Source file src/strconv/atof.go

Documentation: strconv

		 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  
		15  var optimize = true // set to false to force slow-path conversions for testing
		16  
		17  // commonPrefixLenIgnoreCase returns the length of the common
		18  // prefix of s and prefix, with the character case of s ignored.
		19  // The prefix argument must be all lower-case.
		20  func commonPrefixLenIgnoreCase(s, prefix string) int {
		21  	n := len(prefix)
		22  	if n > len(s) {
		23  		n = len(s)
		24  	}
		25  	for i := 0; i < n; i++ {
		26  		c := s[i]
		27  		if 'A' <= c && c <= 'Z' {
		28  			c += 'a' - 'A'
		29  		}
		30  		if c != prefix[i] {
		31  			return i
		32  		}
		33  	}
		34  	return n
		35  }
		36  
		37  // special returns the floating-point value for the special,
		38  // possibly signed floating-point representations inf, infinity,
		39  // and NaN. The result is ok if a prefix of s contains one
		40  // of these representations and n is the length of that prefix.
		41  // The character case is ignored.
		42  func special(s string) (f float64, n int, ok bool) {
		43  	if len(s) == 0 {
		44  		return 0, 0, false
		45  	}
		46  	sign := 1
		47  	nsign := 0
		48  	switch s[0] {
		49  	case '+', '-':
		50  		if s[0] == '-' {
		51  			sign = -1
		52  		}
		53  		nsign = 1
		54  		s = s[1:]
		55  		fallthrough
		56  	case 'i', 'I':
		57  		n := commonPrefixLenIgnoreCase(s, "infinity")
		58  		// Anything longer than "inf" is ok, but if we
		59  		// don't have "infinity", only consume "inf".
		60  		if 3 < n && n < 8 {
		61  			n = 3
		62  		}
		63  		if n == 3 || n == 8 {
		64  			return math.Inf(sign), nsign + n, true
		65  		}
		66  	case 'n', 'N':
		67  		if commonPrefixLenIgnoreCase(s, "nan") == 3 {
		68  			return math.NaN(), 3, true
		69  		}
		70  	}
		71  	return 0, 0, false
		72  }
		73  
		74  func (b *decimal) set(s string) (ok bool) {
		75  	i := 0
		76  	b.neg = false
		77  	b.trunc = false
		78  
		79  	// optional sign
		80  	if i >= len(s) {
		81  		return
		82  	}
		83  	switch {
		84  	case s[i] == '+':
		85  		i++
		86  	case s[i] == '-':
		87  		b.neg = true
		88  		i++
		89  	}
		90  
		91  	// digits
		92  	sawdot := false
		93  	sawdigits := false
		94  	for ; i < len(s); i++ {
		95  		switch {
		96  		case s[i] == '_':
		97  			// readFloat already checked underscores
		98  			continue
		99  		case s[i] == '.':
	 100  			if sawdot {
	 101  				return
	 102  			}
	 103  			sawdot = true
	 104  			b.dp = b.nd
	 105  			continue
	 106  
	 107  		case '0' <= s[i] && s[i] <= '9':
	 108  			sawdigits = true
	 109  			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
	 110  				b.dp--
	 111  				continue
	 112  			}
	 113  			if b.nd < len(b.d) {
	 114  				b.d[b.nd] = s[i]
	 115  				b.nd++
	 116  			} else if s[i] != '0' {
	 117  				b.trunc = true
	 118  			}
	 119  			continue
	 120  		}
	 121  		break
	 122  	}
	 123  	if !sawdigits {
	 124  		return
	 125  	}
	 126  	if !sawdot {
	 127  		b.dp = b.nd
	 128  	}
	 129  
	 130  	// optional exponent moves decimal point.
	 131  	// if we read a very large, very long number,
	 132  	// just be sure to move the decimal point by
	 133  	// a lot (say, 100000).	it doesn't matter if it's
	 134  	// not the exact number.
