ceremonyclient/ec/bls48581/BIG.go

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2023-04-15 04:05:26 +00:00
/*
* Copyright (c) 2012-2020 MIRACL UK Ltd.
*
* This file is part of MIRACL Core
* (see https://github.com/miracl/core).
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* core BIG number class */
package bls48581
import (
"strconv"
"source.quilibrium.com/quilibrium/ceremonyclient/ec/bls48581/core"
)
//import "fmt"
type BIG struct {
w [NLEN]Chunk
}
type DBIG struct {
w [2 * NLEN]Chunk
}
/***************** 32-bit specific code ****************/
/* First the 32/64-bit dependent BIG code */
/* Note that because of the lack of a 128-bit integer, 32 and 64-bit code needs to be done differently */
/* return a*b as DBIG */
func mul(a *BIG, b *BIG) *DBIG {
c := NewDBIG()
// BIGMULS+=1;
var d [NLEN]DChunk
for i := 0; i < NLEN; i++ {
d[i] = DChunk(a.w[i]) * DChunk(b.w[i])
}
s := d[0]
t := s
c.w[0] = Chunk(t) & BMASK
co := t >> BASEBITS
for k := 1; k < NLEN; k++ {
s += d[k]
t = co + s
for i := k; i >= 1+k/2; i-- {
t += DChunk(a.w[i]-a.w[k-i]) * DChunk(b.w[k-i]-b.w[i])
}
c.w[k] = Chunk(t) & BMASK
co = t >> BASEBITS
}
for k := NLEN; k < 2*NLEN-1; k++ {
s -= d[k-NLEN]
t = co + s
for i := NLEN - 1; i >= 1+k/2; i-- {
t += DChunk(a.w[i]-a.w[k-i]) * DChunk(b.w[k-i]-b.w[i])
}
c.w[k] = Chunk(t) & BMASK
co = t >> BASEBITS
}
c.w[2*NLEN-1] = Chunk(co)
return c
}
/* return a^2 as DBIG */
func sqr(a *BIG) *DBIG {
c := NewDBIG()
// BIGSQRS+=1;
t := DChunk(a.w[0]) * DChunk(a.w[0])
c.w[0] = Chunk(t) & BMASK
co := t >> BASEBITS
for j := 1; j < NLEN-1; {
t = DChunk(a.w[j]) * DChunk(a.w[0])
for i := 1; i < (j+1)/2; i++ {
t += DChunk(a.w[j-i]) * DChunk(a.w[i])
}
t += t
t += co
c.w[j] = Chunk(t) & BMASK
co = t >> BASEBITS
j++
t = DChunk(a.w[j]) * DChunk(a.w[0])
for i := 1; i < (j+1)/2; i++ {
t += DChunk(a.w[j-i]) * DChunk(a.w[i])
}
t += t
t += co
t += DChunk(a.w[j/2]) * DChunk(a.w[j/2])
c.w[j] = Chunk(t) & BMASK
co = t >> BASEBITS
j++
}
for j := NLEN - 1 + (NLEN % 2); j < DNLEN-3; {
t = DChunk(a.w[NLEN-1]) * DChunk(a.w[j-NLEN+1])
for i := j - NLEN + 2; i < (j+1)/2; i++ {
t += DChunk(a.w[j-i]) * DChunk(a.w[i])
}
t += t
t += co
c.w[j] = Chunk(t) & BMASK
co = t >> BASEBITS
j++
t = DChunk(a.w[NLEN-1]) * DChunk(a.w[j-NLEN+1])
for i := j - NLEN + 2; i < (j+1)/2; i++ {
t += DChunk(a.w[j-i]) * DChunk(a.w[i])
}
t += t
t += co
t += DChunk(a.w[j/2]) * DChunk(a.w[j/2])
c.w[j] = Chunk(t) & BMASK
