + + /* x^201792 mod p(x), x^201728 mod p(x) */ +DATA ·CastConst+928(SB)/8,$0x0000000179e9e730 +DATA ·CastConst+936(SB)/8,$0x00000001f1c022a2 + + /* x^200768 mod p(x), x^200704 mod p(x) */ +DATA ·CastConst+944(SB)/8,$0x00000001ce1368d6 +DATA ·CastConst+952(SB)/8,$0x0000000173d00ae2 + + /* x^199744 mod p(x), x^199680 mod p(x) */ +DATA ·CastConst+960(SB)/8,$0x0000000112c3a84c +DATA ·CastConst+968(SB)/8,$0x00000001d4ffe4ac + + /* x^198720 mod p(x), x^198656 mod p(x) */ +DATA ·CastConst+976(SB)/8,$0x00000000de940fee +DATA ·CastConst+984(SB)/8,$0x000000016edc5ae4 + + /* x^197696 mod p(x), x^197632 mod p(x) */ +DATA ·CastConst+992(SB)/8,$0x00000000fe896b7e +DATA ·CastConst+1000(SB)/8,$0x00000001f1a02140 + + /* x^196672 mod p(x), x^196608 mod p(x) */ +DATA ·CastConst+1008(SB)/8,$0x00000001f797431c +DATA ·CastConst+1016(SB)/8,$0x00000000ca0b28a0 + + /* x^195648 mod p(x), x^195584 mod p(x) */ +DATA ·CastConst+1024(SB)/8,$0x0000000053e989ba +DATA ·CastConst+1032(SB)/8,$0x00000001928e30a2 + + /* x^194624 mod p(x), x^194560 mod p(x) */ +DATA ·CastConst+1040(SB)/8,$0x000000003920cd16 +DATA ·CastConst+1048(SB)/8,$0x0000000097b1b002 + + /* x^193600 mod p(x), x^193536 mod p(x) */ +DATA ·CastConst+1056(SB)/8,$0x00000001e6f579b8 +DATA ·CastConst+1064(SB)/8,$0x00000000b15bf906 + + /* x^192576 mod p(x), x^192512 mod p(x) */ +DATA ·CastConst+1072(SB)/8,$0x000000007493cb0a +DATA ·CastConst+1080(SB)/8,$0x00000000411c5d52 + + /* x^191552 mod p(x), x^191488 mod p(x) */ +DATA ·CastConst+1088(SB)/8,$0x00000001bdd376d8 +DATA ·CastConst+1096(SB)/8,$0x00000001c36f3300 + + /* x^190528 mod p(x), x^190464 mod p(x) */ +DATA ·CastConst+1104(SB)/8,$0x000000016badfee6 +DATA ·CastConst+1112(SB)/8,$0x00000001119227e0 + + /* x^189504 mod p(x), x^189440 mod p(x) */ +DATA ·CastConst+1120(SB)/8,$0x0000000071de5c58 +DATA ·CastConst+1128(SB)/8,$0x00000000114d4702 + + /* x^188480 mod p(x), x^188416 mod p(x) */ +DATA ·CastConst+1136(SB)/8,$0x00000000453f317c +DATA ·CastConst+1144(SB)/8,$0x00000000458b5b98 + + /* x^187456 mod p(x), x^187392 mod p(x) */ +DATA ·CastConst+1152(SB)/8,$0x0000000121675cce +DATA ·CastConst+1160(SB)/8,$0x000000012e31fb8e + + /* x^186432 mod p(x), x^186368 mod p(x) */ +DATA ·CastConst+1168(SB)/8,$0x00000001f409ee92 +DATA ·CastConst+1176(SB)/8,$0x000000005cf619d8 + + /* x^185408 mod p(x), x^185344 mod p(x) */ +DATA ·CastConst+1184(SB)/8,$0x00000000f36b9c88 +DATA ·CastConst+1192(SB)/8,$0x0000000063f4d8b2 + + /* x^184384 mod p(x), x^184320 mod p(x) */ +DATA ·CastConst+1200(SB)/8,$0x0000000036b398f4 +DATA ·CastConst+1208(SB)/8,$0x000000004138dc8a + + /* x^183360 mod p(x), x^183296 mod p(x) */ +DATA ·CastConst+1216(SB)/8,$0x00000001748f9adc +DATA ·CastConst+1224(SB)/8,$0x00000001d29ee8e0 + + /* x^182336 mod p(x), x^182272 mod p(x) */ +DATA ·CastConst+1232(SB)/8,$0x00000001be94ec00 +DATA ·CastConst+1240(SB)/8,$0x000000006a08ace8 + + /* x^181312 mod p(x), x^181248 mod p(x) */ +DATA ·CastConst+1248(SB)/8,$0x00000000b74370d6 +DATA ·CastConst+1256(SB)/8,$0x0000000127d42010 + + /* x^180288 mod p(x), x^180224 mod p(x) */ +DATA ·CastConst+1264(SB)/8,$0x00000001174d0b98 +DATA ·CastConst+1272(SB)/8,$0x0000000019d76b62 + + /* x^179264 mod p(x), x^179200 mod p(x) */ +DATA ·CastConst+1280(SB)/8,$0x00000000befc06a4 +DATA ·CastConst+1288(SB)/8,$0x00000001b1471f6e + + /* x^178240 mod p(x), x^178176 mod p(x) */ +DATA ·CastConst+1296(SB)/8,$0x00000001ae125288 +DATA ·CastConst+1304(SB)/8,$0x00000001f64c19cc + + /* x^177216 mod p(x), x^177152 mod p(x) */ +DATA ·CastConst+1312(SB)/8,$0x0000000095c19b34 +DATA ·CastConst+1320(SB)/8,$0x00000000003c0ea0 + + /* x^176192 mod p(x), x^176128 mod p(x) */ +DATA ·CastConst+1328(SB)/8,$0x00000001a78496f2 +DATA ·CastConst+1336(SB)/8,$0x000000014d73abf6 + + /* x^175168 mod p(x), x^175104 mod p(x) */ +DATA ·CastConst+1344(SB)/8,$0x00000001ac5390a0 +DATA ·CastConst+1352(SB)/8,$0x00000001620eb844 + + /* x^174144 mod p(x), x^174080 mod p(x) */ +DATA ·CastConst+1360(SB)/8,$0x000000002a80ed6e +DATA ·CastConst+1368(SB)/8,$0x0000000147655048 + + /* x^173120 mod p(x), x^173056 mod p(x) */ +DATA ·CastConst+1376(SB)/8,$0x00000001fa9b0128 +DATA ·CastConst+1384(SB)/8,$0x0000000067b5077e + + /* x^172096 mod p(x), x^172032 mod p(x) */ +DATA ·CastConst+1392(SB)/8,$0x00000001ea94929e +DATA ·CastConst+1400(SB)/8,$0x0000000010ffe206 + + /* x^171072 mod p(x), x^171008 mod p(x) */ +DATA ·CastConst+1408(SB)/8,$0x0000000125f4305c +DATA ·CastConst+1416(SB)/8,$0x000000000fee8f1e + + /* x^170048 mod p(x), x^169984 mod p(x) */ +DATA ·CastConst+1424(SB)/8,$0x00000001471e2002 +DATA ·CastConst+1432(SB)/8,$0x00000001da26fbae + + /* x^169024 mod p(x), x^168960 mod p(x) */ +DATA ·CastConst+1440(SB)/8,$0x0000000132d2253a +DATA ·CastConst+1448(SB)/8,$0x00000001b3a8bd88 + + /* x^168000 mod p(x), x^167936 mod p(x) */ +DATA ·CastConst+1456(SB)/8,$0x00000000f26b3592 +DATA ·CastConst+1464(SB)/8,$0x00000000e8f3898e + + /* x^166976 mod p(x), x^166912 mod p(x) */ +DATA ·CastConst+1472(SB)/8,$0x00000000bc8b67b0 +DATA ·CastConst+1480(SB)/8,$0x00000000b0d0d28c + + /* x^165952 mod p(x), x^165888 mod p(x) */ +DATA ·CastConst+1488(SB)/8,$0x000000013a826ef2 +DATA ·CastConst+1496(SB)/8,$0x0000000030f2a798 + + /* x^164928 mod p(x), x^164864 mod p(x) */ +DATA ·CastConst+1504(SB)/8,$0x0000000081482c84 +DATA ·CastConst+1512(SB)/8,$0x000000000fba1002 + + /* x^163904 mod p(x), x^163840 mod p(x) */ +DATA ·CastConst+1520(SB)/8,$0x00000000e77307c2 +DATA ·CastConst+1528(SB)/8,$0x00000000bdb9bd72 + + /* x^162880 mod p(x), x^162816 mod p(x) */ +DATA ·CastConst+1536(SB)/8,$0x00000000d4a07ec8 +DATA ·CastConst+1544(SB)/8,$0x0000000075d3bf5a + + /* x^161856 mod p(x), x^161792 mod p(x) */ +DATA ·CastConst+1552(SB)/8,$0x0000000017102100 +DATA ·CastConst+1560(SB)/8,$0x00000000ef1f98a0 + + /* x^160832 mod p(x), x^160768 mod p(x) */ +DATA ·CastConst+1568(SB)/8,$0x00000000db406486 +DATA ·CastConst+1576(SB)/8,$0x00000000689c7602 + + /* x^159808 mod p(x), x^159744 mod p(x) */ +DATA ·CastConst+1584(SB)/8,$0x0000000192db7f88 +DATA ·CastConst+1592(SB)/8,$0x000000016d5fa5fe + + /* x^158784 mod p(x), x^158720 mod p(x) */ +DATA ·CastConst+1600(SB)/8,$0x000000018bf67b1e +DATA ·CastConst+1608(SB)/8,$0x00000001d0d2b9ca + + /* x^157760 mod p(x), x^157696 mod p(x) */ +DATA ·CastConst+1616(SB)/8,$0x000000007c09163e +DATA ·CastConst+1624(SB)/8,$0x0000000041e7b470 + + /* x^156736 mod p(x), x^156672 mod p(x) */ +DATA ·CastConst+1632(SB)/8,$0x000000000adac060 +DATA ·CastConst+1640(SB)/8,$0x00000001cbb6495e + + /* x^155712 mod p(x), x^155648 mod p(x) */ +DATA ·CastConst+1648(SB)/8,$0x00000000bd8316ae +DATA ·CastConst+1656(SB)/8,$0x000000010052a0b0 + + /* x^154688 mod p(x), x^154624 mod p(x) */ +DATA ·CastConst+1664(SB)/8,$0x000000019f09ab54 +DATA ·CastConst+1672(SB)/8,$0x00000001d8effb5c + + /* x^153664 mod p(x), x^153600 mod p(x) */ +DATA ·CastConst+1680(SB)/8,$0x0000000125155542 +DATA ·CastConst+1688(SB)/8,$0x00000001d969853c + + /* x^152640 mod p(x), x^152576 mod p(x) */ +DATA ·CastConst+1696(SB)/8,$0x000000018fdb5882 +DATA ·CastConst+1704(SB)/8,$0x00000000523ccce2 + + /* x^151616 mod p(x), x^151552 mod p(x) */ +DATA ·CastConst+1712(SB)/8,$0x00000000e794b3f4 +DATA ·CastConst+1720(SB)/8,$0x000000001e2436bc + + /* x^150592 mod p(x), x^150528 mod p(x) */ +DATA ·CastConst+1728(SB)/8,$0x000000016f9bb022 +DATA ·CastConst+1736(SB)/8,$0x00000000ddd1c3a2 + + /* x^149568 mod p(x), x^149504 mod p(x) */ +DATA ·CastConst+1744(SB)/8,$0x00000000290c9978 +DATA ·CastConst+1752(SB)/8,$0x0000000019fcfe38 + + /* x^148544 mod p(x), x^148480 mod p(x) */ +DATA ·CastConst+1760(SB)/8,$0x0000000083c0f350 +DATA ·CastConst+1768(SB)/8,$0x00000001ce95db64 + + /* x^147520 mod p(x), x^147456 mod p(x) */ +DATA ·CastConst+1776(SB)/8,$0x0000000173ea6628 +DATA ·CastConst+1784(SB)/8,$0x00000000af582806 + + /* x^146496 mod p(x), x^146432 mod p(x) */ +DATA ·CastConst+1792(SB)/8,$0x00000001c8b4e00a +DATA ·CastConst+1800(SB)/8,$0x00000001006388f6 + + /* x^145472 mod p(x), x^145408 mod p(x) */ +DATA ·CastConst+1808(SB)/8,$0x00000000de95d6aa +DATA ·CastConst+1816(SB)/8,$0x0000000179eca00a + + /* x^144448 mod p(x), x^144384 mod p(x) */ +DATA ·CastConst+1824(SB)/8,$0x000000010b7f7248 +DATA ·CastConst+1832(SB)/8,$0x0000000122410a6a + + /* x^143424 mod p(x), x^143360 mod p(x) */ +DATA ·CastConst+1840(SB)/8,$0x00000001326e3a06 +DATA ·CastConst+1848(SB)/8,$0x000000004288e87c + + /* x^142400 mod p(x), x^142336 mod p(x) */ +DATA ·CastConst+1856(SB)/8,$0x00000000bb62c2e6 +DATA ·CastConst+1864(SB)/8,$0x000000016c5490da + + /* x^141376 mod p(x), x^141312 mod p(x) */ +DATA ·CastConst+1872(SB)/8,$0x0000000156a4b2c2 +DATA ·CastConst+1880(SB)/8,$0x00000000d1c71f6e + + /* x^140352 mod p(x), x^140288 mod p(x) */ +DATA ·CastConst+1888(SB)/8,$0x000000011dfe763a +DATA ·CastConst+1896(SB)/8,$0x00000001b4ce08a6 + + /* x^139328 mod p(x), x^139264 mod p(x) */ +DATA ·CastConst+1904(SB)/8,$0x000000007bcca8e2 +DATA ·CastConst+1912(SB)/8,$0x00000001466ba60c + + /* x^138304 mod p(x), x^138240 mod p(x) */ +DATA ·CastConst+1920(SB)/8,$0x0000000186118faa +DATA ·CastConst+1928(SB)/8,$0x00000001f6c488a4 + + /* x^137280 mod p(x), x^137216 mod p(x) */ +DATA ·CastConst+1936(SB)/8,$0x0000000111a65a88 +DATA ·CastConst+1944(SB)/8,$0x000000013bfb0682 + + /* x^136256 mod p(x), x^136192 mod p(x) */ +DATA ·CastConst+1952(SB)/8,$0x000000003565e1c4 +DATA ·CastConst+1960(SB)/8,$0x00000000690e9e54 + + /* x^135232 mod p(x), x^135168 mod p(x) */ +DATA ·CastConst+1968(SB)/8,$0x000000012ed02a82 +DATA ·CastConst+1976(SB)/8,$0x00000000281346b6 + + /* x^134208 mod p(x), x^134144 mod p(x) */ +DATA ·CastConst+1984(SB)/8,$0x00000000c486ecfc +DATA ·CastConst+1992(SB)/8,$0x0000000156464024 + + /* x^133184 mod p(x), x^133120 mod p(x) */ +DATA ·CastConst+2000(SB)/8,$0x0000000001b951b2 +DATA ·CastConst+2008(SB)/8,$0x000000016063a8dc + + /* x^132160 mod p(x), x^132096 mod p(x) */ +DATA ·CastConst+2016(SB)/8,$0x0000000048143916 +DATA ·CastConst+2024(SB)/8,$0x0000000116a66362 + + /* x^131136 mod p(x), x^131072 mod p(x) */ +DATA ·CastConst+2032(SB)/8,$0x00000001dc2ae124 +DATA ·CastConst+2040(SB)/8,$0x000000017e8aa4d2 + + /* x^130112 mod p(x), x^130048 mod p(x) */ +DATA ·CastConst+2048(SB)/8,$0x00000001416c58d6 +DATA ·CastConst+2056(SB)/8,$0x00000001728eb10c + + /* x^129088 mod p(x), x^129024 mod p(x) */ +DATA ·CastConst+2064(SB)/8,$0x00000000a479744a +DATA ·CastConst+2072(SB)/8,$0x00000001b08fd7fa + + /* x^128064 mod p(x), x^128000 mod p(x) */ +DATA ·CastConst+2080(SB)/8,$0x0000000096ca3a26 +DATA ·CastConst+2088(SB)/8,$0x00000001092a16e8 + + /* x^127040 mod p(x), x^126976 mod p(x) */ +DATA ·CastConst+2096(SB)/8,$0x00000000ff223d4e +DATA ·CastConst+2104(SB)/8,$0x00000000a505637c + + /* x^126016 mod p(x), x^125952 mod p(x) */ +DATA ·CastConst+2112(SB)/8,$0x000000010e84da42 +DATA ·CastConst+2120(SB)/8,$0x00000000d94869b2 + + /* x^124992 mod p(x), x^124928 mod p(x) */ +DATA ·CastConst+2128(SB)/8,$0x00000001b61ba3d0 +DATA ·CastConst+2136(SB)/8,$0x00000001c8b203ae + + /* x^123968 mod p(x), x^123904 mod p(x) */ +DATA ·CastConst+2144(SB)/8,$0x00000000680f2de8 +DATA ·CastConst+2152(SB)/8,$0x000000005704aea0 + + /* x^122944 mod p(x), x^122880 mod p(x) */ +DATA ·CastConst+2160(SB)/8,$0x000000008772a9a8 +DATA ·CastConst+2168(SB)/8,$0x000000012e295fa2 + + /* x^121920 mod p(x), x^121856 mod p(x) */ +DATA ·CastConst+2176(SB)/8,$0x0000000155f295bc +DATA ·CastConst+2184(SB)/8,$0x000000011d0908bc + + /* x^120896 mod p(x), x^120832 mod p(x) */ +DATA ·CastConst+2192(SB)/8,$0x00000000595f9282 +DATA ·CastConst+2200(SB)/8,$0x0000000193ed97ea + + /* x^119872 mod p(x), x^119808 mod p(x) */ +DATA ·CastConst+2208(SB)/8,$0x0000000164b1c25a +DATA ·CastConst+2216(SB)/8,$0x000000013a0f1c52 + + /* x^118848 mod p(x), x^118784 mod p(x) */ +DATA ·CastConst+2224(SB)/8,$0x00000000fbd67c50 +DATA ·CastConst+2232(SB)/8,$0x000000010c2c40c0 + + /* x^117824 mod p(x), x^117760 mod p(x) */ +DATA ·CastConst+2240(SB)/8,$0x0000000096076268 +DATA ·CastConst+2248(SB)/8,$0x00000000ff6fac3e + + /* x^116800 mod p(x), x^116736 mod p(x) */ +DATA ·CastConst+2256(SB)/8,$0x00000001d288e4cc +DATA ·CastConst+2264(SB)/8,$0x000000017b3609c0 + + /* x^115776 mod p(x), x^115712 mod p(x) */ +DATA ·CastConst+2272(SB)/8,$0x00000001eaac1bdc +DATA ·CastConst+2280(SB)/8,$0x0000000088c8c922 + + /* x^114752 mod p(x), x^114688 mod p(x) */ +DATA ·CastConst+2288(SB)/8,$0x00000001f1ea39e2 +DATA ·CastConst+2296(SB)/8,$0x00000001751baae6 + + /* x^113728 mod p(x), x^113664 mod p(x) */ +DATA ·CastConst+2304(SB)/8,$0x00000001eb6506fc +DATA ·CastConst+2312(SB)/8,$0x0000000107952972 + + /* x^112704 mod p(x), x^112640 mod p(x) */ +DATA ·CastConst+2320(SB)/8,$0x000000010f806ffe +DATA ·CastConst+2328(SB)/8,$0x0000000162b00abe + + /* x^111680 mod p(x), x^111616 mod p(x) */ +DATA ·CastConst+2336(SB)/8,$0x000000010408481e +DATA ·CastConst+2344(SB)/8,$0x000000000d7b404c + + /* x^110656 mod p(x), x^110592 mod p(x) */ +DATA ·CastConst+2352(SB)/8,$0x0000000188260534 +DATA ·CastConst+2360(SB)/8,$0x00000000763b13d4 + + /* x^109632 mod p(x), x^109568 mod p(x) */ +DATA ·CastConst+2368(SB)/8,$0x0000000058fc73e0 +DATA ·CastConst+2376(SB)/8,$0x00000000f6dc22d8 + + /* x^108608 mod p(x), x^108544 mod p(x) */ +DATA ·CastConst+2384(SB)/8,$0x00000000391c59b8 +DATA ·CastConst+2392(SB)/8,$0x000000007daae060 + + /* x^107584 mod p(x), x^107520 mod p(x) */ +DATA ·CastConst+2400(SB)/8,$0x000000018b638400 +DATA ·CastConst+2408(SB)/8,$0x000000013359ab7c + + /* x^106560 mod p(x), x^106496 mod p(x) */ +DATA ·CastConst+2416(SB)/8,$0x000000011738f5c4 +DATA ·CastConst+2424(SB)/8,$0x000000008add438a + + /* x^105536 mod p(x), x^105472 mod p(x) */ +DATA ·CastConst+2432(SB)/8,$0x000000008cf7c6da +DATA ·CastConst+2440(SB)/8,$0x00000001edbefdea + + /* x^104512 mod p(x), x^104448 mod p(x) */ +DATA ·CastConst+2448(SB)/8,$0x00000001ef97fb16 +DATA ·CastConst+2456(SB)/8,$0x000000004104e0f8 + + /* x^103488 mod p(x), x^103424 mod p(x) */ +DATA ·CastConst+2464(SB)/8,$0x0000000102130e20 +DATA ·CastConst+2472(SB)/8,$0x00000000b48a8222 + + /* x^102464 mod p(x), x^102400 mod p(x) */ +DATA ·CastConst+2480(SB)/8,$0x00000000db968898 +DATA ·CastConst+2488(SB)/8,$0x00000001bcb46844 + + /* x^101440 mod p(x), x^101376 mod p(x) */ +DATA ·CastConst+2496(SB)/8,$0x00000000b5047b5e +DATA ·CastConst+2504(SB)/8,$0x000000013293ce0a + + /* x^100416 mod p(x), x^100352 mod p(x) */ +DATA ·CastConst+2512(SB)/8,$0x000000010b90fdb2 +DATA ·CastConst+2520(SB)/8,$0x00000001710d0844 + + /* x^99392 mod p(x), x^99328 mod p(x) */ +DATA ·CastConst+2528(SB)/8,$0x000000004834a32e +DATA ·CastConst+2536(SB)/8,$0x0000000117907f6e + + /* x^98368 mod p(x), x^98304 mod p(x) */ +DATA ·CastConst+2544(SB)/8,$0x0000000059c8f2b0 +DATA ·CastConst+2552(SB)/8,$0x0000000087ddf93e + + /* x^97344 mod p(x), x^97280 mod p(x) */ +DATA ·CastConst+2560(SB)/8,$0x0000000122cec508 +DATA ·CastConst+2568(SB)/8,$0x000000005970e9b0 + + /* x^96320 mod p(x), x^96256 mod p(x) */ +DATA ·CastConst+2576(SB)/8,$0x000000000a330cda +DATA ·CastConst+2584(SB)/8,$0x0000000185b2b7d0 + + /* x^95296 mod p(x), x^95232 mod p(x) */ +DATA ·CastConst+2592(SB)/8,$0x000000014a47148c +DATA ·CastConst+2600(SB)/8,$0x00000001dcee0efc + + /* x^94272 mod p(x), x^94208 mod p(x) */ +DATA ·CastConst+2608(SB)/8,$0x0000000042c61cb8 +DATA ·CastConst+2616(SB)/8,$0x0000000030da2722 + + /* x^93248 mod p(x), x^93184 mod p(x) */ +DATA ·CastConst+2624(SB)/8,$0x0000000012fe6960 +DATA ·CastConst+2632(SB)/8,$0x000000012f925a18 + + /* x^92224 mod p(x), x^92160 mod p(x) */ +DATA ·CastConst+2640(SB)/8,$0x00000000dbda2c20 +DATA ·CastConst+2648(SB)/8,$0x00000000dd2e357c + + /* x^91200 mod p(x), x^91136 mod p(x) */ +DATA ·CastConst+2656(SB)/8,$0x000000011122410c +DATA ·CastConst+2664(SB)/8,$0x00000000071c80de + + /* x^90176 mod p(x), x^90112 mod p(x) */ +DATA ·CastConst+2672(SB)/8,$0x00000000977b2070 +DATA ·CastConst+2680(SB)/8,$0x000000011513140a + + /* x^89152 mod p(x), x^89088 mod p(x) */ +DATA ·CastConst+2688(SB)/8,$0x000000014050438e +DATA ·CastConst+2696(SB)/8,$0x00000001df876e8e + + /* x^88128 mod p(x), x^88064 mod p(x) */ +DATA ·CastConst+2704(SB)/8,$0x0000000147c840e8 +DATA ·CastConst+2712(SB)/8,$0x000000015f81d6ce + + /* x^87104 mod p(x), x^87040 mod p(x) */ +DATA ·CastConst+2720(SB)/8,$0x00000001cc7c88ce +DATA ·CastConst+2728(SB)/8,$0x000000019dd94dbe + + /* x^86080 mod p(x), x^86016 mod p(x) */ +DATA ·CastConst+2736(SB)/8,$0x00000001476b35a4 +DATA ·CastConst+2744(SB)/8,$0x00000001373d206e + + /* x^85056 mod p(x), x^84992 mod p(x) */ +DATA ·CastConst+2752(SB)/8,$0x000000013d52d508 +DATA ·CastConst+2760(SB)/8,$0x00000000668ccade + + /* x^84032 mod p(x), x^83968 mod p(x) */ +DATA ·CastConst+2768(SB)/8,$0x000000008e4be32e +DATA ·CastConst+2776(SB)/8,$0x00000001b192d268 + + /* x^83008 mod p(x), x^82944 mod p(x) */ +DATA ·CastConst+2784(SB)/8,$0x00000000024120fe +DATA ·CastConst+2792(SB)/8,$0x00000000e30f3a78 + + /* x^81984 mod p(x), x^81920 mod p(x) */ +DATA ·CastConst+2800(SB)/8,$0x00000000ddecddb4 +DATA ·CastConst+2808(SB)/8,$0x000000010ef1f7bc + + /* x^80960 mod p(x), x^80896 mod p(x) */ +DATA ·CastConst+2816(SB)/8,$0x00000000d4d403bc +DATA ·CastConst+2824(SB)/8,$0x00000001f5ac7380 + + /* x^79936 mod p(x), x^79872 mod p(x) */ +DATA ·CastConst+2832(SB)/8,$0x00000001734b89aa +DATA ·CastConst+2840(SB)/8,$0x000000011822ea70 + + /* x^78912 mod p(x), x^78848 mod p(x) */ +DATA ·CastConst+2848(SB)/8,$0x000000010e7a58d6 +DATA ·CastConst+2856(SB)/8,$0x00000000c3a33848 + + /* x^77888 mod p(x), x^77824 mod p(x) */ +DATA ·CastConst+2864(SB)/8,$0x00000001f9f04e9c +DATA ·CastConst+2872(SB)/8,$0x00000001bd151c24 + + /* x^76864 mod p(x), x^76800 mod p(x) */ +DATA ·CastConst+2880(SB)/8,$0x00000000b692225e +DATA ·CastConst+2888(SB)/8,$0x0000000056002d76 + + /* x^75840 mod p(x), x^75776 mod p(x) */ +DATA ·CastConst+2896(SB)/8,$0x000000019b8d3f3e +DATA ·CastConst+2904(SB)/8,$0x000000014657c4f4 + + /* x^74816 mod p(x), x^74752 mod p(x) */ +DATA ·CastConst+2912(SB)/8,$0x00000001a874f11e +DATA ·CastConst+2920(SB)/8,$0x0000000113742d7c + + /* x^73792 mod p(x), x^73728 mod p(x) */ +DATA ·CastConst+2928(SB)/8,$0x000000010d5a4254 +DATA ·CastConst+2936(SB)/8,$0x000000019c5920ba + + /* x^72768 mod p(x), x^72704 mod p(x) */ +DATA ·CastConst+2944(SB)/8,$0x00000000bbb2f5d6 +DATA ·CastConst+2952(SB)/8,$0x000000005216d2d6 + + /* x^71744 mod p(x), x^71680 mod p(x) */ +DATA ·CastConst+2960(SB)/8,$0x0000000179cc0e36 +DATA ·CastConst+2968(SB)/8,$0x0000000136f5ad8a + + /* x^70720 mod p(x), x^70656 mod p(x) */ +DATA ·CastConst+2976(SB)/8,$0x00000001dca1da4a +DATA ·CastConst+2984(SB)/8,$0x000000018b07beb6 + + /* x^69696 mod p(x), x^69632 mod p(x) */ +DATA ·CastConst+2992(SB)/8,$0x00000000feb1a192 +DATA ·CastConst+3000(SB)/8,$0x00000000db1e93b0 + + /* x^68672 mod p(x), x^68608 mod p(x) */ +DATA ·CastConst+3008(SB)/8,$0x00000000d1eeedd6 +DATA ·CastConst+3016(SB)/8,$0x000000000b96fa3a + + /* x^67648 mod p(x), x^67584 mod p(x) */ +DATA ·CastConst+3024(SB)/8,$0x000000008fad9bb4 +DATA ·CastConst+3032(SB)/8,$0x00000001d9968af0 + + /* x^66624 mod p(x), x^66560 mod p(x) */ +DATA ·CastConst+3040(SB)/8,$0x00000001884938e4 +DATA ·CastConst+3048(SB)/8,$0x000000000e4a77a2 + + /* x^65600 mod p(x), x^65536 mod p(x) */ +DATA ·CastConst+3056(SB)/8,$0x00000001bc2e9bc0 +DATA ·CastConst+3064(SB)/8,$0x00000000508c2ac8 + + /* x^64576 mod p(x), x^64512 mod p(x) */ +DATA ·CastConst+3072(SB)/8,$0x00000001f9658a68 +DATA ·CastConst+3080(SB)/8,$0x0000000021572a80 + + /* x^63552 mod p(x), x^63488 mod p(x) */ +DATA ·CastConst+3088(SB)/8,$0x000000001b9224fc +DATA ·CastConst+3096(SB)/8,$0x00000001b859daf2 + + /* x^62528 mod p(x), x^62464 mod p(x) */ +DATA ·CastConst+3104(SB)/8,$0x0000000055b2fb84 +DATA ·CastConst+3112(SB)/8,$0x000000016f788474 + + /* x^61504 mod p(x), x^61440 mod p(x) */ +DATA ·CastConst+3120(SB)/8,$0x000000018b090348 +DATA ·CastConst+3128(SB)/8,$0x00000001b438810e + + /* x^60480 mod p(x), x^60416 mod p(x) */ +DATA ·CastConst+3136(SB)/8,$0x000000011ccbd5ea +DATA ·CastConst+3144(SB)/8,$0x0000000095ddc6f2 + + /* x^59456 mod p(x), x^59392 mod p(x) */ +DATA ·CastConst+3152(SB)/8,$0x0000000007ae47f8 +DATA ·CastConst+3160(SB)/8,$0x00000001d977c20c + + /* x^58432 mod p(x), x^58368 mod p(x) */ +DATA ·CastConst+3168(SB)/8,$0x0000000172acbec0 +DATA ·CastConst+3176(SB)/8,$0x00000000ebedb99a + + /* x^57408 mod p(x), x^57344 mod p(x) */ +DATA ·CastConst+3184(SB)/8,$0x00000001c6e3ff20 +DATA ·CastConst+3192(SB)/8,$0x00000001df9e9e92 + + /* x^56384 mod p(x), x^56320 mod p(x) */ +DATA ·CastConst+3200(SB)/8,$0x00000000e1b38744 +DATA ·CastConst+3208(SB)/8,$0x00000001a4a3f952 + + /* x^55360 mod p(x), x^55296 mod p(x) */ +DATA ·CastConst+3216(SB)/8,$0x00000000791585b2 +DATA ·CastConst+3224(SB)/8,$0x00000000e2f51220 + + /* x^54336 mod p(x), x^54272 mod p(x) */ +DATA ·CastConst+3232(SB)/8,$0x00000000ac53b894 +DATA ·CastConst+3240(SB)/8,$0x000000004aa01f3e + + /* x^53312 mod p(x), x^53248 mod p(x) */ +DATA ·CastConst+3248(SB)/8,$0x00000001ed5f2cf4 +DATA ·CastConst+3256(SB)/8,$0x00000000b3e90a58 + + /* x^52288 mod p(x), x^52224 mod p(x) */ +DATA ·CastConst+3264(SB)/8,$0x00000001df48b2e0 +DATA ·CastConst+3272(SB)/8,$0x000000000c9ca2aa + + /* x^51264 mod p(x), x^51200 mod p(x) */ +DATA ·CastConst+3280(SB)/8,$0x00000000049c1c62 +DATA ·CastConst+3288(SB)/8,$0x0000000151682316 + + /* x^50240 mod p(x), x^50176 mod p(x) */ +DATA ·CastConst+3296(SB)/8,$0x000000017c460c12 +DATA ·CastConst+3304(SB)/8,$0x0000000036fce78c + + /* x^49216 mod p(x), x^49152 mod p(x) */ +DATA ·CastConst+3312(SB)/8,$0x000000015be4da7e +DATA ·CastConst+3320(SB)/8,$0x000000009037dc10 + + /* x^48192 mod p(x), x^48128 mod p(x) */ +DATA ·CastConst+3328(SB)/8,$0x000000010f38f668 +DATA ·CastConst+3336(SB)/8,$0x00000000d3298582 + + /* x^47168 mod p(x), x^47104 mod p(x) */ +DATA ·CastConst+3344(SB)/8,$0x0000000039f40a00 +DATA ·CastConst+3352(SB)/8,$0x00000001b42e8ad6 + + /* x^46144 mod p(x), x^46080 mod p(x) */ +DATA ·CastConst+3360(SB)/8,$0x00000000bd4c10c4 +DATA ·CastConst+3368(SB)/8,$0x00000000142a9838 + + /* x^45120 mod p(x), x^45056 mod p(x) */ +DATA ·CastConst+3376(SB)/8,$0x0000000042db1d98 +DATA ·CastConst+3384(SB)/8,$0x0000000109c7f190 + + /* x^44096 mod p(x), x^44032 mod p(x) */ +DATA ·CastConst+3392(SB)/8,$0x00000001c905bae6 +DATA ·CastConst+3400(SB)/8,$0x0000000056ff9310 + + /* x^43072 mod p(x), x^43008 mod p(x) */ +DATA ·CastConst+3408(SB)/8,$0x00000000069d40ea +DATA ·CastConst+3416(SB)/8,$0x00000001594513aa + + /* x^42048 mod p(x), x^41984 mod p(x) */ +DATA ·CastConst+3424(SB)/8,$0x000000008e4fbad0 +DATA ·CastConst+3432(SB)/8,$0x00000001e3b5b1e8 + + /* x^41024 mod p(x), x^40960 mod p(x) */ +DATA ·CastConst+3440(SB)/8,$0x0000000047bedd46 +DATA ·CastConst+3448(SB)/8,$0x000000011dd5fc08 + + /* x^40000 mod p(x), x^39936 mod p(x) */ +DATA ·CastConst+3456(SB)/8,$0x0000000026396bf8 +DATA ·CastConst+3464(SB)/8,$0x00000001675f0cc2 + + /* x^38976 mod p(x), x^38912 mod p(x) */ +DATA ·CastConst+3472(SB)/8,$0x00000000379beb92 +DATA ·CastConst+3480(SB)/8,$0x00000000d1c8dd44 + + /* x^37952 mod p(x), x^37888 mod p(x) */ +DATA ·CastConst+3488(SB)/8,$0x000000000abae54a +DATA ·CastConst+3496(SB)/8,$0x0000000115ebd3d8 + + /* x^36928 mod p(x), x^36864 mod p(x) */ +DATA ·CastConst+3504(SB)/8,$0x0000000007e6a128 +DATA ·CastConst+3512(SB)/8,$0x00000001ecbd0dac + + /* x^35904 mod p(x), x^35840 mod p(x) */ +DATA ·CastConst+3520(SB)/8,$0x000000000ade29d2 +DATA ·CastConst+3528(SB)/8,$0x00000000cdf67af2 + + /* x^34880 mod p(x), x^34816 mod p(x) */ +DATA ·CastConst+3536(SB)/8,$0x00000000f974c45c +DATA ·CastConst+3544(SB)/8,$0x000000004c01ff4c + + /* x^33856 mod p(x), x^33792 mod p(x) */ +DATA ·CastConst+3552(SB)/8,$0x00000000e77ac60a +DATA ·CastConst+3560(SB)/8,$0x00000000f2d8657e + + /* x^32832 mod p(x), x^32768 mod p(x) */ +DATA ·CastConst+3568(SB)/8,$0x0000000145895816 +DATA ·CastConst+3576(SB)/8,$0x000000006bae74c4 + + /* x^31808 mod p(x), x^31744 mod p(x) */ +DATA ·CastConst+3584(SB)/8,$0x0000000038e362be +DATA ·CastConst+3592(SB)/8,$0x0000000152af8aa0 + + /* x^30784 mod p(x), x^30720 mod p(x) */ +DATA ·CastConst+3600(SB)/8,$0x000000007f991a64 +DATA ·CastConst+3608(SB)/8,$0x0000000004663802 + + /* x^29760 mod p(x), x^29696 mod p(x) */ +DATA ·CastConst+3616(SB)/8,$0x00000000fa366d3a +DATA ·CastConst+3624(SB)/8,$0x00000001ab2f5afc + + /* x^28736 mod p(x), x^28672 mod p(x) */ +DATA ·CastConst+3632(SB)/8,$0x00000001a2bb34f0 +DATA ·CastConst+3640(SB)/8,$0x0000000074a4ebd4 + + /* x^27712 mod p(x), x^27648 mod p(x) */ +DATA ·CastConst+3648(SB)/8,$0x0000000028a9981e +DATA ·CastConst+3656(SB)/8,$0x00000001d7ab3a4c + + /* x^26688 mod p(x), x^26624 mod p(x) */ +DATA ·CastConst+3664(SB)/8,$0x00000001dbc672be +DATA ·CastConst+3672(SB)/8,$0x00000001a8da60c6 + + /* x^25664 mod p(x), x^25600 mod p(x) */ +DATA ·CastConst+3680(SB)/8,$0x00000000b04d77f6 +DATA ·CastConst+3688(SB)/8,$0x000000013cf63820 + + /* x^24640 mod p(x), x^24576 mod p(x) */ +DATA ·CastConst+3696(SB)/8,$0x0000000124400d96 +DATA ·CastConst+3704(SB)/8,$0x00000000bec12e1e + + /* x^23616 mod p(x), x^23552 mod p(x) */ +DATA ·CastConst+3712(SB)/8,$0x000000014ca4b414 +DATA ·CastConst+3720(SB)/8,$0x00000001c6368010 + + /* x^22592 mod p(x), x^22528 mod p(x) */ +DATA ·CastConst+3728(SB)/8,$0x000000012fe2c938 +DATA ·CastConst+3736(SB)/8,$0x00000001e6e78758 + + /* x^21568 mod p(x), x^21504 mod p(x) */ +DATA ·CastConst+3744(SB)/8,$0x00000001faed01e6 +DATA ·CastConst+3752(SB)/8,$0x000000008d7f2b3c + + /* x^20544 mod p(x), x^20480 mod p(x) */ +DATA ·CastConst+3760(SB)/8,$0x000000007e80ecfe +DATA ·CastConst+3768(SB)/8,$0x000000016b4a156e + + /* x^19520 mod p(x), x^19456 mod p(x) */ +DATA ·CastConst+3776(SB)/8,$0x0000000098daee94 +DATA ·CastConst+3784(SB)/8,$0x00000001c63cfeb6 + + /* x^18496 mod p(x), x^18432 mod p(x) */ +DATA ·CastConst+3792(SB)/8,$0x000000010a04edea +DATA ·CastConst+3800(SB)/8,$0x000000015f902670 + + /* x^17472 mod p(x), x^17408 mod p(x) */ +DATA ·CastConst+3808(SB)/8,$0x00000001c00b4524 +DATA ·CastConst+3816(SB)/8,$0x00000001cd5de11e + + /* x^16448 mod p(x), x^16384 mod p(x) */ +DATA ·CastConst+3824(SB)/8,$0x0000000170296550 +DATA ·CastConst+3832(SB)/8,$0x000000001acaec54 + + /* x^15424 mod p(x), x^15360 mod p(x) */ +DATA ·CastConst+3840(SB)/8,$0x0000000181afaa48 +DATA ·CastConst+3848(SB)/8,$0x000000002bd0ca78 + + /* x^14400 mod p(x), x^14336 mod p(x) */ +DATA ·CastConst+3856(SB)/8,$0x0000000185a31ffa +DATA ·CastConst+3864(SB)/8,$0x0000000032d63d5c + + /* x^13376 mod p(x), x^13312 mod p(x) */ +DATA ·CastConst+3872(SB)/8,$0x000000002469f608 +DATA ·CastConst+3880(SB)/8,$0x000000001c6d4e4c + + /* x^12352 mod p(x), x^12288 mod p(x) */ +DATA ·CastConst+3888(SB)/8,$0x000000006980102a +DATA ·CastConst+3896(SB)/8,$0x0000000106a60b92 + + /* x^11328 mod p(x), x^11264 mod p(x) */ +DATA ·CastConst+3904(SB)/8,$0x0000000111ea9ca8 +DATA ·CastConst+3912(SB)/8,$0x00000000d3855e12 + + /* x^10304 mod p(x), x^10240 mod p(x) */ +DATA ·CastConst+3920(SB)/8,$0x00000001bd1d29ce +DATA ·CastConst+3928(SB)/8,$0x00000000e3125636 + + /* x^9280 mod p(x), x^9216 mod p(x) */ +DATA ·CastConst+3936(SB)/8,$0x00000001b34b9580 +DATA ·CastConst+3944(SB)/8,$0x000000009e8f7ea4 + + /* x^8256 mod p(x), x^8192 mod p(x) */ +DATA ·CastConst+3952(SB)/8,$0x000000003076054e +DATA ·CastConst+3960(SB)/8,$0x00000001c82e562c + + /* x^7232 mod p(x), x^7168 mod p(x) */ +DATA ·CastConst+3968(SB)/8,$0x000000012a608ea4 +DATA ·CastConst+3976(SB)/8,$0x00000000ca9f09ce + + /* x^6208 mod p(x), x^6144 mod p(x) */ +DATA ·CastConst+3984(SB)/8,$0x00000000784d05fe +DATA ·CastConst+3992(SB)/8,$0x00000000c63764e6 + + /* x^5184 mod p(x), x^5120 mod p(x) */ +DATA ·CastConst+4000(SB)/8,$0x000000016ef0d82a +DATA ·CastConst+4008(SB)/8,$0x0000000168d2e49e + + /* x^4160 mod p(x), x^4096 mod p(x) */ +DATA ·CastConst+4016(SB)/8,$0x0000000075bda454 +DATA ·CastConst+4024(SB)/8,$0x00000000e986c148 + + /* x^3136 mod p(x), x^3072 mod p(x) */ +DATA ·CastConst+4032(SB)/8,$0x000000003dc0a1c4 +DATA ·CastConst+4040(SB)/8,$0x00000000cfb65894 + + /* x^2112 mod p(x), x^2048 mod p(x) */ +DATA ·CastConst+4048(SB)/8,$0x00000000e9a5d8be +DATA ·CastConst+4056(SB)/8,$0x0000000111cadee4 + + /* x^1088 mod p(x), x^1024 mod p(x) */ +DATA ·CastConst+4064(SB)/8,$0x00000001609bc4b4 +DATA ·CastConst+4072(SB)/8,$0x0000000171fb63ce + + /* x^2048 mod p(x), x^2016 mod p(x), x^1984 mod p(x), x^1952 mod p(x) */ +DATA ·CastConst+4080(SB)/8,$0x5cf015c388e56f72 +DATA ·CastConst+4088(SB)/8,$0x7fec2963e5bf8048 + + /* x^1920 mod p(x), x^1888 mod p(x), x^1856 mod p(x), x^1824 mod p(x) */ +DATA ·CastConst+4096(SB)/8,$0x963a18920246e2e6 +DATA ·CastConst+4104(SB)/8,$0x38e888d4844752a9 + + /* x^1792 mod p(x), x^1760 mod p(x), x^1728 mod p(x), x^1696 mod p(x) */ +DATA ·CastConst+4112(SB)/8,$0x419a441956993a31 +DATA ·CastConst+4120(SB)/8,$0x42316c00730206ad + + /* x^1664 mod p(x), x^1632 mod p(x), x^1600 mod p(x), x^1568 mod p(x) */ +DATA ·CastConst+4128(SB)/8,$0x924752ba2b830011 +DATA ·CastConst+4136(SB)/8,$0x543d5c543e65ddf9 + + /* x^1536 mod p(x), x^1504 mod p(x), x^1472 mod p(x), x^1440 mod p(x) */ +DATA ·CastConst+4144(SB)/8,$0x55bd7f9518e4a304 +DATA ·CastConst+4152(SB)/8,$0x78e87aaf56767c92 + + /* x^1408 mod p(x), x^1376 mod p(x), x^1344 mod p(x), x^1312 mod p(x) */ +DATA ·CastConst+4160(SB)/8,$0x6d76739fe0553f1e +DATA ·CastConst+4168(SB)/8,$0x8f68fcec1903da7f + + /* x^1280 mod p(x), x^1248 mod p(x), x^1216 mod p(x), x^1184 mod p(x) */ +DATA ·CastConst+4176(SB)/8,$0xc133722b1fe0b5c3 +DATA ·CastConst+4184(SB)/8,$0x3f4840246791d588 + + /* x^1152 mod p(x), x^1120 mod p(x), x^1088 mod p(x), x^1056 mod p(x) */ +DATA ·CastConst+4192(SB)/8,$0x64b67ee0e55ef1f3 +DATA ·CastConst+4200(SB)/8,$0x34c96751b04de25a + + /* x^1024 mod p(x), x^992 mod p(x), x^960 mod p(x), x^928 mod p(x) */ +DATA ·CastConst+4208(SB)/8,$0x069db049b8fdb1e7 +DATA ·CastConst+4216(SB)/8,$0x156c8e180b4a395b + + /* x^896 mod p(x), x^864 mod p(x), x^832 mod p(x), x^800 mod p(x) */ +DATA ·CastConst+4224(SB)/8,$0xa11bfaf3c9e90b9e +DATA ·CastConst+4232(SB)/8,$0xe0b99ccbe661f7be + + /* x^768 mod p(x), x^736 mod p(x), x^704 mod p(x), x^672 mod p(x) */ +DATA ·CastConst+4240(SB)/8,$0x817cdc5119b29a35 +DATA ·CastConst+4248(SB)/8,$0x041d37768cd75659 + + /* x^640 mod p(x), x^608 mod p(x), x^576 mod p(x), x^544 mod p(x) */ +DATA ·CastConst+4256(SB)/8,$0x1ce9d94b36c41f1c +DATA ·CastConst+4264(SB)/8,$0x3a0777818cfaa965 + + /* x^512 mod p(x), x^480 mod p(x), x^448 mod p(x), x^416 mod p(x) */ +DATA ·CastConst+4272(SB)/8,$0x4f256efcb82be955 +DATA ·CastConst+4280(SB)/8,$0x0e148e8252377a55 + + /* x^384 mod p(x), x^352 mod p(x), x^320 mod p(x), x^288 mod p(x) */ +DATA ·CastConst+4288(SB)/8,$0xec1631edb2dea967 +DATA ·CastConst+4296(SB)/8,$0x9c25531d19e65dde + + /* x^256 mod p(x), x^224 mod p(x), x^192 mod p(x), x^160 mod p(x) */ +DATA ·CastConst+4304(SB)/8,$0x5d27e147510ac59a +DATA ·CastConst+4312(SB)/8,$0x790606ff9957c0a6 + + /* x^128 mod p(x), x^96 mod p(x), x^64 mod p(x), x^32 mod p(x) */ +DATA ·CastConst+4320(SB)/8,$0xa66805eb18b8ea18 +DATA ·CastConst+4328(SB)/8,$0x82f63b786ea2d55c + +GLOBL ·CastConst(SB),RODATA,$4336 + + /* Barrett constant m - (4^32)/n */ +DATA ·CastBarConst(SB)/8,$0x00000000dea713f1 +DATA ·CastBarConst+8(SB)/8,$0x0000000000000000 +DATA ·CastBarConst+16(SB)/8,$0x0000000105ec76f1 +DATA ·CastBarConst+24(SB)/8,$0x0000000000000000 +GLOBL ·CastBarConst(SB),RODATA,$32 + + /* Reduce 262144 kbits to 1024 bits */ + /* x^261184 mod p(x), x^261120 mod p(x) */ +DATA ·KoopConst+0(SB)/8,$0x00000000d72535b2 +DATA ·KoopConst+8(SB)/8,$0x000000007fd74916 + + /* x^260160 mod p(x), x^260096 mod p(x) */ +DATA ·KoopConst+16(SB)/8,$0x0000000118a2a1b4 +DATA ·KoopConst+24(SB)/8,$0x000000010e944b56 + + /* x^259136 mod p(x), x^259072 mod p(x) */ +DATA ·KoopConst+32(SB)/8,$0x0000000147b5c49c +DATA ·KoopConst+40(SB)/8,$0x00000000bfe71c20 + + /* x^258112 mod p(x), x^258048 mod p(x) */ +DATA ·KoopConst+48(SB)/8,$0x00000001ca76a040 +DATA ·KoopConst+56(SB)/8,$0x0000000021324d9a + + /* x^257088 mod p(x), x^257024 mod p(x) */ +DATA ·KoopConst+64(SB)/8,$0x00000001e3152efc +DATA ·KoopConst+72(SB)/8,$0x00000000d20972ce + + /* x^256064 mod p(x), x^256000 mod p(x) */ +DATA ·KoopConst+80(SB)/8,$0x00000001b0349792 +DATA ·KoopConst+88(SB)/8,$0x000000003475ea06 + + /* x^255040 mod p(x), x^254976 mod p(x) */ +DATA ·KoopConst+96(SB)/8,$0x0000000120a60fe0 +DATA ·KoopConst+104(SB)/8,$0x00000001e40e36c4 + + /* x^254016 mod p(x), x^253952 mod p(x) */ +DATA ·KoopConst+112(SB)/8,$0x00000000b3c4b082 +DATA ·KoopConst+120(SB)/8,$0x00000000b2490102 + + /* x^252992 mod p(x), x^252928 mod p(x) */ +DATA ·KoopConst+128(SB)/8,$0x000000017fe9f3d2 +DATA ·KoopConst+136(SB)/8,$0x000000016b9e1332 + + /* x^251968 mod p(x), x^251904 mod p(x) */ +DATA ·KoopConst+144(SB)/8,$0x0000000145703cbe +DATA ·KoopConst+152(SB)/8,$0x00000001d6c378f4 + + /* x^250944 mod p(x), x^250880 mod p(x) */ +DATA ·KoopConst+160(SB)/8,$0x0000000107551c9c +DATA ·KoopConst+168(SB)/8,$0x0000000085796eac + + /* x^249920 mod p(x), x^249856 mod p(x) */ +DATA ·KoopConst+176(SB)/8,$0x000000003865a702 +DATA ·KoopConst+184(SB)/8,$0x000000019d2f3aaa + + /* x^248896 mod p(x), x^248832 mod p(x) */ +DATA ·KoopConst+192(SB)/8,$0x000000005504f9b8 +DATA ·KoopConst+200(SB)/8,$0x00000001554ddbd4 + + /* x^247872 mod p(x), x^247808 mod p(x) */ +DATA ·KoopConst+208(SB)/8,$0x00000000239bcdd4 +DATA ·KoopConst+216(SB)/8,$0x00000000a76376b0 + + /* x^246848 mod p(x), x^246784 mod p(x) */ +DATA ·KoopConst+224(SB)/8,$0x00000000caead774 +DATA ·KoopConst+232(SB)/8,$0x0000000139b7283c + + /* x^245824 mod p(x), x^245760 mod p(x) */ +DATA ·KoopConst+240(SB)/8,$0x0000000022a3fa16 +DATA ·KoopConst+248(SB)/8,$0x0000000111087030 + + /* x^244800 mod p(x), x^244736 mod p(x) */ +DATA ·KoopConst+256(SB)/8,$0x000000011f89160e +DATA ·KoopConst+264(SB)/8,$0x00000000ad786dc2 + + /* x^243776 mod p(x), x^243712 mod p(x) */ +DATA ·KoopConst+272(SB)/8,$0x00000001a976c248 +DATA ·KoopConst+280(SB)/8,$0x00000000b7a1d068 + + /* x^242752 mod p(x), x^242688 mod p(x) */ +DATA ·KoopConst+288(SB)/8,$0x00000000c20d09c8 +DATA ·KoopConst+296(SB)/8,$0x000000009c5c591c + + /* x^241728 mod p(x), x^241664 mod p(x) */ +DATA ·KoopConst+304(SB)/8,$0x000000016264fe38 +DATA ·KoopConst+312(SB)/8,$0x000000016482aa1a + + /* x^240704 mod p(x), x^240640 mod p(x) */ +DATA ·KoopConst+320(SB)/8,$0x00000001b57aee6a +DATA ·KoopConst+328(SB)/8,$0x000000009a409ba8 + + /* x^239680 mod p(x), x^239616 mod p(x) */ +DATA ·KoopConst+336(SB)/8,$0x00000000e8f1be0a +DATA ·KoopConst+344(SB)/8,$0x00000001ad8eaed8 + + /* x^238656 mod p(x), x^238592 mod p(x) */ +DATA ·KoopConst+352(SB)/8,$0x0000000053fcd0fc +DATA ·KoopConst+360(SB)/8,$0x000000017558b57a + + /* x^237632 mod p(x), x^237568 mod p(x) */ +DATA ·KoopConst+368(SB)/8,$0x000000012df9d496 +DATA ·KoopConst+376(SB)/8,$0x00000000cbb749c8 + + /* x^236608 mod p(x), x^236544 mod p(x) */ +DATA ·KoopConst+384(SB)/8,$0x000000004cb0db26 +DATA ·KoopConst+392(SB)/8,$0x000000008524fc5a + + /* x^235584 mod p(x), x^235520 mod p(x) */ +DATA ·KoopConst+400(SB)/8,$0x00000001150c4584 +DATA ·KoopConst+408(SB)/8,$0x0000000028ce6b76 + + /* x^234560 mod p(x), x^234496 mod p(x) */ +DATA ·KoopConst+416(SB)/8,$0x0000000104f52056 +DATA ·KoopConst+424(SB)/8,$0x00000000e0c48bdc + + /* x^233536 mod p(x), x^233472 mod p(x) */ +DATA ·KoopConst+432(SB)/8,$0x000000008ea11ac8 +DATA ·KoopConst+440(SB)/8,$0x000000003dd3bf9a + + /* x^232512 mod p(x), x^232448 mod p(x) */ +DATA ·KoopConst+448(SB)/8,$0x00000001cc0a3942 +DATA ·KoopConst+456(SB)/8,$0x00000000cb71066c + + /* x^231488 mod p(x), x^231424 mod p(x) */ +DATA ·KoopConst+464(SB)/8,$0x00000000d26231e6 +DATA ·KoopConst+472(SB)/8,$0x00000001d4ee1540 + + /* x^230464 mod p(x), x^230400 mod p(x) */ +DATA ·KoopConst+480(SB)/8,$0x00000000c70d5730 +DATA ·KoopConst+488(SB)/8,$0x00000001d82bed0a + + /* x^229440 mod p(x), x^229376 mod p(x) */ +DATA ·KoopConst+496(SB)/8,$0x00000000e215dfc4 +DATA ·KoopConst+504(SB)/8,$0x000000016e0c7d86 + + /* x^228416 mod p(x), x^228352 mod p(x) */ +DATA ·KoopConst+512(SB)/8,$0x000000013870d0dc +DATA ·KoopConst+520(SB)/8,$0x00000001437051b0 + + /* x^227392 mod p(x), x^227328 mod p(x) */ +DATA ·KoopConst+528(SB)/8,$0x0000000153e4cf3c +DATA ·KoopConst+536(SB)/8,$0x00000000f9a8d4be + + /* x^226368 mod p(x), x^226304 mod p(x) */ +DATA ·KoopConst+544(SB)/8,$0x0000000125f6fdf0 +DATA ·KoopConst+552(SB)/8,$0x000000016b09be1c + + /* x^225344 mod p(x), x^225280 mod p(x) */ +DATA ·KoopConst+560(SB)/8,$0x0000000157ba3a82 +DATA ·KoopConst+568(SB)/8,$0x0000000105f50ed6 + + /* x^224320 mod p(x), x^224256 mod p(x) */ +DATA ·KoopConst+576(SB)/8,$0x00000001cf711064 +DATA ·KoopConst+584(SB)/8,$0x00000001ca7fe3cc + + /* x^223296 mod p(x), x^223232 mod p(x) */ +DATA ·KoopConst+592(SB)/8,$0x00000001006353d2 +DATA ·KoopConst+600(SB)/8,$0x0000000192372e78 + + /* x^222272 mod p(x), x^222208 mod p(x) */ +DATA ·KoopConst+608(SB)/8,$0x000000010cd9faec +DATA ·KoopConst+616(SB)/8,$0x000000008a47af7e + + /* x^221248 mod p(x), x^221184 mod p(x) */ +DATA ·KoopConst+624(SB)/8,$0x000000012148b190 +DATA ·KoopConst+632(SB)/8,$0x00000000a67473e8 + + /* x^220224 mod p(x), x^220160 mod p(x) */ +DATA ·KoopConst+640(SB)/8,$0x00000000776473d6 +DATA ·KoopConst+648(SB)/8,$0x000000013689f2fa + + /* x^219200 mod p(x), x^219136 mod p(x) */ +DATA ·KoopConst+656(SB)/8,$0x00000001ce765bd6 +DATA ·KoopConst+664(SB)/8,$0x00000000e7231774 + + /* x^218176 mod p(x), x^218112 mod p(x) */ +DATA ·KoopConst+672(SB)/8,$0x00000000b29165e8 +DATA ·KoopConst+680(SB)/8,$0x0000000011b5ae68 + + /* x^217152 mod p(x), x^217088 mod p(x) */ +DATA ·KoopConst+688(SB)/8,$0x0000000084ff5a68 +DATA ·KoopConst+696(SB)/8,$0x000000004fd5c188 + + /* x^216128 mod p(x), x^216064 mod p(x) */ +DATA ·KoopConst+704(SB)/8,$0x00000001921e9076 +DATA ·KoopConst+712(SB)/8,$0x000000012148fa22 + + /* x^215104 mod p(x), x^215040 mod p(x) */ +DATA ·KoopConst+720(SB)/8,$0x000000009a753a3c +DATA ·KoopConst+728(SB)/8,$0x000000010cff4f3e + + /* x^214080 mod p(x), x^214016 mod p(x) */ +DATA ·KoopConst+736(SB)/8,$0x000000000251401e +DATA ·KoopConst+744(SB)/8,$0x00000001f9d991d4 + + /* x^213056 mod p(x), x^212992 mod p(x) */ +DATA ·KoopConst+752(SB)/8,$0x00000001f65541fa +DATA ·KoopConst+760(SB)/8,$0x00000001c31db214 + + /* x^212032 mod p(x), x^211968 mod p(x) */ +DATA ·KoopConst+768(SB)/8,$0x00000001d8c8117a +DATA ·KoopConst+776(SB)/8,$0x00000001849fba4a + + /* x^211008 mod p(x), x^210944 mod p(x) */ +DATA ·KoopConst+784(SB)/8,$0x000000014f7a2200 +DATA ·KoopConst+792(SB)/8,$0x00000001cb603184 + + /* x^209984 mod p(x), x^209920 mod p(x) */ +DATA ·KoopConst+800(SB)/8,$0x000000005154a9f4 +DATA ·KoopConst+808(SB)/8,$0x0000000132db7116 + + /* x^208960 mod p(x), x^208896 mod p(x) */ +DATA ·KoopConst+816(SB)/8,$0x00000001dfc69196 +DATA ·KoopConst+824(SB)/8,$0x0000000010694e22 + + /* x^207936 mod p(x), x^207872 mod p(x) */ +DATA ·KoopConst+832(SB)/8,$0x00000001c29f1aa0 +DATA ·KoopConst+840(SB)/8,$0x0000000103b7b478 + + /* x^206912 mod p(x), x^206848 mod p(x) */ +DATA ·KoopConst+848(SB)/8,$0x000000013785f232 +DATA ·KoopConst+856(SB)/8,$0x000000000ab44030 + + /* x^205888 mod p(x), x^205824 mod p(x) */ +DATA ·KoopConst+864(SB)/8,$0x000000010133536e +DATA ·KoopConst+872(SB)/8,$0x0000000131385b68 + + /* x^204864 mod p(x), x^204800 mod p(x) */ +DATA ·KoopConst+880(SB)/8,$0x00000001d45421dc +DATA ·KoopConst+888(SB)/8,$0x00000001761dab66 + + /* x^203840 mod p(x), x^203776 mod p(x) */ +DATA ·KoopConst+896(SB)/8,$0x000000000b59cc28 +DATA ·KoopConst+904(SB)/8,$0x000000012cf0a2a6 + + /* x^202816 mod p(x), x^202752 mod p(x) */ +DATA ·KoopConst+912(SB)/8,$0x00000001f2f74aba +DATA ·KoopConst+920(SB)/8,$0x00000001f4ce25a2 + + /* x^201792 mod p(x), x^201728 mod p(x) */ +DATA ·KoopConst+928(SB)/8,$0x00000000fb308e7e +DATA ·KoopConst+936(SB)/8,$0x000000014c2aae20 + + /* x^200768 mod p(x), x^200704 mod p(x) */ +DATA ·KoopConst+944(SB)/8,$0x0000000167583fa6 +DATA ·KoopConst+952(SB)/8,$0x00000001c162a55a + + /* x^199744 mod p(x), x^199680 mod p(x) */ +DATA ·KoopConst+960(SB)/8,$0x000000017ebb13e0 +DATA ·KoopConst+968(SB)/8,$0x0000000185681a40 + + /* x^198720 mod p(x), x^198656 mod p(x) */ +DATA ·KoopConst+976(SB)/8,$0x00000001ca653306 +DATA ·KoopConst+984(SB)/8,$0x00000001f2642b48 + + /* x^197696 mod p(x), x^197632 mod p(x) */ +DATA ·KoopConst+992(SB)/8,$0x0000000093bb6946 +DATA ·KoopConst+1000(SB)/8,$0x00000001d9cb5a78 + + /* x^196672 mod p(x), x^196608 mod p(x) */ +DATA ·KoopConst+1008(SB)/8,$0x00000000cbc1553e +DATA ·KoopConst+1016(SB)/8,$0x000000008059328c + + /* x^195648 mod p(x), x^195584 mod p(x) */ +DATA ·KoopConst+1024(SB)/8,$0x00000001f9a86fec +DATA ·KoopConst+1032(SB)/8,$0x000000009373c360 + + /* x^194624 mod p(x), x^194560 mod p(x) */ +DATA ·KoopConst+1040(SB)/8,$0x0000000005c52d8a +DATA ·KoopConst+1048(SB)/8,$0x00000001a14061d6 + + /* x^193600 mod p(x), x^193536 mod p(x) */ +DATA ·KoopConst+1056(SB)/8,$0x000000010d8dc668 +DATA ·KoopConst+1064(SB)/8,$0x00000000a9864d48 + + /* x^192576 mod p(x), x^192512 mod p(x) */ +DATA ·KoopConst+1072(SB)/8,$0x0000000158571310 +DATA ·KoopConst+1080(SB)/8,$0x000000011df8c040 + + /* x^191552 mod p(x), x^191488 mod p(x) */ +DATA ·KoopConst+1088(SB)/8,$0x0000000166102348 +DATA ·KoopConst+1096(SB)/8,$0x0000000023a3e6b6 + + /* x^190528 mod p(x), x^190464 mod p(x) */ +DATA ·KoopConst+1104(SB)/8,$0x0000000009513050 +DATA ·KoopConst+1112(SB)/8,$0x00000001207db28a + + /* x^189504 mod p(x), x^189440 mod p(x) */ +DATA ·KoopConst+1120(SB)/8,$0x00000000b0725c74 +DATA ·KoopConst+1128(SB)/8,$0x00000000f94bc632 + + /* x^188480 mod p(x), x^188416 mod p(x) */ +DATA ·KoopConst+1136(SB)/8,$0x000000002985c7e2 +DATA ·KoopConst+1144(SB)/8,$0x00000000ea32cbf6 + + /* x^187456 mod p(x), x^187392 mod p(x) */ +DATA ·KoopConst+1152(SB)/8,$0x00000000a7d4da9e +DATA ·KoopConst+1160(SB)/8,$0x0000000004eb981a + + /* x^186432 mod p(x), x^186368 mod p(x) */ +DATA ·KoopConst+1168(SB)/8,$0x000000000a3f8792 +DATA ·KoopConst+1176(SB)/8,$0x00000000ca8ce712 + + /* x^185408 mod p(x), x^185344 mod p(x) */ +DATA ·KoopConst+1184(SB)/8,$0x00000001ca2c1ce4 +DATA ·KoopConst+1192(SB)/8,$0x0000000065ba801c + + /* x^184384 mod p(x), x^184320 mod p(x) */ +DATA ·KoopConst+1200(SB)/8,$0x00000000e2900196 +DATA ·KoopConst+1208(SB)/8,$0x0000000194aade7a + + /* x^183360 mod p(x), x^183296 mod p(x) */ +DATA ·KoopConst+1216(SB)/8,$0x00000001fbadf0e4 +DATA ·KoopConst+1224(SB)/8,$0x00000001e7939fb2 + + /* x^182336 mod p(x), x^182272 mod p(x) */ +DATA ·KoopConst+1232(SB)/8,$0x00000000d5d96c40 +DATA ·KoopConst+1240(SB)/8,$0x0000000098e5fe22 + + /* x^181312 mod p(x), x^181248 mod p(x) */ +DATA ·KoopConst+1248(SB)/8,$0x000000015c11d3f2 +DATA ·KoopConst+1256(SB)/8,$0x000000016bba0324 + + /* x^180288 mod p(x), x^180224 mod p(x) */ +DATA ·KoopConst+1264(SB)/8,$0x0000000111fb2648 +DATA ·KoopConst+1272(SB)/8,$0x0000000104dce052 + + /* x^179264 mod p(x), x^179200 mod p(x) */ +DATA ·KoopConst+1280(SB)/8,$0x00000001d9f3a564 +DATA ·KoopConst+1288(SB)/8,$0x00000001af31a42e + + /* x^178240 mod p(x), x^178176 mod p(x) */ +DATA ·KoopConst+1296(SB)/8,$0x00000001b556cd1e +DATA ·KoopConst+1304(SB)/8,$0x00000001c56c57ba + + /* x^177216 mod p(x), x^177152 mod p(x) */ +DATA ·KoopConst+1312(SB)/8,$0x0000000101994d2c +DATA ·KoopConst+1320(SB)/8,$0x00000000f6bb1a2e + + /* x^176192 mod p(x), x^176128 mod p(x) */ +DATA ·KoopConst+1328(SB)/8,$0x00000001e8dbf09c +DATA ·KoopConst+1336(SB)/8,$0x00000001abdbf2b2 + + /* x^175168 mod p(x), x^175104 mod p(x) */ +DATA ·KoopConst+1344(SB)/8,$0x000000015580543a +DATA ·KoopConst+1352(SB)/8,$0x00000001a665a880 + + /* x^174144 mod p(x), x^174080 mod p(x) */ +DATA ·KoopConst+1360(SB)/8,$0x00000000c7074f24 +DATA ·KoopConst+1368(SB)/8,$0x00000000c102c700 + + /* x^173120 mod p(x), x^173056 mod p(x) */ +DATA ·KoopConst+1376(SB)/8,$0x00000000fa4112b0 +DATA ·KoopConst+1384(SB)/8,$0x00000000ee362a50 + + /* x^172096 mod p(x), x^172032 mod p(x) */ +DATA ·KoopConst+1392(SB)/8,$0x00000000e786c13e +DATA ·KoopConst+1400(SB)/8,$0x0000000045f29038 + + /* x^171072 mod p(x), x^171008 mod p(x) */ +DATA ·KoopConst+1408(SB)/8,$0x00000001e45e3694 +DATA ·KoopConst+1416(SB)/8,$0x0000000117b9ab5c + + /* x^170048 mod p(x), x^169984 mod p(x) */ +DATA ·KoopConst+1424(SB)/8,$0x000000005423dd8c +DATA ·KoopConst+1432(SB)/8,$0x00000001115dff5e + + /* x^169024 mod p(x), x^168960 mod p(x) */ +DATA ·KoopConst+1440(SB)/8,$0x00000001a1e67766 +DATA ·KoopConst+1448(SB)/8,$0x0000000117fad29c + + /* x^168000 mod p(x), x^167936 mod p(x) */ +DATA ·KoopConst+1456(SB)/8,$0x0000000041a3f508 +DATA ·KoopConst+1464(SB)/8,$0x000000017de134e6 + + /* x^166976 mod p(x), x^166912 mod p(x) */ +DATA ·KoopConst+1472(SB)/8,$0x000000003e792f7e +DATA ·KoopConst+1480(SB)/8,$0x00000000a2f5d19c + + /* x^165952 mod p(x), x^165888 mod p(x) */ +DATA ·KoopConst+1488(SB)/8,$0x00000000c8948aaa +DATA ·KoopConst+1496(SB)/8,$0x00000000dee13658 + + /* x^164928 mod p(x), x^164864 mod p(x) */ +DATA ·KoopConst+1504(SB)/8,$0x000000005d4ccb36 +DATA ·KoopConst+1512(SB)/8,$0x000000015355440c + + /* x^163904 mod p(x), x^163840 mod p(x) */ +DATA ·KoopConst+1520(SB)/8,$0x00000000e92a78a2 +DATA ·KoopConst+1528(SB)/8,$0x0000000197a21778 + + /* x^162880 mod p(x), x^162816 mod p(x) */ +DATA ·KoopConst+1536(SB)/8,$0x000000016ba67caa +DATA ·KoopConst+1544(SB)/8,$0x00000001a3835ec0 + + /* x^161856 mod p(x), x^161792 mod p(x) */ +DATA ·KoopConst+1552(SB)/8,$0x000000004838afc6 +DATA ·KoopConst+1560(SB)/8,$0x0000000011f20912 + + /* x^160832 mod p(x), x^160768 mod p(x) */ +DATA ·KoopConst+1568(SB)/8,$0x000000016644e308 +DATA ·KoopConst+1576(SB)/8,$0x00000001cce9d6cc + + /* x^159808 mod p(x), x^159744 mod p(x) */ +DATA ·KoopConst+1584(SB)/8,$0x0000000037c22f42 +DATA ·KoopConst+1592(SB)/8,$0x0000000084d1e71c + + /* x^158784 mod p(x), x^158720 mod p(x) */ +DATA ·KoopConst+1600(SB)/8,$0x00000001dedba6ca +DATA ·KoopConst+1608(SB)/8,$0x0000000197c2ad54 + + /* x^157760 mod p(x), x^157696 mod p(x) */ +DATA ·KoopConst+1616(SB)/8,$0x0000000146a43500 +DATA ·KoopConst+1624(SB)/8,$0x000000018609261e + + /* x^156736 mod p(x), x^156672 mod p(x) */ +DATA ·KoopConst+1632(SB)/8,$0x000000001cf762de +DATA ·KoopConst+1640(SB)/8,$0x00000000b4b4c224 + + /* x^155712 mod p(x), x^155648 mod p(x) */ +DATA ·KoopConst+1648(SB)/8,$0x0000000022ff7eda +DATA ·KoopConst+1656(SB)/8,$0x0000000080817496 + + /* x^154688 mod p(x), x^154624 mod p(x) */ +DATA ·KoopConst+1664(SB)/8,$0x00000001b6df625e +DATA ·KoopConst+1672(SB)/8,$0x00000001aefb473c + + /* x^153664 mod p(x), x^153600 mod p(x) */ +DATA ·KoopConst+1680(SB)/8,$0x00000001cc99ab58 +DATA ·KoopConst+1688(SB)/8,$0x000000013f1aa474 + + /* x^152640 mod p(x), x^152576 mod p(x) */ +DATA ·KoopConst+1696(SB)/8,$0x00000001c53f5ce2 +DATA ·KoopConst+1704(SB)/8,$0x000000010ca2c756 + + /* x^151616 mod p(x), x^151552 mod p(x) */ +DATA ·KoopConst+1712(SB)/8,$0x0000000082a9c60e +DATA ·KoopConst+1720(SB)/8,$0x000000002c63533a + + /* x^150592 mod p(x), x^150528 mod p(x) */ +DATA ·KoopConst+1728(SB)/8,$0x00000000ec78b570 +DATA ·KoopConst+1736(SB)/8,$0x00000001b7f2ad50 + + /* x^149568 mod p(x), x^149504 mod p(x) */ +DATA ·KoopConst+1744(SB)/8,$0x00000001d3fe1e8e +DATA ·KoopConst+1752(SB)/8,$0x00000000acdf4c20 + + /* x^148544 mod p(x), x^148480 mod p(x) */ +DATA ·KoopConst+1760(SB)/8,$0x000000007f9a7bde +DATA ·KoopConst+1768(SB)/8,$0x000000000bd29e8c + + /* x^147520 mod p(x), x^147456 mod p(x) */ +DATA ·KoopConst+1776(SB)/8,$0x00000000e606f518 +DATA ·KoopConst+1784(SB)/8,$0x00000001eef6992e + + /* x^146496 mod p(x), x^146432 mod p(x) */ +DATA ·KoopConst+1792(SB)/8,$0x000000008538cb96 +DATA ·KoopConst+1800(SB)/8,$0x00000000b01644e6 + + /* x^145472 mod p(x), x^145408 mod p(x) */ +DATA ·KoopConst+1808(SB)/8,$0x0000000131d030b2 +DATA ·KoopConst+1816(SB)/8,$0x0000000059c51acc + + /* x^144448 mod p(x), x^144384 mod p(x) */ +DATA ·KoopConst+1824(SB)/8,$0x00000000115a4d0e +DATA ·KoopConst+1832(SB)/8,$0x00000001a2849272 + + /* x^143424 mod p(x), x^143360 mod p(x) */ +DATA ·KoopConst+1840(SB)/8,$0x00000000e8a5356e +DATA ·KoopConst+1848(SB)/8,$0x00000001a4e0b610 + + /* x^142400 mod p(x), x^142336 mod p(x) */ +DATA ·KoopConst+1856(SB)/8,$0x0000000158d988be +DATA ·KoopConst+1864(SB)/8,$0x00000000084e81a6 + + /* x^141376 mod p(x), x^141312 mod p(x) */ +DATA ·KoopConst+1872(SB)/8,$0x00000001240db498 +DATA ·KoopConst+1880(SB)/8,$0x00000001b71f1fd8 + + /* x^140352 mod p(x), x^140288 mod p(x) */ +DATA ·KoopConst+1888(SB)/8,$0x000000009ce87826 +DATA ·KoopConst+1896(SB)/8,$0x000000017f7df380 + + /* x^139328 mod p(x), x^139264 mod p(x) */ +DATA ·KoopConst+1904(SB)/8,$0x0000000021944aae +DATA ·KoopConst+1912(SB)/8,$0x00000001f7f4e190 + + /* x^138304 mod p(x), x^138240 mod p(x) */ +DATA ·KoopConst+1920(SB)/8,$0x00000001cea3d67e +DATA ·KoopConst+1928(SB)/8,$0x0000000150220d86 + + /* x^137280 mod p(x), x^137216 mod p(x) */ +DATA ·KoopConst+1936(SB)/8,$0x000000004434e926 +DATA ·KoopConst+1944(SB)/8,$0x00000001db7d2b2e + + /* x^136256 mod p(x), x^136192 mod p(x) */ +DATA ·KoopConst+1952(SB)/8,$0x0000000011db8cbe +DATA ·KoopConst+1960(SB)/8,$0x00000000b6ba9668 + + /* x^135232 mod p(x), x^135168 mod p(x) */ +DATA ·KoopConst+1968(SB)/8,$0x00000001f6e0b8dc +DATA ·KoopConst+1976(SB)/8,$0x0000000103fdcecc + + /* x^134208 mod p(x), x^134144 mod p(x) */ +DATA ·KoopConst+1984(SB)/8,$0x00000001f163f4a0 +DATA ·KoopConst+1992(SB)/8,$0x0000000079816a22 + + /* x^133184 mod p(x), x^133120 mod p(x) */ +DATA ·KoopConst+2000(SB)/8,$0x000000007b6cc60e +DATA ·KoopConst+2008(SB)/8,$0x0000000173483482 + + /* x^132160 mod p(x), x^132096 mod p(x) */ +DATA ·KoopConst+2016(SB)/8,$0x000000000f26c82c +DATA ·KoopConst+2024(SB)/8,$0x00000000643ea4c0 + + /* x^131136 mod p(x), x^131072 mod p(x) */ +DATA ·KoopConst+2032(SB)/8,$0x00000000b0acad80 +DATA ·KoopConst+2040(SB)/8,$0x00000000a64752d2 + + /* x^130112 mod p(x), x^130048 mod p(x) */ +DATA ·KoopConst+2048(SB)/8,$0x000000013687e91c +DATA ·KoopConst+2056(SB)/8,$0x00000000ca98eb3a + + /* x^129088 mod p(x), x^129024 mod p(x) */ +DATA ·KoopConst+2064(SB)/8,$0x000000006bac3a96 +DATA ·KoopConst+2072(SB)/8,$0x00000001ca6ac8f8 + + /* x^128064 mod p(x), x^128000 mod p(x) */ +DATA ·KoopConst+2080(SB)/8,$0x00000001bf197d5c +DATA ·KoopConst+2088(SB)/8,$0x00000001c48e2e68 + + /* x^127040 mod p(x), x^126976 mod p(x) */ +DATA ·KoopConst+2096(SB)/8,$0x00000000256e84f2 +DATA ·KoopConst+2104(SB)/8,$0x0000000070086782 + + /* x^126016 mod p(x), x^125952 mod p(x) */ +DATA ·KoopConst+2112(SB)/8,$0x000000003eff0d16 +DATA ·KoopConst+2120(SB)/8,$0x00000000f763621c + + /* x^124992 mod p(x), x^124928 mod p(x) */ +DATA ·KoopConst+2128(SB)/8,$0x00000001748e9fd2 +DATA ·KoopConst+2136(SB)/8,$0x00000000ba58646a + + /* x^123968 mod p(x), x^123904 mod p(x) */ +DATA ·KoopConst+2144(SB)/8,$0x000000015bb85b42 +DATA ·KoopConst+2152(SB)/8,$0x0000000138e157d8 + + /* x^122944 mod p(x), x^122880 mod p(x) */ +DATA ·KoopConst+2160(SB)/8,$0x0000000164d1a980 +DATA ·KoopConst+2168(SB)/8,$0x00000001bf0a09dc + + /* x^121920 mod p(x), x^121856 mod p(x) */ +DATA ·KoopConst+2176(SB)/8,$0x000000001415c9f0 +DATA ·KoopConst+2184(SB)/8,$0x0000000098faf300 + + /* x^120896 mod p(x), x^120832 mod p(x) */ +DATA ·KoopConst+2192(SB)/8,$0x0000000195ae2f48 +DATA ·KoopConst+2200(SB)/8,$0x00000001f872f2c6 + + /* x^119872 mod p(x), x^119808 mod p(x) */ +DATA ·KoopConst+2208(SB)/8,$0x0000000059d1d81a +DATA ·KoopConst+2216(SB)/8,$0x00000000f92577be + + /* x^118848 mod p(x), x^118784 mod p(x) */ +DATA ·KoopConst+2224(SB)/8,$0x00000001bf80257a +DATA ·KoopConst+2232(SB)/8,$0x00000001a4d975f4 + + /* x^117824 mod p(x), x^117760 mod p(x) */ +DATA ·KoopConst+2240(SB)/8,$0x000000011e39bfce +DATA ·KoopConst+2248(SB)/8,$0x000000018b74eeca + + /* x^116800 mod p(x), x^116736 mod p(x) */ +DATA ·KoopConst+2256(SB)/8,$0x00000001287a0456 +DATA ·KoopConst+2264(SB)/8,$0x00000000e8980404 + + /* x^115776 mod p(x), x^115712 mod p(x) */ +DATA ·KoopConst+2272(SB)/8,$0x00000000a5eb589c +DATA ·KoopConst+2280(SB)/8,$0x0000000176ef2b74 + + /* x^114752 mod p(x), x^114688 mod p(x) */ +DATA ·KoopConst+2288(SB)/8,$0x000000017d71c452 +DATA ·KoopConst+2296(SB)/8,$0x0000000063c85caa + + /* x^113728 mod p(x), x^113664 mod p(x) */ +DATA ·KoopConst+2304(SB)/8,$0x00000000fa941f08 +DATA ·KoopConst+2312(SB)/8,$0x00000001708012cc + + /* x^112704 mod p(x), x^112640 mod p(x) */ +DATA ·KoopConst+2320(SB)/8,$0x0000000064ea030e +DATA ·KoopConst+2328(SB)/8,$0x00000000474d58f6 + + /* x^111680 mod p(x), x^111616 mod p(x) */ +DATA ·KoopConst+2336(SB)/8,$0x000000019b7cc7ba +DATA ·KoopConst+2344(SB)/8,$0x00000001c76085a6 + + /* x^110656 mod p(x), x^110592 mod p(x) */ +DATA ·KoopConst+2352(SB)/8,$0x00000000225cb7ba +DATA ·KoopConst+2360(SB)/8,$0x000000018fb0681a + + /* x^109632 mod p(x), x^109568 mod p(x) */ +DATA ·KoopConst+2368(SB)/8,$0x000000010ab3e1da +DATA ·KoopConst+2376(SB)/8,$0x00000001fcee1f16 + + /* x^108608 mod p(x), x^108544 mod p(x) */ +DATA ·KoopConst+2384(SB)/8,$0x00000001ce5cc33e +DATA ·KoopConst+2392(SB)/8,$0x00000000cfbffb7c + + /* x^107584 mod p(x), x^107520 mod p(x) */ +DATA ·KoopConst+2400(SB)/8,$0x000000005e980f6e +DATA ·KoopConst+2408(SB)/8,$0x000000017af8ee72 + + /* x^106560 mod p(x), x^106496 mod p(x) */ +DATA ·KoopConst+2416(SB)/8,$0x00000000d3bf3f46 +DATA ·KoopConst+2424(SB)/8,$0x000000001c2ad3e2 + + /* x^105536 mod p(x), x^105472 mod p(x) */ +DATA ·KoopConst+2432(SB)/8,$0x000000018d554ae0 +DATA ·KoopConst+2440(SB)/8,$0x00000000ee05450a + + /* x^104512 mod p(x), x^104448 mod p(x) */ +DATA ·KoopConst+2448(SB)/8,$0x000000018e276eb0 +DATA ·KoopConst+2456(SB)/8,$0x000000000f7d5bac + + /* x^103488 mod p(x), x^103424 mod p(x) */ +DATA ·KoopConst+2464(SB)/8,$0x000000001c0319ce +DATA ·KoopConst+2472(SB)/8,$0x00000001cb26e004 + + /* x^102464 mod p(x), x^102400 mod p(x) */ +DATA ·KoopConst+2480(SB)/8,$0x00000001ca0c75ec +DATA ·KoopConst+2488(SB)/8,$0x00000001553314e2 + + /* x^101440 mod p(x), x^101376 mod p(x) */ +DATA ·KoopConst+2496(SB)/8,$0x00000001fb075330 +DATA ·KoopConst+2504(SB)/8,$0x000000005729be2c + + /* x^100416 mod p(x), x^100352 mod p(x) */ +DATA ·KoopConst+2512(SB)/8,$0x00000000677920e4 +DATA ·KoopConst+2520(SB)/8,$0x0000000192c4479c + + /* x^99392 mod p(x), x^99328 mod p(x) */ +DATA ·KoopConst+2528(SB)/8,$0x00000000332247c8 +DATA ·KoopConst+2536(SB)/8,$0x0000000078d842b6 + + /* x^98368 mod p(x), x^98304 mod p(x) */ +DATA ·KoopConst+2544(SB)/8,$0x00000000ef84fc6c +DATA ·KoopConst+2552(SB)/8,$0x0000000145ffa282 + + /* x^97344 mod p(x), x^97280 mod p(x) */ +DATA ·KoopConst+2560(SB)/8,$0x0000000139ba7690 +DATA ·KoopConst+2568(SB)/8,$0x000000019d679bf4 + + /* x^96320 mod p(x), x^96256 mod p(x) */ +DATA ·KoopConst+2576(SB)/8,$0x00000000029ef444 +DATA ·KoopConst+2584(SB)/8,$0x000000019412f7a0 + + /* x^95296 mod p(x), x^95232 mod p(x) */ +DATA ·KoopConst+2592(SB)/8,$0x00000001d872048c +DATA ·KoopConst+2600(SB)/8,$0x00000000b28c5c96 + + /* x^94272 mod p(x), x^94208 mod p(x) */ +DATA ·KoopConst+2608(SB)/8,$0x000000016535d70a +DATA ·KoopConst+2616(SB)/8,$0x00000000554bfd44 + + /* x^93248 mod p(x), x^93184 mod p(x) */ +DATA ·KoopConst+2624(SB)/8,$0x00000000761dd222 +DATA ·KoopConst+2632(SB)/8,$0x00000000ce9cfa48 + + /* x^92224 mod p(x), x^92160 mod p(x) */ +DATA ·KoopConst+2640(SB)/8,$0x00000001509a3a44 +DATA ·KoopConst+2648(SB)/8,$0x00000000a4702ab2 + + /* x^91200 mod p(x), x^91136 mod p(x) */ +DATA ·KoopConst+2656(SB)/8,$0x000000007e7019f2 +DATA ·KoopConst+2664(SB)/8,$0x00000001c967fbee + + /* x^90176 mod p(x), x^90112 mod p(x) */ +DATA ·KoopConst+2672(SB)/8,$0x00000000fb4c56ea +DATA ·KoopConst+2680(SB)/8,$0x00000000fd514b3e + + /* x^89152 mod p(x), x^89088 mod p(x) */ +DATA ·KoopConst+2688(SB)/8,$0x000000012022e0ee +DATA ·KoopConst+2696(SB)/8,$0x00000001c0b6f95e + + /* x^88128 mod p(x), x^88064 mod p(x) */ +DATA ·KoopConst+2704(SB)/8,$0x0000000004bc6054 +DATA ·KoopConst+2712(SB)/8,$0x0000000180e103ce + + /* x^87104 mod p(x), x^87040 mod p(x) */ +DATA ·KoopConst+2720(SB)/8,$0x000000017a1a0030 +DATA ·KoopConst+2728(SB)/8,$0x00000001a1630916 + + /* x^86080 mod p(x), x^86016 mod p(x) */ +DATA ·KoopConst+2736(SB)/8,$0x00000001c021a864 +DATA ·KoopConst+2744(SB)/8,$0x000000009a727fb2 + + /* x^85056 mod p(x), x^84992 mod p(x) */ +DATA ·KoopConst+2752(SB)/8,$0x000000009c54421e +DATA ·KoopConst+2760(SB)/8,$0x00000000e83b081a + + /* x^84032 mod p(x), x^83968 mod p(x) */ +DATA ·KoopConst+2768(SB)/8,$0x00000001b4e33e6a +DATA ·KoopConst+2776(SB)/8,$0x000000006b1a1f44 + + /* x^83008 mod p(x), x^82944 mod p(x) */ +DATA ·KoopConst+2784(SB)/8,$0x000000015d615af0 +DATA ·KoopConst+2792(SB)/8,$0x00000000cf280394 + + /* x^81984 mod p(x), x^81920 mod p(x) */ +DATA ·KoopConst+2800(SB)/8,$0x00000001914a3ba8 +DATA ·KoopConst+2808(SB)/8,$0x00000001154b8a9a + + /* x^80960 mod p(x), x^80896 mod p(x) */ +DATA ·KoopConst+2816(SB)/8,$0x000000005f72ec44 +DATA ·KoopConst+2824(SB)/8,$0x0000000149ec63e2 + + /* x^79936 mod p(x), x^79872 mod p(x) */ +DATA ·KoopConst+2832(SB)/8,$0x00000000a33746a8 +DATA ·KoopConst+2840(SB)/8,$0x000000018ef902c4 + + /* x^78912 mod p(x), x^78848 mod p(x) */ +DATA ·KoopConst+2848(SB)/8,$0x00000001c91e90d4 +DATA ·KoopConst+2856(SB)/8,$0x0000000069addb88 + + /* x^77888 mod p(x), x^77824 mod p(x) */ +DATA ·KoopConst+2864(SB)/8,$0x00000001052eb05e +DATA ·KoopConst+2872(SB)/8,$0x00000000e90a29ae + + /* x^76864 mod p(x), x^76800 mod p(x) */ +DATA ·KoopConst+2880(SB)/8,$0x000000006a32f754 +DATA ·KoopConst+2888(SB)/8,$0x00000000c53641ae + + /* x^75840 mod p(x), x^75776 mod p(x) */ +DATA ·KoopConst+2896(SB)/8,$0x00000001ecbd6436 +DATA ·KoopConst+2904(SB)/8,$0x00000000a17c3796 + + /* x^74816 mod p(x), x^74752 mod p(x) */ +DATA ·KoopConst+2912(SB)/8,$0x000000000fd3f93a +DATA ·KoopConst+2920(SB)/8,$0x000000015307a62c + + /* x^73792 mod p(x), x^73728 mod p(x) */ +DATA ·KoopConst+2928(SB)/8,$0x00000001686a4c24 +DATA ·KoopConst+2936(SB)/8,$0x000000002f94bbda + + /* x^72768 mod p(x), x^72704 mod p(x) */ +DATA ·KoopConst+2944(SB)/8,$0x00000001e40afca0 +DATA ·KoopConst+2952(SB)/8,$0x0000000072c8b5e6 + + /* x^71744 mod p(x), x^71680 mod p(x) */ +DATA ·KoopConst+2960(SB)/8,$0x000000012779a2b8 +DATA ·KoopConst+2968(SB)/8,$0x00000000f09b7424 + + /* x^70720 mod p(x), x^70656 mod p(x) */ +DATA ·KoopConst+2976(SB)/8,$0x00000000dcdaeb9e +DATA ·KoopConst+2984(SB)/8,$0x00000001c57de3da + + /* x^69696 mod p(x), x^69632 mod p(x) */ +DATA ·KoopConst+2992(SB)/8,$0x00000001674f7a2a +DATA ·KoopConst+3000(SB)/8,$0x000000013922b30e + + /* x^68672 mod p(x), x^68608 mod p(x) */ +DATA ·KoopConst+3008(SB)/8,$0x00000000dcb9e846 +DATA ·KoopConst+3016(SB)/8,$0x000000008759a6c2 + + /* x^67648 mod p(x), x^67584 mod p(x) */ +DATA ·KoopConst+3024(SB)/8,$0x00000000ea9a6af6 +DATA ·KoopConst+3032(SB)/8,$0x00000000545ae424 + + /* x^66624 mod p(x), x^66560 mod p(x) */ +DATA ·KoopConst+3040(SB)/8,$0x000000006d1f7a74 +DATA ·KoopConst+3048(SB)/8,$0x00000001e0cbafd2 + + /* x^65600 mod p(x), x^65536 mod p(x) */ +DATA ·KoopConst+3056(SB)/8,$0x000000006add215e +DATA ·KoopConst+3064(SB)/8,$0x0000000018360c04 + + /* x^64576 mod p(x), x^64512 mod p(x) */ +DATA ·KoopConst+3072(SB)/8,$0x000000010a9ee4b0 +DATA ·KoopConst+3080(SB)/8,$0x00000000941dc432 + + /* x^63552 mod p(x), x^63488 mod p(x) */ +DATA ·KoopConst+3088(SB)/8,$0x00000000304c48d2 +DATA ·KoopConst+3096(SB)/8,$0x0000000004d3566e + + /* x^62528 mod p(x), x^62464 mod p(x) */ +DATA ·KoopConst+3104(SB)/8,$0x0000000163d0e672 +DATA ·KoopConst+3112(SB)/8,$0x0000000096aed14e + + /* x^61504 mod p(x), x^61440 mod p(x) */ +DATA ·KoopConst+3120(SB)/8,$0x0000000010049166 +DATA ·KoopConst+3128(SB)/8,$0x0000000087c13618 + + /* x^60480 mod p(x), x^60416 mod p(x) */ +DATA ·KoopConst+3136(SB)/8,$0x00000001d3913e34 +DATA ·KoopConst+3144(SB)/8,$0x00000001d52f7b0c + + /* x^59456 mod p(x), x^59392 mod p(x) */ +DATA ·KoopConst+3152(SB)/8,$0x00000001e392d54a +DATA ·KoopConst+3160(SB)/8,$0x000000000182058e + + /* x^58432 mod p(x), x^58368 mod p(x) */ +DATA ·KoopConst+3168(SB)/8,$0x0000000173f2704a +DATA ·KoopConst+3176(SB)/8,$0x00000001ed73aa02 + + /* x^57408 mod p(x), x^57344 mod p(x) */ +DATA ·KoopConst+3184(SB)/8,$0x000000019112b480 +DATA ·KoopConst+3192(SB)/8,$0x000000002721a82e + + /* x^56384 mod p(x), x^56320 mod p(x) */ +DATA ·KoopConst+3200(SB)/8,$0x0000000093d295d6 +DATA ·KoopConst+3208(SB)/8,$0x000000012ca83da2 + + /* x^55360 mod p(x), x^55296 mod p(x) */ +DATA ·KoopConst+3216(SB)/8,$0x0000000114e37f44 +DATA ·KoopConst+3224(SB)/8,$0x00000000da358698 + + /* x^54336 mod p(x), x^54272 mod p(x) */ +DATA ·KoopConst+3232(SB)/8,$0x00000000fcfebc86 +DATA ·KoopConst+3240(SB)/8,$0x0000000011fad322 + + /* x^53312 mod p(x), x^53248 mod p(x) */ +DATA ·KoopConst+3248(SB)/8,$0x00000000834c48d6 +DATA ·KoopConst+3256(SB)/8,$0x000000012b25025c + + /* x^52288 mod p(x), x^52224 mod p(x) */ +DATA ·KoopConst+3264(SB)/8,$0x000000017b909372 +DATA ·KoopConst+3272(SB)/8,$0x000000001290cd24 + + /* x^51264 mod p(x), x^51200 mod p(x) */ +DATA ·KoopConst+3280(SB)/8,$0x000000010156b9ac +DATA ·KoopConst+3288(SB)/8,$0x000000016edd0b06 + + /* x^50240 mod p(x), x^50176 mod p(x) */ +DATA ·KoopConst+3296(SB)/8,$0x0000000113a82fa8 +DATA ·KoopConst+3304(SB)/8,$0x00000000c08e222a + + /* x^49216 mod p(x), x^49152 mod p(x) */ +DATA ·KoopConst+3312(SB)/8,$0x0000000182dacb74 +DATA ·KoopConst+3320(SB)/8,$0x00000000cfb4d10e + + /* x^48192 mod p(x), x^48128 mod p(x) */ +DATA ·KoopConst+3328(SB)/8,$0x000000010210dc40 +DATA ·KoopConst+3336(SB)/8,$0x000000013e156ece + + /* x^47168 mod p(x), x^47104 mod p(x) */ +DATA ·KoopConst+3344(SB)/8,$0x000000008ab5ed20 +DATA ·KoopConst+3352(SB)/8,$0x00000000f12d89f8 + + /* x^46144 mod p(x), x^46080 mod p(x) */ +DATA ·KoopConst+3360(SB)/8,$0x00000000810386fa +DATA ·KoopConst+3368(SB)/8,$0x00000001fce3337c + + /* x^45120 mod p(x), x^45056 mod p(x) */ +DATA ·KoopConst+3376(SB)/8,$0x000000011dce2fe2 +DATA ·KoopConst+3384(SB)/8,$0x00000001c4bf3514 + + /* x^44096 mod p(x), x^44032 mod p(x) */ +DATA ·KoopConst+3392(SB)/8,$0x000000004bb0a390 +DATA ·KoopConst+3400(SB)/8,$0x00000001ae67c492 + + /* x^43072 mod p(x), x^43008 mod p(x) */ +DATA ·KoopConst+3408(SB)/8,$0x00000000028d486a +DATA ·KoopConst+3416(SB)/8,$0x00000000302af704 + + /* x^42048 mod p(x), x^41984 mod p(x) */ +DATA ·KoopConst+3424(SB)/8,$0x000000010e4d63fe +DATA ·KoopConst+3432(SB)/8,$0x00000001e375b250 + + /* x^41024 mod p(x), x^40960 mod p(x) */ +DATA ·KoopConst+3440(SB)/8,$0x000000014fd6f458 +DATA ·KoopConst+3448(SB)/8,$0x00000001678b58c0 + + /* x^40000 mod p(x), x^39936 mod p(x) */ +DATA ·KoopConst+3456(SB)/8,$0x00000000db7a83a2 +DATA ·KoopConst+3464(SB)/8,$0x0000000065103c1e + + /* x^38976 mod p(x), x^38912 mod p(x) */ +DATA ·KoopConst+3472(SB)/8,$0x000000016cf9fa3c +DATA ·KoopConst+3480(SB)/8,$0x000000000ccd28ca + + /* x^37952 mod p(x), x^37888 mod p(x) */ +DATA ·KoopConst+3488(SB)/8,$0x000000016bb33912 +DATA ·KoopConst+3496(SB)/8,$0x0000000059c177d4 + + /* x^36928 mod p(x), x^36864 mod p(x) */ +DATA ·KoopConst+3504(SB)/8,$0x0000000135bda8bc +DATA ·KoopConst+3512(SB)/8,$0x00000001d162f83a + + /* x^35904 mod p(x), x^35840 mod p(x) */ +DATA ·KoopConst+3520(SB)/8,$0x000000004e8c6b76 +DATA ·KoopConst+3528(SB)/8,$0x00000001efc0230c + + /* x^34880 mod p(x), x^34816 mod p(x) */ +DATA ·KoopConst+3536(SB)/8,$0x00000000e17cb750 +DATA ·KoopConst+3544(SB)/8,$0x00000001a2a2e2d2 + + /* x^33856 mod p(x), x^33792 mod p(x) */ +DATA ·KoopConst+3552(SB)/8,$0x000000010e8bb9cc +DATA ·KoopConst+3560(SB)/8,$0x00000001145c9dc2 + + /* x^32832 mod p(x), x^32768 mod p(x) */ +DATA ·KoopConst+3568(SB)/8,$0x00000001859d1cae +DATA ·KoopConst+3576(SB)/8,$0x00000000949e4a48 + + /* x^31808 mod p(x), x^31744 mod p(x) */ +DATA ·KoopConst+3584(SB)/8,$0x0000000167802bbe +DATA ·KoopConst+3592(SB)/8,$0x0000000128beecbc + + /* x^30784 mod p(x), x^30720 mod p(x) */ +DATA ·KoopConst+3600(SB)/8,$0x0000000086f5219c +DATA ·KoopConst+3608(SB)/8,$0x00000001ffc96ae4 + + /* x^29760 mod p(x), x^29696 mod p(x) */ +DATA ·KoopConst+3616(SB)/8,$0x00000001349a4faa +DATA ·KoopConst+3624(SB)/8,$0x00000001ba81e0aa + + /* x^28736 mod p(x), x^28672 mod p(x) */ +DATA ·KoopConst+3632(SB)/8,$0x000000007da3353e +DATA ·KoopConst+3640(SB)/8,$0x0000000104d7df14 + + /* x^27712 mod p(x), x^27648 mod p(x) */ +DATA ·KoopConst+3648(SB)/8,$0x00000000440fba4e +DATA ·KoopConst+3656(SB)/8,$0x00000001c2ff8518 + + /* x^26688 mod p(x), x^26624 mod p(x) */ +DATA ·KoopConst+3664(SB)/8,$0x00000000507aba70 +DATA ·KoopConst+3672(SB)/8,$0x00000000ba6d4708 + + /* x^25664 mod p(x), x^25600 mod p(x) */ +DATA ·KoopConst+3680(SB)/8,$0x0000000015b578b6 +DATA ·KoopConst+3688(SB)/8,$0x00000001d49d4bba + + /* x^24640 mod p(x), x^24576 mod p(x) */ +DATA ·KoopConst+3696(SB)/8,$0x0000000141633fb2 +DATA ·KoopConst+3704(SB)/8,$0x00000000d21247e6 + + /* x^23616 mod p(x), x^23552 mod p(x) */ +DATA ·KoopConst+3712(SB)/8,$0x0000000178712680 +DATA ·KoopConst+3720(SB)/8,$0x0000000063b4004a + + /* x^22592 mod p(x), x^22528 mod p(x) */ +DATA ·KoopConst+3728(SB)/8,$0x000000001404c194 +DATA ·KoopConst+3736(SB)/8,$0x0000000094f55d2c + + /* x^21568 mod p(x), x^21504 mod p(x) */ +DATA ·KoopConst+3744(SB)/8,$0x00000000469dbe46 +DATA ·KoopConst+3752(SB)/8,$0x00000001ca68fe74 + + /* x^20544 mod p(x), x^20480 mod p(x) */ +DATA ·KoopConst+3760(SB)/8,$0x00000000fb093fd8 +DATA ·KoopConst+3768(SB)/8,$0x00000001fd7d1b4c + + /* x^19520 mod p(x), x^19456 mod p(x) */ +DATA ·KoopConst+3776(SB)/8,$0x00000000767a2bfe +DATA ·KoopConst+3784(SB)/8,$0x0000000055982d0c + + /* x^18496 mod p(x), x^18432 mod p(x) */ +DATA ·KoopConst+3792(SB)/8,$0x00000001344e22bc +DATA ·KoopConst+3800(SB)/8,$0x00000000221553a6 + + /* x^17472 mod p(x), x^17408 mod p(x) */ +DATA ·KoopConst+3808(SB)/8,$0x0000000161cd9978 +DATA ·KoopConst+3816(SB)/8,$0x000000013d9a153a + + /* x^16448 mod p(x), x^16384 mod p(x) */ +DATA ·KoopConst+3824(SB)/8,$0x00000001d702e906 +DATA ·KoopConst+3832(SB)/8,$0x00000001cd108b3c + + /* x^15424 mod p(x), x^15360 mod p(x) */ +DATA ·KoopConst+3840(SB)/8,$0x00000001c7db9908 +DATA ·KoopConst+3848(SB)/8,$0x00000001d0af0f4a + + /* x^14400 mod p(x), x^14336 mod p(x) */ +DATA ·KoopConst+3856(SB)/8,$0x00000001665d025c +DATA ·KoopConst+3864(SB)/8,$0x00000001196cf0ec + + /* x^13376 mod p(x), x^13312 mod p(x) */ +DATA ·KoopConst+3872(SB)/8,$0x000000012df97c0e +DATA ·KoopConst+3880(SB)/8,$0x00000001c88c9704 + + /* x^12352 mod p(x), x^12288 mod p(x) */ +DATA ·KoopConst+3888(SB)/8,$0x000000006fed84da +DATA ·KoopConst+3896(SB)/8,$0x000000002013d300 + + /* x^11328 mod p(x), x^11264 mod p(x) */ +DATA ·KoopConst+3904(SB)/8,$0x00000000b094146e +DATA ·KoopConst+3912(SB)/8,$0x00000001c458501e + + /* x^10304 mod p(x), x^10240 mod p(x) */ +DATA ·KoopConst+3920(SB)/8,$0x00000001ceb518a6 +DATA ·KoopConst+3928(SB)/8,$0x000000003ce14802 + + /* x^9280 mod p(x), x^9216 mod p(x) */ +DATA ·KoopConst+3936(SB)/8,$0x000000011f16db0a +DATA ·KoopConst+3944(SB)/8,$0x00000000bb72bb98 + + /* x^8256 mod p(x), x^8192 mod p(x) */ +DATA ·KoopConst+3952(SB)/8,$0x00000001d4aa130e +DATA ·KoopConst+3960(SB)/8,$0x00000000fb9aeaba + + /* x^7232 mod p(x), x^7168 mod p(x) */ +DATA ·KoopConst+3968(SB)/8,$0x00000001991f01d2 +DATA ·KoopConst+3976(SB)/8,$0x000000000131f5e6 + + /* x^6208 mod p(x), x^6144 mod p(x) */ +DATA ·KoopConst+3984(SB)/8,$0x000000006bd58b4c +DATA ·KoopConst+3992(SB)/8,$0x0000000089d5799a + + /* x^5184 mod p(x), x^5120 mod p(x) */ +DATA ·KoopConst+4000(SB)/8,$0x000000007272c166 +DATA ·KoopConst+4008(SB)/8,$0x00000000474c43b0 + + /* x^4160 mod p(x), x^4096 mod p(x) */ +DATA ·KoopConst+4016(SB)/8,$0x000000013974e6f8 +DATA ·KoopConst+4024(SB)/8,$0x00000001db991f34 + + /* x^3136 mod p(x), x^3072 mod p(x) */ +DATA ·KoopConst+4032(SB)/8,$0x000000000bd6e03c +DATA ·KoopConst+4040(SB)/8,$0x000000004b1bfd00 + + /* x^2112 mod p(x), x^2048 mod p(x) */ +DATA ·KoopConst+4048(SB)/8,$0x000000005988c652 +DATA ·KoopConst+4056(SB)/8,$0x000000004036b796 + + /* x^1088 mod p(x), x^1024 mod p(x) */ +DATA ·KoopConst+4064(SB)/8,$0x00000000129ef036 +DATA ·KoopConst+4072(SB)/8,$0x000000000c5ec3d4 + + /* x^2048 mod p(x), x^2016 mod p(x), x^1984 mod p(x), x^1952 mod p(x) */ +DATA ·KoopConst+4080(SB)/8,$0xd6f94847201b5bcb +DATA ·KoopConst+4088(SB)/8,$0x1efc02e79571e892 + + /* x^1920 mod p(x), x^1888 mod p(x), x^1856 mod p(x), x^1824 mod p(x) */ +DATA ·KoopConst+4096(SB)/8,$0xce08adcc294c1393 +DATA ·KoopConst+4104(SB)/8,$0x0b269b5c5ab5f161 + + /* x^1792 mod p(x), x^1760 mod p(x), x^1728 mod p(x), x^1696 mod p(x) */ +DATA ·KoopConst+4112(SB)/8,$0x17315505e4201e72 +DATA ·KoopConst+4120(SB)/8,$0x2e841f4784acf3e9 + + /* x^1664 mod p(x), x^1632 mod p(x), x^1600 mod p(x), x^1568 mod p(x) */ +DATA ·KoopConst+4128(SB)/8,$0x37cfc3a67cc667e3 +DATA ·KoopConst+4136(SB)/8,$0x7020425856bc424b + + /* x^1536 mod p(x), x^1504 mod p(x), x^1472 mod p(x), x^1440 mod p(x) */ +DATA ·KoopConst+4144(SB)/8,$0x8e2fa3369218d2c3 +DATA ·KoopConst+4152(SB)/8,$0xdf81bf923f7c6ef1 + + /* x^1408 mod p(x), x^1376 mod p(x), x^1344 mod p(x), x^1312 mod p(x) */ +DATA ·KoopConst+4160(SB)/8,$0x5ce20d2d39ed1981 +DATA ·KoopConst+4168(SB)/8,$0x9d0898a0af5ddc43 + + /* x^1280 mod p(x), x^1248 mod p(x), x^1216 mod p(x), x^1184 mod p(x) */ +DATA ·KoopConst+4176(SB)/8,$0x6f7f4546ca081e03 +DATA ·KoopConst+4184(SB)/8,$0x4992836903fda047 + + /* x^1152 mod p(x), x^1120 mod p(x), x^1088 mod p(x), x^1056 mod p(x) */ +DATA ·KoopConst+4192(SB)/8,$0xfd4f413b9bf11d68 +DATA ·KoopConst+4200(SB)/8,$0xf4ddf452094f781b + + /* x^1024 mod p(x), x^992 mod p(x), x^960 mod p(x), x^928 mod p(x) */ +DATA ·KoopConst+4208(SB)/8,$0x11d84204062f61ea +DATA ·KoopConst+4216(SB)/8,$0x9487f1e51f3588cf + + /* x^896 mod p(x), x^864 mod p(x), x^832 mod p(x), x^800 mod p(x) */ +DATA ·KoopConst+4224(SB)/8,$0xfaedf111abf58a1f +DATA ·KoopConst+4232(SB)/8,$0x31da2c22b1384ec9 + + /* x^768 mod p(x), x^736 mod p(x), x^704 mod p(x), x^672 mod p(x) */ +DATA ·KoopConst+4240(SB)/8,$0x0246b541e8f81b22 +DATA ·KoopConst+4248(SB)/8,$0xc857ede58a42eb47 + + /* x^640 mod p(x), x^608 mod p(x), x^576 mod p(x), x^544 mod p(x) */ +DATA ·KoopConst+4256(SB)/8,$0xd4dbfa9b92b0372e +DATA ·KoopConst+4264(SB)/8,$0xe0354c0b2cd1c09a + + /* x^512 mod p(x), x^480 mod p(x), x^448 mod p(x), x^416 mod p(x) */ +DATA ·KoopConst+4272(SB)/8,$0x5f36c79cfc4417ec +DATA ·KoopConst+4280(SB)/8,$0x4b92cf8d54b8f25b + + /* x^384 mod p(x), x^352 mod p(x), x^320 mod p(x), x^288 mod p(x) */ +DATA ·KoopConst+4288(SB)/8,$0xdad234918345041e +DATA ·KoopConst+4296(SB)/8,$0x4e44c81828229301 + + /* x^256 mod p(x), x^224 mod p(x), x^192 mod p(x), x^160 mod p(x) */ +DATA ·KoopConst+4304(SB)/8,$0x56fd28cc8e02f1d0 +DATA ·KoopConst+4312(SB)/8,$0x3da5e43c8ee9ee84 + + /* x^128 mod p(x), x^96 mod p(x), x^64 mod p(x), x^32 mod p(x) */ +DATA ·KoopConst+4320(SB)/8,$0xa583017cdfcb9f08 +DATA ·KoopConst+4328(SB)/8,$0xeb31d82e0c62ab26 + +GLOBL ·KoopConst(SB),RODATA,$4336 + + /* Barrett constant m - (4^32)/n */ +DATA ·KoopBarConst(SB)/8,$0x0000000017d232cd +DATA ·KoopBarConst+8(SB)/8,$0x0000000000000000 +DATA ·KoopBarConst+16(SB)/8,$0x00000001d663b05d +DATA ·KoopBarConst+24(SB)/8,$0x0000000000000000 +GLOBL ·KoopBarConst(SB),RODATA,$32 diff --git a/src/hash/crc32/crc32_test.go b/src/hash/crc32/crc32_test.go new file mode 100644 index 0000000..f084612 --- /dev/null +++ b/src/hash/crc32/crc32_test.go @@ -0,0 +1,342 @@ +// Copyright 2009 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package crc32 + +import ( + "encoding" + "fmt" + "hash" + "io" + "math/rand" + "testing" +) + +// First test, so that it can be the one to initialize castagnoliTable. +func TestCastagnoliRace(t *testing.T) { + // The MakeTable(Castagnoli) lazily initializes castagnoliTable, + // which races with the switch on tab during Write to check + // whether tab == castagnoliTable. + ieee := NewIEEE() + go MakeTable(Castagnoli) + ieee.Write([]byte("hello")) +} + +type test struct { + ieee, castagnoli uint32 + in string + halfStateIEEE string // IEEE marshaled hash state after first half of in written, used by TestGoldenMarshal + halfStateCastagnoli string // Castagnoli marshaled hash state after first half of in written, used by TestGoldenMarshal +} + +var golden = []test{ + {0x0, 0x0, "", "crc\x01ʇ\x91M\x00\x00\x00\x00", "crc\x01wB\x84\x81\x00\x00\x00\x00"}, + {0xe8b7be43, 0xc1d04330, "a", "crc\x01ʇ\x91M\x00\x00\x00\x00", "crc\x01wB\x84\x81\x00\x00\x00\x00"}, + {0x9e83486d, 0xe2a22936, "ab", "crc\x01ʇ\x91M跾C", "crc\x01wB\x84\x81\xc1\xd0C0"}, + {0x352441c2, 0x364b3fb7, "abc", "crc\x01ʇ\x91M跾C", "crc\x01wB\x84\x81\xc1\xd0C0"}, + {0xed82cd11, 0x92c80a31, "abcd", "crc\x01ʇ\x91M\x9e\x83Hm", "crc\x01wB\x84\x81\xe2\xa2)6"}, + {0x8587d865, 0xc450d697, "abcde", "crc\x01ʇ\x91M\x9e\x83Hm", "crc\x01wB\x84\x81\xe2\xa2)6"}, + {0x4b8e39ef, 0x53bceff1, "abcdef", "crc\x01ʇ\x91M5$A\xc2", "crc\x01wB\x84\x816K?\xb7"}, + {0x312a6aa6, 0xe627f441, "abcdefg", "crc\x01ʇ\x91M5$A\xc2", "crc\x01wB\x84\x816K?\xb7"}, + {0xaeef2a50, 0xa9421b7, "abcdefgh", "crc\x01ʇ\x91M\xed\x82\xcd\x11", "crc\x01wB\x84\x81\x92\xc8\n1"}, + {0x8da988af, 0x2ddc99fc, "abcdefghi", "crc\x01ʇ\x91M\xed\x82\xcd\x11", "crc\x01wB\x84\x81\x92\xc8\n1"}, + {0x3981703a, 0xe6599437, "abcdefghij", "crc\x01ʇ\x91M\x85\x87\xd8e", "crc\x01wB\x84\x81\xc4P֗"}, + {0x6b9cdfe7, 0xb2cc01fe, "Discard medicine more than two years old.", "crc\x01ʇ\x91M\xfd\xe5\xc2J", "crc\x01wB\x84\x81S\"(\xe0"}, + {0xc90ef73f, 0xe28207f, "He who has a shady past knows that nice guys finish last.", "crc\x01ʇ\x91M\x01Nj+", "crc\x01wB\x84\x81'\xdaR\x15"}, + {0xb902341f, 0xbe93f964, "I wouldn't marry him with a ten foot pole.", "crc\x01ʇ\x91M\x9d\x13\xce\x10", "crc\x01wB\x84\x81\xc3\xed\xabG"}, + {0x42080e8, 0x9e3be0c3, "Free! Free!/A trip/to Mars/for 900/empty jars/Burma Shave", "crc\x01ʇ\x91M-\xed\xf7\x94", "crc\x01wB\x84\x81\xce\xceb\x81"}, + {0x154c6d11, 0xf505ef04, "The days of the digital watch are numbered. -Tom Stoppard", "crc\x01ʇ\x91MOa\xa5\r", "crc\x01wB\x84\x81\xd3s\x9dP"}, + {0x4c418325, 0x85d3dc82, "Nepal premier won't resign.", "crc\x01ʇ\x91M\xa8S9\x85", "crc\x01wB\x84\x81{\x90\x8a\x14"}, + {0x33955150, 0xc5142380, "For every action there is an equal and opposite government program.", "crc\x01ʇ\x91Ma\xe9>\x86", "crc\x01wB\x84\x81\xaa@\xc4\x1c"}, + {0x26216a4b, 0x75eb77dd, "His money is twice tainted: 'taint yours and 'taint mine.", "crc\x01ʇ\x91M\\\x1an\x88", "crc\x01wB\x84\x81W\a8Z"}, + {0x1abbe45e, 0x91ebe9f7, "There is no reason for any individual to have a computer in their home. -Ken Olsen, 1977", "crc\x01ʇ\x91M\xb7\xf5\xf2\xca", "crc\x01wB\x84\x81\xc4o\x9d\x85"}, + {0xc89a94f7, 0xf0b1168e, "It's a tiny change to the code and not completely disgusting. - Bob Manchek", "crc\x01ʇ\x91M\x84g1\xe8", "crc\x01wB\x84\x81#\x98\f\xab"}, + {0xab3abe14, 0x572b74e2, "size: a.out: bad magic", "crc\x01ʇ\x91M\x8a\x0f\xad\b", "crc\x01wB\x84\x81\x80\xc9n\xd8"}, + {0xbab102b6, 0x8a58a6d5, "The major problem is with sendmail. -Mark Horton", "crc\x01ʇ\x91M\a\xf0\xb3\x15", "crc\x01wB\x84\x81liS\xcc"}, + {0x999149d7, 0x9c426c50, "Give me a rock, paper and scissors and I will move the world. CCFestoon", "crc\x01ʇ\x91M\x0fa\xbc.", "crc\x01wB\x84\x81\xdb͏C"}, + {0x6d52a33c, 0x735400a4, "If the enemy is within range, then so are you.", "crc\x01ʇ\x91My\x1b\x99\xf8", "crc\x01wB\x84\x81\xaaB\x037"}, + {0x90631e8d, 0xbec49c95, "It's well we cannot hear the screams/That we create in others' dreams.", "crc\x01ʇ\x91M\bqfY", "crc\x01wB\x84\x81\x16y\xa1\xd2"}, + {0x78309130, 0xa95a2079, "You remind me of a TV show, but that's all right: I watch it anyway.", "crc\x01ʇ\x91M\xbdO,\xc2", "crc\x01wB\x84\x81f&\xc5\xe4"}, + {0x7d0a377f, 0xde2e65c5, "C is as portable as Stonehedge!!", "crc\x01ʇ\x91M\xf7\xd6\x00\xd5", "crc\x01wB\x84\x81de\\\xf8"}, + {0x8c79fd79, 0x297a88ed, "Even if I could be Shakespeare, I think I should still choose to be Faraday. - A. Huxley", "crc\x01ʇ\x91Ml+\xb8\xa7", "crc\x01wB\x84\x81\xbf\xd6S\xdd"}, + {0xa20b7167, 0x66ed1d8b, "The fugacity of a constituent in a mixture of gases at a given temperature is proportional to its mole fraction. Lewis-Randall Rule", "crc\x01ʇ\x91M<lR[", "crc\x01wB\x84\x81{\xaco\xb1"}, + {0x8e0bb443, 0xdcded527, "How can you write a big system without C++? -Paul Glick", "crc\x01ʇ\x91M\x0e\x88\x89\xed", "crc\x01wB\x84\x813\xd7C\u007f"}, +} + +// testGoldenIEEE verifies that the given function returns +// correct IEEE checksums. +func testGoldenIEEE(t *testing.T, crcFunc func(b []byte) uint32) { + for _, g := range golden { + if crc := crcFunc([]byte(g.in)); crc != g.ieee { + t.Errorf("IEEE(%s) = 0x%x want 0x%x", g.in, crc, g.ieee) + } + } +} + +// testGoldenCastagnoli verifies that the given function returns +// correct IEEE checksums. +func testGoldenCastagnoli(t *testing.T, crcFunc func(b []byte) uint32) { + for _, g := range golden { + if crc := crcFunc([]byte(g.in)); crc != g.castagnoli { + t.Errorf("Castagnoli(%s) = 0x%x want 0x%x", g.in, crc, g.castagnoli) + } + } +} + +// testCrossCheck generates random buffers of various lengths and verifies that +// the two "update" functions return the same result. +func testCrossCheck(t *testing.T, crcFunc1, crcFunc2 func(crc uint32, b []byte) uint32) { + // The AMD64 implementation has some cutoffs at lengths 168*3=504 and + // 1344*3=4032. We should make sure lengths around these values are in the + // list. + lengths := []int{0, 1, 2, 3, 4, 5, 10, 16, 50, 63, 64, 65, 100, + 127, 128, 129, 255, 256, 257, 300, 312, 384, 416, 448, 480, + 500, 501, 502, 503, 504, 505, 512, 513, 1000, 1024, 2000, + 4030, 4031, 4032, 4033, 4036, 4040, 4048, 4096, 5000, 10000} + for _, length := range lengths { + p := make([]byte, length) + _, _ = rand.Read(p) + crcInit := uint32(rand.Int63()) + crc1 := crcFunc1(crcInit, p) + crc2 := crcFunc2(crcInit, p) + if crc1 != crc2 { + t.Errorf("mismatch: 0x%x vs 0x%x (buffer length %d)", crc1, crc2, length) + } + } +} + +// TestSimple tests the simple generic algorithm. +func TestSimple(t *testing.T) { + tab := simpleMakeTable(IEEE) + testGoldenIEEE(t, func(b []byte) uint32 { + return simpleUpdate(0, tab, b) + }) + + tab = simpleMakeTable(Castagnoli) + testGoldenCastagnoli(t, func(b []byte) uint32 { + return simpleUpdate(0, tab, b) + }) +} + +func TestGoldenMarshal(t *testing.T) { + t.Run("IEEE", func(t *testing.T) { + for _, g := range golden { + h := New(IEEETable) + h2 := New(IEEETable) + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfStateIEEE { + t.Errorf("IEEE(%q) state = %q, want %q", g.in, state, g.halfStateIEEE) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if h.Sum32() != h2.Sum32() { + t.Errorf("IEEE(%s) = 0x%x != marshaled 0x%x", g.in, h.Sum32(), h2.Sum32()) + } + } + }) + t.Run("Castagnoli", func(t *testing.T) { + table := MakeTable(Castagnoli) + for _, g := range golden { + h := New(table) + h2 := New(table) + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfStateCastagnoli { + t.Errorf("Castagnoli(%q) state = %q, want %q", g.in, state, g.halfStateCastagnoli) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if h.Sum32() != h2.Sum32() { + t.Errorf("Castagnoli(%s) = 0x%x != marshaled 0x%x", g.in, h.Sum32(), h2.Sum32()) + } + } + }) +} + +func TestMarshalTableMismatch(t *testing.T) { + h1 := New(IEEETable) + h2 := New(MakeTable(Castagnoli)) + + state1, err := h1.