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 implements conversions to and from string representations
   6 // of basic data types.
   7 package strconv
   8
   9 // decimal to binary floating point conversion.
  10 // Algorithm:
  11 //   1) Store input in multiprecision decimal.
  12 //   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
  13 //   3) Multiply by 2^precision and round to get mantissa.
  14
  15 import "math"
  16 import "runtime"
  17
  18 var optimize = true // can change for testing
  19
  20 func equalIgnoreCase(s1, s2 string) bool {
  21         if len(s1) != len(s2) {
  22                 return false
  23         }
  24         for i := 0; i < len(s1); i++ {
  25                 c1 := s1[i]
  26                 if 'A' <= c1 && c1 <= 'Z' {
  27                         c1 += 'a' - 'A'
  28                 }
  29                 c2 := s2[i]
  30                 if 'A' <= c2 && c2 <= 'Z' {
  31                         c2 += 'a' - 'A'
  32                 }
  33                 if c1 != c2 {
  34                         return false
  35                 }
  36         }
  37         return true
  38 }
  39
  40 func special(s string) (f float64, ok bool) {
  41         if len(s) == 0 {
  42                 return
  43         }
  44         switch s[0] {
  45         default:
  46                 return
  47         case '+':
  48                 if equalIgnoreCase(s, "+inf") || equalIgnoreCase(s, "+infinity") {
  49                         return math.Inf(1), true
  50                 }
  51         case '-':
  52                 if equalIgnoreCase(s, "-inf") || equalIgnoreCase(s, "-infinity") {
  53                         return math.Inf(-1), true
  54                 }
  55         case 'n', 'N':
  56                 if equalIgnoreCase(s, "nan") {
  57                         return math.NaN(), true
  58                 }
  59         case 'i', 'I':
  60                 if equalIgnoreCase(s, "inf") || equalIgnoreCase(s, "infinity") {
  61                         return math.Inf(1), true
  62                 }
  63         }
  64         return
  65 }
  66
  67 func (b *decimal) set(s string) (ok bool) {
  68         i := 0
  69         b.neg = false
  70         b.trunc = false
  71
  72         // optional sign
  73         if i >= len(s) {
  74                 return
  75         }
  76         switch {
  77         case s[i] == '+':
  78                 i++
  79         case s[i] == '-':
  80                 b.neg = true
  81                 i++
  82         }
  83
  84         // digits
  85         sawdot := false
  86         sawdigits := false
  87         for ; i < len(s); i++ {
  88                 switch {
  89                 case s[i] == '.':
  90                         if sawdot {
  91                                 return
  92                         }
  93                         sawdot = true
  94                         b.dp = b.nd
  95                         continue
  96
  97                 case '0' <= s[i] && s[i] <= '9':
  98                         sawdigits = true
  99                         if s[i] == '0' && b.nd == 0 { // ignore leading zeros
 100                                 b.dp--
 101                                 continue
 102                         }
 103                         if b.nd < len(b.d) {
 104                                 b.d[b.nd] = s[i]
 105                                 b.nd++
 106                         } else if s[i] != '0' {
 107                                 b.trunc = true
 108                         }
 109                         continue
 110                 }
 111                 break
 112         }
 113         if !sawdigits {
 114                 return
 115         }
 116         if !sawdot {
 117                 b.dp = b.nd
 118         }
 119
 120         // optional exponent moves decimal point.
 121         // if we read a very large, very long number,
 122         // just be sure to move the decimal point by
 123         // a lot (say, 100000).  it doesn't matter if it's
 124         // not the exact number.
 125         if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
 126                 i++
 127                 if i >= len(s) {
 128                         return
 129                 }
 130                 esign := 1
 131                 if s[i] == '+' {
 132                         i++
 133                 } else if s[i] == '-' {
 134                         i++
 135                         esign = -1
 136                 }
 137                 if i >= len(s) || s[i] < '0' || s[i] > '9' {
 138                         return
 139                 }
 140                 e := 0
 141                 for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
 142                         if e < 10000 {
 143                                 e = e*10 + int(s[i]) - '0'
 144                         }
 145                 }
 146                 b.dp += e * esign
 147         }
 148
 149         if i != len(s) {
 150                 return
 151         }
 152
 153         ok = true
 154         return
 155 }
 156
 157 // readFloat reads a decimal mantissa and exponent from a float
 158 // string representation. It sets ok to false if the number could
 159 // not fit return types or is invalid.
 160 func readFloat(s string) (mantissa uint64, exp int, neg, trunc, ok bool) {
 161         const uint64digits = 19
 162         i := 0
 163
 164         // optional sign
 165         if i >= len(s) {
 166                 return
 167         }
 168         switch {
 169         case s[i] == '+':
 170                 i++
 171         case s[i] == '-':
 172                 neg = true
 173                 i++
 174         }
 175
 176         // digits
 177         sawdot := false
 178         sawdigits := false
 179         nd := 0
 180         ndMant := 0
 181         dp := 0
 182         for ; i < len(s); i++ {
 183                 switch c := s[i]; true {
 184                 case c == '.':
 185                         if sawdot {
 186                                 return
 187                         }
 188                         sawdot = true
 189                         dp = nd
 190                         continue
 191
 192                 case '0' <= c && c <= '9':
 193                         sawdigits = true
 194                         if c == '0' && nd == 0 { // ignore leading zeros
 195                                 dp--
 196                                 continue
 197                         }
 198                         nd++
 199                         if ndMant < uint64digits {
 200                                 mantissa *= 10
 201                                 mantissa += uint64(c - '0')
 202                                 ndMant++
 203                         } else if s[i] != '0' {
 204                                 trunc = true
 205                         }
 206                         continue
 207                 }
 208                 break
 209         }
 210         if !sawdigits {
 211                 return
 212         }
 213         if !sawdot {
 214                 dp = nd
 215         }
 216
 217         // optional exponent moves decimal point.
 218         // if we read a very large, very long number,
 219         // just be sure to move the decimal point by
 220         // a lot (say, 100000).  it doesn't matter if it's
 221         // not the exact number.
 222         if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
 223                 i++
 224                 if i >= len(s) {
 225                         return
 226                 }
 227                 esign := 1
 228                 if s[i] == '+' {
 229                         i++
 230                 } else if s[i] == '-' {
 231                         i++
 232                         esign = -1
 233                 }
 234                 if i >= len(s) || s[i] < '0' || s[i] > '9' {
 235                         return
 236                 }
 237                 e := 0
 238                 for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
 239                         if e < 10000 {
 240                                 e = e*10 + int(s[i]) - '0'
 241                         }
 242                 }
 243                 dp += e * esign
 244         }
 245
 246         if i != len(s) {
 247                 return
 248         }
 249
 250         exp = dp - ndMant
 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) (f float64, err error) {
 540         if bitSize == 32 {
 541                 f1, err1 := atof32(s)
 542                 return float64(f1), err1
 543         }
 544         f1, err1 := atof64(s)
 545         return f1, err1
 546 }