libgo/go/strconv/atof.go

   1 // Copyright 2009 The Go 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 package strconv
   6
   7 // decimal to binary floating point conversion.
   8 // Algorithm:
   9 //   1) Store input in multiprecision decimal.
  10 //   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
  11 //   3) Multiply by 2^precision and round to get mantissa.
  12
  13 import "math"
  14 import "runtime"
  15
  16 var optimize = true // can change for testing
  17
  18 func equalIgnoreCase(s1, s2 string) bool {
  19         if len(s1) != len(s2) {
  20                 return false
  21         }
  22         for i := 0; i < len(s1); i++ {
  23                 c1 := s1[i]
  24                 if 'A' <= c1 && c1 <= 'Z' {
  25                         c1 += 'a' - 'A'
  26                 }
  27                 c2 := s2[i]
  28                 if 'A' <= c2 && c2 <= 'Z' {
  29                         c2 += 'a' - 'A'
  30                 }
  31                 if c1 != c2 {
  32                         return false
  33                 }
  34         }
  35         return true
  36 }
  37
  38 func special(s string) (f float64, ok bool) {
  39         if len(s) == 0 {
  40                 return
  41         }
  42         switch s[0] {
  43         default:
  44                 return
  45         case '+':
  46                 if equalIgnoreCase(s, "+inf") || equalIgnoreCase(s, "+infinity") {
  47                         return math.Inf(1), true
  48                 }
  49         case '-':
  50                 if equalIgnoreCase(s, "-inf") || equalIgnoreCase(s, "-infinity") {
  51                         return math.Inf(-1), true
  52                 }
  53         case 'n', 'N':
  54                 if equalIgnoreCase(s, "nan") {
  55                         return math.NaN(), true
  56                 }
  57         case 'i', 'I':
  58                 if equalIgnoreCase(s, "inf") || equalIgnoreCase(s, "infinity") {
  59                         return math.Inf(1), true
  60                 }
  61         }
  62         return
  63 }
  64
  65 func (b *decimal) set(s string) (ok bool) {
  66         i := 0
  67         b.neg = false
  68         b.trunc = false
  69
  70         // optional sign
  71         if i >= len(s) {
  72                 return
  73         }
  74         switch {
  75         case s[i] == '+':
  76                 i++
  77         case s[i] == '-':
  78                 b.neg = true
  79                 i++
  80         }
  81
  82         // digits
  83         sawdot := false
  84         sawdigits := false
  85         for ; i < len(s); i++ {
  86                 switch {
  87                 case s[i] == '.':
  88                         if sawdot {
  89                                 return
  90                         }
  91                         sawdot = true
  92                         b.dp = b.nd
  93                         continue
  94
  95                 case '0' <= s[i] && s[i] <= '9':
  96                         sawdigits = true
  97                         if s[i] == '0' && b.nd == 0 { // ignore leading zeros
  98                                 b.dp--
  99                                 continue
 100                         }
 101                         if b.nd < len(b.d) {
 102                                 b.d[b.nd] = s[i]
 103                                 b.nd++
 104                         } else if s[i] != '0' {
 105                                 b.trunc = true
 106                         }
 107                         continue
 108                 }
 109                 break
 110         }
 111         if !sawdigits {
 112                 return
 113         }
 114         if !sawdot {
 115                 b.dp = b.nd
 116         }
 117
 118         // optional exponent moves decimal point.
 119         // if we read a very large, very long number,
 120         // just be sure to move the decimal point by
 121         // a lot (say, 100000).  it doesn't matter if it's
 122         // not the exact number.
 123         if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
 124                 i++
 125                 if i >= len(s) {
 126                         return
 127                 }
 128                 esign := 1
 129                 if s[i] == '+' {
 130                         i++
 131                 } else if s[i] == '-' {
 132                         i++
 133                         esign = -1
 134                 }
 135                 if i >= len(s) || s[i] < '0' || s[i] > '9' {
 136                         return
 137                 }
 138                 e := 0
 139                 for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
 140                         if e < 10000 {
 141                                 e = e*10 + int(s[i]) - '0'
 142                         }
 143                 }
 144                 b.dp += e * esign
 145         }
 146
 147         if i != len(s) {
 148                 return
 149         }
 150
 151         ok = true
 152         return
 153 }
 154
 155 // readFloat reads a decimal mantissa and exponent from a float
 156 // string representation. It sets ok to false if the number could
 157 // not fit return types or is invalid.