co = t >> BASEBITS
j++
}
t = DChunk(a.w[NLEN-2]) * DChunk(a.w[NLEN-1])
t += t
t += co
c.w[DNLEN-3] = Chunk(t) & BMASK
co = t >> BASEBITS
t = DChunk(a.w[NLEN-1])*DChunk(a.w[NLEN-1]) + co
c.w[DNLEN-2] = Chunk(t) & BMASK
co = t >> BASEBITS
c.w[DNLEN-1] = Chunk(co)
return c
}
func monty(m *BIG, mc Chunk, d *DBIG) *BIG {
var dd [NLEN]DChunk
var v [NLEN]Chunk
b := NewBIG()
t := DChunk(d.w[0])
v[0] = (Chunk(t) * mc) & BMASK
t += DChunk(v[0]) * DChunk(m.w[0])
c := (t >> BASEBITS) + DChunk(d.w[1])
s := DChunk(0)
for k := 1; k < NLEN; k++ {
t = c + s + DChunk(v[0])*DChunk(m.w[k])
for i := k - 1; i > k/2; i-- {
t += DChunk(v[k-i]-v[i]) * DChunk(m.w[i]-m.w[k-i])
}
v[k] = (Chunk(t) * mc) & BMASK
t += DChunk(v[k]) * DChunk(m.w[0])
c = (t >> BASEBITS) + DChunk(d.w[k+1])
dd[k] = DChunk(v[k]) * DChunk(m.w[k])
s += dd[k]
}
for k := NLEN; k < 2*NLEN-1; k++ {
t = c + s
for i := NLEN - 1; i >= 1+k/2; i-- {
t += DChunk(v[k-i]-v[i]) * DChunk(m.w[i]-m.w[k-i])
}
b.w[k-NLEN] = Chunk(t) & BMASK
c = (t >> BASEBITS) + DChunk(d.w[k+1])
s -= dd[k-NLEN+1]
}
b.w[NLEN-1] = Chunk(c) & BMASK
return b
}
/* set this[i]+=x*y+c, and return high part */
func muladd(a Chunk, b Chunk, c Chunk, r Chunk) (Chunk, Chunk) {
var prod = DChunk(a)*DChunk(b) + DChunk(c) + DChunk(r)
bot := Chunk(prod) & BMASK
top := Chunk(prod >> BASEBITS)
return top, bot
}
/***************************************************************************/
func (r *BIG) get(i int) Chunk {
return r.w[i]
}
func (r *BIG) set(i int, x Chunk) {
r.w[i] = x
}
func (r *BIG) xortop(x Chunk) {
r.w[NLEN-1] ^= x
}
/* normalise BIG - force all digits < 2^BASEBITS */
func (r *BIG) norm() Chunk {
carry := Chunk(0)
for i := 0; i < NLEN-1; i++ {
d := r.w[i] + carry
r.w[i] = d & BMASK
carry = d >> BASEBITS
}
r.w[NLEN-1] = (r.w[NLEN-1] + carry)
return (r.w[NLEN-1] >> ((8 * MODBYTES) % BASEBITS))
}
/* Shift right by less than a word */
func (r *BIG) fshr(k uint) int {
w := r.w[0] & ((Chunk(1) << k) - 1) /* shifted out part */
for i := 0; i < NLEN-1; i++ {
r.w[i] = (r.w[i] >> k) | ((r.w[i+1] << (BASEBITS - k)) & BMASK)
}
r.w[NLEN-1] = r.w[NLEN-1] >> k
return int(w)
}
/* Shift right by less than a word */
func (r *BIG) fshl(k uint) int {
r.w[NLEN-1] = (r.w[NLEN-1] << k) | (r.w[NLEN-2] >> (BASEBITS - k))
for i := NLEN - 2; i > 0; i-- {
r.w[i] = ((r.w[i] << k) & BMASK) | (r.w[i-1] >> (BASEBITS - k))
}
r.w[0] = (r.w[0] << k) & BMASK
