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element.go
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element.go
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// Copyright 2020 ConsenSys Software Inc.
//
// 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.
// Code generated by consensys/gnark-crypto DO NOT EDIT
package fr
import (
"crypto/rand"
"encoding/binary"
"errors"
"io"
"math/big"
"math/bits"
"reflect"
"strconv"
"strings"
"github.com/bits-and-blooms/bitset"
"github.com/consensys/gnark-crypto/field/hash"
"github.com/consensys/gnark-crypto/field/pool"
)
// Element represents a field element stored on 4 words (uint64)
//
// Element are assumed to be in Montgomery form in all methods.
//
// Modulus q =
//
// q[base10] = 11502027791375260645628074404575422495959608200132055716665986169834464870401
// q[base16] = 0x196deac24a9da12b25fc7ec9cf927a98c8c480ece644e36419d0c5fd00c00001
//
// # Warning
//
// This code has not been audited and is provided as-is. In particular, there is no security guarantees such as constant time implementation or side-channel attack resistance.
type Element [4]uint64
const (
Limbs = 4 // number of 64 bits words needed to represent a Element
Bits = 253 // number of bits needed to represent a Element
Bytes = 32 // number of bytes needed to represent a Element
)
// Field modulus q
const (
q0 uint64 = 1860204336533995521
q1 uint64 = 14466829657984787300
q2 uint64 = 2737202078770428568
q3 uint64 = 1832378743606059307
)
var qElement = Element{
q0,
q1,
q2,
q3,
}
var _modulus big.Int // q stored as big.Int
// Modulus returns q as a big.Int
//
// q[base10] = 11502027791375260645628074404575422495959608200132055716665986169834464870401
// q[base16] = 0x196deac24a9da12b25fc7ec9cf927a98c8c480ece644e36419d0c5fd00c00001
func Modulus() *big.Int {
return new(big.Int).Set(&_modulus)
}
// q + r'.r = 1, i.e., qInvNeg = - q⁻¹ mod r
// used for Montgomery reduction
const qInvNeg uint64 = 2184305180030271487
func init() {
_modulus.SetString("196deac24a9da12b25fc7ec9cf927a98c8c480ece644e36419d0c5fd00c00001", 16)
}
// NewElement returns a new Element from a uint64 value
//
// it is equivalent to
//
// var v Element
// v.SetUint64(...)
func NewElement(v uint64) Element {
z := Element{v}
z.Mul(&z, &rSquare)
return z
}
// SetUint64 sets z to v and returns z
func (z *Element) SetUint64(v uint64) *Element {
// sets z LSB to v (non-Montgomery form) and convert z to Montgomery form
*z = Element{v}
return z.Mul(z, &rSquare) // z.toMont()
}
// SetInt64 sets z to v and returns z
func (z *Element) SetInt64(v int64) *Element {
// absolute value of v
m := v >> 63
z.SetUint64(uint64((v ^ m) - m))
if m != 0 {
// v is negative
z.Neg(z)
}
return z
}
// Set z = x and returns z
func (z *Element) Set(x *Element) *Element {
z[0] = x[0]
z[1] = x[1]
z[2] = x[2]
z[3] = x[3]
return z
}
// SetInterface converts provided interface into Element
// returns an error if provided type is not supported
// supported types:
//
// Element
// *Element
// uint64
// int
// string (see SetString for valid formats)
// *big.Int
// big.Int
// []byte
func (z *Element) SetInterface(i1 interface{}) (*Element, error) {
if i1 == nil {
return nil, errors.New("can't set fr.Element with <nil>")
}
switch c1 := i1.(type) {
case Element:
return z.Set(&c1), nil
case *Element:
if c1 == nil {
return nil, errors.New("can't set fr.Element with <nil>")
}
return z.Set(c1), nil
case uint8:
return z.SetUint64(uint64(c1)), nil