 158 func readFloat(s string) (mantissa uint64, exp int, neg, trunc, ok bool) {
 159         const uint64digits = 19
 160         i := 0
 161
 162         // optional sign
 163         if i >= len(s) {
 164                 return
 165         }
 166         switch {
 167         case s[i] == '+':
 168                 i++
 169         case s[i] == '-':
 170                 neg = true
 171                 i++
 172         }
 173
 174         // digits
 175         sawdot := false
 176         sawdigits := false
 177         nd := 0
 178         ndMant := 0
 179         dp := 0
 180         for ; i < len(s); i++ {
 181                 switch c := s[i]; true {
 182                 case c == '.':
 183                         if sawdot {
 184                                 return
 185                         }
 186                         sawdot = true
 187                         dp = nd
 188                         continue
 189
 190                 case '0' <= c && c <= '9':
 191                         sawdigits = true
 192                         if c == '0' && nd == 0 { // ignore leading zeros
 193                                 dp--
 194                                 continue
 195                         }
 196                         nd++
 197                         if ndMant < uint64digits {
 198                                 mantissa *= 10
 199                                 mantissa += uint64(c - '0')
 200                                 ndMant++
 201                         } else if s[i] != '0' {
 202                                 trunc = true
 203                         }
 204                         continue
 205                 }
 206                 break
 207         }
 208         if !sawdigits {
 209                 return
 210         }
 211         if !sawdot {
 212                 dp = nd
 213         }
 214
 215         // optional exponent moves decimal point.
 216         // if we read a very large, very long number,
 217         // just be sure to move the decimal point by
 218         // a lot (say, 100000).  it doesn't matter if it's
 219         // not the exact number.
 220         if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
 221                 i++
 222                 if i >= len(s) {
 223                         return
 224                 }
 225                 esign := 1
 226                 if s[i] == '+' {
 227                         i++
 228                 } else if s[i] == '-' {
 229                         i++
 230                         esign = -1
 231                 }
 232                 if i >= len(s) || s[i] < '0' || s[i] > '9' {
 233                         return
 234                 }
 235                 e := 0
 236                 for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
 237                         if e < 10000 {
 238                                 e = e*10 + int(s[i]) - '0'
 239                         }
 240                 }
 241                 dp += e * esign
 242         }
 243
 244         if i != len(s) {
 245                 return
 246         }
 247
 248         if mantissa != 0 {
 249                 exp = dp - ndMant
 250         }
 251         ok = true
 252         return
 253
 254 }
 255
 256 // decimal power of ten to binary power of two.
 257 var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
 258
 259 func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
 260         var exp int
 261         var mant uint64
 262
 263         // Zero is always a special case.
 264         if d.nd == 0 {
 265                 mant = 0
 266                 exp = flt.bias
 267                 goto out
 268         }
 269
 270         // Obvious overflow/underflow.
 271         // These bounds are for 64-bit floats.
 272         // Will have to change if we want to support 80-bit floats in the future.
 273         if d.dp > 310 {
 274                 goto overflow
 275         }
 276         if d.dp < -330 {
 277                 // zero
 278                 mant = 0
 279                 exp = flt.bias
 280                 goto out
 281         }
 282
 283         // Scale by powers of two until in range [0.5, 1.0)
 284         exp = 0
 285         for d.dp > 0 {
 286                 var n int
 287                 if d.dp >= len(powtab) {
 288                         n = 27
 289                 } else {
 290                         n = powtab[d.dp]
 291                 }
 292                 d.Shift(-n)
 293                 exp += n
 294         }
 295         for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
 296                 var n int
 297                 if -d.dp >= len(powtab) {
 298                         n = 27
 299                 } else {
 300                         n = powtab[-d.dp]
 301                 }
 302                 d.Shift(n)
 303                 exp -= n
 304         }
 305
 306         // Our range is [0.5,1) but floating point range is [1,2).