return int(r.w[NLEN-1] >> ((8 * MODBYTES) % BASEBITS)) /* return excess - only used in ff.c */
}
func NewBIG() *BIG {
b := new(BIG)
for i := 0; i < NLEN; i++ {
b.w[i] = 0
}
return b
}
func NewBIGints(x [21]Chunk) *BIG {
b := new(BIG)
for i := 0; i < NLEN; i++ {
b.w[i] = x[i]
}
return b
}
func NewBIGint(x int) *BIG {
b := new(BIG)
b.w[0] = Chunk(x)
for i := 1; i < NLEN; i++ {
b.w[i] = 0
}
return b
}
func NewBIGcopy(x *BIG) *BIG {
b := new(BIG)
for i := 0; i < NLEN; i++ {
b.w[i] = x.w[i]
}
return b
}
func NewBIGdcopy(x *DBIG) *BIG {
b := new(BIG)
for i := 0; i < NLEN; i++ {
b.w[i] = x.w[i]
}
return b
}
/* test for zero */
func (r *BIG) iszilch() bool {
d := Chunk(0)
for i := 0; i < NLEN; i++ {
d |= r.w[i]
}
return (1 & ((d - 1) >> BASEBITS)) != 0
}
/* set to zero */
func (r *BIG) zero() {
for i := 0; i < NLEN; i++ {
r.w[i] = 0
}
}
/* Test for equal to one */
func (r *BIG) isunity() bool {
d := Chunk(0)
for i := 1; i < NLEN; i++ {
d |= r.w[i]
}
return (1 & ((d - 1) >> BASEBITS) & (((r.w[0] ^ 1) - 1) >> BASEBITS)) != 0
}
/* set to one */
func (r *BIG) one() {
r.w[0] = 1
for i := 1; i < NLEN; i++ {
r.w[i] = 0
}
}
/* Copy from another BIG */
func (r *BIG) copy(x *BIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = x.w[i]
}
}
/* Copy from another DBIG */
func (r *BIG) dcopy(x *DBIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = x.w[i]
}
}
/* Conditional swap of two bigs depending on d using XOR - no branches */
func (r *BIG) cswap(b *BIG, d int) Chunk {
c := Chunk(-d)
s := Chunk(0)
v := r.w[0] ^ b.w[1]
va := v + v
va >>= 1
for i := 0; i < NLEN; i++ {
t := c & (r.w[i] ^ b.w[i])
t ^= v
e := r.w[i] ^ t
s ^= e // to force calculation of e
r.w[i] = e ^ va
e = b.w[i] ^ t
s ^= e
b.w[i] = e ^ va
}
return s
}
func (r *BIG) cmove(g *BIG, d int) Chunk {
b := Chunk(-d)
s := Chunk(0)
v := r.w[0] ^ g.w[1]
va := v + v
va >>= 1
for i := 0; i < NLEN; i++ {
t := (r.w[i] ^ g.w[i]) & b
t ^= v
e := r.w[i] ^ t
s ^= e
r.w[i] = e ^ va
}
return s
}
/* general shift right */
func (r *BIG) shr(k uint) {
n := (k % BASEBITS)
m := int(k / BASEBITS)
for i := 0; i < NLEN-m-1; i++ {
r.w[i] = (r.w[m+i] >> n) | ((r.w[m+i+1] << (BASEBITS - n)) & BMASK)
}
r.w[NLEN-m-1] = r.w[NLEN-1] >> n
for i := NLEN - m; i < NLEN; i++ {
r.w[i] = 0
}
}
/* general shift left */
func (r *BIG) shl(k uint) {
n := k % BASEBITS
m := int(k / BASEBITS)
r.w[NLEN-1] = (r.w[NLEN-1-m] << n)
if NLEN >= m+2 {
r.w[NLEN-1] |= (r.w[NLEN-m-2] >> (BASEBITS - n))