case uint16:
return z.SetUint64(uint64(c1)), nil
case uint32:
return z.SetUint64(uint64(c1)), nil
case uint:
return z.SetUint64(uint64(c1)), nil
case uint64:
return z.SetUint64(c1), nil
case int8:
return z.SetInt64(int64(c1)), nil
case int16:
return z.SetInt64(int64(c1)), nil
case int32:
return z.SetInt64(int64(c1)), nil
case int64:
return z.SetInt64(c1), nil
case int:
return z.SetInt64(int64(c1)), nil
case string:
return z.SetString(c1)
case *big.Int:
if c1 == nil {
return nil, errors.New("can't set fr.Element with <nil>")
}
return z.SetBigInt(c1), nil
case big.Int:
return z.SetBigInt(&c1), nil
case []byte:
return z.SetBytes(c1), nil
default:
return nil, errors.New("can't set fr.Element from type " + reflect.TypeOf(i1).String())
}
}
// SetZero z = 0
func (z *Element) SetZero() *Element {
z[0] = 0
z[1] = 0
z[2] = 0
z[3] = 0
return z
}
// SetOne z = 1 (in Montgomery form)
func (z *Element) SetOne() *Element {
z[0] = 18291444782079148022
z[1] = 2905656009828539926
z[2] = 9521467359714817544
z[3] = 122956637648958544
return z
}
// Div z = x*y⁻¹ (mod q)
func (z *Element) Div(x, y *Element) *Element {
var yInv Element
yInv.Inverse(y)
z.Mul(x, &yInv)
return z
}
// Equal returns z == x; constant-time
func (z *Element) Equal(x *Element) bool {
return z.NotEqual(x) == 0
}
// NotEqual returns 0 if and only if z == x; constant-time
func (z *Element) NotEqual(x *Element) uint64 {
return (z[3] ^ x[3]) | (z[2] ^ x[2]) | (z[1] ^ x[1]) | (z[0] ^ x[0])
}
// IsZero returns z == 0
func (z *Element) IsZero() bool {
return (z[3] | z[2] | z[1] | z[0]) == 0
}
// IsOne returns z == 1
func (z *Element) IsOne() bool {
return ((z[3] ^ 122956637648958544) | (z[2] ^ 9521467359714817544) | (z[1] ^ 2905656009828539926) | (z[0] ^ 18291444782079148022)) == 0
}
// IsUint64 reports whether z can be represented as an uint64.
func (z *Element) IsUint64() bool {
zz := *z
zz.fromMont()
return zz.FitsOnOneWord()
}
// Uint64 returns the uint64 representation of x. If x cannot be represented in a uint64, the result is undefined.
func (z *Element) Uint64() uint64 {
return z.Bits()[0]
}
// FitsOnOneWord reports whether z words (except the least significant word) are 0
//
// It is the responsibility of the caller to convert from Montgomery to Regular form if needed.
func (z *Element) FitsOnOneWord() bool {
return (z[3] | z[2] | z[1]) == 0
}
// Cmp compares (lexicographic order) z and x and returns:
//
// -1 if z < x
// 0 if z == x
// +1 if z > x
func (z *Element) Cmp(x *Element) int {
_z := z.Bits()
_x := x.Bits()
if _z[3] > _x[3] {
return 1
} else if _z[3] < _x[3] {
return -1
}
if _z[2] > _x[2] {
return 1
} else if _z[2] < _x[2] {
return -1
}
if _z[1] > _x[1] {
return 1
} else if _z[1] < _x[1] {
return -1
}
if _z[0] > _x[0] {
return 1
} else if _z[0] < _x[0] {
return -1
}
return 0
}
// LexicographicallyLargest returns true if this element is strictly lexicographically
// larger than its negation, false otherwise
func (z *Element) LexicographicallyLargest() bool {
// adapted from github.com/zkcrypto/bls12_381
// we check if the element is larger than (q-1) / 2
// if z - (((q -1) / 2) + 1) have no underflow, then z > (q-1) / 2
_z := z.Bits()
var b uint64
_, b = bits.Sub64(_z[0], 930102168266997761, 0)
_, b = bits.Sub64(_z[1], 7233414828992393650, b)
_, b = bits.Sub64(_z[2], 10591973076239990092, b)
_, b = bits.Sub64(_z[3], 916189371803029653, b)
return b == 0
}
// SetRandom sets z to a uniform random value in [0, q).
