271 lines
6.9 KiB
Go
271 lines
6.9 KiB
Go
// Copyright 2017 The go-ethereum Authors
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// This file is part of the go-ethereum library.
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//
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// The go-ethereum library is free software: you can redistribute it and/or modify
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// it under the terms of the GNU Lesser General Public License as published by
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// the Free Software Foundation, either version 3 of the License, or
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// (at your option) any later version.
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//
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// The go-ethereum library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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// GNU Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public License
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// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
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// Package math provides integer math utilities.
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package math
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import (
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"fmt"
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"math/big"
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)
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// Various big integer limit values.
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var (
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tt255 = BigPow(2, 255)
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tt256 = BigPow(2, 256)
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tt256m1 = new(big.Int).Sub(tt256, big.NewInt(1))
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tt63 = BigPow(2, 63)
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MaxBig256 = new(big.Int).Set(tt256m1)
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MaxBig63 = new(big.Int).Sub(tt63, big.NewInt(1))
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)
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const (
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// number of bits in a big.Word
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wordBits = 32 << (uint64(^big.Word(0)) >> 63)
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// number of bytes in a big.Word
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wordBytes = wordBits / 8
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)
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// HexOrDecimal256 marshals big.Int as hex or decimal.
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type HexOrDecimal256 big.Int
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// NewHexOrDecimal256 creates a new HexOrDecimal256
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func NewHexOrDecimal256(x int64) *HexOrDecimal256 {
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b := big.NewInt(x)
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h := HexOrDecimal256(*b)
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return &h
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}
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// UnmarshalJSON implements json.Unmarshaler.
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//
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// It is similar to UnmarshalText, but allows parsing real decimals too, not just
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// quoted decimal strings.
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func (i *HexOrDecimal256) UnmarshalJSON(input []byte) error {
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if len(input) > 0 && input[0] == '"' {
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input = input[1 : len(input)-1]
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}
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return i.UnmarshalText(input)
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}
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// UnmarshalText implements encoding.TextUnmarshaler.
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func (i *HexOrDecimal256) UnmarshalText(input []byte) error {
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bigint, ok := ParseBig256(string(input))
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if !ok {
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return fmt.Errorf("invalid hex or decimal integer %q", input)
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}
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*i = HexOrDecimal256(*bigint)
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return nil
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}
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// MarshalText implements encoding.TextMarshaler.
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func (i *HexOrDecimal256) MarshalText() ([]byte, error) {
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if i == nil {
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return []byte("0x0"), nil
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}
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return []byte(fmt.Sprintf("%#x", (*big.Int)(i))), nil
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}
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// Decimal256 unmarshals big.Int as a decimal string. When unmarshalling,
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// it however accepts either "0x"-prefixed (hex encoded) or non-prefixed (decimal)
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type Decimal256 big.Int
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// NewDecimal256 creates a new Decimal256
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func NewDecimal256(x int64) *Decimal256 {
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b := big.NewInt(x)
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d := Decimal256(*b)
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return &d
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}
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// UnmarshalText implements encoding.TextUnmarshaler.
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func (i *Decimal256) UnmarshalText(input []byte) error {
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bigint, ok := ParseBig256(string(input))
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if !ok {
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return fmt.Errorf("invalid hex or decimal integer %q", input)
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}
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*i = Decimal256(*bigint)
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return nil
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}
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// MarshalText implements encoding.TextMarshaler.
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func (i *Decimal256) MarshalText() ([]byte, error) {
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return []byte(i.String()), nil
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}
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// String implements Stringer.
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func (i *Decimal256) String() string {
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if i == nil {
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return "0"
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}
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return fmt.Sprintf("%#d", (*big.Int)(i))
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}
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// ParseBig256 parses s as a 256 bit integer in decimal or hexadecimal syntax.
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// Leading zeros are accepted. The empty string parses as zero.
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func ParseBig256(s string) (*big.Int, bool) {
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if s == "" {
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return new(big.Int), true
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}
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var bigint *big.Int
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var ok bool
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if len(s) >= 2 && (s[:2] == "0x" || s[:2] == "0X") {
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bigint, ok = new(big.Int).SetString(s[2:], 16)
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} else {
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bigint, ok = new(big.Int).SetString(s, 10)
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}
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if ok && bigint.BitLen() > 256 {
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bigint, ok = nil, false
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}
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return bigint, ok
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}
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// MustParseBig256 parses s as a 256 bit big integer and panics if the string is invalid.