}
for i := NLEN - 2; i > m; i-- {
r.w[i] = ((r.w[i-m] << n) & BMASK) | (r.w[i-m-1] >> (BASEBITS - n))
}
r.w[m] = (r.w[0] << n) & BMASK
for i := 0; i < m; i++ {
r.w[i] = 0
}
}
/* return number of bits */
func (r *BIG) nbits() int {
t := NewBIGcopy(r)
k := NLEN - 1
t.norm()
for k >= 0 && t.w[k] == 0 {
k--
}
if k < 0 {
return 0
}
bts := int(BASEBITS) * k
c := t.w[k]
for c != 0 {
c /= 2
bts++
}
return bts
}
func (r *BIG) Nbits() int {
return r.nbits()
}
/* Convert to Hex String */
func (r *BIG) ToString() string {
s := ""
len := r.nbits()
if len%4 == 0 {
len /= 4
} else {
len /= 4
len++
}
MB := int(MODBYTES * 2)
if len < MB {
len = MB
}
for i := len - 1; i >= 0; i-- {
b := NewBIGcopy(r)
b.shr(uint(i * 4))
s += strconv.FormatInt(int64(b.w[0]&15), 16)
}
return s
}
func (r *BIG) add(x *BIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = r.w[i] + x.w[i]
}
}
func (r *BIG) or(x *BIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = r.w[i] | x.w[i]
}
}
/* return this+x */
func (r *BIG) Plus(x *BIG) *BIG {
s := new(BIG)
for i := 0; i < NLEN; i++ {
s.w[i] = r.w[i] + x.w[i]
}
s.norm()
return s
}
/* this+=x, where x is int */
func (r *BIG) inc(x int) {
r.norm()
r.w[0] += Chunk(x)
}
/* this*=c and catch overflow in DBIG */
func (r *BIG) pxmul(c int) *DBIG {
m := NewDBIG()
carry := Chunk(0)
for j := 0; j < NLEN; j++ {
carry, m.w[j] = muladd(r.w[j], Chunk(c), carry, m.w[j])
}
m.w[NLEN] = carry
return m
}
/* return this-x */
func (r *BIG) Minus(x *BIG) *BIG {
d := new(BIG)
for i := 0; i < NLEN; i++ {
d.w[i] = r.w[i] - x.w[i]
}
return d
}
/* this-=x */
func (r *BIG) sub(x *BIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = r.w[i] - x.w[i]
}
}
/* reverse subtract this=x-this */
func (r *BIG) rsub(x *BIG) {
for i := 0; i < NLEN; i++ {
r.w[i] = x.w[i] - r.w[i]
}
}
/* this-=x, where x is int */
func (r *BIG) dec(x int) {
r.norm()
r.w[0] -= Chunk(x)
}
/* this*=x, where x is small int<NEXCESS */
func (r *BIG) imul(c int) {
for i := 0; i < NLEN; i++ {
r.w[i] *= Chunk(c)
}
}
/* this*=x, where x is >NEXCESS */
func (r *BIG) pmul(c int) Chunk {
carry := Chunk(0)
// r.norm();
for i := 0; i < NLEN; i++ {
ak := r.w[i]
r.w[i] = 0
carry, r.w[i] = muladd(ak, Chunk(c), carry, r.w[i])
}
return carry
}
/* convert this BIG to byte array */
func (r *BIG) tobytearray(b []byte, n int) {
//r.norm();
c := NewBIGcopy(r)
c.norm()
for i := int(MODBYTES) - 1; i >= 0; i-- {