//
// This might error only if reading from crypto/rand.Reader errors,
// in which case, value of z is undefined.
func (z *Element) SetRandom() (*Element, error) {
// this code is generated for all modulus
// and derived from go/src/crypto/rand/util.go
// l is number of limbs * 8; the number of bytes needed to reconstruct 4 uint64
const l = 32
// bitLen is the maximum bit length needed to encode a value < q.
const bitLen = 253
// k is the maximum byte length needed to encode a value < q.
const k = (bitLen + 7) / 8
// b is the number of bits in the most significant byte of q-1.
b := uint(bitLen % 8)
if b == 0 {
b = 8
}
var bytes [l]byte
for {
// note that bytes[k:l] is always 0
if _, err := io.ReadFull(rand.Reader, bytes[:k]); err != nil {
return nil, err
}
// Clear unused bits in in the most significant byte to increase probability
// that the candidate is < q.
bytes[k-1] &= uint8(int(1<<b) - 1)
z[0] = binary.LittleEndian.Uint64(bytes[0:8])
z[1] = binary.LittleEndian.Uint64(bytes[8:16])
z[2] = binary.LittleEndian.Uint64(bytes[16:24])
z[3] = binary.LittleEndian.Uint64(bytes[24:32])
if !z.smallerThanModulus() {
continue // ignore the candidate and re-sample
}
return z, nil
}
}
// smallerThanModulus returns true if z < q
// This is not constant time
func (z *Element) smallerThanModulus() bool {
return (z[3] < q3 || (z[3] == q3 && (z[2] < q2 || (z[2] == q2 && (z[1] < q1 || (z[1] == q1 && (z[0] < q0)))))))
}
// One returns 1
func One() Element {
var one Element
one.SetOne()
return one
}
// Halve sets z to z / 2 (mod q)
func (z *Element) Halve() {
var carry uint64
if z[0]&1 == 1 {
// z = z + q
z[0], carry = bits.Add64(z[0], q0, 0)
z[1], carry = bits.Add64(z[1], q1, carry)
z[2], carry = bits.Add64(z[2], q2, carry)
z[3], _ = bits.Add64(z[3], q3, carry)
}
// z = z >> 1
z[0] = z[0]>>1 | z[1]<<63
z[1] = z[1]>>1 | z[2]<<63
z[2] = z[2]>>1 | z[3]<<63
z[3] >>= 1
}
// fromMont converts z in place (i.e. mutates) from Montgomery to regular representation
// sets and returns z = z * 1
func (z *Element) fromMont() *Element {
fromMont(z)
return z
}
// Add z = x + y (mod q)
func (z *Element) Add(x, y *Element) *Element {
var carry uint64
z[0], carry = bits.Add64(x[0], y[0], 0)
z[1], carry = bits.Add64(x[1], y[1], carry)
z[2], carry = bits.Add64(x[2], y[2], carry)
z[3], _ = bits.Add64(x[3], y[3], carry)
// if z ⩾ q → z -= q
if !z.smallerThanModulus() {
var b uint64
z[0], b = bits.Sub64(z[0], q0, 0)
z[1], b = bits.Sub64(z[1], q1, b)
z[2], b = bits.Sub64(z[2], q2, b)
z[3], _ = bits.Sub64(z[3], q3, b)
}
return z
}
// Double z = x + x (mod q), aka Lsh 1
func (z *Element) Double(x *Element) *Element {
var carry uint64
z[0], carry = bits.Add64(x[0], x[0], 0)
z[1], carry = bits.Add64(x[1], x[1], carry)
z[2], carry = bits.Add64(x[2], x[2], carry)
z[3], _ = bits.Add64(x[3], x[3], carry)
// if z ⩾ q → z -= q
if !z.smallerThanModulus() {
var b uint64
z[0], b = bits.Sub64(z[0], q0, 0)
z[1], b = bits.Sub64(z[1], q1, b)
z[2], b = bits.Sub64(z[2], q2, b)
z[3], _ = bits.Sub64(z[3], q3, b)
}
return z
}
// Sub z = x - y (mod q)
func (z *Element) Sub(x, y *Element) *Element {
var b uint64
z[0], b = bits.Sub64(x[0], y[0], 0)
z[1], b = bits.Sub64(x[1], y[1], b)
z[2], b = bits.Sub64(x[2], y[2], b)
z[3], b = bits.Sub64(x[3], y[3], b)
if b != 0 {
var c uint64
z[0], c = bits.Add64(z[0], q0, 0)
z[1], c = bits.Add64(z[1], q1, c)
z[2], c = bits.Add64(z[2], q2, c)
z[3], _ = bits.Add64(z[3], q3, c)
}
return z
}
// Neg z = q - x
func (z *Element) Neg(x *Element) *Element {
if x.IsZero() {
z.SetZero()
return z
}
var borrow uint64
z[0], borrow = bits.Sub64(q0, x[0], 0)
z[1], borrow = bits.Sub64(q1, x[1], borrow)
z[2], borrow = bits.Sub64(q2, x[2], borrow)
z[3], _ = bits.Sub64(q3, x[3], borrow)
return z
}
// Select is a constant-time conditional move.