 307         exp--
 308
 309         // Minimum representable exponent is flt.bias+1.
 310         // If the exponent is smaller, move it up and
 311         // adjust d accordingly.
 312         if exp < flt.bias+1 {
 313                 n := flt.bias + 1 - exp
 314                 d.Shift(-n)
 315                 exp += n
 316         }
 317
 318         if exp-flt.bias >= 1<<flt.expbits-1 {
 319                 goto overflow
 320         }
 321
 322         // Extract 1+flt.mantbits bits.
 323         d.Shift(int(1 + flt.mantbits))
 324         mant = d.RoundedInteger()
 325
 326         // Rounding might have added a bit; shift down.
 327         if mant == 2<<flt.mantbits {
 328                 mant >>= 1
 329                 exp++
 330                 if exp-flt.bias >= 1<<flt.expbits-1 {
 331                         goto overflow
 332                 }
 333         }
 334
 335         // Denormalized?
 336         if mant&(1<<flt.mantbits) == 0 {
 337                 exp = flt.bias
 338         }
 339         goto out
 340
 341 overflow:
 342         // ±Inf
 343         mant = 0
 344         exp = 1<<flt.expbits - 1 + flt.bias
 345         overflow = true
 346
 347 out:
 348         // Assemble bits.
 349         bits := mant & (uint64(1)<<flt.mantbits - 1)
 350         bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
 351         if d.neg {
 352                 bits |= 1 << flt.mantbits << flt.expbits
 353         }
 354         return bits, overflow
 355 }
 356
 357 // Exact powers of 10.
 358 var float64pow10 = []float64{
 359         1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
 360         1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
 361         1e20, 1e21, 1e22,
 362 }
 363 var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
 364
 365 // If possible to convert decimal representation to 64-bit float f exactly,
 366 // entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
 367 // Three common cases:
 368 //      value is exact integer
 369 //      value is exact integer * exact power of ten
 370 //      value is exact integer / exact power of ten
 371 // These all produce potentially inexact but correctly rounded answers.
 372 func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
 373         if mantissa>>float64info.mantbits != 0 {
 374                 return
 375         }
 376         // gccgo gets this wrong on 32-bit i386 when not using -msse.
 377         // See TestRoundTrip in atof_test.go for a test case.
 378         if runtime.GOARCH == "386" {
 379                 return
 380         }
 381         f = float64(mantissa)
 382         if neg {
 383                 f = -f
 384         }
 385         switch {
 386         case exp == 0:
 387                 // an integer.
 388                 return f, true
 389         // Exact integers are <= 10^15.
 390         // Exact powers of ten are <= 10^22.
 391         case exp > 0 && exp <= 15+22: // int * 10^k
 392                 // If exponent is big but number of digits is not,
 393                 // can move a few zeros into the integer part.
 394                 if exp > 22 {
 395                         f *= float64pow10[exp-22]
 396                         exp = 22
 397                 }
 398                 if f > 1e15 || f < -1e15 {
 399                         // the exponent was really too large.
 400                         return
 401                 }
 402                 return f * float64pow10[exp], true
 403         case exp < 0 && exp >= -22: // int / 10^k
 404                 return f / float64pow10[-exp], true
 405         }
 406         return
 407 }
 408
 409 // If possible to compute mantissa*10^exp to 32-bit float f exactly,
 410 // entirely in floating-point math, do so, avoiding the machinery above.
 411 func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
 412         if mantissa>>float32info.mantbits != 0 {
 413                 return
 414         }
 415         f = float32(mantissa)
 416         if neg {
 417                 f = -f
 418         }
 419         switch {
 420         case exp == 0:
 421                 return f, true
 422         // Exact integers are <= 10^7.
 423         // Exact powers of ten are <= 10^10.
 424         case exp > 0 && exp <= 7+10: // int * 10^k
 425                 // If exponent is big but number of digits is not,
 426                 // can move a few zeros into the integer part.
