github.com/arieschain/arieschain@v0.0.0-20191023063405-37c074544356/common/math/big.go (about) 1 // Package math provides integer math utilities. 2 package math 3 4 import ( 5 "fmt" 6 "math/big" 7 ) 8 9 var ( 10 tt255 = BigPow(2, 255) 11 tt256 = BigPow(2, 256) 12 tt256m1 = new(big.Int).Sub(tt256, big.NewInt(1)) 13 MaxBig256 = new(big.Int).Set(tt256m1) 14 tt63 = BigPow(2, 63) 15 MaxBig63 = new(big.Int).Sub(tt63, big.NewInt(1)) 16 ) 17 18 const ( 19 // number of bits in a big.Word 20 wordBits = 32 << (uint64(^big.Word(0)) >> 63) 21 // number of bytes in a big.Word 22 wordBytes = wordBits / 8 23 ) 24 25 // HexOrDecimal256 marshals big.Int as hex or decimal. 26 type HexOrDecimal256 big.Int 27 28 // UnmarshalText implements encoding.TextUnmarshaler. 29 func (i *HexOrDecimal256) UnmarshalText(input []byte) error { 30 bigint, ok := ParseBig256(string(input)) 31 if !ok { 32 return fmt.Errorf("invalid hex or decimal integer %q", input) 33 } 34 *i = HexOrDecimal256(*bigint) 35 return nil 36 } 37 38 // MarshalText implements encoding.TextMarshaler. 39 func (i *HexOrDecimal256) MarshalText() ([]byte, error) { 40 if i == nil { 41 return []byte("0x0"), nil 42 } 43 return []byte(fmt.Sprintf("%#x", (*big.Int)(i))), nil 44 } 45 46 // ParseBig256 parses s as a 256 bit integer in decimal or hexadecimal syntax. 47 // Leading zeros are accepted. The empty string parses as zero. 48 func ParseBig256(s string) (*big.Int, bool) { 49 if s == "" { 50 return new(big.Int), true 51 } 52 var bigint *big.Int 53 var ok bool 54 if len(s) >= 2 && (s[:2] == "0x" || s[:2] == "0X") { 55 bigint, ok = new(big.Int).SetString(s[2:], 16) 56 } else { 57 bigint, ok = new(big.Int).SetString(s, 10) 58 } 59 if ok && bigint.BitLen() > 256 { 60 bigint, ok = nil, false 61 } 62 return bigint, ok 63 } 64 65 // MustParseBig parses s as a 256 bit big integer and panics if the string is invalid. 66 func MustParseBig256(s string) *big.Int { 67 v, ok := ParseBig256(s) 68 if !ok { 69 panic("invalid 256 bit integer: " + s) 70 } 71 return v 72 } 73 74 // BigPow returns a ** b as a big integer. 75 func BigPow(a, b int64) *big.Int { 76 r := big.NewInt(a) 77 return r.Exp(r, big.NewInt(b), nil) 78 } 79 80 // BigMax returns the larger of x or y. 81 func BigMax(x, y *big.Int) *big.Int { 82 if x.Cmp(y) < 0 { 83 return y 84 } 85 return x 86 } 87 88 // BigMin returns the smaller of x or y. 89 func BigMin(x, y *big.Int) *big.Int { 90 if x.Cmp(y) > 0 { 91 return y 92 } 93 return x 94 } 95 96 // FirstBitSet returns the index of the first 1 bit in v, counting from LSB. 97 func FirstBitSet(v *big.Int) int { 98 for i := 0; i < v.BitLen(); i++ { 99 if v.Bit(i) > 0 { 100 return i 101 } 102 } 103 return v.BitLen() 104 } 105 106 // PaddedBigBytes encodes a big integer as a big-endian byte slice. The length 107 // of the slice is at least n bytes. 108 func PaddedBigBytes(bigint *big.Int, n int) []byte { 109 if bigint.BitLen()/8 >= n { 110 return bigint.Bytes() 111 } 112 ret := make([]byte, n) 113 ReadBits(bigint, ret) 114 return ret 115 } 116 117 // bigEndianByteAt returns the byte at position n, 118 // in Big-Endian encoding 119 // So n==0 returns the least significant byte 120 func bigEndianByteAt(bigint *big.Int, n int) byte { 121 words := bigint.Bits() 122 // Check word-bucket the byte will reside in 123 i := n / wordBytes 124 if i >= len(words) { 125 return byte(0) 126 } 127 word := words[i] 128 // Offset of the byte 129 shift := 8 * uint(n%wordBytes) 130 131 return byte(word >> shift) 132 } 133 134 // Byte returns the byte at position n, 135 // with the supplied padlength in Little-Endian encoding. 136 // n==0 returns the MSB 137 // Example: bigint '5', padlength 32, n=31 => 5 138 func Byte(bigint *big.Int, padlength, n int) byte { 139 if n >= padlength { 140 return byte(0) 141 } 142 return bigEndianByteAt(bigint, padlength-1-n) 143 } 144 145 // ReadBits encodes the absolute value of bigint as big-endian bytes. Callers must ensure 146 // that buf has enough space. If buf is too short the result will be incomplete. 147 func ReadBits(bigint *big.Int, buf []byte) { 148 i := len(buf) 149 for _, d := range bigint.Bits() { 150 for j := 0; j < wordBytes && i > 0; j++ { 151 i-- 152 buf[i] = byte(d) 153 d >>= 8 154 } 155 } 156 } 157 158 // U256 encodes as a 256 bit two's complement number. This operation is destructive. 159 func U256(x *big.Int) *big.Int { 160 return x.And(x, tt256m1) 161 } 162 163 // S256 interprets x as a two's complement number. 164 // x must not exceed 256 bits (the result is undefined if it does) and is not modified. 165 // 166 // S256(0) = 0 167 // S256(1) = 1 168 // S256(2**255) = -2**255 169 // S256(2**256-1) = -1 170 func S256(x *big.Int) *big.Int { 171 if x.Cmp(tt255) < 0 { 172 return x 173 } else { 174 return new(big.Int).Sub(x, tt256) 175 } 176 } 177 178 // Exp implements exponentiation by squaring. 179 // Exp returns a newly-allocated big integer and does not change 180 // base or exponent. The result is truncated to 256 bits. 181 // 182 // Courtesy @karalabe and @chfast 183 func Exp(base, exponent *big.Int) *big.Int { 184 result := big.NewInt(1) 185 186 for _, word := range exponent.Bits() { 187 for i := 0; i < wordBits; i++ { 188 if word&1 == 1 { 189 U256(result.Mul(result, base)) 190 } 191 U256(base.Mul(base, base)) 192 word >>= 1 193 } 194 } 195 return result 196 }