b[i+n] = byte(c.w[0])
c.fshr(8)
}
}
/* convert from byte array to BIG */
func frombytearray(b []byte, n int) *BIG {
m := NewBIG()
l := len(b)
for i := 0; i < int(MODBYTES); i++ {
m.fshl(8)
if i < l {
m.w[0] += Chunk(int(b[i+n] & 0xff))
} else {
m.w[0] += Chunk(int(0 & 0xff))
}
}
return m
}
func (r *BIG) ToBytes(b []byte) {
r.tobytearray(b, 0)
}
func FromBytes(b []byte) *BIG {
return frombytearray(b, 0)
}
/* divide by 3 */
func (r *BIG) div3() int {
carry := Chunk(0)
r.norm()
base := (Chunk(1) << BASEBITS)
for i := NLEN - 1; i >= 0; i-- {
ak := (carry*base + r.w[i])
r.w[i] = ak / 3
carry = ak % 3
}
return int(carry)
}
/* return a*b where result fits in a BIG */
func smul(a *BIG, b *BIG) *BIG {
carry := Chunk(0)
c := NewBIG()
for i := 0; i < NLEN; i++ {
carry = 0
for j := 0; j < NLEN; j++ {
if i+j < NLEN {
carry, c.w[i+j] = muladd(a.w[i], b.w[j], carry, c.w[i+j])
}
}
}
return c
}
/* Compare a and b, return 0 if a==b, -1 if a<b, +1 if a>b. Inputs must be normalised */
func Comp(a *BIG, b *BIG) int {
gt := Chunk(0)
eq := Chunk(1)
for i := NLEN - 1; i >= 0; i-- {
gt |= ((b.w[i] - a.w[i]) >> BASEBITS) & eq
eq &= ((b.w[i] ^ a.w[i]) - 1) >> BASEBITS
}
return int(gt + gt + eq - 1)
}
/* return parity */
func (r *BIG) parity() int {
return int(r.w[0] % 2)
}
/* return n-th bit */
func (r *BIG) bit(n int) int {
return int((r.w[n/int(BASEBITS)] & (Chunk(1) << (uint(n) % BASEBITS))) >> (uint(n) % BASEBITS))
// if (r.w[n/int(BASEBITS)] & (Chunk(1) << (uint(n) % BASEBITS))) > 0 {
// return 1
// }
// return 0
}
/* return n last bits */
func (r *BIG) lastbits(n int) int {
msk := (1 << uint(n)) - 1
r.norm()
return (int(r.w[0])) & msk
}
/* set x = x mod 2^m */
func (r *BIG) mod2m(m uint) {
wd := int(m / BASEBITS)
bt := m % BASEBITS
msk := (Chunk(1) << bt) - 1
r.w[wd] &= msk
for i := wd + 1; i < NLEN; i++ {
r.w[i] = 0
}
}
/* a=1/a mod 2^256. This is very fast! */
func (r *BIG) invmod2m() {
U := NewBIG()
b := NewBIG()
c := NewBIG()
U.inc(invmod256(r.lastbits(8)))
for i := 8; i < BIGBITS; i <<= 1 {
U.norm()
ui := uint(i)
b.copy(r)
b.mod2m(ui)
t1 := smul(U, b)
t1.shr(ui)
c.copy(r)
c.shr(ui)
c.mod2m(ui)
t2 := smul(U, c)
t2.mod2m(ui)
t1.add(t2)
t1.norm()
b = smul(t1, U)
t1.copy(b)
t1.mod2m(ui)
t2.one()
t2.shl(ui)
t1.rsub(t2)
t1.norm()
t1.shl(ui)
U.add(t1)
}
U.mod2m(8 * MODBYTES)
r.copy(U)
r.norm()
}
func (r *BIG) ctmod(m *BIG, bd uint) {
k := bd
sr := NewBIG()
c := NewBIGcopy(m)
r.norm()
c.shl(k)
