Source file src/pkg/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	
    17	var optimize = true // can change for testing
    18	
    19	func equalIgnoreCase(s1, s2 string) bool {
    20		if len(s1) != len(s2) {
    21			return false
    22		}
    23		for i := 0; i < len(s1); i++ {
    24			c1 := s1[i]
    25			if 'A' <= c1 && c1 <= 'Z' {
    26				c1 += 'a' - 'A'
    27			}
    28			c2 := s2[i]
    29			if 'A' <= c2 && c2 <= 'Z' {
    30				c2 += 'a' - 'A'
    31			}
    32			if c1 != c2 {
    33				return false
    34			}
    35		}
    36		return true
    37	}
    38	
    39	func special(s string) (f float64, ok bool) {
    40		switch {
    41		case equalIgnoreCase(s, "nan"):
    42			return math.NaN(), true
    43		case equalIgnoreCase(s, "-inf"),
    44			equalIgnoreCase(s, "-infinity"):
    45			return math.Inf(-1), true
    46		case equalIgnoreCase(s, "+inf"),
    47			equalIgnoreCase(s, "+infinity"),
    48			equalIgnoreCase(s, "inf"),
    49			equalIgnoreCase(s, "infinity"):
    50			return math.Inf(1), true
    51		}
    52		return
    53	}
    54	
    55	func (b *decimal) set(s string) (ok bool) {
    56		i := 0
    57		b.neg = false
    58		b.trunc = false
    59	
    60		// optional sign
    61		if i >= len(s) {
    62			return
    63		}
    64		switch {
    65		case s[i] == '+':
    66			i++
    67		case s[i] == '-':
    68			b.neg = true
    69			i++
    70		}
    71	
    72		// digits
    73		sawdot := false
    74		sawdigits := false
    75		for ; i < len(s); i++ {
    76			switch {
    77			case s[i] == '.':
    78				if sawdot {
    79					return
    80				}
    81				sawdot = true
    82				b.dp = b.nd
    83				continue
    84	
    85			case '0' <= s[i] && s[i] <= '9':
    86				sawdigits = true
    87				if s[i] == '0' && b.nd == 0 { // ignore leading zeros
    88					b.dp--
    89					continue
    90				}
    91				if b.nd < len(b.d) {
    92					b.d[b.nd] = s[i]
    93					b.nd++
    94				} else if s[i] != '0' {
    95					b.trunc = true
    96				}
    97				continue
    98			}
    99			break
   100		}
   101		if !sawdigits {
   102			return
   103		}
   104		if !sawdot {
   105			b.dp = b.nd
   106		}
   107	
   108		// optional exponent moves decimal point.
   109		// if we read a very large, very long number,
   110		// just be sure to move the decimal point by
   111		// a lot (say, 100000).  it doesn't matter if it's
   112		// not the exact number.
   113		if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
   114			i++
   115			if i >= len(s) {
   116				return
   117			}
   118			esign := 1
   119			if s[i] == '+' {
   120				i++
   121			} else if s[i] == '-' {
   122				i++
   123				esign = -1
   124			}
   125			if i >= len(s) || s[i] < '0' || s[i] > '9' {
   126				return
   127			}
   128			e := 0
   129			for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
   130				if e < 10000 {
   131					e = e*10 + int(s[i]) - '0'
   132				}
   133			}
   134			b.dp += e * esign
   135		}
   136	
   137		if i != len(s) {
   138			return
   139		}
   140	
   141		ok = true
   142		return
   143	}
   144	
   145	// decimal power of ten to binary power of two.
   146	var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
   147	
   148	func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
   149		var exp int
   150		var mant uint64
   151	
   152		// Zero is always a special case.
   153		if d.nd == 0 {
   154			mant = 0
   155			exp = flt.bias
   156			goto out
   157		}
   158	
   159		// Obvious overflow/underflow.
   160		// These bounds are for 64-bit floats.
   161		// Will have to change if we want to support 80-bit floats in the future.