// If c=0, z = x0. Else z = x1
func (z *Element) Select(c int, x0 *Element, x1 *Element) *Element {
cC := uint64((int64(c) | -int64(c)) >> 63) // "canonicized" into: 0 if c=0, -1 otherwise
z[0] = x0[0] ^ cC&(x0[0]^x1[0])
z[1] = x0[1] ^ cC&(x0[1]^x1[1])
z[2] = x0[2] ^ cC&(x0[2]^x1[2])
z[3] = x0[3] ^ cC&(x0[3]^x1[3])
return z
}
// _mulGeneric is unoptimized textbook CIOS
// it is a fallback solution on x86 when ADX instruction set is not available
// and is used for testing purposes.
func _mulGeneric(z, x, y *Element) {
// Implements CIOS multiplication -- section 2.3.2 of Tolga Acar's thesis
// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
//
// The algorithm:
//
// for i=0 to N-1
// C := 0
// for j=0 to N-1
// (C,t[j]) := t[j] + x[j]*y[i] + C
// (t[N+1],t[N]) := t[N] + C
//
// C := 0
// m := t[0]*q'[0] mod D
// (C,_) := t[0] + m*q[0]
// for j=1 to N-1
// (C,t[j-1]) := t[j] + m*q[j] + C
//
// (C,t[N-1]) := t[N] + C
// t[N] := t[N+1] + C
//
// → N is the number of machine words needed to store the modulus q
// → D is the word size. For example, on a 64-bit architecture D is 2 64
// → x[i], y[i], q[i] is the ith word of the numbers x,y,q
// → q'[0] is the lowest word of the number -q⁻¹ mod r. This quantity is pre-computed, as it does not depend on the inputs.
// → t is a temporary array of size N+2
// → C, S are machine words. A pair (C,S) refers to (hi-bits, lo-bits) of a two-word number
var t [5]uint64
var D uint64
var m, C uint64
// -----------------------------------
// First loop
C, t[0] = bits.Mul64(y[0], x[0])
C, t[1] = madd1(y[0], x[1], C)
C, t[2] = madd1(y[0], x[2], C)
C, t[3] = madd1(y[0], x[3], C)
t[4], D = bits.Add64(t[4], C, 0)
// m = t[0]n'[0] mod W
m = t[0] * qInvNeg
// -----------------------------------
// Second loop
C = madd0(m, q0, t[0])
C, t[0] = madd2(m, q1, t[1], C)
C, t[1] = madd2(m, q2, t[2], C)
C, t[2] = madd2(m, q3, t[3], C)
t[3], C = bits.Add64(t[4], C, 0)
t[4], _ = bits.Add64(0, D, C)
// -----------------------------------
// First loop
C, t[0] = madd1(y[1], x[0], t[0])
C, t[1] = madd2(y[1], x[1], t[1], C)
C, t[2] = madd2(y[1], x[2], t[2], C)
C, t[3] = madd2(y[1], x[3], t[3], C)
t[4], D = bits.Add64(t[4], C, 0)
// m = t[0]n'[0] mod W
m = t[0] * qInvNeg
// -----------------------------------
// Second loop
C = madd0(m, q0, t[0])
C, t[0] = madd2(m, q1, t[1], C)
C, t[1] = madd2(m, q2, t[2], C)
C, t[2] = madd2(m, q3, t[3], C)
t[3], C = bits.Add64(t[4], C, 0)
t[4], _ = bits.Add64(0, D, C)
// -----------------------------------
// First loop
C, t[0] = madd1(y[2], x[0], t[0])
C, t[1] = madd2(y[2], x[1], t[1], C)
C, t[2] = madd2(y[2], x[2], t[2], C)
C, t[3] = madd2(y[2], x[3], t[3], C)