for {
sr.copy(r)
sr.sub(c)
sr.norm()
r.cmove(sr, int(1-((sr.w[NLEN-1]>>uint(CHUNK-1))&1)))
if k == 0 {
break
}
c.fshr(1)
k -= 1
}
}
/* reduce this mod m */
func (r *BIG) Mod(m *BIG) {
k := r.nbits() - m.nbits()
if k < 0 {
k = 0
}
r.ctmod(m, uint(k))
}
func (r *BIG) ctdiv(m *BIG, bd uint) {
k := bd
e := NewBIGint(1)
sr := NewBIG()
a := NewBIGcopy(r)
c := NewBIGcopy(m)
r.norm()
r.zero()
c.shl(k)
e.shl(k)
for {
sr.copy(a)
sr.sub(c)
sr.norm()
d := int(1 - ((sr.w[NLEN-1] >> uint(CHUNK-1)) & 1))
a.cmove(sr, d)
sr.copy(r)
sr.add(e)
sr.norm()
r.cmove(sr, d)
if k == 0 {
break
}
c.fshr(1)
e.fshr(1)
k -= 1
}
}
/* divide this by m */
func (r *BIG) div(m *BIG) {
k := r.nbits() - m.nbits()
if k < 0 {
k = 0
}
r.ctdiv(m, uint(k))
}
/* get 8*MODBYTES size random number */
func Random(rng *core.RAND) *BIG {
m := NewBIG()
var j int = 0
var r byte = 0
/* generate random BIG */
for i := 0; i < 8*int(MODBYTES); i++ {
if j == 0 {
r = rng.GetByte()
} else {
r >>= 1
}
b := Chunk(int(r & 1))
m.shl(1)
m.w[0] += b
j++
j &= 7
}
return m
}
/* Create random BIG in portable way, one bit at a time */
func Randomnum(q *BIG, rng *core.RAND) *BIG {
d := NewDBIG()
var j int = 0
var r byte = 0
for i := 0; i < 2*q.nbits(); i++ {
if j == 0 {
r = rng.GetByte()
} else {
r >>= 1
}
b := Chunk(int(r & 1))
d.shl(1)
d.w[0] += b
j++
j &= 7
}
m := d.Mod(q)
return m
}
func Randtrunc(q *BIG, trunc int, rng *core.RAND) *BIG {
m := Randomnum(q, rng)
if q.nbits() > trunc {
m.mod2m(uint(trunc))
}
return m
}
/* return a*b mod m */
func Modmul(a1, b1, m *BIG) *BIG {
a := NewBIGcopy(a1)
b := NewBIGcopy(b1)
a.Mod(m)
b.Mod(m)
d := mul(a, b)
return d.ctmod(m, uint(m.nbits()))
}
/* return a^2 mod m */
func Modsqr(a1, m *BIG) *BIG {
a := NewBIGcopy(a1)
a.Mod(m)
d := sqr(a)
return d.ctmod(m, uint(m.nbits()))
}
/* return -a mod m */
func Modneg(a1, m *BIG) *BIG {
a := NewBIGcopy(a1)
a.Mod(m)
a.rsub(m)
a.norm()
return a
}
/* return a+b mod m */
func Modadd(a1, b1, m *BIG) *BIG {
a := NewBIGcopy(a1)
b := NewBIGcopy(b1)
a.Mod(m)
b.Mod(m)
a.add(b)
a.norm()
a.ctmod(m, 1)
return a
}
/* Jacobi Symbol (this/p). Returns 0, 1 or -1 */
func (r *BIG) Jacobi(p *BIG) int {
m := 0
t := NewBIGint(0)
x := NewBIGint(0)
n := NewBIGint(0)
zilch := NewBIGint(0)
one := NewBIGint(1)
if p.parity() == 0 || Comp(r, zilch) == 0 || Comp(p, one) <= 0 {
return 0
}
r.norm()
x.copy(r)
n.copy(p)
x.Mod(p)
for Comp(n, one) > 0 {
if Comp(x, zilch) == 0 {
return 0