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state1); err == nil { + t.Errorf("no error when one was expected") + } +} + +// TestSimple tests the slicing-by-8 algorithm. +func TestSlicing(t *testing.T) { + tab := slicingMakeTable(IEEE) + testGoldenIEEE(t, func(b []byte) uint32 { + return slicingUpdate(0, tab, b) + }) + + tab = slicingMakeTable(Castagnoli) + testGoldenCastagnoli(t, func(b []byte) uint32 { + return slicingUpdate(0, tab, b) + }) + + // Cross-check various polys against the simple algorithm. + for _, poly := range []uint32{IEEE, Castagnoli, Koopman, 0xD5828281} { + t1 := simpleMakeTable(poly) + f1 := func(crc uint32, b []byte) uint32 { + return simpleUpdate(crc, t1, b) + } + t2 := slicingMakeTable(poly) + f2 := func(crc uint32, b []byte) uint32 { + return slicingUpdate(crc, t2, b) + } + testCrossCheck(t, f1, f2) + } +} + +func TestArchIEEE(t *testing.T) { + if !archAvailableIEEE() { + t.Skip("Arch-specific IEEE not available.") + } + archInitIEEE() + slicingTable := slicingMakeTable(IEEE) + testCrossCheck(t, archUpdateIEEE, func(crc uint32, b []byte) uint32 { + return slicingUpdate(crc, slicingTable, b) + }) +} + +func TestArchCastagnoli(t *testing.T) { + if !archAvailableCastagnoli() { + t.Skip("Arch-specific Castagnoli not available.") + } + archInitCastagnoli() + slicingTable := slicingMakeTable(Castagnoli) + testCrossCheck(t, archUpdateCastagnoli, func(crc uint32, b []byte) uint32 { + return slicingUpdate(crc, slicingTable, b) + }) +} + +func TestGolden(t *testing.T) { + testGoldenIEEE(t, ChecksumIEEE) + + // Some implementations have special code to deal with misaligned + // data; test that as well. + for delta := 1; delta <= 7; delta++ { + testGoldenIEEE(t, func(b []byte) uint32 { + ieee := NewIEEE() + d := delta + if d >= len(b) { + d = len(b) + } + ieee.Write(b[:d]) + ieee.Write(b[d:]) + return ieee.Sum32() + }) + } + + castagnoliTab := MakeTable(Castagnoli) + if castagnoliTab == nil { + t.Errorf("nil Castagnoli Table") + } + + testGoldenCastagnoli(t, func(b []byte) uint32 { + castagnoli := New(castagnoliTab) + castagnoli.Write(b) + return castagnoli.Sum32() + }) + + // Some implementations have special code to deal with misaligned + // data; test that as well. + for delta := 1; delta <= 7; delta++ { + testGoldenCastagnoli(t, func(b []byte) uint32 { + castagnoli := New(castagnoliTab) + d := delta + if d >= len(b) { + d = len(b) + } + castagnoli.Write(b[:d]) + castagnoli.Write(b[d:]) + return castagnoli.Sum32() + }) + } +} + +func BenchmarkCRC32(b *testing.B) { + b.Run("poly=IEEE", benchmarkAll(NewIEEE())) + b.Run("poly=Castagnoli", benchmarkAll(New(MakeTable(Castagnoli)))) + b.Run("poly=Koopman", benchmarkAll(New(MakeTable(Koopman)))) +} + +func benchmarkAll(h hash.Hash32) func(b *testing.B) { + return func(b *testing.B) { + for _, size := range []int{15, 40, 512, 1 << 10, 4 << 10, 32 << 10} { + name := fmt.Sprint(size) + if size >= 1024 { + name = fmt.Sprintf("%dkB", size/1024) + } + b.Run("size="+name, func(b *testing.B) { + for align := 0; align <= 1; align++ { + b.Run(fmt.Sprintf("align=%d", align), func(b *testing.B) { + benchmark(b, h, int64(size), int64(align)) + }) + } + }) + } + } +} + +func benchmark(b *testing.B, h hash.Hash32, n, alignment int64) { + b.SetBytes(n) + data := make([]byte, n+alignment) + data = data[alignment:] + for i := range data { + data[i] = byte(i) + } + in := make([]byte, 0, h.Size()) + + // Warm up + h.Reset() + h.Write(data) + h.Sum(in) + // Avoid further allocations + in = in[:0] + + b.ResetTimer() + for i := 0; i < b.N; i++ { + h.Reset() + h.Write(data) + h.Sum(in) + in = in[:0] + } +} diff --git a/src/hash/crc32/example_test.go b/src/hash/crc32/example_test.go new file mode 100644 index 0000000..621bf83 --- /dev/null +++ b/src/hash/crc32/example_test.go @@ -0,0 +1,28 @@ +// Copyright 2015 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_test + +import ( + "fmt" + "hash/crc32" +) + +func ExampleMakeTable() { + // In this package, the CRC polynomial is represented in reversed notation, + // or LSB-first representation. + // + // LSB-first representation is a hexadecimal number with n bits, in which the + // most significant bit represents the coefficient of x⁰ and the least significant + // bit represents the coefficient of xⁿ⁻¹ (the coefficient for xⁿ is implicit). + // + // For example, CRC32-Q, as defined by the following polynomial, + // x³²+ x³¹+ x²⁴+ x²²+ x¹⁶+ x¹⁴+ x⁸+ x⁷+ x⁵+ x³+ x¹+ x⁰ + // has the reversed notation 0b11010101100000101000001010000001, so the value + // that should be passed to MakeTable is 0xD5828281. + crc32q := crc32.MakeTable(0xD5828281) + fmt.Printf("%08x\n", crc32.Checksum([]byte("Hello world"), crc32q)) + // Output: + // 2964d064 +} diff --git a/src/hash/crc32/gen_const_ppc64le.go b/src/hash/crc32/gen_const_ppc64le.go new file mode 100644 index 0000000..2f15a60 --- /dev/null +++ b/src/hash/crc32/gen_const_ppc64le.go @@ -0,0 +1,150 @@ +// Copyright 2017 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. + +//go:build ignore + +// Generate the constant table associated with the poly used by the +// vpmsumd crc32 algorithm. +// +// go run gen_const_ppc64le.go +// +// generates crc32_table_ppc64le.s + +// The following is derived from code written by Anton Blanchard +// <anton@au.ibm.com> found at https://github.com/antonblanchard/crc32-vpmsum. +// The original is dual licensed under GPL and Apache 2. As the copyright holder +// for the work, IBM has contributed this new work under the golang license. + +// This code was written in Go based on the original C implementation. + +// This is a tool needed to generate the appropriate constants needed for +// the vpmsum algorithm. It is included to generate new constant tables if +// new polynomial values are included in the future. + +package main + +import ( + "bytes" + "fmt" + "os" +) + +var blocking = 32 * 1024 + +func reflect_bits(b uint64, nr uint) uint64 { + var ref uint64 + + for bit := uint64(0); bit < uint64(nr); bit++ { + if (b & uint64(1)) == 1 { + ref |= (1 << (uint64(nr-1) - bit)) + } + b = (b >> 1) + } + return ref +} + +func get_remainder(poly uint64, deg uint, n uint) uint64 { + + rem, _ := xnmodp(n, poly, deg) + return rem +} + +func get_quotient(poly uint64, bits, n uint) uint64 { + + _, div := xnmodp(n, poly, bits) + return div +} + +// xnmodp returns two values, p and div: +// p is the representation of the binary polynomial x**n mod (x ** deg + "poly") +// That is p is the binary representation of the modulus polynomial except for its highest-order term. +// div is the binary representation of the polynomial x**n / (x ** deg + "poly") +func xnmodp(n uint, poly uint64, deg uint) (uint64, uint64) { + + var mod, mask, high, div uint64 + + if n < deg { + div = 0 + return poly, div + } + mask = 1<<deg - 1 + poly &= mask + mod = poly + div = 1 + deg-- + n-- + for n > deg { + high = (mod >> deg) & 1 + div = (div << 1) | high + mod <<= 1 + if high != 0 { + mod ^= poly + } + n-- + } + return mod & mask, div +} + +func main() { + w := new(bytes.Buffer) + + fmt.Fprintf(w, "// autogenerated: do not edit!\n") + fmt.Fprintf(w, "// generated from crc32/gen_const_ppc64le.go\n") + fmt.Fprintln(w) + fmt.Fprintf(w, "#include \"textflag.h\"\n") + + // These are the polynomials supported in vector now. + // If adding others, include the polynomial and a name + // to identify it. + + genCrc32ConstTable(w, 0xedb88320, "IEEE") + genCrc32ConstTable(w, 0x82f63b78, "Cast") + genCrc32ConstTable(w, 0xeb31d82e, "Koop") + b := w.Bytes() + + err := os.WriteFile("crc32_table_ppc64le.s", b, 0666) + if err != nil { + fmt.Printf("can't write output: %s\n", err) + } +} + +func genCrc32ConstTable(w *bytes.Buffer, poly uint32, polyid string) { + + ref_poly := reflect_bits(uint64(poly), 32) + fmt.Fprintf(w, "\n\t/* Reduce %d kbits to 1024 bits */\n", blocking*8) + j := 0 + for i := (blocking * 8) - 1024; i > 0; i -= 1024 { + a := reflect_bits(get_remainder(ref_poly, 32, uint(i)), 32) << 1 + b := reflect_bits(get_remainder(ref_poly, 32, uint(i+64)), 32) << 1 + + fmt.Fprintf(w, "\t/* x^%d mod p(x)%s, x^%d mod p(x)%s */\n", uint(i+64), "", uint(i), "") + fmt.Fprintf(w, "DATA ·%sConst+%d(SB)/8,$0x%016x\n", polyid, j*8, b) + fmt.Fprintf(w, "DATA ·%sConst+%d(SB)/8,$0x%016x\n", polyid, (j+1)*8, a) + + j += 2 + fmt.Fprintf(w, "\n") + } + + for i := (1024 * 2) - 128; i >= 0; i -= 128 { + a := reflect_bits(get_remainder(ref_poly, 32, uint(i+32)), 32) + b := reflect_bits(get_remainder(ref_poly, 32, uint(i+64)), 32) + c := reflect_bits(get_remainder(ref_poly, 32, uint(i+96)), 32) + d := reflect_bits(get_remainder(ref_poly, 32, uint(i+128)), 32) + + fmt.Fprintf(w, "\t/* x^%d mod p(x)%s, x^%d mod p(x)%s, x^%d mod p(x)%s, x^%d mod p(x)%s */\n", i+128, "", i+96, "", i+64, "", i+32, "") + fmt.Fprintf(w, "DATA ·%sConst+%d(SB)/8,$0x%08x%08x\n", polyid, j*8, c, d) + fmt.Fprintf(w, "DATA ·%sConst+%d(SB)/8,$0x%08x%08x\n", polyid, (j+1)*8, a, b) + + j += 2 + fmt.Fprintf(w, "\n") + } + + fmt.Fprintf(w, "GLOBL ·%sConst(SB),RODATA,$4336\n", polyid) + fmt.Fprintf(w, "\n /* Barrett constant m - (4^32)/n */\n") + fmt.Fprintf(w, "DATA ·%sBarConst(SB)/8,$0x%016x\n", polyid, reflect_bits(get_quotient(ref_poly, 32, 64), 33)) + fmt.Fprintf(w, "DATA ·%sBarConst+8(SB)/8,$0x0000000000000000\n", polyid) + fmt.Fprintf(w, "DATA ·%sBarConst+16(SB)/8,$0x%016x\n", polyid, reflect_bits((uint64(1)<<32)|ref_poly, 33)) // reflected? + fmt.Fprintf(w, "DATA ·%sBarConst+24(SB)/8,$0x0000000000000000\n", polyid) + fmt.Fprintf(w, "GLOBL ·%sBarConst(SB),RODATA,$32\n", polyid) +} diff --git a/src/hash/crc64/crc64.go b/src/hash/crc64/crc64.go new file mode 100644 index 0000000..26b2573 --- /dev/null +++ b/src/hash/crc64/crc64.go @@ -0,0 +1,226 @@ +// 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 crc64 implements the 64-bit cyclic redundancy check, or CRC-64, +// checksum. See https://en.wikipedia.org/wiki/Cyclic_redundancy_check for +// information. +package crc64 + +import ( + "errors" + "hash" + "sync" +) + +// The size of a CRC-64 checksum in bytes. +const Size = 8 + +// Predefined polynomials. +const ( + // The ISO polynomial, defined in ISO 3309 and used in HDLC. + ISO = 0xD800000000000000 + + // The ECMA polynomial, defined in ECMA 182. + ECMA = 0xC96C5795D7870F42 +) + +// Table is a 256-word table representing the polynomial for efficient processing. +type Table [256]uint64 + +var ( + slicing8TablesBuildOnce sync.Once + slicing8TableISO *[8]Table + slicing8TableECMA *[8]Table +) + +func buildSlicing8TablesOnce() { + slicing8TablesBuildOnce.Do(buildSlicing8Tables) +} + +func buildSlicing8Tables() { + slicing8TableISO = makeSlicingBy8Table(makeTable(ISO)) + slicing8TableECMA = makeSlicingBy8Table(makeTable(ECMA)) +} + +// MakeTable returns a Table constructed from the specified polynomial. +// The contents of this Table must not be modified. +func MakeTable(poly uint64) *Table { + buildSlicing8TablesOnce() + switch poly { + case ISO: + return &slicing8TableISO[0] + case ECMA: + return &slicing8TableECMA[0] + default: + return makeTable(poly) + } +} + +func makeTable(poly uint64) *Table { + t := new(Table) + for i := 0; i < 256; i++ { + crc := uint64(i) + for j := 0; j < 8; j++ { + if crc&1 == 1 { + crc = (crc >> 1) ^ poly + } else { + crc >>= 1 + } + } + t[i] = crc + } + return t +} + +func makeSlicingBy8Table(t *Table) *[8]Table { + var helperTable [8]Table + helperTable[0] = *t + for i := 0; i < 256; i++ { + crc := t[i] + for j := 1; j < 8; j++ { + crc = t[crc&0xff] ^ (crc >> 8) + helperTable[j][i] = crc + } + } + return &helperTable +} + +// digest represents the partial evaluation of a checksum. +type digest struct { + crc uint64 + tab *Table +} + +// New creates a new hash.Hash64 computing the CRC-64 checksum using the +// polynomial represented by the Table. Its Sum method will lay the +// value out in big-endian byte order. The returned Hash64 also +// implements encoding.BinaryMarshaler and encoding.BinaryUnmarshaler to +// marshal and unmarshal the internal state of the hash. +func New(tab *Table) hash.Hash64 { return &digest{0, tab} } + +func (d *digest) Size() int { return Size } + +func (d *digest) BlockSize() int { return 1 } + +func (d *digest) Reset() { d.crc = 0 } + +const ( + magic = "crc\x02" + marshaledSize = len(magic) + 8 + 8 +) + +func (d *digest) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize) + b = append(b, magic...) + b = appendUint64(b, tableSum(d.tab)) + b = appendUint64(b, d.crc) + return b, nil +} + +func (d *digest) UnmarshalBinary(b []byte) error { + if len(b) < len(magic) || string(b[:len(magic)]) != magic { + return errors.New("hash/crc64: invalid hash state identifier") + } + if len(b) != marshaledSize { + return errors.New("hash/crc64: invalid hash state size") + } + if tableSum(d.tab) != readUint64(b[4:]) { + return errors.New("hash/crc64: tables do not match") + } + d.crc = readUint64(b[12:]) + return nil +} + +func appendUint64(b []byte, x uint64) []byte { + a := [8]byte{ + byte(x >> 56), + byte(x >> 48), + byte(x >> 40), + byte(x >> 32), + byte(x >> 24), + byte(x >> 16), + byte(x >> 8), + byte(x), + } + return append(b, a[:]...) +} + +func readUint64(b []byte) uint64 { + _ = b[7] + return uint64(b[7]) | uint64(b[6])<<8 | uint64(b[5])<<16 | uint64(b[4])<<24 | + uint64(b[3])<<32 | uint64(b[2])<<40 | uint64(b[1])<<48 | uint64(b[0])<<56 +} + +func update(crc uint64, tab *Table, p []byte) uint64 { + buildSlicing8TablesOnce() + crc = ^crc + // Table comparison is somewhat expensive, so avoid it for small sizes + for len(p) >= 64 { + var helperTable *[8]Table + if *tab == slicing8TableECMA[0] { + helperTable = slicing8TableECMA + } else if *tab == slicing8TableISO[0] { + helperTable = slicing8TableISO + // For smaller sizes creating extended table takes too much time + } else if len(p) >= 2048 { + // According to the tests between various x86 and arm CPUs, 2k is a reasonable + // threshold for now. This may change in the future. + helperTable = makeSlicingBy8Table(tab) + } else { + break + } + // Update using slicing-by-8 + for len(p) > 8 { + crc ^= uint64(p[0]) | uint64(p[1])<<8 | uint64(p[2])<<16 | uint64(p[3])<<24 | + uint64(p[4])<<32 | uint64(p[5])<<40 | uint64(p[6])<<48 | uint64(p[7])<<56 + crc = helperTable[7][crc&0xff] ^ + helperTable[6][(crc>>8)&0xff] ^ + helperTable[5][(crc>>16)&0xff] ^ + helperTable[4][(crc>>24)&0xff] ^ + helperTable[3][(crc>>32)&0xff] ^ + helperTable[2][(crc>>40)&0xff] ^ + helperTable[1][(crc>>48)&0xff] ^ + helperTable[0][crc>>56] + p = p[8:] + } + } + // For reminders or small sizes + for _, v := range p { + crc = tab[byte(crc)^v] ^ (crc >> 8) + } + return ^crc +} + +// Update returns the result of adding the bytes in p to the crc. +func Update(crc uint64, tab *Table, p []byte) uint64 { + return update(crc, tab, p) +} + +func (d *digest) Write(p []byte) (n int, err error) { + d.crc = update(d.crc, d.tab, p) + return len(p), nil +} + +func (d *digest) Sum64() uint64 { return d.crc } + +func (d *digest) Sum(in []byte) []byte { + s := d.Sum64() + return append(in, byte(s>>56), byte(s>>48), byte(s>>40), byte(s>>32), byte(s>>24), byte(s>>16), byte(s>>8), byte(s)) +} + +// Checksum returns the CRC-64 checksum of data +// using the polynomial represented by the Table. +func Checksum(data []byte, tab *Table) uint64 { return update(0, tab, data) } + +// tableSum returns the ISO checksum of table t. +func tableSum(t *Table) uint64 { + var a [2048]byte + b := a[:0] + if t != nil { + for _, x := range t { + b = appendUint64(b, x) + } + } + return Checksum(b, MakeTable(ISO)) +} diff --git a/src/hash/crc64/crc64_test.go b/src/hash/crc64/crc64_test.go new file mode 100644 index 0000000..9cf602c --- /dev/null +++ b/src/hash/crc64/crc64_test.go @@ -0,0 +1,193 @@ +// 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 crc64 + +import ( + "encoding" + "io" + "testing" +) + +type test struct { + outISO uint64 + outECMA uint64 + in string + halfStateISO string // ISO marshaled hash state after first half of in written, used by TestGoldenMarshal + halfStateECMA string // ECMA marshaled hash state after first half of in written, used by TestGoldenMarshal +} + +var golden = []test{ + {0x0, 0x0, "", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\x00\x00\x00\x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee\x00\x00\x00\x00\x00\x00\x00\x00"}, + {0x3420000000000000, 0x330284772e652b05, "a", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\x00\x00\x00\x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee\x00\x00\x00\x00\x00\x00\x00\x00"}, + {0x36c4200000000000, 0xbc6573200e84b046, "ab", "crc\x02s\xba\x84\x84\xbb\xcd]\xef4 \x00\x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee3\x02\x84w.e+\x05"}, + {0x3776c42000000000, 0x2cd8094a1a277627, "abc", "crc\x02s\xba\x84\x84\xbb\xcd]\xef4 \x00\x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee3\x02\x84w.e+\x05"}, + {0x336776c420000000, 0x3c9d28596e5960ba, "abcd", "crc\x02s\xba\x84\x84\xbb\xcd]\xef6\xc4 \x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee\xbces \x0e\x84\xb0F"}, + {0x32d36776c4200000, 0x40bdf58fb0895f2, "abcde", "crc\x02s\xba\x84\x84\xbb\xcd]\xef6\xc4 \x00\x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee\xbces \x0e\x84\xb0F"}, + {0x3002d36776c42000, 0xd08e9f8545a700f4, "abcdef", "crc\x02s\xba\x84\x84\xbb\xcd]\xef7v\xc4 \x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee,\xd8\tJ\x1a'v'"}, + {0x31b002d36776c420, 0xec20a3a8cc710e66, "abcdefg", "crc\x02s\xba\x84\x84\xbb\xcd]\xef7v\xc4 \x00\x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee,\xd8\tJ\x1a'v'"}, + {0xe21b002d36776c4, 0x67b4f30a647a0c59, "abcdefgh", "crc\x02s\xba\x84\x84\xbb\xcd]\xef3gv\xc4 \x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee<\x9d(YnY`\xba"}, + {0x8b6e21b002d36776, 0x9966f6c89d56ef8e, "abcdefghi", "crc\x02s\xba\x84\x84\xbb\xcd]\xef3gv\xc4 \x00\x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee<\x9d(YnY`\xba"}, + {0x7f5b6e21b002d367, 0x32093a2ecd5773f4, "abcdefghij", "crc\x02s\xba\x84\x84\xbb\xcd]\xef2\xd3gv\xc4 \x00\x00", "crc\x02`&\x9aR\xe1\xb7\xfee\x04\v\xdfX\xfb\b\x95\xf2"}, + {0x8ec0e7c835bf9cdf, 0x8a0825223ea6d221, "Discard medicine more than two years old.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xc6\xc0\f\xac'\x11\x12\xd5", "crc\x02`&\x9aR\xe1\xb7\xfee\xfd%\xc0&\xa0R\xef\x95"}, + {0xc7db1759e2be5ab4, 0x8562c0ac2ab9a00d, "He who has a shady past knows that nice guys finish last.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\t\xcb\xd15X[r\t", "crc\x02`&\x9aR\xe1\xb7\xfee\a\x02\xe8|+\xc1\x06\xe3"}, + {0xfbf9d9603a6fa020, 0x3ee2a39c083f38b4, "I wouldn't marry him with a ten foot pole.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\x19\xc8d\xbe\x84\x14\x87_", "crc\x02`&\x9aR\xe1\xb7\xfee˷\xd3\xeeG\xdcE\x8c"}, + {0xeafc4211a6daa0ef, 0x1f603830353e518a, "Free! Free!/A trip/to Mars/for 900/empty jars/Burma Shave", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xad\x1b*\xc0\xb1\xf3i(", "crc\x02`&\x9aR\xe1\xb7\xfee\xa7\x8a\xdb\xf6\xd2R\t\x96"}, + {0x3e05b21c7a4dc4da, 0x2fd681d7b2421fd, "The days of the digital watch are numbered. -Tom Stoppard", "crc\x02s\xba\x84\x84\xbb\xcd]\xefv78\x1ak\x02\x8f\xff", "crc\x02`&\x9aR\xe1\xb7\xfeeT\xcbl\x10\xfb\x87K*"}, + {0x5255866ad6ef28a6, 0x790ef2b16a745a41, "Nepal premier won't resign.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xcbf\x11R\xbfh\xde\xc9", "crc\x02`&\x9aR\xe1\xb7\xfee6\x13ُ\x06_\xbd\x9a"}, + {0x8a79895be1e9c361, 0x3ef8f06daccdcddf, "For every action there is an equal and opposite government program.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xf3pV\x01c_Wu", "crc\x02`&\x9aR\xe1\xb7\xfee\xe7\xc6\n\b\x12FL\xa0"}, + {0x8878963a649d4916, 0x49e41b2660b106d, "His money is twice tainted: 'taint yours and 'taint mine.", "crc\x02s\xba\x84\x84\xbb\xcd]\xefñ\xff\xf1\xe0/Δ", "crc\x02`&\x9aR\xe1\xb7\xfeeOL/\xb1\xec\xa2\x14\x87"}, + {0xa7b9d53ea87eb82f, 0x561cc0cfa235ac68, "There is no reason for any individual to have a computer in their home. -Ken Olsen, 1977", "crc\x02s\xba\x84\x84\xbb\xcd]\xefݸa\xe1\xb5\xf8\xb9W", "crc\x02`&\x9aR\xe1\xb7\xfee\x87)GQ\x03\xf4K\t"}, + {0xdb6805c0966a2f9c, 0xd4fe9ef082e69f59, "It's a tiny change to the code and not completely disgusting. - Bob Manchek", "crc\x02s\xba\x84\x84\xbb\xcd]\xefV\xba\x12\x91\x81\x1fNU", "crc\x02`&\x9aR\xe1\xb7\xfee\n\xb8\x81v?