	 135  	if i < len(s) && lower(s[i]) == 'e' {
	 136  		i++
	 137  		if i >= len(s) {
	 138  			return
	 139  		}
	 140  		esign := 1
	 141  		if s[i] == '+' {
	 142  			i++
	 143  		} else if s[i] == '-' {
	 144  			i++
	 145  			esign = -1
	 146  		}
	 147  		if i >= len(s) || s[i] < '0' || s[i] > '9' {
	 148  			return
	 149  		}
	 150  		e := 0
	 151  		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
	 152  			if s[i] == '_' {
	 153  				// readFloat already checked underscores
	 154  				continue
	 155  			}
	 156  			if e < 10000 {
	 157  				e = e*10 + int(s[i]) - '0'
	 158  			}
	 159  		}
	 160  		b.dp += e * esign
	 161  	}
	 162  
	 163  	if i != len(s) {
	 164  		return
	 165  	}
	 166  
	 167  	ok = true
	 168  	return
	 169  }
	 170  
	 171  // readFloat reads a decimal or hexadecimal mantissa and exponent from a float
	 172  // string representation in s; the number may be followed by other characters.
	 173  // readFloat reports the number of bytes consumed (i), and whether the number
	 174  // is valid (ok).
	 175  func readFloat(s string) (mantissa uint64, exp int, neg, trunc, hex bool, i int, ok bool) {
	 176  	underscores := false
	 177  
	 178  	// optional sign
	 179  	if i >= len(s) {
	 180  		return
	 181  	}
	 182  	switch {
	 183  	case s[i] == '+':
	 184  		i++
	 185  	case s[i] == '-':
	 186  		neg = true
	 187  		i++
	 188  	}
	 189  
	 190  	// digits
	 191  	base := uint64(10)
	 192  	maxMantDigits := 19 // 10^19 fits in uint64
	 193  	expChar := byte('e')
	 194  	if i+2 < len(s) && s[i] == '0' && lower(s[i+1]) == 'x' {
	 195  		base = 16
	 196  		maxMantDigits = 16 // 16^16 fits in uint64
	 197  		i += 2
	 198  		expChar = 'p'
	 199  		hex = true
	 200  	}
	 201  	sawdot := false
	 202  	sawdigits := false
	 203  	nd := 0
	 204  	ndMant := 0
	 205  	dp := 0
	 206  loop:
	 207  	for ; i < len(s); i++ {
	 208  		switch c := s[i]; true {
	 209  		case c == '_':
	 210  			underscores = true
	 211  			continue
	 212  
	 213  		case c == '.':
	 214  			if sawdot {
	 215  				break loop
	 216  			}
	 217  			sawdot = true
	 218  			dp = nd
	 219  			continue
	 220  
	 221  		case '0' <= c && c <= '9':
	 222  			sawdigits = true
	 223  			if c == '0' && nd == 0 { // ignore leading zeros
	 224  				dp--
	 225  				continue
	 226  			}
	 227  			nd++
	 228  			if ndMant < maxMantDigits {
	 229  				mantissa *= base
	 230  				mantissa += uint64(c - '0')
	 231  				ndMant++
	 232  			} else if c != '0' {
	 233  				trunc = true
	 234  			}
	 235  			continue
	 236  
	 237  		case base == 16 && 'a' <= lower(c) && lower(c) <= 'f':
	 238  			sawdigits = true
	 239  			nd++
	 240  			if ndMant < maxMantDigits {
	 241  				mantissa *= 16
	 242  				mantissa += uint64(lower(c) - 'a' + 10)
	 243  				ndMant++
	 244  			} else {
	 245  				trunc = true
	 246  			}
	 247  			continue
	 248  		}
	 249  		break
	 250  	}
	 251  	if !sawdigits {
	 252  		return
	 253  	}
	 254  	if !sawdot {
	 255  		dp = nd
	 256  	}
	 257  
	 258  	if base == 16 {
	 259  		dp *= 4
	 260  		ndMant *= 4
	 261  	}
	 262  
	 263  	// optional exponent moves decimal point.
	 264  	// if we read a very large, very long number,
	 265  	// just be sure to move the decimal point by
	 266  	// a lot (say, 100000).	it doesn't matter if it's
	 267  	// not the exact number.
