tzhash/gf127/avx/gf127.go
Evgenii Stratonikov 0f8b498b58 Alias gf127.GF127
2019-10-15 13:22:36 +03:00

104 lines
2 KiB
Go

// Copyright 2018 (c) NSPCC
//
// Package gf127 implements the GF(2^127) arithmetic
// modulo reduction polynomial x^127 + x^63 + 1 .
// This is rather straight-forward re-implementation of C library
// available here https://github.com/srijs/hwsl2-core .
// Interfaces are highly influenced by math/big .
package avx
import (
"math/bits"
"github.com/nspcc-dev/tzhash/gf127"
)
// GF127 is an alias for a main type.
type GF127 = gf127.GF127
const msb64 = uint64(1) << 63
var (
// x127x63 represents x^127 + x^63. Used in assembly file.
x127x63 = GF127{msb64, msb64}
// x126x631 is reduction polynomial x^127+x^63+1
x127x631 = GF127{msb64 + 1, msb64}
)
// 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 mul 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 a to b.
func Mul1(a, b *GF127) {
b[0] = a[0]
b[1] = a[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]
}
// Add sets c to a+b.
func Add(a, b, c *GF127)
// Mul sets c to a*b.
func Mul(a, b, c *GF127)
// Mul10 sets b to a*x.
func Mul10(a, b *GF127)
// Mul11 sets b to a*(x+1).
func Mul11(a, b *GF127)