   162		if d.dp > 310 {
   163			goto overflow
   164		}
   165		if d.dp < -330 {
   166			// zero
   167			mant = 0
   168			exp = flt.bias
   169			goto out
   170		}
   171	
   172		// Scale by powers of two until in range [0.5, 1.0)
   173		exp = 0
   174		for d.dp > 0 {
   175			var n int
   176			if d.dp >= len(powtab) {
   177				n = 27
   178			} else {
   179				n = powtab[d.dp]
   180			}
   181			d.Shift(-n)
   182			exp += n
   183		}
   184		for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
   185			var n int
   186			if -d.dp >= len(powtab) {
   187				n = 27
   188			} else {
   189				n = powtab[-d.dp]
   190			}
   191			d.Shift(n)
   192			exp -= n
   193		}
   194	
   195		// Our range is [0.5,1) but floating point range is [1,2).
   196		exp--
   197	
   198		// Minimum representable exponent is flt.bias+1.
   199		// If the exponent is smaller, move it up and
   200		// adjust d accordingly.
   201		if exp < flt.bias+1 {
   202			n := flt.bias + 1 - exp
   203			d.Shift(-n)
   204			exp += n
   205		}
   206	
   207		if exp-flt.bias >= 1<<flt.expbits-1 {
   208			goto overflow
   209		}
   210	
   211		// Extract 1+flt.mantbits bits.
   212		d.Shift(int(1 + flt.mantbits))
   213		mant = d.RoundedInteger()
   214	
   215		// Rounding might have added a bit; shift down.
   216		if mant == 2<<flt.mantbits {
   217			mant >>= 1
   218			exp++
   219			if exp-flt.bias >= 1<<flt.expbits-1 {
   220				goto overflow
   221			}
   222		}
   223	
   224		// Denormalized?
   225		if mant&(1<<flt.mantbits) == 0 {
   226			exp = flt.bias
   227		}
   228		goto out
   229	
   230	overflow:
   231		// ±Inf
   232		mant = 0
   233		exp = 1<<flt.expbits - 1 + flt.bias
   234		overflow = true
   235	
   236	out:
   237		// Assemble bits.
   238		bits := mant & (uint64(1)<<flt.mantbits - 1)
   239		bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
   240		if d.neg {
   241			bits |= 1 << flt.mantbits << flt.expbits
   242		}
   243		return bits, overflow
   244	}
   245	
   246	// Compute exact floating-point integer from d's digits.
   247	// Caller is responsible for avoiding overflow.
   248	func (d *decimal) atof64int() float64 {
   249		f := 0.0
   250		for i := 0; i < d.nd; i++ {
   251			f = f*10 + float64(d.d[i]-'0')
   252		}
   253		if d.neg {
   254			f = -f
   255		}
   256		return f
   257	}
   258	
   259	func (d *decimal) atof32int() float32 {
   260		f := float32(0)
   261		for i := 0; i < d.nd; i++ {
   262			f = f*10 + float32(d.d[i]-'0')
   263		}
   264		if d.neg {
   265			f = -f
   266		}
   267		return f
   268	}
   269	
   270	// Reads a uint64 decimal mantissa, which might be truncated.
   271	func (d *decimal) atou64() (mant uint64, digits int) {
   272		const uint64digits = 19
   273		for i, c := range d.d[:d.nd] {
   274			if i == uint64digits {
   275				return mant, i
   276			}
   277			mant = 10*mant + uint64(c-'0')
   278		}
   279		return mant, d.nd
   280	}
   281	
   282	// Exact powers of 10.
   283	var float64pow10 = []float64{
   284		1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
   285		1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
   286		1e20, 1e21, 1e22,
   287	}
   288	var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
   289	
   290	// If possible to convert decimal d to 64-bit float f exactly,
   291	// entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
   292	// Three common cases:
   293	//	value is exact integer
   294	//	value is exact integer * exact power of ten
   295	//	value is exact integer / exact power of ten
   296	// These all produce potentially inexact but correctly rounded answers.
   297	func (d *decimal) atof64() (f float64, ok bool) {
   298		// Exact integers are <= 10^15.
   299		// Exact powers of ten are <= 10^22.
   300		if d.nd > 15 {
   301			return
   302		}
   303		switch {
   304		case d.dp == d.nd: // int
   305			f := d.atof64int()
   306			return f, true
   307	
   308		case d.dp > d.nd && d.dp <= 15+22: // int * 10^k
   309			f := d.atof64int()
   310			k := d.dp - d.nd
   311			// If exponent is big but number of digits is not,
   312			// can move a few zeros into the integer part.