	 268  	if i < len(s) && lower(s[i]) == expChar {
	 269  		i++
	 270  		if i >= len(s) {
	 271  			return
	 272  		}
	 273  		esign := 1
	 274  		if s[i] == '+' {
	 275  			i++
	 276  		} else if s[i] == '-' {
	 277  			i++
	 278  			esign = -1
	 279  		}
	 280  		if i >= len(s) || s[i] < '0' || s[i] > '9' {
	 281  			return
	 282  		}
	 283  		e := 0
	 284  		for ; i < len(s) && ('0' <= s[i] && s[i] <= '9' || s[i] == '_'); i++ {
	 285  			if s[i] == '_' {
	 286  				underscores = true
	 287  				continue
	 288  			}
	 289  			if e < 10000 {
	 290  				e = e*10 + int(s[i]) - '0'
	 291  			}
	 292  		}
	 293  		dp += e * esign
	 294  	} else if base == 16 {
	 295  		// Must have exponent.
	 296  		return
	 297  	}
	 298  
	 299  	if mantissa != 0 {
	 300  		exp = dp - ndMant
	 301  	}
	 302  
	 303  	if underscores && !underscoreOK(s[:i]) {
	 304  		return
	 305  	}
	 306  
	 307  	ok = true
	 308  	return
	 309  }
	 310  
	 311  // decimal power of ten to binary power of two.
	 312  var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
	 313  
	 314  func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
	 315  	var exp int
	 316  	var mant uint64
	 317  
	 318  	// Zero is always a special case.
	 319  	if d.nd == 0 {
	 320  		mant = 0
	 321  		exp = flt.bias
	 322  		goto out
	 323  	}
	 324  
	 325  	// Obvious overflow/underflow.
	 326  	// These bounds are for 64-bit floats.
	 327  	// Will have to change if we want to support 80-bit floats in the future.
	 328  	if d.dp > 310 {
	 329  		goto overflow
	 330  	}
	 331  	if d.dp < -330 {
	 332  		// zero
	 333  		mant = 0
	 334  		exp = flt.bias
	 335  		goto out
	 336  	}
	 337  
	 338  	// Scale by powers of two until in range [0.5, 1.0)
	 339  	exp = 0
	 340  	for d.dp > 0 {
	 341  		var n int
	 342  		if d.dp >= len(powtab) {
	 343  			n = 27
	 344  		} else {
	 345  			n = powtab[d.dp]
	 346  		}
	 347  		d.Shift(-n)
	 348  		exp += n
	 349  	}
	 350  	for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
	 351  		var n int
	 352  		if -d.dp >= len(powtab) {
	 353  			n = 27
	 354  		} else {
	 355  			n = powtab[-d.dp]
	 356  		}
	 357  		d.Shift(n)
	 358  		exp -= n
	 359  	}
	 360  
	 361  	// Our range is [0.5,1) but floating point range is [1,2).
	 362  	exp--
	 363  
	 364  	// Minimum representable exponent is flt.bias+1.
	 365  	// If the exponent is smaller, move it up and
	 366  	// adjust d accordingly.
	 367  	if exp < flt.bias+1 {
	 368  		n := flt.bias + 1 - exp
	 369  		d.Shift(-n)
	 370  		exp += n
	 371  	}
	 372  
	 373  	if exp-flt.bias >= 1<<flt.expbits-1 {
	 374  		goto overflow
	 375  	}
	 376  
	 377  	// Extract 1+flt.mantbits bits.
	 378  	d.Shift(int(1 + flt.mantbits))
	 379  	mant = d.RoundedInteger()
	 380  
	 381  	// Rounding might have added a bit; shift down.
	 382  	if mant == 2<<flt.mantbits {
	 383  		mant >>= 1
	 384  		exp++
	 385  		if exp-flt.bias >= 1<<flt.expbits-1 {
	 386  			goto overflow
	 387  		}
	 388  	}
	 389  
	 390  	// Denormalized?
	 391  	if mant&(1<<flt.mantbits) == 0 {
	 392  		exp = flt.bias
	 393  	}
	 394  	goto out
	 395  
	 396  overflow:
	 397  	// ±Inf
	 398  	mant = 0
	 399  	exp = 1<<flt.expbits - 1 + flt.bias
	 400  	overflow = true
	 401  
	 402  out:
	 403  	// Assemble bits.
