path: root/common/math/big.go

// 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"
)

var (
    tt255     = BigPow(2, 255)
    tt256     = BigPow(2, 256)
    tt256m1   = new(big.Int).Sub(tt256, big.NewInt(1))
    MaxBig256 = new(big.Int).Set(tt256m1)
    tt63      = BigPow(2, 63)
    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
}