 427                 if exp > 10 {
 428                         f *= float32pow10[exp-10]
 429                         exp = 10
 430                 }
 431                 if f > 1e7 || f < -1e7 {
 432                         // the exponent was really too large.
 433                         return
 434                 }
 435                 return f * float32pow10[exp], true
 436         case exp < 0 && exp >= -10: // int / 10^k
 437                 return f / float32pow10[-exp], true
 438         }
 439         return
 440 }
 441
 442 const fnParseFloat = "ParseFloat"
 443
 444 func atof32(s string) (f float32, err error) {
 445         if val, ok := special(s); ok {
 446                 return float32(val), nil
 447         }
 448
 449         if optimize {
 450                 // Parse mantissa and exponent.
 451                 mantissa, exp, neg, trunc, ok := readFloat(s)
 452                 if ok {
 453                         // Try pure floating-point arithmetic conversion.
 454                         if !trunc {
 455                                 if f, ok := atof32exact(mantissa, exp, neg); ok {
 456                                         return f, nil
 457                                 }
 458                         }
 459                         // Try another fast path.
 460                         ext := new(extFloat)
 461                         if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
 462                                 b, ovf := ext.floatBits(&float32info)
 463                                 f = math.Float32frombits(uint32(b))
 464                                 if ovf {
 465                                         err = rangeError(fnParseFloat, s)
 466                                 }
 467                                 return f, err
 468                         }
 469                 }
 470         }
 471         var d decimal
 472         if !d.set(s) {
 473                 return 0, syntaxError(fnParseFloat, s)
 474         }
 475         b, ovf := d.floatBits(&float32info)
 476         f = math.Float32frombits(uint32(b))
 477         if ovf {
 478                 err = rangeError(fnParseFloat, s)
 479         }
 480         return f, err
 481 }
 482
 483 func atof64(s string) (f float64, err error) {
 484         if val, ok := special(s); ok {
 485                 return val, nil
 486         }
 487
 488         if optimize {
 489                 // Parse mantissa and exponent.
 490                 mantissa, exp, neg, trunc, ok := readFloat(s)
 491                 if ok {
 492                         // Try pure floating-point arithmetic conversion.
 493                         if !trunc {
 494                                 if f, ok := atof64exact(mantissa, exp, neg); ok {
 495                                         return f, nil
 496                                 }
 497                         }
 498                         // Try another fast path.
 499                         ext := new(extFloat)
 500                         if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
 501                                 b, ovf := ext.floatBits(&float64info)
 502                                 f = math.Float64frombits(b)
 503                                 if ovf {
 504                                         err = rangeError(fnParseFloat, s)
 505                                 }
 506                                 return f, err
 507                         }
 508                 }
 509         }
 510         var d decimal
 511         if !d.set(s) {
 512                 return 0, syntaxError(fnParseFloat, s)
 513         }
 514         b, ovf := d.floatBits(&float64info)
 515         f = math.Float64frombits(b)
 516         if ovf {
 517                 err = rangeError(fnParseFloat, s)
 518         }
 519         return f, err
 520 }
 521
 522 // ParseFloat converts the string s to a floating-point number
 523 // with the precision specified by bitSize: 32 for float32, or 64 for float64.
 524 // When bitSize=32, the result still has type float64, but it will be
 525 // convertible to float32 without changing its value.
 526 //
 527 // If s is well-formed and near a valid floating point number,
 528 // ParseFloat returns the nearest floating point number rounded
 529 // using IEEE754 unbiased rounding.
 530 //
 531 // The errors that ParseFloat returns have concrete type *NumError
 532 // and include err.Num = s.
 533 //
 534 // If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
 535 //
 536 // If s is syntactically well-formed but is more than 1/2 ULP
 537 // away from the largest floating point number of the given size,
 538 // ParseFloat returns f = ±Inf, err.Err = ErrRange.
 539 func ParseFloat(s string, bitSize int) (float64, error) {
 540         if bitSize == 32 {
 541                 f, err := atof32(s)
 542                 return float64(f), err
 543         }
 544         return atof64(s)
 545 }