t[4], D = bits.Add64(t[4], C, 0)
// m = t[0]n'[0] mod W
m = t[0] * qInvNeg
// -----------------------------------
// Second loop
C = madd0(m, q0, t[0])
C, t[0] = madd2(m, q1, t[1], C)
C, t[1] = madd2(m, q2, t[2], C)
C, t[2] = madd2(m, q3, t[3], C)
t[3], C = bits.Add64(t[4], C, 0)
t[4], _ = bits.Add64(0, D, C)
// -----------------------------------
// First loop
C, t[0] = madd1(y[3], x[0], t[0])
C, t[1] = madd2(y[3], x[1], t[1], C)
C, t[2] = madd2(y[3], x[2], t[2], C)
C, t[3] = madd2(y[3], x[3], t[3], C)
t[4], D = bits.Add64(t[4], C, 0)
// m = t[0]n'[0] mod W
m = t[0] * qInvNeg
// -----------------------------------
// Second loop
C = madd0(m, q0, t[0])
C, t[0] = madd2(m, q1, t[1], C)
C, t[1] = madd2(m, q2, t[2], C)
C, t[2] = madd2(m, q3, t[3], C)
t[3], C = bits.Add64(t[4], C, 0)
t[4], _ = bits.Add64(0, D, C)
if t[4] != 0 {
// we need to reduce, we have a result on 5 words
var b uint64
z[0], b = bits.Sub64(t[0], q0, 0)
z[1], b = bits.Sub64(t[1], q1, b)
z[2], b = bits.Sub64(t[2], q2, b)
z[3], _ = bits.Sub64(t[3], q3, b)
return
}
// copy t into z
z[0] = t[0]
z[1] = t[1]
z[2] = t[2]
z[3] = t[3]
// if z ⩾ q → z -= q
if !z.smallerThanModulus() {
var b uint64
z[0], b = bits.Sub64(z[0], q0, 0)
z[1], b = bits.Sub64(z[1], q1, b)
z[2], b = bits.Sub64(z[2], q2, b)
z[3], _ = bits.Sub64(z[3], q3, b)
}
}
func _fromMontGeneric(z *Element) {
// the following lines implement z = z * 1
// with a modified CIOS montgomery multiplication
// see Mul for algorithm documentation
{
// m = z[0]n'[0] mod W
m := z[0] * qInvNeg
C := madd0(m, q0, z[0])
C, z[0] = madd2(m, q1, z[1], C)
C, z[1] = madd2(m, q2, z[2], C)
C, z[2] = madd2(m, q3, z[3], C)
z[3] = C
}
{
// m = z[0]n'[0] mod W
m := z[0] * qInvNeg
C := madd0(m, q0, z[0])
C, z[0] = madd2(m, q1, z[1], C)
C, z[1] = madd2(m, q2, z[2], C)
C, z[2] = madd2(m, q3, z[3], C)
z[3] = C
}
{
// m = z[0]n'[0] mod W
m := z[0] * qInvNeg
C := madd0(m, q0, z[0])
C, z[0] = madd2(m, q1, z[1], C)
C, z[1] = madd2(m, q2, z[2], C)
C, z[2] = madd2(m, q3, z[3], C)
z[3] = C
}
{
// m = z[0]n'[0] mod W
m := z[0] * qInvNeg
C := madd0(m, q0, z[0])
C, z[0] = madd2(m, q1, z[1], C)
C, z[1] = madd2(m, q2, z[2], C)
C, z[2] = madd2(m, q3, z[3], C)
z[3] = C
}
// if z ⩾ q → z -= q
if !z.smallerThanModulus() {
var b uint64
z[0], b = bits.Sub64(z[0], q0, 0)
z[1], b = bits.Sub64(z[1], q1, b)
z[2], b = bits.Sub64(z[2], q2, b)
z[3], _ = bits.Sub64(z[3], q3, b)
}
}
func _reduceGeneric(z *Element) {
// if z ⩾ q → z -= q
if !z.smallerThanModulus() {
var b uint64
z[0], b = bits.Sub64(z[0], q0, 0)
z[1], b = bits.Sub64(z[1], q1, b)
z[2], b = bits.Sub64(z[2], q2, b)
z[3], _ = bits.Sub64(z[3], q3, b)
}
}
// BatchInvert returns a new slice with every element inverted.