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func MustParseBig256(s string) *big.Int {
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v, ok := ParseBig256(s)
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if !ok {
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panic("invalid 256 bit integer: " + s)
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}
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return v
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}
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// BigPow returns a ** b as a big integer.
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func BigPow(a, b int64) *big.Int {
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r := big.NewInt(a)
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return r.Exp(r, big.NewInt(b), nil)
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}
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// BigMax returns the larger of x or y.
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func BigMax(x, y *big.Int) *big.Int {
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if x.Cmp(y) < 0 {
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return y
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}
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return x
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}
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// BigMin returns the smaller of x or y.
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func BigMin(x, y *big.Int) *big.Int {
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if x.Cmp(y) > 0 {
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return y
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}
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return x
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}
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// FirstBitSet returns the index of the first 1 bit in v, counting from LSB.
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func FirstBitSet(v *big.Int) int {
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for i := 0; i < v.BitLen(); i++ {
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if v.Bit(i) > 0 {
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return i
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}
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}
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return v.BitLen()
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}
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// PaddedBigBytes encodes a big integer as a big-endian byte slice. The length
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// of the slice is at least n bytes.
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func PaddedBigBytes(bigint *big.Int, n int) []byte {
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if bigint.BitLen()/8 >= n {
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return bigint.Bytes()
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}
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ret := make([]byte, n)
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ReadBits(bigint, ret)
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return ret
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}
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// bigEndianByteAt returns the byte at position n,
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// in Big-Endian encoding
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// So n==0 returns the least significant byte
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func bigEndianByteAt(bigint *big.Int, n int) byte {
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words := bigint.Bits()
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// Check word-bucket the byte will reside in
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i := n / wordBytes
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if i >= len(words) {
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return byte(0)
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}
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word := words[i]
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// Offset of the byte
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shift := 8 * uint(n%wordBytes)
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return byte(word >> shift)
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}
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// Byte returns the byte at position n,
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// with the supplied padlength in Little-Endian encoding.
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// n==0 returns the MSB
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// Example: bigint '5', padlength 32, n=31 => 5
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func Byte(bigint *big.Int, padlength, n int) byte {
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if n >= padlength {
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return byte(0)
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}
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return bigEndianByteAt(bigint, padlength-1-n)
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}
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// ReadBits encodes the absolute value of bigint as big-endian bytes. Callers must ensure
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// that buf has enough space. If buf is too short the result will be incomplete.
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func ReadBits(bigint *big.Int, buf []byte) {
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i := len(buf)
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for _, d := range bigint.Bits() {
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for j := 0; j < wordBytes && i > 0; j++ {
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i--
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buf[i] = byte(d)
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d >>= 8
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}
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}
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}
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// U256 encodes as a 256 bit two's complement number. This operation is destructive.
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func U256(x *big.Int) *big.Int {
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return x.And(x, tt256m1)
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}
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// U256Bytes converts a big Int into a 256bit EVM number.
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// This operation is destructive.
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func U256Bytes(n *big.Int) []byte {
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return PaddedBigBytes(U256(n), 32)
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}
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// S256 interprets x as a two's complement number.
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// x must not exceed 256 bits (the result is undefined if it does) and is not modified.
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//
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// S256(0) = 0
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// S256(1) = 1
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// S256(2**255) = -2**255
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// S256(2**256-1) = -1
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func S256(x *big.Int) *big.Int {
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if x.Cmp(tt255) < 0 {
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return x
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}
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return new(big.Int).Sub(x, tt256)
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}
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// Exp implements exponentiation by squaring.
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// Exp returns a newly-allocated big integer and does not change
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// base or exponent. The result is truncated to 256 bits.
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//
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// Courtesy @karalabe and @chfast
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func Exp(base, exponent *big.Int) *big.Int {
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result := big.NewInt(1)
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for _, word := range exponent.Bits() {
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for i := 0; i < wordBits; i++ {
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if word&1 == 1 {
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U256(result.Mul(result, base))
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}
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U256(base.Mul(base, base))
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word >>= 1
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}
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}
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return result
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}
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