// Copyright 2017 The go-ethereum Authors
// This file is part of the go-ethereum library.
//
// The go-ethereum library is free software: you can redistribute it and/or modify
// it under the terms of the GNU Lesser General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
//
// The go-ethereum library is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU Lesser General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public License
// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
// Package math provides integer math utilities.
package math
import (
"fmt"
"math/big"
)
// Various big integer limit values.
var (
tt255 = BigPow(2, 255)
tt256 = BigPow(2, 256)
tt256m1 = new(big.Int).Sub(tt256, big.NewInt(1))
tt63 = BigPow(2, 63)
MaxBig256 = new(big.Int).Set(tt256m1)
MaxBig63 = new(big.Int).Sub(tt63, big.NewInt(1))
)
const (
// number of bits in a big.Word
wordBits = 32 << (uint64(^big.Word(0)) >> 63)
// number of bytes in a big.Word
wordBytes = wordBits / 8
)
// HexOrDecimal256 marshals big.Int as hex or decimal.
type HexOrDecimal256 big.Int
// UnmarshalText implements encoding.TextUnmarshaler.
func (i *HexOrDecimal256) UnmarshalText(input []byte) error {
bigint, ok := ParseBig256(string(input))
if !ok {
return fmt.Errorf("invalid hex or decimal integer %q", input)
}
*i = HexOrDecimal256(*bigint)
return nil
}
// MarshalText implements encoding.TextMarshaler.
func (i *HexOrDecimal256) MarshalText() ([]byte, error) {
if i == nil {
return []byte("0x0"), nil
}
return []byte(fmt.Sprintf("%#x", (*big.Int)(i))), nil
}
// ParseBig256 parses s as a 256 bit integer in decimal or hexadecimal syntax.
// Leading zeros are accepted. The empty string parses as zero.
func ParseBig256(s string) (*big.Int, bool) {
if s == "" {
return new(big.Int), true
}
var bigint *big.Int
var ok bool
if len(s) >= 2 && (s[:2] == "0x" || s[:2] == "0X") {
bigint, ok = new(big.Int).SetString(s[2:], 16)
} else {
bigint, ok = new(big.Int).SetString(s, 10)
}
if ok && bigint.BitLen() > 256 {
bigint, ok = nil, false
}
return bigint, ok
}
// MustParseBig256 parses s as a 256 bit big integer and panics if the string is invalid.
func MustParseBig256(s string) *big.Int {
v, ok := ParseBig256(s)
if !ok {
panic("invalid 256 bit integer: " + s)
}
return v
}
// BigPow returns a ** b as a big integer.
func BigPow(a, b int64) *big.Int {
r := big.NewInt(a)
return r.Exp(r, big.NewInt(b), nil)
}
// BigMax returns the larger of x or y.
func BigMax(x, y *big.Int) *big.Int {
if x.Cmp(y) < 0 {
return y
}
return x
}
// BigMin returns the smaller of x or y.
func BigMin(x, y *big.Int) *big.Int {
if x.Cmp(y) > 0 {
return y
}
return x
}
// FirstBitSet returns the index of the first 1 bit in v, counting from LSB.
func FirstBitSet(v *big.Int) int {
for i := 0; i < v.BitLen(); i++ {
if v.Bit(i) > 0 {
return i
}
}
return v.BitLen()
}
// PaddedBigBytes encodes a big integer as a big-endian byte slice. The length
// of the slice is at least n bytes.
func PaddedBigBytes(bigint *big.Int, n int) []byte {
if bigint.BitLen()/8 >= n {
return bigint.Bytes()
}
ret := make([]byte, n)
ReadBits(bigint, ret)
return ret
}
// bigEndianByteAt returns the byte at position n,
// in Big-Endian encoding
// So n==0 returns the least significant byte
func bigEndianByteAt(bigint *big.Int, n int) byte {
words := bigint.Bits()
// Check word-bucket the byte will reside in
i := n / wordBytes
if i >= len(words) {
return byte(0)
}
word := words[i]
// Offset of the byte
shift := 8 * uint(n%wordBytes)
return byte(word >> shift)
}
// Byte returns the byte at position n,
// with the supplied padlength in Little-Endian encoding.
// n==0 returns the MSB
// Example: bigint '5', padlength 32, n=31 => 5
func Byte(bigint *big.Int, padlength, n int) byte {
if n >= padlength {
return byte(0)
}
return bigEndianByteAt(bigint, padlength-1-n)
}
// ReadBits encodes the absolute value of bigint as big-endian bytes. Callers must ensure
// that buf has enough space. If buf is too short the result will be incomplete.
func ReadBits(bigint *big.Int, buf []byte) {
i := len(buf)
for _, d := range bigint.Bits() {
for j := 0; j < wordBytes && i > 0; j++ {
i--
buf[i] = byte(d)
d >>= 8
}
}
}
// U256 encodes as a 256 bit two's complement number. This operation is destructive.
func U256(x *big.Int) *big.Int {
return x.And(x, tt256m1)
}
// S256 interprets x as a two's complement number.
// x must not exceed 256 bits (the result is undefined if it does) and is not modified.
//
// S256(0) = 0
// S256(1) = 1
// S256(2**255) = -2**255
// S256(2**256-1) = -1
func S256(x *big.Int) *big.Int {
if x.Cmp(tt255) < 0 {
return x
}
return new(big.Int).Sub(x, tt256)
}
// Exp implements exponentiation by squaring.
// Exp returns a newly-allocated big integer and does not change
// base or exponent. The result is truncated to 256 bits.
//
// Courtesy @karalabe and @chfast
func Exp(base, exponent *big.Int) *big.Int {
result := big.NewInt(1)
for _, word := range exponent.Bits() {
for i := 0; i < wordBits; i++ {
if word&1 == 1 {
U256(result.Mul(result, base))
}
U256(base.Mul(base, base))
word >>= 1
}
}
return result
}