\xdeL\xcb"}, + {0xf3553c65dacdadd2, 0xe3b5e46cd8d63a4d, "size: a.out: bad magic", "crc\x02s\xba\x84\x84\xbb\xcd]\xefG\xad\xbc\xb2\xa8y\xc9\xdc", "crc\x02`&\x9aR\xe1\xb7\xfee\xcc\xce\xe5\xe6\x89p\x01\xb8"}, + {0x9d5e034087a676b9, 0x865aaf6b94f2a051, "The major problem is with sendmail. -Mark Horton", "crc\x02s\xba\x84\x84\xbb\xcd]\uf8acn\x8aT;&\xd5", "crc\x02`&\x9aR\xe1\xb7\xfeeFf\x9c\x1f\xc9x\xbfa"}, + {0xa6db2d7f8da96417, 0x7eca10d2f8136eb4, "Give me a rock, paper and scissors and I will move the world. CCFestoon", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xeb\x18\xbf\xf9}\x91\xe5|", "crc\x02`&\x9aR\xe1\xb7\xfeea\x9e\x05:\xce[\xe7\x19"}, + {0x325e00cd2fe819f9, 0xd7dd118c98e98727, "If the enemy is within range, then so are you.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef^5k\xd0Aj_{", "crc\x02`&\x9aR\xe1\xb7\xfee\v#\x99\xa8r\x83YR"}, + {0x88c6600ce58ae4c6, 0x70fb33c119c29318, "It's well we cannot hear the screams/That we create in others' dreams.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef|\xb5\x02\xdcw\x18/\x86", "crc\x02`&\x9aR\xe1\xb7\xfee]\x9d-\xed\x8c\xf9r9"}, + {0x28c4a3f3b769e078, 0x57c891e39a97d9b7, "You remind me of a TV show, but that's all right: I watch it anyway.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\x03\x8bd\x1c\xb0_\x16\x98", "crc\x02`&\x9aR\xe1\xb7\xfee\xafW\x98\xaa\"\xe7\xd7|"}, + {0xa698a34c9d9f1dca, 0xa1f46ba20ad06eb7, "C is as portable as Stonehedge!!", "crc\x02s\xba\x84\x84\xbb\xcd]\xef.P\xe1I\xc6pi\xdc", "crc\x02`&\x9aR\xe1\xb7\xfee֚\x06\x01(\xc0\x1e\x8b"}, + {0xf6c1e2a8c26c5cfc, 0x7ad25fafa1710407, "Even if I could be Shakespeare, I think I should still choose to be Faraday. - A. Huxley", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\xf7\xa04\x8a\xf2o\xe0;", "crc\x02`&\x9aR\xe1\xb7\xfee<[\xd2%\x9em\x94\x04"}, + {0xd402559dfe9b70c, 0x73cef1666185c13f, "The fugacity of a constituent in a mixture of gases at a given temperature is proportional to its mole fraction. Lewis-Randall Rule", "crc\x02s\xba\x84\x84\xbb\xcd]\xef\u007f\xae\xb9\xbaX=\x19v", "crc\x02`&\x9aR\xe1\xb7\xfee\xb2˦Y\xc5\xd0G\x03"}, + {0xdb6efff26aa94946, 0xb41858f73c389602, "How can you write a big system without C++? -Paul Glick", "crc\x02s\xba\x84\x84\xbb\xcd]\xefa\xed$js\xb9\xa5A", "crc\x02`&\x9aR\xe1\xb7\xfeeZm\x96\x8a\xe2\xaf\x13p"}, + {0xe7fcf1006b503b61, 0x27db187fc15bbc72, "This is a test of the emergency broadcast system.", "crc\x02s\xba\x84\x84\xbb\xcd]\xef}\xee[q\x16\xcb\xe4\x8d", "crc\x02`&\x9aR\xe1\xb7\xfee\xb1\x93] \xeb\xa9am"}, +} + +func TestGolden(t *testing.T) { + tabISO := MakeTable(ISO) + tabECMA := MakeTable(ECMA) + for i := 0; i < len(golden); i++ { + g := golden[i] + c := New(tabISO) + io.WriteString(c, g.in) + s := c.Sum64() + if s != g.outISO { + t.Fatalf("ISO crc64(%s) = 0x%x want 0x%x", g.in, s, g.outISO) + } + c = New(tabECMA) + io.WriteString(c, g.in) + s = c.Sum64() + if s != g.outECMA { + t.Fatalf("ECMA crc64(%s) = 0x%x want 0x%x", g.in, s, g.outECMA) + } + } +} + +func TestGoldenMarshal(t *testing.T) { + t.Run("ISO", func(t *testing.T) { + table := MakeTable(ISO) + for _, g := range golden { + h := New(table) + h2 := New(table) + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfStateISO { + t.Errorf("ISO crc64(%q) state = %q, want %q", g.in, state, g.halfStateISO) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if h.Sum64() != h2.Sum64() { + t.Errorf("ISO crc64(%s) = 0x%x != marshaled (0x%x)", g.in, h.Sum64(), h2.Sum64()) + } + } + }) + t.Run("ECMA", func(t *testing.T) { + table := MakeTable(ECMA) + for _, g := range golden { + h := New(table) + h2 := New(table) + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfStateECMA { + t.Errorf("ECMA crc64(%q) state = %q, want %q", g.in, state, g.halfStateECMA) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if h.Sum64() != h2.Sum64() { + t.Errorf("ECMA crc64(%s) = 0x%x != marshaled (0x%x)", g.in, h.Sum64(), h2.Sum64()) + } + } + }) +} + +func TestMarshalTableMismatch(t *testing.T) { + h1 := New(MakeTable(ISO)) + h2 := New(MakeTable(ECMA)) + + state1, err := h1.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state1); err == nil { + t.Errorf("no error when one was expected") + } +} + +func bench(b *testing.B, poly uint64, size int64) { + b.SetBytes(size) + data := make([]byte, size) + for i := range data { + data[i] = byte(i) + } + h := New(MakeTable(poly)) + in := make([]byte, 0, h.Size()) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + h.Reset() + h.Write(data) + h.Sum(in) + } +} + +func BenchmarkCrc64(b *testing.B) { + b.Run("ISO64KB", func(b *testing.B) { + bench(b, ISO, 64<<10) + }) + b.Run("ISO4KB", func(b *testing.B) { + bench(b, ISO, 4<<10) + }) + b.Run("ISO1KB", func(b *testing.B) { + bench(b, ISO, 1<<10) + }) + b.Run("ECMA64KB", func(b *testing.B) { + bench(b, ECMA, 64<<10) + }) + b.Run("Random64KB", func(b *testing.B) { + bench(b, 0x777, 64<<10) + }) + b.Run("Random16KB", func(b *testing.B) { + bench(b, 0x777, 16<<10) + }) +} diff --git a/src/hash/example_test.go b/src/hash/example_test.go new file mode 100644 index 0000000..f07b9aa --- /dev/null +++ b/src/hash/example_test.go @@ -0,0 +1,51 @@ +// Copyright 2017 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 hash_test + +import ( + "bytes" + "crypto/sha256" + "encoding" + "fmt" + "log" +) + +func Example_binaryMarshaler() { + const ( + input1 = "The tunneling gopher digs downwards, " + input2 = "unaware of what he will find." + ) + + first := sha256.New() + first.Write([]byte(input1)) + + marshaler, ok := first.(encoding.BinaryMarshaler) + if !ok { + log.Fatal("first does not implement encoding.BinaryMarshaler") + } + state, err := marshaler.MarshalBinary() + if err != nil { + log.Fatal("unable to marshal hash:", err) + } + + second := sha256.New() + + unmarshaler, ok := second.(encoding.BinaryUnmarshaler) + if !ok { + log.Fatal("second does not implement encoding.BinaryUnmarshaler") + } + if err := unmarshaler.UnmarshalBinary(state); err != nil { + log.Fatal("unable to unmarshal hash:", err) + } + + first.Write([]byte(input2)) + second.Write([]byte(input2)) + + fmt.Printf("%x\n", first.Sum(nil)) + fmt.Println(bytes.Equal(first.Sum(nil), second.Sum(nil))) + // Output: + // 57d51a066f3a39942649cd9a76c77e97ceab246756ff3888659e6aa5a07f4a52 + // true +} diff --git a/src/hash/fnv/fnv.go b/src/hash/fnv/fnv.go new file mode 100644 index 0000000..0fce177 --- /dev/null +++ b/src/hash/fnv/fnv.go @@ -0,0 +1,371 @@ +// 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. + +// Package fnv implements FNV-1 and FNV-1a, non-cryptographic hash functions +// created by Glenn Fowler, Landon Curt Noll, and Phong Vo. +// See +// https://en.wikipedia.org/wiki/Fowler-Noll-Vo_hash_function. +// +// All the hash.Hash implementations returned by this package also +// implement encoding.BinaryMarshaler and encoding.BinaryUnmarshaler to +// marshal and unmarshal the internal state of the hash. +package fnv + +import ( + "errors" + "hash" + "math/bits" +) + +type ( + sum32 uint32 + sum32a uint32 + sum64 uint64 + sum64a uint64 + sum128 [2]uint64 + sum128a [2]uint64 +) + +const ( + offset32 = 2166136261 + offset64 = 14695981039346656037 + offset128Lower = 0x62b821756295c58d + offset128Higher = 0x6c62272e07bb0142 + prime32 = 16777619 + prime64 = 1099511628211 + prime128Lower = 0x13b + prime128Shift = 24 +) + +// New32 returns a new 32-bit FNV-1 hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New32() hash.Hash32 { + var s sum32 = offset32 + return &s +} + +// New32a returns a new 32-bit FNV-1a hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New32a() hash.Hash32 { + var s sum32a = offset32 + return &s +} + +// New64 returns a new 64-bit FNV-1 hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New64() hash.Hash64 { + var s sum64 = offset64 + return &s +} + +// New64a returns a new 64-bit FNV-1a hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New64a() hash.Hash64 { + var s sum64a = offset64 + return &s +} + +// New128 returns a new 128-bit FNV-1 hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New128() hash.Hash { + var s sum128 + s[0] = offset128Higher + s[1] = offset128Lower + return &s +} + +// New128a returns a new 128-bit FNV-1a hash.Hash. +// Its Sum method will lay the value out in big-endian byte order. +func New128a() hash.Hash { + var s sum128a + s[0] = offset128Higher + s[1] = offset128Lower + return &s +} + +func (s *sum32) Reset() { *s = offset32 } +func (s *sum32a) Reset() { *s = offset32 } +func (s *sum64) Reset() { *s = offset64 } +func (s *sum64a) Reset() { *s = offset64 } +func (s *sum128) Reset() { s[0] = offset128Higher; s[1] = offset128Lower } +func (s *sum128a) Reset() { s[0] = offset128Higher; s[1] = offset128Lower } + +func (s *sum32) Sum32() uint32 { return uint32(*s) } +func (s *sum32a) Sum32() uint32 { return uint32(*s) } +func (s *sum64) Sum64() uint64 { return uint64(*s) } +func (s *sum64a) Sum64() uint64 { return uint64(*s) } + +func (s *sum32) Write(data []byte) (int, error) { + hash := *s + for _, c := range data { + hash *= prime32 + hash ^= sum32(c) + } + *s = hash + return len(data), nil +} + +func (s *sum32a) Write(data []byte) (int, error) { + hash := *s + for _, c := range data { + hash ^= sum32a(c) + hash *= prime32 + } + *s = hash + return len(data), nil +} + +func (s *sum64) Write(data []byte) (int, error) { + hash := *s + for _, c := range data { + hash *= prime64 + hash ^= sum64(c) + } + *s = hash + return len(data), nil +} + +func (s *sum64a) Write(data []byte) (int, error) { + hash := *s + for _, c := range data { + hash ^= sum64a(c) + hash *= prime64 + } + *s = hash + return len(data), nil +} + +func (s *sum128) Write(data []byte) (int, error) { + for _, c := range data { + // Compute the multiplication + s0, s1 := bits.Mul64(prime128Lower, s[1]) + s0 += s[1]<<prime128Shift + prime128Lower*s[0] + // Update the values + s[1] = s1 + s[0] = s0 + s[1] ^= uint64(c) + } + return len(data), nil +} + +func (s *sum128a) Write(data []byte) (int, error) { + for _, c := range data { + s[1] ^= uint64(c) + // Compute the multiplication + s0, s1 := bits.Mul64(prime128Lower, s[1]) + s0 += s[1]<<prime128Shift + prime128Lower*s[0] + // Update the values + s[1] = s1 + s[0] = s0 + } + return len(data), nil +} + +func (s *sum32) Size() int { return 4 } +func (s *sum32a) Size() int { return 4 } +func (s *sum64) Size() int { return 8 } +func (s *sum64a) Size() int { return 8 } +func (s *sum128) Size() int { return 16 } +func (s *sum128a) Size() int { return 16 } + +func (s *sum32) BlockSize() int { return 1 } +func (s *sum32a) BlockSize() int { return 1 } +func (s *sum64) BlockSize() int { return 1 } +func (s *sum64a) BlockSize() int { return 1 } +func (s *sum128) BlockSize() int { return 1 } +func (s *sum128a) BlockSize() int { return 1 } + +func (s *sum32) Sum(in []byte) []byte { + v := uint32(*s) + return append(in, byte(v>>24), byte(v>>16), byte(v>>8), byte(v)) +} + +func (s *sum32a) Sum(in []byte) []byte { + v := uint32(*s) + return append(in, byte(v>>24), byte(v>>16), byte(v>>8), byte(v)) +} + +func (s *sum64) Sum(in []byte) []byte { + v := uint64(*s) + return append(in, byte(v>>56), byte(v>>48), byte(v>>40), byte(v>>32), byte(v>>24), byte(v>>16), byte(v>>8), byte(v)) +} + +func (s *sum64a) Sum(in []byte) []byte { + v := uint64(*s) + return append(in, byte(v>>56), byte(v>>48), byte(v>>40), byte(v>>32), byte(v>>24), byte(v>>16), byte(v>>8), byte(v)) +} + +func (s *sum128) Sum(in []byte) []byte { + return append(in, + byte(s[0]>>56), byte(s[0]>>48), byte(s[0]>>40), byte(s[0]>>32), byte(s[0]>>24), byte(s[0]>>16), byte(s[0]>>8), byte(s[0]), + byte(s[1]>>56), byte(s[1]>>48), byte(s[1]>>40), byte(s[1]>>32), byte(s[1]>>24), byte(s[1]>>16), byte(s[1]>>8), byte(s[1]), + ) +} + +func (s *sum128a) Sum(in []byte) []byte { + return append(in, + byte(s[0]>>56), byte(s[0]>>48), byte(s[0]>>40), byte(s[0]>>32), byte(s[0]>>24), byte(s[0]>>16), byte(s[0]>>8), byte(s[0]), + byte(s[1]>>56), byte(s[1]>>48), byte(s[1]>>40), byte(s[1]>>32), byte(s[1]>>24), byte(s[1]>>16), byte(s[1]>>8), byte(s[1]), + ) +} + +const ( + magic32 = "fnv\x01" + magic32a = "fnv\x02" + magic64 = "fnv\x03" + magic64a = "fnv\x04" + magic128 = "fnv\x05" + magic128a = "fnv\x06" + marshaledSize32 = len(magic32) + 4 + marshaledSize64 = len(magic64) + 8 + marshaledSize128 = len(magic128) + 8*2 +) + +func (s *sum32) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize32) + b = append(b, magic32...) + b = appendUint32(b, uint32(*s)) + return b, nil +} + +func (s *sum32a) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize32) + b = append(b, magic32a...) + b = appendUint32(b, uint32(*s)) + return b, nil +} + +func (s *sum64) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize64) + b = append(b, magic64...) + b = appendUint64(b, uint64(*s)) + return b, nil + +} + +func (s *sum64a) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize64) + b = append(b, magic64a...) + b = appendUint64(b, uint64(*s)) + return b, nil +} + +func (s *sum128) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize128) + b = append(b, magic128...) + b = appendUint64(b, s[0]) + b = appendUint64(b, s[1]) + return b, nil +} + +func (s *sum128a) MarshalBinary() ([]byte, error) { + b := make([]byte, 0, marshaledSize128) + b = append(b, magic128a...) + b = appendUint64(b, s[0]) + b = appendUint64(b, s[1]) + return b, nil +} + +func (s *sum32) UnmarshalBinary(b []byte) error { + if len(b) < len(magic32) || string(b[:len(magic32)]) != magic32 { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize32 { + return errors.New("hash/fnv: invalid hash state size") + } + *s = sum32(readUint32(b[4:])) + return nil +} + +func (s *sum32a) UnmarshalBinary(b []byte) error { + if len(b) < len(magic32a) || string(b[:len(magic32a)]) != magic32a { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize32 { + return errors.New("hash/fnv: invalid hash state size") + } + *s = sum32a(readUint32(b[4:])) + return nil +} + +func (s *sum64) UnmarshalBinary(b []byte) error { + if len(b) < len(magic64) || string(b[:len(magic64)]) != magic64 { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize64 { + return errors.New("hash/fnv: invalid hash state size") + } + *s = sum64(readUint64(b[4:])) + return nil +} + +func (s *sum64a) UnmarshalBinary(b []byte) error { + if len(b) < len(magic64a) || string(b[:len(magic64a)]) != magic64a { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize64 { + return errors.New("hash/fnv: invalid hash state size") + } + *s = sum64a(readUint64(b[4:])) + return nil +} + +func (s *sum128) UnmarshalBinary(b []byte) error { + if len(b) < len(magic128) || string(b[:len(magic128)]) != magic128 { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize128 { + return errors.New("hash/fnv: invalid hash state size") + } + s[0] = readUint64(b[4:]) + s[1] = readUint64(b[12:]) + return nil +} + +func (s *sum128a) UnmarshalBinary(b []byte) error { + if len(b) < len(magic128a) || string(b[:len(magic128a)]) != magic128a { + return errors.New("hash/fnv: invalid hash state identifier") + } + if len(b) != marshaledSize128 { + return errors.New("hash/fnv: invalid hash state size") + } + s[0] = readUint64(b[4:]) + s[1] = readUint64(b[12:]) + return nil +} + +func readUint32(b []byte) uint32 { + _ = b[3] + return uint32(b[3]) | uint32(b[2])<<8 | uint32(b[1])<<16 | uint32(b[0])<<24 +} + +func appendUint32(b []byte, x uint32) []byte { + a := [4]byte{ + byte(x >> 24), + byte(x >> 16), + byte(x >> 8), + byte(x), + } + return append(b, a[:]...) +} + +func appendUint64(b []byte, x uint64) []byte { + a := [8]byte{ + byte(x >> 56), + byte(x >> 48), + byte(x >> 40), + byte(x >> 32), + byte(x >> 24), + byte(x >> 16), + byte(x >> 8), + byte(x), + } + return append(b, a[:]...) +} + +func readUint64(b []byte) uint64 { + _ = b[7] + return uint64(b[7]) | uint64(b[6])<<8 | uint64(b[5])<<16 | uint64(b[4])<<24 | + uint64(b[3])<<32 | uint64(b[2])<<40 | uint64(b[1])<<48 | uint64(b[0])<<56 +} diff --git a/src/hash/fnv/fnv_test.go b/src/hash/fnv/fnv_test.go new file mode 100644 index 0000000..7b1f7a3 --- /dev/null +++ b/src/hash/fnv/fnv_test.go @@ -0,0 +1,255 @@ +// 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. + +package fnv + +import ( + "bytes" + "encoding" + "encoding/binary" + "hash" + "io" + "testing" +) + +type golden struct { + out []byte + in string + halfState string // marshaled hash state after first half of in written, used by TestGoldenMarshal +} + +var golden32 = []golden{ + {[]byte{0x81, 0x1c, 0x9d, 0xc5}, "", "fnv\x01\x81\x1c\x9d\xc5"}, + {[]byte{0x05, 0x0c, 0x5d, 0x7e}, "a", "fnv\x01\x81\x1c\x9d\xc5"}, + {[]byte{0x70, 0x77, 0x2d, 0x38}, "ab", "fnv\x01\x05\f]~"}, + {[]byte{0x43, 0x9c, 0x2f, 0x4b}, "abc", "fnv\x01\x05\f]~"}, +} + +var golden32a = []golden{ + {[]byte{0x81, 0x1c, 0x9d, 0xc5}, "", "fnv\x02\x81\x1c\x9d\xc5"}, + {[]byte{0xe4, 0x0c, 0x29, 0x2c}, "a", "fnv\x02\x81\x1c\x9d\xc5"}, + {[]byte{0x4d, 0x25, 0x05, 0xca}, "ab", "fnv\x02\xe4\f),"}, + {[]byte{0x1a, 0x47, 0xe9, 0x0b}, "abc", "fnv\x02\xe4\f),"}, +} + +var golden64 = []golden{ + {[]byte{0xcb, 0xf2, 0x9c, 0xe4, 0x84, 0x22, 0x23, 0x25}, "", "fnv\x03\xcb\xf2\x9c\xe4\x84\"#%"}, + {[]byte{0xaf, 0x63, 0xbd, 0x4c, 0x86, 0x01, 0xb7, 0xbe}, "a", "fnv\x03\xcb\xf2\x9c\xe4\x84\"#%"}, + {[]byte{0x08, 0x32, 0x67, 0x07, 0xb4, 0xeb, 0x37, 0xb8}, "ab", "fnv\x03\xafc\xbdL\x86\x01\xb7\xbe"}, + {[]byte{0xd8, 0xdc, 0xca, 0x18, 0x6b, 0xaf, 0xad, 0xcb}, "abc", "fnv\x03\xafc\xbdL\x86\x01\xb7\xbe"}, +} + +var golden64a = []golden{ + {[]byte{0xcb, 0xf2, 0x9c, 0xe4, 0x84, 0x22, 0x23, 0x25}, "", "fnv\x04\xcb\xf2\x9c\xe4\x84\"#%"}, + {[]byte{0xaf, 0x63, 0xdc, 0x4c, 0x86, 0x01, 0xec, 0x8c}, "a", "fnv\x04\xcb\xf2\x9c\xe4\x84\"#%"}, + {[]byte{0x08, 0x9c, 0x44, 0x07, 0xb5, 0x45, 0x98, 0x6a}, "ab", "fnv\x04\xafc\xdcL\x86\x01\xec\x8c"}, + {[]byte{0xe7, 0x1f, 0xa2, 0x19, 0x05, 0x41, 0x57, 0x4b}, "abc", "fnv\x04\xafc\xdcL\x86\x01\xec\x8c"}, +} + +var golden128 = []golden{ + {[]byte{0x6c, 0x62, 0x27, 0x2e, 0x07, 0xbb, 0x01, 0x42, 0x62, 0xb8, 0x21, 0x75, 0x62, 0x95, 0xc5, 0x8d}, "", "fnv\x05lb'.\a\xbb\x01Bb\xb8!ub\x95ō"}, + {[]byte{0xd2, 0x28, 0xcb, 0x69, 0x10, 0x1a, 0x8c, 0xaf, 0x78, 0x91, 0x2b, 0x70, 0x4e, 0x4a, 0x14, 0x1e}, "a", "fnv\x05lb'.\a\xbb\x01Bb\xb8!ub\x95ō"}, + {[]byte{0x8, 0x80, 0x94, 0x5a, 0xee, 0xab, 0x1b, 0xe9, 0x5a, 0xa0, 0x73, 0x30, 0x55, 0x26, 0xc0, 0x88}, "ab", "fnv\x05\xd2(\xcbi\x10\x1a\x8c\xafx\x91+pNJ\x14\x1e"}, + {[]byte{0xa6, 0x8b, 0xb2, 0xa4, 0x34, 0x8b, 0x58, 0x22, 0x83, 0x6d, 0xbc, 0x78, 0xc6, 0xae, 0xe7, 0x3b}, "abc", "fnv\x05\xd2(\xcbi\x10\x1a\x8c\xafx\x91+pNJ\x14\x1e"}, +} + +var golden128a = []golden{ + {[]byte{0x6c, 0x62, 0x27, 0x2e, 0x07, 0xbb, 0x01, 0x42, 0x62, 0xb8, 0x21, 0x75, 0x62, 0x95, 0xc5, 0x8d}, "", "fnv\x06lb'.\a\xbb\x01Bb\xb8!ub\x95ō"}, + {[]byte{0xd2, 0x28, 0xcb, 0x69, 0x6f, 0x1a, 0x8c, 0xaf, 0x78, 0x91, 0x2b, 0x70, 0x4e, 0x4a, 0x89, 0x64}, "a", "fnv\x06lb'.\a\xbb\x01Bb\xb8!ub\x95ō"}, + {[]byte{0x08, 0x80, 0x95, 0x44, 0xbb, 0xab, 0x1b, 0xe9, 0x5a, 0xa0, 0x73, 0x30, 0x55, 0xb6, 0x9a, 0x62}, "ab", "fnv\x06\xd2(\xcbio\x1a\x8c\xafx\x91+pNJ\x89d"}, + {[]byte{0xa6, 0x8d, 0x62, 0x2c, 0xec, 0x8b, 0x58, 0x22, 0x83, 0x6d, 0xbc, 0x79, 0x77, 0xaf, 0x7f, 0x3b}, "abc", "fnv\x06\xd2(\xcbio\x1a\x8c\xafx\x91+pNJ\x89d"}, +} + +func TestGolden32(t *testing.T) { + testGolden(t, New32(), golden32) +} + +func TestGolden32a(t *testing.T) { + testGolden(t, New32a(), golden32a) +} + +func TestGolden64(t *testing.T) { + testGolden(t, New64(), golden64) +} + +func TestGolden64a(t *testing.T) { + testGolden(t, New64a(), golden64a) +} + +func TestGolden128(t *testing.T) { + testGolden(t, New128(), golden128) +} + +func TestGolden128a(t *testing.T) { + testGolden(t, New128a(), golden128a) +} + +func testGolden(t *testing.T, hash hash.Hash, gold []golden) { + for _, g := range gold { + hash.Reset() + done, error := hash.Write([]byte(g.in)) + if error != nil { + t.Fatalf("write error: %s", error) + } + if done != len(g.in) { + t.Fatalf("wrote only %d out of %d bytes", done, len(g.in)) + } + if actual := hash.Sum(nil); !bytes.Equal(g.out, actual) { + t.Errorf("hash(%q) = 0x%x want 0x%x", g.in, actual, g.out) + } + } +} + +func TestGoldenMarshal(t *testing.T) { + tests := []struct { + name string + newHash func() hash.Hash + gold []golden + }{ + {"32", func() hash.Hash { return New32() }, golden32}, + {"32a", func() hash.Hash { return New32a() }, golden32a}, + {"64", func() hash.Hash { return New64() }, golden64}, + {"64a", func() hash.Hash { return New64a() }, golden64a}, + {"128", func() hash.Hash { return New128() }, golden128}, + {"128a", func() hash.Hash { return New128a() }, golden128a}, + } + for _, tt := range tests { + t.Run(tt.name, func(t *testing.T) { + for _, g := range tt.gold { + h := tt.newHash() + h2 := tt.newHash() + + io.WriteString(h, g.in[:len(g.in)/2]) + + state, err := h.