	 404  	bits := mant & (uint64(1)<<flt.mantbits - 1)
	 405  	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
	 406  	if d.neg {
	 407  		bits |= 1 << flt.mantbits << flt.expbits
	 408  	}
	 409  	return bits, overflow
	 410  }
	 411  
	 412  // Exact powers of 10.
	 413  var float64pow10 = []float64{
	 414  	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
	 415  	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
	 416  	1e20, 1e21, 1e22,
	 417  }
	 418  var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
	 419  
	 420  // If possible to convert decimal representation to 64-bit float f exactly,
	 421  // entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
	 422  // Three common cases:
	 423  //	value is exact integer
	 424  //	value is exact integer * exact power of ten
	 425  //	value is exact integer / exact power of ten
	 426  // These all produce potentially inexact but correctly rounded answers.
	 427  func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
	 428  	if mantissa>>float64info.mantbits != 0 {
	 429  		return
	 430  	}
	 431  	f = float64(mantissa)
	 432  	if neg {
	 433  		f = -f
	 434  	}
	 435  	switch {
	 436  	case exp == 0:
	 437  		// an integer.
	 438  		return f, true
	 439  	// Exact integers are <= 10^15.
	 440  	// Exact powers of ten are <= 10^22.
	 441  	case exp > 0 && exp <= 15+22: // int * 10^k
	 442  		// If exponent is big but number of digits is not,
	 443  		// can move a few zeros into the integer part.
	 444  		if exp > 22 {
	 445  			f *= float64pow10[exp-22]
	 446  			exp = 22
	 447  		}
	 448  		if f > 1e15 || f < -1e15 {
	 449  			// the exponent was really too large.
	 450  			return
	 451  		}
	 452  		return f * float64pow10[exp], true
	 453  	case exp < 0 && exp >= -22: // int / 10^k
	 454  		return f / float64pow10[-exp], true
	 455  	}
	 456  	return
	 457  }
	 458  
	 459  // If possible to compute mantissa*10^exp to 32-bit float f exactly,
	 460  // entirely in floating-point math, do so, avoiding the machinery above.
	 461  func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
	 462  	if mantissa>>float32info.mantbits != 0 {
	 463  		return
	 464  	}
	 465  	f = float32(mantissa)
	 466  	if neg {
	 467  		f = -f
	 468  	}
	 469  	switch {
	 470  	case exp == 0:
	 471  		return f, true
	 472  	// Exact integers are <= 10^7.
	 473  	// Exact powers of ten are <= 10^10.
	 474  	case exp > 0 && exp <= 7+10: // int * 10^k
	 475  		// If exponent is big but number of digits is not,
	 476  		// can move a few zeros into the integer part.
	 477  		if exp > 10 {
	 478  			f *= float32pow10[exp-10]
	 479  			exp = 10
	 480  		}
	 481  		if f > 1e7 || f < -1e7 {
	 482  			// the exponent was really too large.
	 483  			return
	 484  		}
	 485  		return f * float32pow10[exp], true
	 486  	case exp < 0 && exp >= -10: // int / 10^k
	 487  		return f / float32pow10[-exp], true
	 488  	}
	 489  	return
	 490  }
	 491  
	 492  // atofHex converts the hex floating-point string s
	 493  // to a rounded float32 or float64 value (depending on flt==&float32info or flt==&float64info)
	 494  // and returns it as a float64.
	 495  // The string s has already been parsed into a mantissa, exponent, and sign (neg==true for negative).
	 496  // If trunc is true, trailing non-zero bits have been omitted from the mantissa.
	 497  func atofHex(s string, flt *floatInfo, mantissa uint64, exp int, neg, trunc bool) (float64, error) {
	 498  	maxExp := 1<<flt.expbits + flt.bias - 2
	 499  	minExp := flt.bias + 1
	 500  	exp += int(flt.mantbits) // mantissa now implicitly divided by 2^mantbits.
	 501  
	 502  	// Shift mantissa and exponent to bring representation into float range.
