int128.go (10133B)
1 // Copyright 2020 The Libc Authors. All rights reserved. 2 // Use of this source code is governed by a BSD-style 3 // license that can be found in the LICENSE file. 4 5 // Some code is copied and adjusted from 6 // https://github.com/lukechampine/uint128, the original LICENSE file 7 // reproduced below in full as of 2021-01-19: 8 9 /* 10 The MIT License (MIT) 11 12 Copyright (c) 2019 Luke Champine 13 14 Permission is hereby granted, free of charge, to any person obtaining a copy 15 of this software and associated documentation files (the "Software"), to deal 16 in the Software without restriction, including without limitation the rights 17 to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 18 copies of the Software, and to permit persons to whom the Software is 19 furnished to do so, subject to the following conditions: 20 21 The above copyright notice and this permission notice shall be included in 22 all copies or substantial portions of the Software. 23 24 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 25 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 26 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 27 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 28 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 29 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 30 THE SOFTWARE. 31 */ 32 33 package libc // import "modernc.org/libc" 34 35 import ( 36 mbits "math/bits" 37 38 "modernc.org/mathutil" 39 ) 40 41 type Int128 mathutil.Int128 42 43 var ( 44 int128Minus1 = Int128{-1, -1} 45 int128Plus1 = Int128{Lo: 1} 46 ) 47 48 func Int128FromFloat32(n float32) Int128 { return Int128(mathutil.NewInt128FromFloat32(n)) } 49 func Int128FromFloat64(n float64) Int128 { return Int128(mathutil.NewInt128FromFloat64(n)) } 50 func Int128FromInt16(n int16) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 51 func Int128FromInt32(n int32) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 52 func Int128FromInt64(n int64) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 53 func Int128FromInt8(n int8) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 54 func Int128FromUint16(n uint16) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 55 func Int128FromUint32(n uint32) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 56 func Int128FromUint64(n uint64) Int128 { return Int128(mathutil.NewInt128FromUint64(n)) } 57 func Int128FromUint8(n uint8) Int128 { return Int128(mathutil.NewInt128FromInt64(int64(n))) } 58 func Int128FromUint128(n Uint128) Int128 { return Int128{Lo: int64(n.Lo), Hi: int64(n.Hi)} } 59 60 func (n *Int128) LValueDec() { *n = n.Add(int128Minus1) } 61 func (n *Int128) LValueInc() { *n = n.Add(int128Plus1) } 62 func (n *Int128) LValueShl(c int32) { *n = n.Shl(c) } 63 func (n *Int128) LValueShr(c int32) { *n = n.Shr(c) } 64 func (n Int128) And(v Int128) Int128 { return Int128{n.Lo & v.Lo, n.Hi & v.Hi} } 65 func (n Int128) Cmp(y Int128) int { return mathutil.Int128(n).Cmp(mathutil.Int128(y)) } 66 func (n Int128) Int16() int16 { return int16(n.Lo) } 67 func (n Int128) Int32() int32 { return int32(n.Lo) } 68 func (n Int128) Int64() int64 { return int64(n.Lo) } 69 func (n Int128) Int8() int8 { return int8(n.Lo) } 70 func (n Int128) Or(v Int128) Int128 { return Int128{n.Lo | v.Lo, n.Hi | v.Hi} } 71 func (n Int128) Uint128() (r Uint128) { return Uint128{uint64(n.Lo), uint64(n.Hi)} } 72 func (n Int128) Uint16() uint16 { return uint16(n.Lo) } 73 func (n Int128) Uint32() uint32 { return uint32(n.Lo) } 74 func (n Int128) Uint64() uint64 { return uint64(n.Lo) } 75 func (n Int128) Uint8() uint8 { return uint8(n.Lo) } 76 func (n Int128) Xor(v Int128) Int128 { return Int128{n.Lo ^ v.Lo, n.Hi ^ v.Hi} } 77 78 func (n Int128) Neg() Int128 { 79 n.Lo ^= -1 80 n.Hi ^= -1 81 return n.Add(int128Plus1) 82 } 83 84 func (n Int128) Float32() float32 { 85 switch n.Hi { 86 case 0: 87 return float32(uint64(n.Lo)) 88 case -1: 89 return -float32(uint64(n.Lo)) 90 } 91 92 if n.Hi < 0 { 93 n = n.Neg() 94 return -float32(n.Hi)*(1<<64) + float32(uint64(n.Lo)) 95 } 96 97 return -float32(n.Hi)*(1<<64) + float32(uint64(n.Lo)) 98 } 99 100 func (n Int128) Float64() float64 { 101 switch n.Hi { 102 case 0: 103 return float64(uint64(n.Lo)) 104 case -1: 105 return -float64(uint64(n.Lo)) 106 } 107 108 if n.Hi < 0 { 109 n = n.Neg() 110 return -float64(n.Hi)*(1<<64) + float64(uint64(n.Lo)) 111 } 112 113 return float64(n.Hi)*(1<<64) + float64(uint64(n.Lo)) 114 } 115 116 func (n Int128) Add(m Int128) (r Int128) { 117 r.Lo = n.Lo + m.Lo 118 r.Hi = n.Hi + m.Hi 119 if uint64(r.Lo) < uint64(n.Lo) { 120 r.Hi++ 121 } 122 return r 123 } 124 125 func (n Int128) Mul(m Int128) Int128 { 126 hi, lo := mbits.Mul64(uint64(n.Lo), uint64(m.Lo)) 127 _, p1 := mbits.Mul64(uint64(n.Hi), uint64(m.Lo)) 128 _, p3 := mbits.Mul64(uint64(n.Lo), uint64(m.Hi)) 129 hi, _ = mbits.Add64(hi, p1, 0) 130 hi, _ = mbits.Add64(hi, p3, 0) 131 return Int128{int64(lo), int64(hi)} 132 } 133 134 func (n Int128) Shl(c int32) (r Int128) { 135 if c > 64 { 136 r.Lo = 0 137 r.Hi = n.Lo << (c - 64) 138 } else { 139 r.Lo = n.Lo << c 140 r.Hi = n.Hi<<c | n.Lo>>(64-c) 141 } 142 return r 143 } 144 145 func (n Int128) Shr(c int32) (r Int128) { 146 if c > 64 { 147 r.Lo = n.Hi >> (c - 64) 148 switch { 149 case n.Hi < 0: 150 r.Hi = -1 151 default: 152 r.Hi = 0 153 } 154 } else { 155 r.Lo = n.Lo>>c | n.Hi<<(64-c) 156 r.Hi = n.Hi >> c 157 } 158 return r 159 } 160 161 type Uint128 mathutil.Uint128 162 163 func Uint128FromFloat32(n float32) Uint128 { return Uint128(mathutil.NewUint128FromFloat32(n)) } 164 func Uint128FromFloat64(n float64) Uint128 { return Uint128(mathutil.NewUint128FromFloat64(n)) } 165 func Uint128FromInt128(n Int128) Uint128 { return Uint128{Lo: uint64(n.Lo), Hi: uint64(n.Hi)} } 166 func Uint128FromInt16(n int16) Uint128 { return Uint128FromInt64(int64(n)) } 167 func Uint128FromInt32(n int32) Uint128 { return Uint128FromInt64(int64(n)) } 168 func Uint128FromInt8(n int8) Uint128 { return Uint128FromInt64(int64(n)) } 169 func Uint128FromUint16(n uint16) Uint128 { return Uint128{Lo: uint64(n)} } 170 func Uint128FromUint32(n uint32) Uint128 { return Uint128{Lo: uint64(n)} } 171 func Uint128FromUint64(n uint64) Uint128 { return Uint128{Lo: n} } 172 func Uint128FromUint8(n uint8) Uint128 { return Uint128{Lo: uint64(n)} } 173 174 func Uint128FromInt64(n int64) (r Uint128) { 175 r.Lo = uint64(n) 176 if n < 0 { 177 r.Hi = ^uint64(0) 178 } 179 return r 180 } 181 182 func (n *Uint128) LValueShl(c int32) { *n = n.Shl(c) } 183 func (n *Uint128) LValueShr(c int32) { *n = n.Shr(c) } 184 func (n Uint128) And(m Uint128) Uint128 { return Uint128{n.Lo & m.Lo, n.Hi & m.Hi} } 185 func (n Uint128) Int128() Int128 { return Int128{int64(n.Lo), int64(n.Hi)} } 186 func (n Uint128) Int16() int16 { return int16(n.Lo) } 187 func (n Uint128) Int32() int32 { return int32(n.Lo) } 188 func (n Uint128) Int64() int64 { return int64(n.Lo) } 189 func (n Uint128) Int8() int8 { return int8(n.Lo) } 190 func (n Uint128) Or(m Uint128) Uint128 { return Uint128{n.Lo | m.Lo, n.Hi | m.Hi} } 191 func (n Uint128) Uint16() uint16 { return uint16(n.Lo) } 