// Uses Montgomery batch inversion trick
func BatchInvert(a []Element) []Element {
res := make([]Element, len(a))
if len(a) == 0 {
return res
}
zeroes := bitset.New(uint(len(a)))
accumulator := One()
for i := 0; i < len(a); i++ {
if a[i].IsZero() {
zeroes.Set(uint(i))
continue
}
res[i] = accumulator
accumulator.Mul(&accumulator, &a[i])
}
accumulator.Inverse(&accumulator)
for i := len(a) - 1; i >= 0; i-- {
if zeroes.Test(uint(i)) {
continue
}
res[i].Mul(&res[i], &accumulator)
accumulator.Mul(&accumulator, &a[i])
}
return res
}
func _butterflyGeneric(a, b *Element) {
t := *a
a.Add(a, b)
b.Sub(&t, b)
}
// BitLen returns the minimum number of bits needed to represent z
// returns 0 if z == 0
func (z *Element) BitLen() int {
if z[3] != 0 {
return 192 + bits.Len64(z[3])
}
if z[2] != 0 {
return 128 + bits.Len64(z[2])
}
if z[1] != 0 {
return 64 + bits.Len64(z[1])
}
return bits.Len64(z[0])
}
// Hash msg to count prime field elements.
// https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-06#section-5.2
func Hash(msg, dst []byte, count int) ([]Element, error) {
// 128 bits of security
// L = ceil((ceil(log2(p)) + k) / 8), where k is the security parameter = 128
const Bytes = 1 + (Bits-1)/8
const L = 16 + Bytes
lenInBytes := count * L
pseudoRandomBytes, err := hash.ExpandMsgXmd(msg, dst, lenInBytes)
if err != nil {
return nil, err
}
// get temporary big int from the pool
vv := pool.BigInt.Get()
res := make([]Element, count)
for i := 0; i < count; i++ {
vv.SetBytes(pseudoRandomBytes[i*L : (i+1)*L])
res[i].SetBigInt(vv)
}
// release object into pool
pool.BigInt.Put(vv)
return res, nil
}
// Exp z = xᵏ (mod q)
func (z *Element) Exp(x Element, k *big.Int) *Element {
if k.IsUint64() && k.Uint64() == 0 {
return z.SetOne()
}
e := k
if k.Sign() == -1 {
// negative k, we invert
// if k < 0: xᵏ (mod q) == (x⁻¹)ᵏ (mod q)
x.Inverse(&x)
// we negate k in a temp big.Int since
// Int.Bit(_) of k and -k is different
e = pool.BigInt.Get()
defer pool.BigInt.Put(e)
e.Neg(k)
}
z.Set(&x)
for i := e.BitLen() - 2; i >= 0; i-- {
z.Square(z)
if e.Bit(i) == 1 {
z.Mul(z, &x)
}
}
return z
}
// rSquare where r is the Montgommery constant
// see section 2.3.2 of Tolga Acar's thesis
// https://www.microsoft.com/en-us/research/wp-content/uploads/1998/06/97Acar.pdf
var rSquare = Element{
6242551132904523857,
16951295617263545407,
10923821274252739203,
584663452775307866,
}
// toMont converts z to Montgomery form
// sets and returns z = z * r²
func (z *Element) toMont() *Element {
return z.Mul(z, &rSquare)
}
// String returns the decimal representation of z as generated by
// z.Text(10).
func (z *Element) String() string {
return z.Text(10)
}
// toBigInt returns z as a big.Int in Montgomery form
func (z *Element) toBigInt(res *big.Int) *big.Int {
var b [Bytes]byte
binary.BigEndian.PutUint64(b[24:32], z[0])
binary.BigEndian.PutUint64(b[16:24], z[1])
binary.BigEndian.PutUint64(b[8:16], z[2])
binary.BigEndian.PutUint64(b[0:8], z[3])
return res.SetBytes(b[:])
}
// Text returns the string representation of z in the given base.
// Base must be between 2 and 36, inclusive. The result uses the
// lower-case letters 'a' to 'z' for digit values 10 to 35.
