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