192 func (n Uint128) Uint32() uint32 { return uint32(n.Lo) } 193 func (n Uint128) Uint64() uint64 { return n.Lo } 194 func (n Uint128) Uint8() uint8 { return uint8(n.Lo) } 195 func (n Uint128) Xor(m Uint128) Uint128 { return Uint128{n.Lo ^ m.Lo, n.Hi ^ m.Hi} } 196 197 func (n Uint128) Add(m Uint128) (r Uint128) { 198 var carry uint64 199 r.Lo, carry = mbits.Add64(n.Lo, m.Lo, 0) 200 r.Hi, _ = mbits.Add64(n.Hi, m.Hi, carry) 201 return r 202 } 203 204 func (n Uint128) Mul(m Uint128) Uint128 { 205 hi, lo := mbits.Mul64(n.Lo, m.Lo) 206 _, p1 := mbits.Mul64(n.Hi, m.Lo) 207 _, p3 := mbits.Mul64(n.Lo, m.Hi) 208 hi, _ = mbits.Add64(hi, p1, 0) 209 hi, _ = mbits.Add64(hi, p3, 0) 210 return Uint128{lo, hi} 211 } 212 213 func (n Uint128) Shr(c int32) (r Uint128) { 214 if c > 64 { 215 r.Lo = n.Hi >> (c - 64) 216 r.Hi = 0 217 } else { 218 r.Lo = n.Lo>>c | n.Hi<<(64-c) 219 r.Hi = n.Hi >> c 220 } 221 return r 222 } 223 224 func (n Uint128) mulOvf(m Uint128) (_ Uint128, ovf bool) { 225 hi, lo := mbits.Mul64(n.Lo, m.Lo) 226 p0, p1 := mbits.Mul64(n.Hi, m.Lo) 227 p2, p3 := mbits.Mul64(n.Lo, m.Hi) 228 hi, c0 := mbits.Add64(hi, p1, 0) 229 hi, c1 := mbits.Add64(hi, p3, 0) 230 ovf = p0 != 0 || p2 != 0 || c0 != 0 || c1 != 0 231 return Uint128{lo, hi}, ovf 232 } 233 234 func (n Uint128) quoRem(m Uint128) (q, r Uint128) { 235 if m.Hi == 0 { 236 var r64 uint64 237 q, r64 = n.quoRem64(m.Lo) 238 r = Uint128FromUint64(r64) 239 } else { 240 // generate a "trial quotient," guaranteed to be within 1 of the actual 241 // quotient, then adjust. 242 nz := mbits.LeadingZeros64(m.Hi) 243 v1 := m.Shl(int32(nz)) 244 u1 := n.Shr(1) 245 tq, _ := mbits.Div64(u1.Hi, u1.Lo, v1.Hi) 246 tq >>= 63 - nz 247 if tq != 0 { 248 tq-- 249 } 250 q = Uint128FromUint64(tq) 251 // calculate remainder using trial quotient, then adjust if remainder is 252 // greater than divisor 253 r = n.Sub(m.mul64(tq)) 254 if r.Cmp(m) >= 0 { 255 q = q.add64(1) 256 r = r.Sub(m) 257 } 258 } 259 return 260 } 261 262 func (n Uint128) quoRem64(m uint64) (q Uint128, r uint64) { 263 if n.Hi < m { 264 q.Lo, r = mbits.Div64(n.Hi, n.Lo, m) 265 } else { 266 q.Hi, r = mbits.Div64(0, n.Hi, m) 267 q.Lo, r = mbits.Div64(r, n.Lo, m) 268 } 269 return 270 } 271 272 func (n Uint128) Div(m Uint128) (r Uint128) { 273 r, _ = n.quoRem(m) 274 return r 275 } 276 277 func (n Uint128) Shl(c int32) (r Uint128) { 278 if c > 64 { 279 r.Lo = 0 280 r.Hi = n.Lo << (c - 64) 281 } else { 282 r.Lo = n.Lo << c 283 r.Hi = n.Hi<<c | n.Lo>>(64-c) 284 } 285 return 286 } 287 288 func (n Uint128) Sub(m Uint128) Uint128 { 289 lo, borrow := mbits.Sub64(n.Lo, m.Lo, 0) 290 hi, _ := mbits.Sub64(n.Hi, m.Hi, borrow) 291 return Uint128{lo, hi} 292 } 293 294 func (n Uint128) mul64(m uint64) Uint128 { 295 hi, lo := mbits.Mul64(n.Lo, m) 296 _, p1 := mbits.Mul64(n.Hi, m) 297 hi, _ = mbits.Add64(hi, p1, 0) 298 return Uint128{lo, hi} 299 } 300 301 func (n Uint128) Cmp(m Uint128) int { 302 if n == m { 303 return 0 304 } else if n.Hi < m.Hi || (n.Hi == m.Hi && n.Lo < m.Lo) { 305 return -1 306 } else { 307 return 1 308 } 309 } 310 311 func (n Uint128) add64(m uint64) Uint128 { 312 lo, carry := mbits.Add64(n.Lo, m, 0) 313 hi, _ := mbits.Add64(n.Hi, 0, carry) 314 return Uint128{lo, hi} 315 } 316 317 func (n Uint128) Float32() float32 { 318 if n.Hi == 0 { 319 return float32(uint64(n.Lo)) 320 } 321 322 return float32(n.Hi)*(1<<64) + float32(uint64(n.Lo)) 323 } 324 325 func (n Uint128) Float64() float64 { 326 if n.Hi == 0 { 327 return float64(uint64(n.Lo)) 328 } 329 330 return float64(n.Hi)*(1<<64) + float64(uint64(n.Lo)) 331 }