// No prefix (such as "0x") is added to the string. If z is a nil
// pointer it returns "<nil>".
// If base == 10 and -z fits in a uint16 prefix "-" is added to the string.
func (z *Element) Text(base int) string {
if base < 2 || base > 36 {
panic("invalid base")
}
if z == nil {
return "<nil>"
}
const maxUint16 = 65535
if base == 10 {
var zzNeg Element
zzNeg.Neg(z)
zzNeg.fromMont()
if zzNeg.FitsOnOneWord() && zzNeg[0] <= maxUint16 && zzNeg[0] != 0 {
return "-" + strconv.FormatUint(zzNeg[0], base)
}
}
zz := *z
zz.fromMont()
if zz.FitsOnOneWord() {
return strconv.FormatUint(zz[0], base)
}
vv := pool.BigInt.Get()
r := zz.toBigInt(vv).Text(base)
pool.BigInt.Put(vv)
return r
}
// BigInt sets and return z as a *big.Int
func (z *Element) BigInt(res *big.Int) *big.Int {
_z := *z
_z.fromMont()
return _z.toBigInt(res)
}
// ToBigIntRegular returns z as a big.Int in regular form
//
// Deprecated: use BigInt(*big.Int) instead
func (z Element) ToBigIntRegular(res *big.Int) *big.Int {
z.fromMont()
return z.toBigInt(res)
}
// Bits provides access to z by returning its value as a little-endian [4]uint64 array.
// Bits is intended to support implementation of missing low-level Element
// functionality outside this package; it should be avoided otherwise.
func (z *Element) Bits() [4]uint64 {
_z := *z
fromMont(&_z)
return _z
}
// Bytes returns the value of z as a big-endian byte array
func (z *Element) Bytes() (res [Bytes]byte) {
BigEndian.PutElement(&res, *z)
return
}
// Marshal returns the value of z as a big-endian byte slice
func (z *Element) Marshal() []byte {
b := z.Bytes()
return b[:]
}
// Unmarshal is an alias for SetBytes, it sets z to the value of e.
func (z *Element) Unmarshal(e []byte) {
z.SetBytes(e)
}
// SetBytes interprets e as the bytes of a big-endian unsigned integer,
// sets z to that value, and returns z.
func (z *Element) SetBytes(e []byte) *Element {
if len(e) == Bytes {
// fast path
v, err := BigEndian.Element((*[Bytes]byte)(e))
if err == nil {
*z = v
return z
}
}
// slow path.
// get a big int from our pool
vv := pool.BigInt.Get()
vv.SetBytes(e)
// set big int
z.SetBigInt(vv)
// put temporary object back in pool
pool.BigInt.Put(vv)
return z
}
// SetBytesCanonical interprets e as the bytes of a big-endian 32-byte integer.
// If e is not a 32-byte slice or encodes a value higher than q,
// SetBytesCanonical returns an error.
func (z *Element) SetBytesCanonical(e []byte) error {
if len(e) != Bytes {
return errors.New("invalid fr.Element encoding")
}
v, err := BigEndian.Element((*[Bytes]byte)(e))
if err != nil {
return err
}
*z = v
return nil
}
// SetBigInt sets z to v and returns z
func (z *Element) SetBigInt(v *big.Int) *Element {
z.SetZero()
var zero big.Int
// fast path
c := v.Cmp(&_modulus)
if c == 0 {
// v == 0
return z
} else if c != 1 && v.Cmp(&zero) != -1 {
// 0 < v < q
return z.setBigInt(v)
}
// get temporary big int from the pool
vv := pool.BigInt.Get()
// copy input + modular reduction
vv.Mod(v, &_modulus)
// set big int byte value
z.setBigInt(vv)
// release object into pool
pool.BigInt.Put(vv)
return z
}
// setBigInt assumes 0 ⩽ v < q
func (z *Element) setBigInt(v *big.Int) *Element {
vBits := v.Bits()
if bits.UintSize == 64 {
for i := 0; i < len(vBits); i++ {
z[i] = uint64(vBits[i])
}
} else {
for i := 0; i < len(vBits); i++ {
if i%2 == 0 {
z[i/2] = uint64(vBits[i])
} else {
z[i/2] |= uint64(vBits[i]) << 32
}
}
}
return z.toMont()
}