// 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 . // Package math provides integer math utilities. package math import ( "math/big" ) var ( tt255 = BigPow(2, 255) tt256 = BigPow(2, 256) tt256m1 = new(big.Int).Sub(tt256, big.NewInt(1)) MaxBig256 = new(big.Int).Set(tt256m1) ) // 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 } // MustParseBig 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 { bytes := bigint.Bytes() if len(bytes) >= n { return bytes } ret := make([]byte, n) return append(ret[:len(ret)-len(bytes)], bytes...) } // 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 } else { return new(big.Int).Sub(x, tt256) } } // wordSize is the size number of bits in a big.Word. const wordSize = 32 << (uint64(^big.Word(0)) >> 63) // 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 < wordSize; i++ { if word&1 == 1 { U256(result.Mul(result, base)) } U256(base.Mul(base, base)) word >>= 1 } } return result }