}
n8 := n.lastbits(3)
k := 0
for x.parity() == 0 {
k++
x.shr(1)
}
if k%2 == 1 {
m += (n8*n8 - 1) / 8
}
m += (n8 - 1) * (x.lastbits(2) - 1) / 4
t.copy(n)
t.Mod(x)
n.copy(x)
x.copy(t)
m %= 2
}
if m == 0 {
return 1
}
return -1
}
/* this=1/this mod p. Binary method */
func (r *BIG) Invmodp(p *BIG) {
r.Mod(p)
if r.iszilch() {
return
}
u := NewBIGcopy(r)
v := NewBIGcopy(p)
x1 := NewBIGint(1)
x2 := NewBIGint(0)
t := NewBIGint(0)
one := NewBIGint(1)
for Comp(u, one) != 0 && Comp(v, one) != 0 {
for u.parity() == 0 {
u.fshr(1)
t.copy(x1)
t.add(p)
x1.cmove(t, x1.parity())
x1.norm()
x1.fshr(1)
}
for v.parity() == 0 {
v.fshr(1)
t.copy(x2)
t.add(p)
x2.cmove(t, x2.parity())
x2.norm()
x2.fshr(1)
}
if Comp(u, v) >= 0 {
u.sub(v)
u.norm()
t.copy(x1)
t.add(p)
x1.cmove(t, (Comp(x1, x2)>>1)&1)
x1.sub(x2)
x1.norm()
} else {
v.sub(u)
v.norm()
t.copy(x2)
t.add(p)
x2.cmove(t, (Comp(x2, x1)>>1)&1)
x2.sub(x1)
x2.norm()
}
}
r.copy(x1)
r.cmove(x2, Comp(u, one)&1)
}
/* return this^e mod m */
func (r *BIG) Powmod(e1 *BIG, m *BIG) *BIG {
e := NewBIGcopy(e1)
r.norm()
e.norm()
a := NewBIGint(1)
z := NewBIGcopy(e)
s := NewBIGcopy(r)
for true {
bt := z.parity()
z.fshr(1)
if bt == 1 {
a = Modmul(a, s, m)
}
if z.iszilch() {
break
}
s = Modsqr(s, m)
}
return a
}
/* Arazi and Qi inversion mod 256 */
func invmod256(a int) int {
var t1 int = 0
c := (a >> 1) & 1
t1 += c
t1 &= 1
t1 = 2 - t1
t1 <<= 1
U := t1 + 1
// i=2
b := a & 3
t1 = U * b
t1 >>= 2
c = (a >> 2) & 3
t2 := (U * c) & 3
t1 += t2
t1 *= U
t1 &= 3
t1 = 4 - t1
t1 <<= 2
U += t1
// i=4
b = a & 15
t1 = U * b
t1 >>= 4
c = (a >> 4) & 15
t2 = (U * c) & 15
t1 += t2
t1 *= U
t1 &= 15
t1 = 16 - t1
t1 <<= 4
U += t1
return U
}
func logb2(w uint32) uint {
v := w
v |= (v >> 1)
v |= (v >> 2)
v |= (v >> 4)
v |= (v >> 8)
v |= (v >> 16)
v = v - ((v >> 1) & 0x55555555)
v = (v & 0x33333333) + ((v >> 2) & 0x33333333)
r := uint((((v + (v >> 4)) & 0xF0F0F0F) * 0x1010101) >> 24)
return (r)
}
// Optimized combined shift, subtract and norm
func ssn(r *BIG, a *BIG, m *BIG) int {
n := NLEN - 1
m.w[0] = (m.w[0] >> 1) | ((m.w[1] << (BASEBITS - 1)) & BMASK)
r.w[0] = a.w[0] - m.w[0]
carry := r.w[0] >> BASEBITS
r.w[0] &= BMASK
for i := 1; i < n; i++ {
m.w[i] = (m.w[i] >> 1) | ((m.w[i+1] << (BASEBITS - 1)) & BMASK)
r.w[i] = a.w[i] - m.w[i] + carry
carry = r.w[i] >> BASEBITS
r.w[i] &= BMASK
}
m.w[n] >>= 1
r.w[n] = a.w[n] - m.w[n] + carry
return int((r.w[n] >> uint(CHUNK-1)) & 1)
}