	 503  	// Eventually we want a mantissa with a leading 1-bit followed by mantbits other bits.
	 504  	// For rounding, we need two more, where the bottom bit represents
	 505  	// whether that bit or any later bit was non-zero.
	 506  	// (If the mantissa has already lost non-zero bits, trunc is true,
	 507  	// and we OR in a 1 below after shifting left appropriately.)
	 508  	for mantissa != 0 && mantissa>>(flt.mantbits+2) == 0 {
	 509  		mantissa <<= 1
	 510  		exp--
	 511  	}
	 512  	if trunc {
	 513  		mantissa |= 1
	 514  	}
	 515  	for mantissa>>(1+flt.mantbits+2) != 0 {
	 516  		mantissa = mantissa>>1 | mantissa&1
	 517  		exp++
	 518  	}
	 519  
	 520  	// If exponent is too negative,
	 521  	// denormalize in hopes of making it representable.
	 522  	// (The -2 is for the rounding bits.)
	 523  	for mantissa > 1 && exp < minExp-2 {
	 524  		mantissa = mantissa>>1 | mantissa&1
	 525  		exp++
	 526  	}
	 527  
	 528  	// Round using two bottom bits.
	 529  	round := mantissa & 3
	 530  	mantissa >>= 2
	 531  	round |= mantissa & 1 // round to even (round up if mantissa is odd)
	 532  	exp += 2
	 533  	if round == 3 {
	 534  		mantissa++
	 535  		if mantissa == 1<<(1+flt.mantbits) {
	 536  			mantissa >>= 1
	 537  			exp++
	 538  		}
	 539  	}
	 540  
	 541  	if mantissa>>flt.mantbits == 0 { // Denormal or zero.
	 542  		exp = flt.bias
	 543  	}
	 544  	var err error
	 545  	if exp > maxExp { // infinity and range error
	 546  		mantissa = 1 << flt.mantbits
	 547  		exp = maxExp + 1
	 548  		err = rangeError(fnParseFloat, s)
	 549  	}
	 550  
	 551  	bits := mantissa & (1<<flt.mantbits - 1)
	 552  	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
	 553  	if neg {
	 554  		bits |= 1 << flt.mantbits << flt.expbits
	 555  	}
	 556  	if flt == &float32info {
	 557  		return float64(math.Float32frombits(uint32(bits))), err
	 558  	}
	 559  	return math.Float64frombits(bits), err
	 560  }
	 561  
	 562  const fnParseFloat = "ParseFloat"
	 563  
	 564  func atof32(s string) (f float32, n int, err error) {
	 565  	if val, n, ok := special(s); ok {
	 566  		return float32(val), n, nil
	 567  	}
	 568  
	 569  	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
	 570  	if !ok {
	 571  		return 0, n, syntaxError(fnParseFloat, s)
	 572  	}
	 573  
	 574  	if hex {
	 575  		f, err := atofHex(s[:n], &float32info, mantissa, exp, neg, trunc)
	 576  		return float32(f), n, err
	 577  	}
	 578  
	 579  	if optimize {
	 580  		// Try pure floating-point arithmetic conversion, and if that fails,
	 581  		// the Eisel-Lemire algorithm.
	 582  		if !trunc {
	 583  			if f, ok := atof32exact(mantissa, exp, neg); ok {
	 584  				return f, n, nil
	 585  			}
	 586  		}
	 587  		f, ok := eiselLemire32(mantissa, exp, neg)
	 588  		if ok {
	 589  			if !trunc {
	 590  				return f, n, nil
	 591  			}
	 592  			// Even if the mantissa was truncated, we may
	 593  			// have found the correct result. Confirm by
	 594  			// converting the upper mantissa bound.
	 595  			fUp, ok := eiselLemire32(mantissa+1, exp, neg)
	 596  			if ok && f == fUp {
	 597  				return f, n, nil
	 598  			}
	 599  		}
	 600  	}
	 601  
	 602  	// Slow fallback.