   313			if k > 22 {
   314				f *= float64pow10[k-22]
   315				k = 22
   316			}
   317			return f * float64pow10[k], true
   318	
   319		case d.dp < d.nd && d.nd-d.dp <= 22: // int / 10^k
   320			f := d.atof64int()
   321			return f / float64pow10[d.nd-d.dp], true
   322		}
   323		return
   324	}
   325	
   326	// If possible to convert decimal d to 32-bit float f exactly,
   327	// entirely in floating-point math, do so, avoiding the machinery above.
   328	func (d *decimal) atof32() (f float32, ok bool) {
   329		// Exact integers are <= 10^7.
   330		// Exact powers of ten are <= 10^10.
   331		if d.nd > 7 {
   332			return
   333		}
   334		switch {
   335		case d.dp == d.nd: // int
   336			f := d.atof32int()
   337			return f, true
   338	
   339		case d.dp > d.nd && d.dp <= 7+10: // int * 10^k
   340			f := d.atof32int()
   341			k := d.dp - d.nd
   342			// If exponent is big but number of digits is not,
   343			// can move a few zeros into the integer part.
   344			if k > 10 {
   345				f *= float32pow10[k-10]
   346				k = 10
   347			}
   348			return f * float32pow10[k], true
   349	
   350		case d.dp < d.nd && d.nd-d.dp <= 10: // int / 10^k
   351			f := d.atof32int()
   352			return f / float32pow10[d.nd-d.dp], true
   353		}
   354		return
   355	}
   356	
   357	const fnParseFloat = "ParseFloat"
   358	
   359	func atof32(s string) (f float32, err error) {
   360		if val, ok := special(s); ok {
   361			return float32(val), nil
   362		}
   363	
   364		var d decimal
   365		if !d.set(s) {
   366			return 0, syntaxError(fnParseFloat, s)
   367		}
   368		if optimize {
   369			if f, ok := d.atof32(); ok {
   370				return f, nil
   371			}
   372		}
   373		b, ovf := d.floatBits(&float32info)
   374		f = math.Float32frombits(uint32(b))
   375		if ovf {
   376			err = rangeError(fnParseFloat, s)
   377		}
   378		return f, err
   379	}
   380	
   381	func atof64(s string) (f float64, err error) {
   382		if val, ok := special(s); ok {
   383			return val, nil
   384		}
   385	
   386		var d decimal
   387		if !d.set(s) {
   388			return 0, syntaxError(fnParseFloat, s)
   389		}
   390		if optimize {
   391			if f, ok := d.atof64(); ok {
   392				return f, nil
   393			}
   394	
   395			// Try another fast path.
   396			ext := new(extFloat)
   397			if ok := ext.AssignDecimal(&d); ok {
   398				b, ovf := ext.floatBits()
   399				f = math.Float64frombits(b)
   400				if ovf {
   401					err = rangeError(fnParseFloat, s)
   402				}
   403				return f, err
   404			}
   405		}
   406		b, ovf := d.floatBits(&float64info)
   407		f = math.Float64frombits(b)
   408		if ovf {
   409			err = rangeError(fnParseFloat, s)
   410		}
   411		return f, err
   412	}
   413	
   414	// ParseFloat converts the string s to a floating-point number
   415	// with the precision specified by bitSize: 32 for float32, or 64 for float64.
   416	// When bitSize=32, the result still has type float64, but it will be
   417	// convertible to float32 without changing its value.
   418	//
   419	// If s is well-formed and near a valid floating point number,
   420	// ParseFloat returns the nearest floating point number rounded
   421	// using IEEE754 unbiased rounding.
   422	//
   423	// The errors that ParseFloat returns have concrete type *NumError
   424	// and include err.Num = s.
   425	//
   426	// If s is not syntactically well-formed, ParseFloat returns err.Error = ErrSyntax.
   427	//
   428	// If s is syntactically well-formed but is more than 1/2 ULP
   429	// away from the largest floating point number of the given size,
   430	// ParseFloat returns f = ±Inf, err.Error = ErrRange.
   431	func ParseFloat(s string, bitSize int) (f float64, err error) {
   432		if bitSize == 32 {
   433			f1, err1 := atof32(s)
   434			return float64(f1), err1
   435		}
   436		f1, err1 := atof64(s)
   437		return f1, err1
   438	}