crypto/common/math/big.go

// Copyright 2025 The Lux Authors
// This file is part of the Lux library.
//
// The Lux 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 Lux 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 Lux library. If not, see <http://www.gnu.org/licenses/>.

// Package math provides integer math utilities.
package math

import (
	"fmt"
	"math/big"
	"math/bits"
)

// Various big integer limit values.
var (
	tt256     = new(big.Int).Lsh(big.NewInt(1), 256)
	tt256m1   = new(big.Int).Sub(tt256, big.NewInt(1))
	tt255     = new(big.Int).Lsh(big.NewInt(1), 255)
	MaxBig256 = new(big.Int).Sub(new(big.Int).Lsh(big.NewInt(1), 256), big.NewInt(1))
	MaxBig63  = new(big.Int).Sub(new(big.Int).Lsh(big.NewInt(1), 63), big.NewInt(1))
)

// 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
}

// 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)
	bigint.FillBytes(ret)
	return ret
}

// ReadBits encodes the absolute value of bigint as big-endian bytes. Callers must ensure
// that bigint is non-negative.
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)
}

// U256Bytes converts a big Int into a 256bit EVM number.
// This operation is destructive.
func U256Bytes(n *big.Int) []byte {
	return PaddedBigBytes(U256(n), 32)
}

// 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)
}

// SafeSub returns x-y and checks for overflow.
func SafeSub(x, y uint64) (uint64, bool) {
	diff, borrowOut := bits.Sub64(x, y, 0)
	return diff, borrowOut != 0
}

// SafeAdd returns x+y and checks for overflow.
func SafeAdd(x, y uint64) (uint64, bool) {
	sum, carryOut := bits.Add64(x, y, 0)
	return sum, carryOut != 0
}

// SafeMul returns x*y and checks for overflow.
func SafeMul(x, y uint64) (uint64, bool) {
	hi, lo := bits.Mul64(x, y)
	return lo, hi != 0
}

// SafeDiv returns x/y and checks for division by zero.
func SafeDiv(x, y uint64) (uint64, error) {
	if y == 0 {
		return 0, fmt.Errorf("division by zero")
	}
	return x / y, nil
}

// 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)
}

// 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)
}

// 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 {
	copyBase := new(big.Int).Set(base)
	result := big.NewInt(1)

	for _, word := range exponent.Bits() {
		for i := 0; i < wordBits; i++ {
			if word&1 == 1 {
				U256(result.Mul(result, copyBase))
			}
			U256(copyBase.Mul(copyBase, copyBase))
			word >>= 1
		}
	}
	return result
}

// Architecture-dependent constants
const (
	// wordBits is the number of bits in a big.Word.
	wordBits = 32 << (uint64(^big.Word(0)) >> 63)
	// wordBytes is the number of bytes in a big.Word.
	wordBytes = wordBits / 8
)