(encoding.BinaryMarshaler).MarshalBinary() + if err != nil { + t.Errorf("could not marshal: %v", err) + continue + } + + if string(state) != g.halfState { + t.Errorf("checksum(%q) state = %q, want %q", g.in, state, g.halfState) + continue + } + + if err := h2.(encoding.BinaryUnmarshaler).UnmarshalBinary(state); err != nil { + t.Errorf("could not unmarshal: %v", err) + continue + } + + io.WriteString(h, g.in[len(g.in)/2:]) + io.WriteString(h2, g.in[len(g.in)/2:]) + + if actual, actual2 := h.Sum(nil), h2.Sum(nil); !bytes.Equal(actual, actual2) { + t.Errorf("hash(%q) = 0x%x != marshaled 0x%x", g.in, actual, actual2) + } + } + }) + } +} + +func TestIntegrity32(t *testing.T) { + testIntegrity(t, New32()) +} + +func TestIntegrity32a(t *testing.T) { + testIntegrity(t, New32a()) +} + +func TestIntegrity64(t *testing.T) { + testIntegrity(t, New64()) +} + +func TestIntegrity64a(t *testing.T) { + testIntegrity(t, New64a()) +} +func TestIntegrity128(t *testing.T) { + testIntegrity(t, New128()) +} + +func TestIntegrity128a(t *testing.T) { + testIntegrity(t, New128a()) +} + +func testIntegrity(t *testing.T, h hash.Hash) { + data := []byte{'1', '2', 3, 4, 5} + h.Write(data) + sum := h.Sum(nil) + + if size := h.Size(); size != len(sum) { + t.Fatalf("Size()=%d but len(Sum())=%d", size, len(sum)) + } + + if a := h.Sum(nil); !bytes.Equal(sum, a) { + t.Fatalf("first Sum()=0x%x, second Sum()=0x%x", sum, a) + } + + h.Reset() + h.Write(data) + if a := h.Sum(nil); !bytes.Equal(sum, a) { + t.Fatalf("Sum()=0x%x, but after Reset() Sum()=0x%x", sum, a) + } + + h.Reset() + h.Write(data[:2]) + h.Write(data[2:]) + if a := h.Sum(nil); !bytes.Equal(sum, a) { + t.Fatalf("Sum()=0x%x, but with partial writes, Sum()=0x%x", sum, a) + } + + switch h.Size() { + case 4: + sum32 := h.(hash.Hash32).Sum32() + if sum32 != binary.BigEndian.Uint32(sum) { + t.Fatalf("Sum()=0x%x, but Sum32()=0x%x", sum, sum32) + } + case 8: + sum64 := h.(hash.Hash64).Sum64() + if sum64 != binary.BigEndian.Uint64(sum) { + t.Fatalf("Sum()=0x%x, but Sum64()=0x%x", sum, sum64) + } + case 16: + // There's no Sum128 function, so we don't need to test anything here. + } +} + +func BenchmarkFnv32KB(b *testing.B) { + benchmarkKB(b, New32()) +} + +func BenchmarkFnv32aKB(b *testing.B) { + benchmarkKB(b, New32a()) +} + +func BenchmarkFnv64KB(b *testing.B) { + benchmarkKB(b, New64()) +} + +func BenchmarkFnv64aKB(b *testing.B) { + benchmarkKB(b, New64a()) +} + +func BenchmarkFnv128KB(b *testing.B) { + benchmarkKB(b, New128()) +} + +func BenchmarkFnv128aKB(b *testing.B) { + benchmarkKB(b, New128a()) +} + +func benchmarkKB(b *testing.B, h hash.Hash) { + b.SetBytes(1024) + data := make([]byte, 1024) + for i := range data { + data[i] = byte(i) + } + in := make([]byte, 0, h.Size()) + + b.ResetTimer() + for i := 0; i < b.N; i++ { + h.Reset() + h.Write(data) + h.Sum(in) + } +} diff --git a/src/hash/hash.go b/src/hash/hash.go new file mode 100644 index 0000000..62cf6a4 --- /dev/null +++ b/src/hash/hash.go @@ -0,0 +1,58 @@ +// 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 hash provides interfaces for hash functions. +package hash + +import "io" + +// Hash is the common interface implemented by all hash functions. +// +// Hash implementations in the standard library (e.g. hash/crc32 and +// crypto/sha256) implement the encoding.BinaryMarshaler and +// encoding.BinaryUnmarshaler interfaces. Marshaling a hash implementation +// allows its internal state to be saved and used for additional processing +// later, without having to re-write the data previously written to the hash. +// The hash state may contain portions of the input in its original form, +// which users are expected to handle for any possible security implications. +// +// Compatibility: Any future changes to hash or crypto packages will endeavor +// to maintain compatibility with state encoded using previous versions. +// That is, any released versions of the packages should be able to +// decode data written with any previously released version, +// subject to issues such as security fixes. +// See the Go compatibility document for background: https://golang.org/doc/go1compat +type Hash interface { + // Write (via the embedded io.Writer interface) adds more data to the running hash. + // It never returns an error. + io.Writer + + // Sum appends the current hash to b and returns the resulting slice. + // It does not change the underlying hash state. + Sum(b []byte) []byte + + // Reset resets the Hash to its initial state. + Reset() + + // Size returns the number of bytes Sum will return. + Size() int + + // BlockSize returns the hash's underlying block size. + // The Write method must be able to accept any amount + // of data, but it may operate more efficiently if all writes + // are a multiple of the block size. + BlockSize() int +} + +// Hash32 is the common interface implemented by all 32-bit hash functions. +type Hash32 interface { + Hash + Sum32() uint32 +} + +// Hash64 is the common interface implemented by all 64-bit hash functions. +type Hash64 interface { + Hash + Sum64() uint64 +} diff --git a/src/hash/maphash/example_test.go b/src/hash/maphash/example_test.go new file mode 100644 index 0000000..78690fd --- /dev/null +++ b/src/hash/maphash/example_test.go @@ -0,0 +1,37 @@ +// Copyright 2020 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 maphash_test + +import ( + "fmt" + "hash/maphash" +) + +func Example() { + // The zero Hash value is valid and ready to use; setting an + // initial seed is not necessary. + var h maphash.Hash + + // Add a string to the hash, and print the current hash value. + h.WriteString("hello, ") + fmt.Printf("%#x\n", h.Sum64()) + + // Append additional data (in the form of a byte array). + h.Write([]byte{'w', 'o', 'r', 'l', 'd'}) + fmt.Printf("%#x\n", h.Sum64()) + + // Reset discards all data previously added to the Hash, without + // changing its seed. + h.Reset() + + // Use SetSeed to create a new Hash h2 which will behave + // identically to h. + var h2 maphash.Hash + h2.SetSeed(h.Seed()) + + h.WriteString("same") + h2.WriteString("same") + fmt.Printf("%#x == %#x\n", h.Sum64(), h2.Sum64()) +} diff --git a/src/hash/maphash/maphash.go b/src/hash/maphash/maphash.go new file mode 100644 index 0000000..690068a --- /dev/null +++ b/src/hash/maphash/maphash.go @@ -0,0 +1,308 @@ +// Copyright 2019 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 maphash provides hash functions on byte sequences. +// These hash functions are intended to be used to implement hash tables or +// other data structures that need to map arbitrary strings or byte +// sequences to a uniform distribution on unsigned 64-bit integers. +// Each different instance of a hash table or data structure should use its own Seed. +// +// The hash functions are not cryptographically secure. +// (See crypto/sha256 and crypto/sha512 for cryptographic use.) +package maphash + +import ( + "unsafe" +) + +// A Seed is a random value that selects the specific hash function +// computed by a Hash. If two Hashes use the same Seeds, they +// will compute the same hash values for any given input. +// If two Hashes use different Seeds, they are very likely to compute +// distinct hash values for any given input. +// +// A Seed must be initialized by calling MakeSeed. +// The zero seed is uninitialized and not valid for use with Hash's SetSeed method. +// +// Each Seed value is local to a single process and cannot be serialized +// or otherwise recreated in a different process. +type Seed struct { + s uint64 +} + +// Bytes returns the hash of b with the given seed. +// +// Bytes is equivalent to, but more convenient and efficient than: +// +// var h Hash +// h.SetSeed(seed) +// h.Write(b) +// return h.Sum64() +func Bytes(seed Seed, b []byte) uint64 { + state := seed.s + if state == 0 { + panic("maphash: use of uninitialized Seed") + } + if len(b) == 0 { + return rthash(nil, 0, state) // avoid &b[0] index panic below + } + if len(b) > bufSize { + b = b[:len(b):len(b)] // merge len and cap calculations when reslicing + for len(b) > bufSize { + state = rthash(&b[0], bufSize, state) + b = b[bufSize:] + } + } + return rthash(&b[0], len(b), state) +} + +// String returns the hash of s with the given seed. +// +// String is equivalent to, but more convenient and efficient than: +// +// var h Hash +// h.SetSeed(seed) +// h.WriteString(s) +// return h.Sum64() +func String(seed Seed, s string) uint64 { + state := seed.s + if state == 0 { + panic("maphash: use of uninitialized Seed") + } + for len(s) > bufSize { + p := (*byte)(unsafe.StringData(s)) + state = rthash(p, bufSize, state) + s = s[bufSize:] + } + p := (*byte)(unsafe.StringData(s)) + return rthash(p, len(s), state) +} + +// A Hash computes a seeded hash of a byte sequence. +// +// The zero Hash is a valid Hash ready to use. +// A zero Hash chooses a random seed for itself during +// the first call to a Reset, Write, Seed, or Sum64 method. +// For control over the seed, use SetSeed. +// +// The computed hash values depend only on the initial seed and +// the sequence of bytes provided to the Hash object, not on the way +// in which the bytes are provided. For example, the three sequences +// +// h.Write([]byte{'f','o','o'}) +// h.WriteByte('f'); h.WriteByte('o'); h.WriteByte('o') +// h.WriteString("foo") +// +// all have the same effect. +// +// Hashes are intended to be collision-resistant, even for situations +// where an adversary controls the byte sequences being hashed. +// +// A Hash is not safe for concurrent use by multiple goroutines, but a Seed is. +// If multiple goroutines must compute the same seeded hash, +// each can declare its own Hash and call SetSeed with a common Seed. +type Hash struct { + _ [0]func() // not comparable + seed Seed // initial seed used for this hash + state Seed // current hash of all flushed bytes + buf [bufSize]byte // unflushed byte buffer + n int // number of unflushed bytes +} + +// bufSize is the size of the Hash write buffer. +// The buffer ensures that writes depend only on the sequence of bytes, +// not the sequence of WriteByte/Write/WriteString calls, +// by always calling rthash with a full buffer (except for the tail). +const bufSize = 128 + +// initSeed seeds the hash if necessary. +// initSeed is called lazily before any operation that actually uses h.seed/h.state. +// Note that this does not include Write/WriteByte/WriteString in the case +// where they only add to h.buf. (If they write too much, they call h.flush, +// which does call h.initSeed.) +func (h *Hash) initSeed() { + if h.seed.s == 0 { + seed := MakeSeed() + h.seed = seed + h.state = seed + } +} + +// WriteByte adds b to the sequence of bytes hashed by h. +// It never fails; the error result is for implementing io.ByteWriter. +func (h *Hash) WriteByte(b byte) error { + if h.n == len(h.buf) { + h.flush() + } + h.buf[h.n] = b + h.n++ + return nil +} + +// Write adds b to the sequence of bytes hashed by h. +// It always writes all of b and never fails; the count and error result are for implementing io.Writer. +func (h *Hash) Write(b []byte) (int, error) { + size := len(b) + // Deal with bytes left over in h.buf. + // h.n <= bufSize is always true. + // Checking it is ~free and it lets the compiler eliminate a bounds check. + if h.n > 0 && h.n <= bufSize { + k := copy(h.buf[h.n:], b) + h.n += k + if h.n < bufSize { + // Copied the entirety of b to h.buf. + return size, nil + } + b = b[k:] + h.flush() + // No need to set h.n = 0 here; it happens just before exit. + } + // Process as many full buffers as possible, without copying, and calling initSeed only once. + if len(b) > bufSize { + h.initSeed() + for len(b) > bufSize { + h.state.s = rthash(&b[0], bufSize, h.state.s) + b = b[bufSize:] + } + } + // Copy the tail. + copy(h.buf[:], b) + h.n = len(b) + return size, nil +} + +// WriteString adds the bytes of s to the sequence of bytes hashed by h. +// It always writes all of s and never fails; the count and error result are for implementing io.StringWriter. +func (h *Hash) WriteString(s string) (int, error) { + // WriteString mirrors Write. See Write for comments. + size := len(s) + if h.n > 0 && h.n <= bufSize { + k := copy(h.buf[h.n:], s) + h.n += k + if h.n < bufSize { + return size, nil + } + s = s[k:] + h.flush() + } + if len(s) > bufSize { + h.initSeed() + for len(s) > bufSize { + ptr := (*byte)(unsafe.StringData(s)) + h.state.s = rthash(ptr, bufSize, h.state.s) + s = s[bufSize:] + } + } + copy(h.buf[:], s) + h.n = len(s) + return size, nil +} + +// Seed returns h's seed value. +func (h *Hash) Seed() Seed { + h.initSeed() + return h.seed +} + +// SetSeed sets h to use seed, which must have been returned by MakeSeed +// or by another Hash's Seed method. +// Two Hash objects with the same seed behave identically. +// Two Hash objects with different seeds will very likely behave differently. +// Any bytes added to h before this call will be discarded. +func (h *Hash) SetSeed(seed Seed) { + if seed.s == 0 { + panic("maphash: use of uninitialized Seed") + } + h.seed = seed + h.state = seed + h.n = 0 +} + +// Reset discards all bytes added to h. +// (The seed remains the same.) +func (h *Hash) Reset() { + h.initSeed() + h.state = h.seed + h.n = 0 +} + +// precondition: buffer is full. +func (h *Hash) flush() { + if h.n != len(h.buf) { + panic("maphash: flush of partially full buffer") + } + h.initSeed() + h.state.s = rthash(&h.buf[0], h.n, h.state.s) + h.n = 0 +} + +// Sum64 returns h's current 64-bit value, which depends on +// h's seed and the sequence of bytes added to h since the +// last call to Reset or SetSeed. +// +// All bits of the Sum64 result are close to uniformly and +// independently distributed, so it can be safely reduced +// by using bit masking, shifting, or modular arithmetic. +func (h *Hash) Sum64() uint64 { + h.initSeed() + return rthash(&h.buf[0], h.n, h.state.s) +} + +// MakeSeed returns a new random seed. +func MakeSeed() Seed { + var s uint64 + for { + s = runtime_fastrand64() + // We use seed 0 to indicate an uninitialized seed/hash, + // so keep trying until we get a non-zero seed. + if s != 0 { + break + } + } + return Seed{s: s} +} + +//go:linkname runtime_fastrand64 runtime.fastrand64 +func runtime_fastrand64() uint64 + +func rthash(ptr *byte, len int, seed uint64) uint64 { + if len == 0 { + return seed + } + // The runtime hasher only works on uintptr. For 64-bit + // architectures, we use the hasher directly. Otherwise, + // we use two parallel hashers on the lower and upper 32 bits. + if unsafe.Sizeof(uintptr(0)) == 8 { + return uint64(runtime_memhash(unsafe.Pointer(ptr), uintptr(seed), uintptr(len))) + } + lo := runtime_memhash(unsafe.Pointer(ptr), uintptr(seed), uintptr(len)) + hi := runtime_memhash(unsafe.Pointer(ptr), uintptr(seed>>32), uintptr(len)) + return uint64(hi)<<32 | uint64(lo) +} + +//go:linkname runtime_memhash runtime.memhash +//go:noescape +func runtime_memhash(p unsafe.Pointer, seed, s uintptr) uintptr + +// Sum appends the hash's current 64-bit value to b. +// It exists for implementing hash.Hash. +// For direct calls, it is more efficient to use Sum64. +func (h *Hash) Sum(b []byte) []byte { + x := h.Sum64() + return append(b, + byte(x>>0), + byte(x>>8), + byte(x>>16), + byte(x>>24), + byte(x>>32), + byte(x>>40), + byte(x>>48), + byte(x>>56)) +} + +// Size returns h's hash value size, 8 bytes. +func (h *Hash) Size() int { return 8 } + +// BlockSize returns h's block size. +func (h *Hash) BlockSize() int { return len(h.buf) } diff --git a/src/hash/maphash/maphash_test.go b/src/hash/maphash/maphash_test.go new file mode 100644 index 0000000..7526989 --- /dev/null +++ b/src/hash/maphash/maphash_test.go @@ -0,0 +1,255 @@ +// Copyright 2019 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 maphash + +import ( + "bytes" + "fmt" + "hash" + "testing" +) + +func TestUnseededHash(t *testing.T) { + m := map[uint64]struct{}{} + for i := 0; i < 1000; i++ { + h := new(Hash) + m[h.Sum64()] = struct{}{} + } + if len(m) < 900 { + t.Errorf("empty hash not sufficiently random: got %d, want 1000", len(m)) + } +} + +func TestSeededHash(t *testing.T) { + s := MakeSeed() + m := map[uint64]struct{}{} + for i := 0; i < 1000; i++ { + h := new(Hash) + h.SetSeed(s) + m[h.Sum64()] = struct{}{} + } + if len(m) != 1 { + t.Errorf("seeded hash is random: got %d, want 1", len(m)) + } +} + +func TestHashGrouping(t *testing.T) { + b := bytes.Repeat([]byte("foo"), 100) + hh := make([]*Hash, 7) + for i := range hh { + hh[i] = new(Hash) + } + for _, h := range hh[1:] { + h.SetSeed(hh[0].Seed()) + } + hh[0].Write(b) + hh[1].WriteString(string(b)) + + writeByte := func(h *Hash, b byte) { + err := h.WriteByte(b) + if err != nil { + t.Fatalf("WriteByte: %v", err) + } + } + writeSingleByte := func(h *Hash, b byte) { + _, err := h.Write([]byte{b}) + if err != nil { + t.Fatalf("Write single byte: %v", err) + } + } + writeStringSingleByte := func(h *Hash, b byte) { + _, err := h.WriteString(string([]byte{b})) + if err != nil { + t.Fatalf("WriteString single byte: %v", err) + } + } + + for i, x := range b { + writeByte(hh[2], x) + writeSingleByte(hh[3], x) + if i == 0 { + writeByte(hh[4], x) + } else { + writeSingleByte(hh[4], x) + } + writeStringSingleByte(hh[5], x) + if i == 0 { + writeByte(hh[6], x) + } else { + writeStringSingleByte(hh[6], x) + } + } + + sum := hh[0].Sum64() + for i, h := range hh { + if sum != h.Sum64() { + t.Errorf("hash %d not identical to a single Write", i) + } + } + + if sum1 := Bytes(hh[0].Seed(), b); sum1 != hh[0].Sum64() { + t.Errorf("hash using Bytes not identical to a single Write") + } + + if sum1 := String(hh[0].Seed(), string(b)); sum1 != hh[0].Sum64() { + t.Errorf("hash using String not identical to a single Write") + } +} + +func TestHashBytesVsString(t *testing.T) { + s := "foo" + b := []byte(s) + h1 := new(Hash) + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + n1, err1 := h1.WriteString(s) + if n1 != len(s) || err1 != nil { + t.Fatalf("WriteString(s) = %d, %v, want %d, nil", n1, err1, len(s)) + } + n2, err2 := h2.Write(b) + if n2 != len(b) || err2 != nil { + t.Fatalf("Write(b) = %d, %v, want %d, nil", n2, err2, len(b)) + } + if h1.Sum64() != h2.Sum64() { + t.Errorf("hash of string and bytes not identical") + } +} + +func TestHashHighBytes(t *testing.T) { + // See issue 34925. + const N = 10 + m := map[uint64]struct{}{} + for i := 0; i < N; i++ { + h := new(Hash) + h.WriteString("foo") + m[h.Sum64()>>32] = struct{}{} + } + if len(m) < N/2 { + t.Errorf("from %d seeds, wanted at least %d different hashes; got %d", N, N/2, len(m)) + } +} + +func TestRepeat(t *testing.T) { + h1 := new(Hash) + h1.WriteString("testing") + sum1 := h1.Sum64() + + h1.Reset() + h1.WriteString("testing") + sum2 := h1.Sum64() + + if sum1 != sum2 { + t.Errorf("different sum after reseting: %#x != %#x", sum1, sum2) + } + + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + h2.WriteString("testing") + sum3 := h2.Sum64() + + if sum1 != sum3 { + t.Errorf("different sum on the same seed: %#x != %#x", sum1, sum3) + } +} + +func TestSeedFromSum64(t *testing.T) { + h1 := new(Hash) + h1.WriteString("foo") + x := h1.Sum64() // seed generated here + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + h2.WriteString("foo") + y := h2.Sum64() + if x != y { + t.Errorf("hashes don't match: want %x, got %x", x, y) + } +} + +func TestSeedFromSeed(t *testing.T) { + h1 := new(Hash) + h1.WriteString("foo") + _ = h1.Seed() // seed generated here + x := h1.Sum64() + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + h2.WriteString("foo") + y := h2.Sum64() + if x != y { + t.Errorf("hashes don't match: want %x, got %x", x, y) + } +} + +func TestSeedFromFlush(t *testing.T) { + b := make([]byte, 65) + h1 := new(Hash) + h1.Write(b) // seed generated here + x := h1.Sum64() + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + h2.Write(b) + y := h2.Sum64() + if x != y { + t.Errorf("hashes don't match: want %x, got %x", x, y) + } +} + +func TestSeedFromReset(t *testing.T) { + h1 := new(Hash) + h1.WriteString("foo") + h1.Reset() // seed generated here + h1.WriteString("foo") + x := h1.Sum64() + h2 := new(Hash) + h2.SetSeed(h1.Seed()) + h2.WriteString("foo") + y := h2.Sum64() + if x != y { + t.Errorf("hashes don't match: want %x, got %x", x, y) + } +} + +// Make sure a Hash implements the hash.Hash and hash.Hash64 interfaces. +var _ hash.Hash = &Hash{} +var _ hash.Hash64 = &Hash{} + +func benchmarkSize(b *testing.B, size int) { + h := &Hash{} + buf := make([]byte, size) + s := string(buf) + + b.Run("Write", func(b *testing.B) { + b.SetBytes(int64(size)) + for i := 0; i < b.N; i++ { + h.Reset() + h.Write(buf) + h.Sum64() + } + }) + + b.Run("Bytes", func(b *testing.B) { + b.SetBytes(int64(size)) + seed := h.Seed() + for i := 0; i < b.N; i++ { + Bytes(seed, buf) + } + }) + + b.Run("String", func(b *testing.B) { + b.SetBytes(int64(size)) + seed := h.Seed() + for i := 0; i < b.N; i++ { + String(seed, s) + } + }) +} + +func BenchmarkHash(b *testing.B) { + sizes := []int{4, 8, 16, 32, 64, 256, 320, 1024, 4096, 16384} + for _, size := range sizes { + b.Run(fmt.Sprint("n=", size), func(b *testing.B) { + benchmarkSize(b, size) + }) + } +} diff --git a/src/hash/maphash/smhasher_test.go b/src/hash/maphash/smhasher_test.go new file mode 100644 index 0000000..27cedc4 --- /dev/null +++ b/src/hash/maphash/smhasher_test.go @@ -0,0 +1,474 @@ +// Copyright 2019 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. + +//go:build !race + +package maphash + +import ( + "fmt" + "math" + "math/rand" + "runtime" + "strings" + "testing" + "unsafe" +) + +// Smhasher is a torture test for hash functions. +// https://code.google.com/p/smhasher/ +// This code is a port of some of the Smhasher tests to Go. + +// Note: due to the long running time of these tests, they are +// currently disabled in -race mode. + +var fixedSeed = MakeSeed() + +// Sanity checks. +// hash should not depend on values outside key. +// hash should not depend on alignment. +func TestSmhasherSanity(t *testing.T) { + r := rand.New(rand.NewSource(1234)) + const REP = 10 + const KEYMAX = 128 + const PAD = 16 + const OFFMAX = 16 + for k := 0; k < REP; k++ { + for n := 0; n < KEYMAX; n++ { + for i := 0; i < OFFMAX; i++ { + var b [KEYMAX + OFFMAX + 2*PAD]byte + var c [KEYMAX + OFFMAX + 2*PAD]byte + randBytes(r, b[:]) + randBytes(r, c[:]) + copy(c[PAD+i:PAD+i+n], b[PAD:PAD+n]) + if bytesHash(b[PAD:PAD+n]) != bytesHash(c[PAD+i:PAD+i+n]) { + t.Errorf("hash depends on bytes outside key") + } + } + } + } +} + +func bytesHash(b []byte) uint64 { + var h Hash + h.SetSeed(fixedSeed) + h.Write(b) + return h.Sum64() +} +func stringHash(s string) uint64 { + var h Hash + h.SetSeed(fixedSeed) + h.WriteString(s) + return h.Sum64() +} + +const hashSize = 64 + +func randBytes(r *rand.Rand, b []byte) { + r.Read(b) // can't fail +} + +// A hashSet measures the frequency of hash collisions. +type hashSet struct { + m map[uint64]struct{} // set of hashes added + n int // number of hashes added +} + +func newHashSet() *hashSet { + return &hashSet{make(map[uint64]struct{}), 0} +} +func (s *hashSet) add(h uint64) { + s.m[h] = struct{}{} + s.n++ +} +func (s *hashSet) addS(x string) { + s.add(stringHash(x)) +} +func (s *hashSet) addB(x []byte) { + s.add(bytesHash(x)) +} +func (s *hashSet) addS_seed(x string, seed Seed) { + var h Hash + h.SetSeed(seed) + h.WriteString(x) + s.add(h.Sum64()) +} +func (s *hashSet) check(t *testing.T) { + const SLOP = 10.0 + collisions := s.n - len(s.m) + pairs := int64(s.n) * int64(s.n-1) / 2 + expected := float64(pairs) / math.Pow(2.0, float64(hashSize)) + stddev := math.Sqrt(expected) + if float64(collisions) > expected+SLOP*(3*stddev+1) { + t.Errorf("unexpected number of collisions: got=%d mean=%f stddev=%f", collisions, expected, stddev) + } +} + +// a string plus adding zeros must make distinct hashes +func TestSmhasherAppendedZeros(t *testing.T) { + s := "hello" + strings.Repeat("\x00", 256) + h := newHashSet() + for i := 0; i <= len(s); i++ { + h.addS(s[:i]) + } + h.check(t) +} + +// All 0-3 byte strings have distinct hashes. +func TestSmhasherSmallKeys(t *testing.T) { + h := newHashSet() + var b [3]byte + for i := 0; i < 256; i++ { + b[0] = byte(i) + h.addB(b[:1]) + for j := 0; j < 256; j++ { + b[1] = byte(j) + h.addB(b[:2]) + if !testing.Short() { + for k := 0; k < 256; k++ { + b[2] = byte(k) + h.addB(b[:3]) + } + } + } + } + h.check(t) +} + +// Different length strings of all zeros have distinct hashes. +func TestSmhasherZeros(t *testing.T) { + N := 256 * 1024 + if testing.Short() { + N = 1024 + } + h := newHashSet() + b := make([]byte, N) + for i := 0; i <= N; i++ { + h.addB(b[:i]) + } + h.check(t) +} + +// Strings with up to two nonzero bytes all have distinct hashes. +func TestSmhasherTwoNonzero(t *testing.T) { + if runtime.GOARCH == "wasm" { + t.Skip("Too slow on wasm") + } + if testing.Short() { + t.Skip("Skipping in short mode") + } + h := newHashSet() + for n := 2; n <= 16; n++ { + twoNonZero(h, n) + } + h.check(t) +} +func twoNonZero(h *hashSet, n int) { + b := make([]byte, n) + + // all zero + h.addB(b) + + // one non-zero byte + for i := 0; i < n; i++ { + for x := 1; x < 256; x++ { + b[i] = byte(x) + h.addB(b) + b[i] = 0 + } + } + + // two non-zero bytes + for i := 0; i < n; i++ { + for x := 1; x < 256; x++ { + b[i] = byte(x) + for j := i + 1; j < n; j++ { + for y := 1; y < 256; y++ { + b[j] = byte(y) + h.addB(b) + b[j] = 0 + } + } + b[i] = 0 + } + } +} + +// Test strings with repeats, like "abcdabcdabcdabcd..." +func TestSmhasherCyclic(t *testing.T) { + if testing.Short() { + t.Skip("Skipping in short mode") + } + r := rand.New(rand.NewSource(1234)) + const REPEAT = 8 + const N = 1000000 + for n := 4; n <= 12; n++ { + h := newHashSet() + b := make([]byte, REPEAT*n) + for i := 0; i < N; i++ { + b[0] = byte(i * 79 % 97) + b[1] = byte(i * 43 % 137) + b[2] = byte(i * 151 % 197) + b[3] = byte(i * 199 % 251) + randBytes(r, b[4:n]) + for j := n; j < n*REPEAT; j++ { + b[j] = b[j-n] + } + h.addB(b) + } + h.check(t) + } +} + +// Test strings with only a few bits set +func TestSmhasherSparse(t *testing.T) { + if runtime.GOARCH == "wasm" { + t.Skip("Too slow on wasm") + } + if testing.Short() { + t.Skip("Skipping in short mode") + } + sparse(t, 32, 6) + sparse(t, 40, 6) + sparse(t, 48, 5) + sparse(t, 56, 5) + sparse(t, 64, 5) + sparse(t, 96, 4) + sparse(t, 256, 3) + sparse(t, 2048, 2) +} +func sparse(t *testing.T, n int, k int) { + b := make([]byte, n/8) + h := newHashSet() + setbits(h, b, 0, k) + h.check(t) +} + +// set up to k bits at index i and greater +func setbits(h *hashSet, b []byte, i int, k int) { + h.addB(b) + if k == 0 { + return + } + for j := i; j < len(b)*8; j++ { + b[j/8] |= byte(1 << uint(j&7)) + setbits(h, b, j+1, k-1) + b[j/8] &= byte(^(1 << uint(j&7))) + } +} + +// Test all possible combinations of n blocks from the set s. +// "permutation" is a bad name here, but it is what Smhasher uses. +func TestSmhasherPermutation(t *testing.T) { + if runtime.GOARCH == "wasm" { + t.Skip("Too slow on wasm") + } + if testing.Short() { + t.Skip("Skipping in short mode") + } + permutation(t, []uint32{0, 1, 2, 3, 4, 5, 6, 7}, 8) + permutation(t, []uint32{0, 1 << 29, 2 << 29, 3 << 29, 4 << 29, 5 << 29, 6 << 29, 7 << 29}, 8) + permutation(t, []uint32{0, 1}, 20) + permutation(t, []uint32{0, 1 << 31}, 20) + permutation(t, []uint32{0, 1, 2, 3, 4, 5, 6, 7, 1 << 29, 2 << 29, 3 << 29, 4 << 29, 5 << 29, 6 << 29, 7 << 29}, 6) +} +func permutation(t *testing.T, s []uint32, n int) { + b := make([]byte, n*4) + h := newHashSet() + genPerm(h, b, s, 0) + h.check(t) +} +func genPerm(h *hashSet, b []byte, s []uint32, n int) { + h.addB(b[:n]) + if n == len(b) { + return + } + for _, v := range s { + b[n] = byte(v) + b[n+1] = byte(v >> 8) + b[n+2] = byte(v >> 16) + b[n+3] = byte(v >> 24) + genPerm(h, b, s, n+4) + } +} + +type key interface { + clear() // set bits all to 0 + random(r *rand.Rand) // set key to something random + bits() int // how many bits key has + flipBit(i int) // flip bit i of the key + hash() uint64 // hash the key + name() string // for error reporting +} + +type bytesKey struct { + b []byte +} + +func (k *bytesKey) clear() { + for i := range k.b { + k.b[i] = 0 + } +} +func (k *bytesKey) random(r *rand.Rand) { + randBytes(r, k.b) +} +func (k *bytesKey) bits() int { + return len(k.b) * 8 +} +func (k *bytesKey) flipBit(i int) { + k.b[i>>3] ^= byte(1 << uint(i&7)) +} +func (k *bytesKey) hash() uint64 { + return bytesHash(k.b) +} +func (k *bytesKey) name() string { + return fmt.Sprintf("bytes%d", len(k.b)) +} + +// Flipping a single bit of a key should flip each output bit with 50% probability. +func TestSmhasherAvalanche(t *testing.T) { + if runtime.GOARCH == "wasm" { + t.Skip("Too slow on wasm") + } + if testing.Short() { + t.Skip("Skipping in short mode") + } + avalancheTest1(t, &bytesKey{make([]byte, 2)}) + avalancheTest1(t, &bytesKey{make([]byte, 4)}) + avalancheTest1(t, &bytesKey{make([]byte, 8)}) + avalancheTest1(t, &bytesKey{make([]byte, 16)}) + avalancheTest1(t, &bytesKey{make([]byte, 32)}) + avalancheTest1(t, &bytesKey{make([]byte, 200)}) +} +func avalancheTest1(t *testing.T, k key) { + const REP = 100000 + r := rand.New(rand.NewSource(1234)) + n := k.bits() + + // grid[i][j] is a count of whether flipping + // input bit i affects output bit j. + grid := make([][hashSize]int, n) + + for z := 0; z < REP; z++ { + // pick a random key, hash it + k.random(r) + h := k.hash() + + // flip each bit, hash & compare the results + for i := 0; i < n; i++ { + k.flipBit(i) + d := h ^ k.hash() + k.flipBit(i) + + // record the effects of that bit flip + g := &grid[i] + for j := 0; j < hashSize; j++ { + g[j] += int(d & 1) + d >>= 1 + } + } + } + + // Each entry in the grid should be about REP/2. + // More precisely, we did N = k.bits() * hashSize experiments where + // each is the sum of REP coin flips. We want to find bounds on the + // sum of coin flips such that a truly random experiment would have + // all sums inside those bounds with 99% probability. + N := n * hashSize + var c float64 + // find c such that Prob(mean-c*stddev < x < mean+c*stddev)^N > .9999 + for c = 0.0; math.Pow(math.Erf(c/math.Sqrt(2)), float64(N)) < .9999; c += .1 { + } + c *= 4.0 // allowed slack - we don't need to be perfectly random + mean := .5 * REP + stddev := .5 * math.Sqrt(REP) + low := int(mean - c*stddev) + high := int(mean + c*stddev) + for i := 0; i < n; i++ { + for j := 0; j < hashSize; j++ { + x := grid[i][j] + if x < low || x > high { + t.Errorf("bad bias for %s bit %d -> bit %d: %d/%d\n", k.name(), i, j, x, REP) + } + } + } +} + +// All bit rotations of a set of distinct keys +func TestSmhasherWindowed(t *testing.T) { + windowed(t, &bytesKey{make([]byte, 128)}) +} +func windowed(t *testing.T, k key) { + if runtime.GOARCH == "wasm" { + t.Skip("Too slow on wasm") + } + if testing.Short() { + t.Skip("Skipping in short mode") + } + const BITS = 16 + + for r := 0; r < k.bits(); r++ { + h := newHashSet() + for i := 0; i < 1<<BITS; i++ { + k.clear() + for j := 0; j < BITS; j++ { + if i>>uint(j)&1 != 0 { + k.flipBit((j + r) % k.bits()) + } + } + h.add(k.hash()) + } + h.check(t) + } +} + +// All keys of the form prefix + [A-Za-z0-9]*N + suffix. +func TestSmhasherText(t *testing.T) { + if testing.Short() { + t.Skip("Skipping in short mode") + } + text(t, "Foo", "Bar") + text(t, "FooBar", "") + text(t, "", "FooBar") +} +func text(t *testing.T, prefix, suffix string) { + const N = 4 + const S = "ABCDEFGHIJKLMNOPQRSTabcdefghijklmnopqrst0123456789" + const L = len(S) + b := make([]byte, len(prefix)+N+len(suffix)) + copy(b, prefix) + copy(b[len(prefix)+N:], suffix) + h := newHashSet() + c := b[len(prefix):] + for i := 0; i < L; i++ { + c[0] = S[i] + for j := 0; j < L; j++ { + c[1] = S[j] + for k := 0; k < L; k++ { + c[2] = S[k] + for x := 0; x < L; x++ { + c[3] = S[x] + h.addB(b) + } + } + } + } + h.check(t) +} + +// Make sure different seed values generate different hashes. +func TestSmhasherSeed(t *testing.T) { + if unsafe.Sizeof(uintptr(0)) == 4 { + t.Skip("32-bit platforms don't have ideal seed-input distributions (see issue 33988)") + } + h := newHashSet() + const N = 100000 + s := "hello" + for i := 0; i < N; i++ { + h.addS_seed(s, Seed{s: uint64(i + 1)}) + h.addS_seed(s, Seed{s: uint64(i+1) << 32}) // make sure high bits are used + } + h.check(t) +} diff --git a/src/hash/marshal_test.go b/src/hash/marshal_test.go new file mode 100644 index 0000000..3091f7a --- /dev/null +++ b/src/hash/marshal_test.go @@ -0,0 +1,107 @@ +// Copyright 2017 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. + +// Test that the hashes in the standard library implement +// BinaryMarshaler, BinaryUnmarshaler, +// and lock in the current representations. + +package hash_test + +import ( + "bytes" + "crypto/md5" + "crypto/sha1" + "crypto/sha256" + "crypto/sha512" + "encoding" + "encoding/hex" + "hash" + "hash/adler32" + "hash/crc32" + "hash/crc64" + "hash/fnv" + "testing" +) + +func fromHex(s string) []byte { + b, err := hex.DecodeString(s) + if err != nil { + panic(err) + } + return b +} + +var marshalTests = []struct { + name string + new func() hash.Hash + golden []byte +}{ + {"adler32", func() hash.Hash { return adler32.New() }, fromHex("61646c01460a789d")}, + {"crc32", func() hash.Hash { return crc32.NewIEEE() }, fromHex("63726301ca87914dc956d3e8")}, + {"crc64", func() hash.Hash { return crc64.New(crc64.MakeTable(crc64.ISO)) }, fromHex("6372630273ba8484bbcd5def5d51c83c581695be")}, + {"fnv32", func() hash.Hash { return fnv.New32() }, fromHex("666e760171ba3d77")}, + {"fnv32a", func() hash.Hash { return fnv.New32a() }, fromHex("666e76027439f86f")}, + {"fnv64", func() hash.Hash { return fnv.New64() }, fromHex("666e7603cc64e0e97692c637")}, + {"fnv64a", func() hash.Hash { return fnv.New64a() }, fromHex("666e7604c522af9b0dede66f")}, + {"fnv128", func() hash.Hash { return fnv.New128() }, fromHex("666e760561587a70a0f66d7981dc980e2cabbaf7")}, + {"fnv128a", func() hash.Hash { return fnv.New128a() }, fromHex("666e7606a955802b0136cb67622b461d9f91e6ff")}, + {"md5", md5.New, fromHex("6d643501a91b0023007aa14740a3979210b5f024c0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha1", sha1.New, fromHex("736861016dad5acb4dc003952f7a0b352ee5537ec381a228c0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha224", sha256.New224, fromHex("73686102f8b92fc047c9b4d82f01a6370841277b7a0d92108440178c83db855a8e66c2d9c0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha256", sha256.New, fromHex("736861032bed68b99987cae48183b2b049d393d0050868e4e8ba3730e9112b08765929b7c0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha384", sha512.New384, fromHex("736861046f1664d213dd802f7c47bc50637cf93592570a2b8695839148bf38341c6eacd05326452ef1cbe64d90f1ef73bb5ac7d2803565467d0ddb10c5ee3fc050f9f0c1808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha512_224", sha512.New512_224, fromHex("736861056f1a450ec15af20572d0d1ee6518104d7cbbbe79a038557af5450ed7dbd420b53b7335209e951b4d9aff401f90549b9604fa3d823fbb8581c73582a88aa84022808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha512_256", sha512.New512_256, fromHex("736861067c541f1d1a72536b1f5dad64026bcc7c508f8a2126b51f46f8b9bff63a26fee70980718031e96832e95547f4fe76160ff84076db53b4549b86354af8e17b5116808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, + {"sha512", sha512.New, fromHex("736861078e03953cd57cd6879321270afa70c5827bb5b69be59a8f0130147e94f2aedf7bdc01c56c92343ca8bd837bb7f0208f5a23e155694516b6f147099d491a30b151808182838485868788898a8b8c8d8e8f909192939495969798999a9b9c9d9e9fa0a1a2a3a4a5a6a7a8a9aaabacadaeafb0b1b2b3b4b5b6b7b8b9babbbcbdbebfc0c1c2c3c4c5c6c7c8c9cacbcccdcecfd0d1d2d3d4d5d6d7d8d9dadbdcdddedfe0e1e2e3e4e5e6e7e8e9eaebecedeeeff0f1f2f3f4f5f6f7f80000000000000000000000000000f9")}, +} + +func TestMarshalHash(t *testing.T) { + for _, tt := range marshalTests { + t.Run(tt.name, func(t *testing.T) { + buf := make([]byte, 256) + for i := range buf { + buf[i] = byte(i) + } + + h := tt.new() + h.Write(buf[:256]) + sum := h.Sum(nil) + + h2 := tt.new() + h3 := tt.new() + const split = 249 + for i := 0; i < split; i++ { + h2.Write(buf[i : i+1]) + } + h2m, ok := h2.(encoding.BinaryMarshaler) + if !ok { + t.Fatalf("Hash does not implement MarshalBinary") + } + enc, err := h2m.MarshalBinary() + if err != nil { + t.Fatalf("MarshalBinary: %v", err) + } + if !bytes.Equal(enc, tt.golden) { + t.Errorf("MarshalBinary = %x, want %x", enc, tt.golden) + } + h3u, ok := h3.(encoding.BinaryUnmarshaler) + if !ok { + t.Fatalf("Hash does not implement UnmarshalBinary") + } + if err := h3u.UnmarshalBinary(enc); err != nil { + t.Fatalf("UnmarshalBinary: %v", err) + } + h2.Write(buf[split:]) + h3.Write(buf[split:]) + sum2 := h2.Sum(nil) + sum3 := h3.Sum(nil) + if !bytes.Equal(sum2, sum) { + t.Fatalf("Sum after MarshalBinary = %x, want %x", sum2, sum) + } + if !bytes.Equal(sum3, sum) { + t.Fatalf("Sum after UnmarshalBinary = %x, want %x", sum3, sum) + } + }) + } +} diff --git a/src/hash/test_cases.txt b/src/hash/test_cases.txt new file mode 100644 index 0000000..26d3ccc --- /dev/null +++ b/src/hash/test_cases.txt @@ -0,0 +1,31 @@ + +a +ab +abc +abcd +abcde +abcdef +abcdefg +abcdefgh +abcdefghi +abcdefghij +Discard medicine more than two years old. +He who has a shady past knows that nice guys finish last. +I wouldn't marry him with a ten foot pole. +Free! Free!/A trip/to Mars/for 900/empty jars/Burma Shave +The days of the digital watch are numbered. -Tom Stoppard +Nepal premier won't resign. +For every action there is an equal and opposite government program. +His money is twice tainted: 'taint yours and 'taint mine. +There is no reason for any individual to have a computer in their home. -Ken Olsen, 1977 +It's a tiny change to the code and not completely disgusting. - Bob Manchek +size: a.out: bad magic +The major problem is with sendmail. -Mark Horton +Give me a rock, paper and scissors and I will move the world. CCFestoon +If the enemy is within range, then so are you. +It's well we cannot hear the screams/That we create in others' dreams. +You remind me of a TV show, but that's all right: I watch it anyway. +C is as portable as Stonehedge!! +Even if I could be Shakespeare, I think I should still choose to be Faraday. - A. Huxley +The fugacity of a constituent in a mixture of gases at a given temperature is proportional to its mole fraction. Lewis-Randall Rule +How can you write a big system without C++? -Paul Glick diff --git a/src/hash/test_gen.awk b/src/hash/test_gen.awk new file mode 100644 index 0000000..804f786 --- /dev/null +++ b/src/hash/test_gen.awk @@ -0,0 +1,14 @@ +# 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. + +# awk -f test_gen.awk test_cases.txt +# generates test case table. +# edit next line to set particular reference implementation and name. +BEGIN { cmd = "echo -n `9 sha1sum`"; name = "Sha1Test" } +{ + printf("\t%s{ \"", name); + printf("%s", $0) |cmd; + close(cmd); + printf("\", \"%s\" },\n", $0); +} |