tzhash/gf127/gf127.go

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package gf127
import (
"encoding/binary"
"encoding/hex"
"errors"
"math/bits"
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"math/rand"
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)
// GF127 represents element of GF(2^127)
type GF127 [2]uint64
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const (
byteSize = 16
maxUint64 = ^uint64(0)
msb64 = uint64(1) << 63
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)
// x127x631 is reduction polynomial x^127 + x^63 + 1
var x127x631 = GF127{msb64 + 1, msb64}
// New constructs new element of GF(2^127) as hi*x^64 + lo.
// It is assumed that hi has zero MSB.
func New(lo, hi uint64) *GF127 {
return &GF127{lo, hi}
}
func addGeneric(a, b, c *GF127) {
c[0] = a[0] ^ b[0]
c[1] = a[1] ^ b[1]
}
func mulGeneric(a, b, c *GF127) {
r := new(GF127)
d := *a
for i := uint(0); i < 64; i++ {
if b[0]&(1<<i) != 0 {
addGeneric(r, &d, r)
}
mul10Generic(&d, &d)
}
for i := uint(0); i < 63; i++ {
if b[1]&(1<<i) != 0 {
addGeneric(r, &d, r)
}
mul10Generic(&d, &d)
}
*c = *r
}
func mul10Generic(a, b *GF127) {
c := a[0] >> 63
b[0] = a[0] << 1
b[1] = (a[1] << 1) ^ c
mask := b[1] & msb64
b[0] ^= mask | (mask >> 63)
b[1] ^= mask
}
func mul11Generic(a, b *GF127) {
c := a[0] >> 63
b[0] = a[0] ^ (a[0] << 1)
b[1] = a[1] ^ (a[1] << 1) ^ c
mask := b[1] & msb64
b[0] ^= mask | (mask >> 63)
b[1] ^= mask
}
// Inv sets b to a^-1
// Algorithm is based on Extended Euclidean Algorithm
// and is described by Hankerson, Hernandez, Menezes in
// https://link.springer.com/content/pdf/10.1007/3-540-44499-8_1.pdf
func Inv(a, b *GF127) {
var (
v = x127x631
u = *a
c, d = &GF127{1, 0}, &GF127{0, 0}
t = new(GF127)
x *GF127
)
// degree of polynomial is a position of most significant bit
for du, dv := msb(&u), msb(&v); du != 0; du, dv = msb(&u), msb(&v) {
if du < dv {
v, u = u, v
dv, du = du, dv
d, c = c, d
}
x = xN(du - dv)
Mul(x, &v, t)
Add(&u, t, &u)
// becasuse mulAVX performs reduction on t, we need
// manually reduce u at first step
if msb(&u) == 127 {
Add(&u, &x127x631, &u)
}
Mul(x, d, t)
Add(c, t, c)
}
*b = *c
}
func xN(n int) *GF127 {
if n < 64 {
return &GF127{1 << uint(n), 0}
}
return &GF127{0, 1 << uint(n-64)}
}
func msb(a *GF127) (x int) {
x = bits.LeadingZeros64(a[1])
if x == 64 {
x = bits.LeadingZeros64(a[0]) + 64
}
return 127 - x
}
// Mul1 copies b into a.
func Mul1(a, b *GF127) {
a[0] = b[0]
a[1] = b[1]
}
// And sets c to a & b (bitwise-and).
func And(a, b, c *GF127) {
c[0] = a[0] & b[0]
c[1] = a[1] & b[1]
}
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// Random returns random element from GF(2^127).
// Is used mostly for testing.
func Random() *GF127 {
return &GF127{rand.Uint64(), rand.Uint64() >> 1}
}
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// String returns hex-encoded representation, starting with MSB.
func (c *GF127) String() string {
buf := c.Bytes()
return hex.EncodeToString(buf[:])
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}
// Equals checks if two reduced (zero MSB) elements of GF(2^127) are equal
func (c *GF127) Equals(b *GF127) bool {
return c[0] == b[0] && c[1] == b[1]
}
// Bytes represents element of GF(2^127) as byte array of length 16.
func (c *GF127) Bytes() [16]byte {
var buf [16]byte
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binary.BigEndian.PutUint64(buf[:8], c[1])
binary.BigEndian.PutUint64(buf[8:], c[0])
return buf
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}
// MarshalBinary implements encoding.BinaryMarshaler.
func (c *GF127) MarshalBinary() (data []byte, err error) {
buf := c.Bytes()
return buf[:], nil
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}
// UnmarshalBinary implements encoding.BinaryUnmarshaler.
func (c *GF127) UnmarshalBinary(data []byte) error {
if len(data) != byteSize {
return errors.New("data must be 16-bytes long")
}
c[0] = binary.BigEndian.Uint64(data[8:])
c[1] = binary.BigEndian.Uint64(data[:8])
if c[1]&msb64 != 0 {
return errors.New("MSB must be zero")
}
return nil
}