	 603  	var d decimal
	 604  	if !d.set(s[:n]) {
	 605  		return 0, n, syntaxError(fnParseFloat, s)
	 606  	}
	 607  	b, ovf := d.floatBits(&float32info)
	 608  	f = math.Float32frombits(uint32(b))
	 609  	if ovf {
	 610  		err = rangeError(fnParseFloat, s)
	 611  	}
	 612  	return f, n, err
	 613  }
	 614  
	 615  func atof64(s string) (f float64, n int, err error) {
	 616  	if val, n, ok := special(s); ok {
	 617  		return val, n, nil
	 618  	}
	 619  
	 620  	mantissa, exp, neg, trunc, hex, n, ok := readFloat(s)
	 621  	if !ok {
	 622  		return 0, n, syntaxError(fnParseFloat, s)
	 623  	}
	 624  
	 625  	if hex {
	 626  		f, err := atofHex(s[:n], &float64info, mantissa, exp, neg, trunc)
	 627  		return f, n, err
	 628  	}
	 629  
	 630  	if optimize {
	 631  		// Try pure floating-point arithmetic conversion, and if that fails,
	 632  		// the Eisel-Lemire algorithm.
	 633  		if !trunc {
	 634  			if f, ok := atof64exact(mantissa, exp, neg); ok {
	 635  				return f, n, nil
	 636  			}
	 637  		}
	 638  		f, ok := eiselLemire64(mantissa, exp, neg)
	 639  		if ok {
	 640  			if !trunc {
	 641  				return f, n, nil
	 642  			}
	 643  			// Even if the mantissa was truncated, we may
	 644  			// have found the correct result. Confirm by
	 645  			// converting the upper mantissa bound.
	 646  			fUp, ok := eiselLemire64(mantissa+1, exp, neg)
	 647  			if ok && f == fUp {
	 648  				return f, n, nil
	 649  			}
	 650  		}
	 651  	}
	 652  
	 653  	// Slow fallback.
	 654  	var d decimal
	 655  	if !d.set(s[:n]) {
	 656  		return 0, n, syntaxError(fnParseFloat, s)
	 657  	}
	 658  	b, ovf := d.floatBits(&float64info)
	 659  	f = math.Float64frombits(b)
	 660  	if ovf {
	 661  		err = rangeError(fnParseFloat, s)
	 662  	}
	 663  	return f, n, err
	 664  }
	 665  
	 666  // ParseFloat converts the string s to a floating-point number
	 667  // with the precision specified by bitSize: 32 for float32, or 64 for float64.
	 668  // When bitSize=32, the result still has type float64, but it will be
	 669  // convertible to float32 without changing its value.
	 670  //
	 671  // ParseFloat accepts decimal and hexadecimal floating-point number syntax.
	 672  // If s is well-formed and near a valid floating-point number,
	 673  // ParseFloat returns the nearest floating-point number rounded
	 674  // using IEEE754 unbiased rounding.
	 675  // (Parsing a hexadecimal floating-point value only rounds when
	 676  // there are more bits in the hexadecimal representation than
	 677  // will fit in the mantissa.)
	 678  //
	 679  // The errors that ParseFloat returns have concrete type *NumError
	 680  // and include err.Num = s.
	 681  //
	 682  // If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
	 683  //
	 684  // If s is syntactically well-formed but is more than 1/2 ULP
	 685  // away from the largest floating point number of the given size,
	 686  // ParseFloat returns f = ±Inf, err.Err = ErrRange.
	 687  //
	 688  // ParseFloat recognizes the strings "NaN", and the (possibly signed) strings "Inf" and "Infinity"
	 689  // as their respective special floating point values. It ignores case when matching.
	 690  func ParseFloat(s string, bitSize int) (float64, error) {
	 691  	f, n, err := parseFloatPrefix(s, bitSize)
	 692  	if n != len(s) && (err == nil || err.(*NumError).Err != ErrSyntax) {
	 693  		return 0, syntaxError(fnParseFloat, s)
	 694  	}
	 695  	return f, err
	 696  }
	 697  
	 698  func parseFloatPrefix(s string, bitSize int) (float64, int, error) {
	 699  	if bitSize == 32 {
	 700  		f, n, err := atof32(s)
	 701  		return float64(f), n, err
	 702  	}
	 703  	return atof64(s)
	 704  }
	 705  

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