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Source file src/strconv/atof.go

Documentation: strconv

  // Copyright 2009 The Go Authors. All rights reserved.
  // Use of this source code is governed by a BSD-style
  // license that can be found in the LICENSE file.
  
  package strconv
  
  // decimal to binary floating point conversion.
  // Algorithm:
  //   1) Store input in multiprecision decimal.
  //   2) Multiply/divide decimal by powers of two until in range [0.5, 1)
  //   3) Multiply by 2^precision and round to get mantissa.
  
  import "math"
  
  var optimize = true // can change for testing
  
  func equalIgnoreCase(s1, s2 string) bool {
  	if len(s1) != len(s2) {
  		return false
  	}
  	for i := 0; i < len(s1); i++ {
  		c1 := s1[i]
  		if 'A' <= c1 && c1 <= 'Z' {
  			c1 += 'a' - 'A'
  		}
  		c2 := s2[i]
  		if 'A' <= c2 && c2 <= 'Z' {
  			c2 += 'a' - 'A'
  		}
  		if c1 != c2 {
  			return false
  		}
  	}
  	return true
  }
  
  func special(s string) (f float64, ok bool) {
  	if len(s) == 0 {
  		return
  	}
  	switch s[0] {
  	default:
  		return
  	case '+':
  		if equalIgnoreCase(s, "+inf") || equalIgnoreCase(s, "+infinity") {
  			return math.Inf(1), true
  		}
  	case '-':
  		if equalIgnoreCase(s, "-inf") || equalIgnoreCase(s, "-infinity") {
  			return math.Inf(-1), true
  		}
  	case 'n', 'N':
  		if equalIgnoreCase(s, "nan") {
  			return math.NaN(), true
  		}
  	case 'i', 'I':
  		if equalIgnoreCase(s, "inf") || equalIgnoreCase(s, "infinity") {
  			return math.Inf(1), true
  		}
  	}
  	return
  }
  
  func (b *decimal) set(s string) (ok bool) {
  	i := 0
  	b.neg = false
  	b.trunc = false
  
  	// optional sign
  	if i >= len(s) {
  		return
  	}
  	switch {
  	case s[i] == '+':
  		i++
  	case s[i] == '-':
  		b.neg = true
  		i++
  	}
  
  	// digits
  	sawdot := false
  	sawdigits := false
  	for ; i < len(s); i++ {
  		switch {
  		case s[i] == '.':
  			if sawdot {
  				return
  			}
  			sawdot = true
  			b.dp = b.nd
  			continue
  
  		case '0' <= s[i] && s[i] <= '9':
  			sawdigits = true
  			if s[i] == '0' && b.nd == 0 { // ignore leading zeros
  				b.dp--
  				continue
  			}
  			if b.nd < len(b.d) {
  				b.d[b.nd] = s[i]
  				b.nd++
  			} else if s[i] != '0' {
  				b.trunc = true
  			}
  			continue
  		}
  		break
  	}
  	if !sawdigits {
  		return
  	}
  	if !sawdot {
  		b.dp = b.nd
  	}
  
  	// optional exponent moves decimal point.
  	// if we read a very large, very long number,
  	// just be sure to move the decimal point by
  	// a lot (say, 100000).  it doesn't matter if it's
  	// not the exact number.
  	if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
  		i++
  		if i >= len(s) {
  			return
  		}
  		esign := 1
  		if s[i] == '+' {
  			i++
  		} else if s[i] == '-' {
  			i++
  			esign = -1
  		}
  		if i >= len(s) || s[i] < '0' || s[i] > '9' {
  			return
  		}
  		e := 0
  		for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
  			if e < 10000 {
  				e = e*10 + int(s[i]) - '0'
  			}
  		}
  		b.dp += e * esign
  	}
  
  	if i != len(s) {
  		return
  	}
  
  	ok = true
  	return
  }
  
  // readFloat reads a decimal mantissa and exponent from a float
  // string representation. It sets ok to false if the number could
  // not fit return types or is invalid.
  func readFloat(s string) (mantissa uint64, exp int, neg, trunc, ok bool) {
  	const uint64digits = 19
  	i := 0
  
  	// optional sign
  	if i >= len(s) {
  		return
  	}
  	switch {
  	case s[i] == '+':
  		i++
  	case s[i] == '-':
  		neg = true
  		i++
  	}
  
  	// digits
  	sawdot := false
  	sawdigits := false
  	nd := 0
  	ndMant := 0
  	dp := 0
  	for ; i < len(s); i++ {
  		switch c := s[i]; true {
  		case c == '.':
  			if sawdot {
  				return
  			}
  			sawdot = true
  			dp = nd
  			continue
  
  		case '0' <= c && c <= '9':
  			sawdigits = true
  			if c == '0' && nd == 0 { // ignore leading zeros
  				dp--
  				continue
  			}
  			nd++
  			if ndMant < uint64digits {
  				mantissa *= 10
  				mantissa += uint64(c - '0')
  				ndMant++
  			} else if s[i] != '0' {
  				trunc = true
  			}
  			continue
  		}
  		break
  	}
  	if !sawdigits {
  		return
  	}
  	if !sawdot {
  		dp = nd
  	}
  
  	// optional exponent moves decimal point.
  	// if we read a very large, very long number,
  	// just be sure to move the decimal point by
  	// a lot (say, 100000).  it doesn't matter if it's
  	// not the exact number.
  	if i < len(s) && (s[i] == 'e' || s[i] == 'E') {
  		i++
  		if i >= len(s) {
  			return
  		}
  		esign := 1
  		if s[i] == '+' {
  			i++
  		} else if s[i] == '-' {
  			i++
  			esign = -1
  		}
  		if i >= len(s) || s[i] < '0' || s[i] > '9' {
  			return
  		}
  		e := 0
  		for ; i < len(s) && '0' <= s[i] && s[i] <= '9'; i++ {
  			if e < 10000 {
  				e = e*10 + int(s[i]) - '0'
  			}
  		}
  		dp += e * esign
  	}
  
  	if i != len(s) {
  		return
  	}
  
  	if mantissa != 0 {
  		exp = dp - ndMant
  	}
  	ok = true
  	return
  
  }
  
  // decimal power of ten to binary power of two.
  var powtab = []int{1, 3, 6, 9, 13, 16, 19, 23, 26}
  
  func (d *decimal) floatBits(flt *floatInfo) (b uint64, overflow bool) {
  	var exp int
  	var mant uint64
  
  	// Zero is always a special case.
  	if d.nd == 0 {
  		mant = 0
  		exp = flt.bias
  		goto out
  	}
  
  	// Obvious overflow/underflow.
  	// These bounds are for 64-bit floats.
  	// Will have to change if we want to support 80-bit floats in the future.
  	if d.dp > 310 {
  		goto overflow
  	}
  	if d.dp < -330 {
  		// zero
  		mant = 0
  		exp = flt.bias
  		goto out
  	}
  
  	// Scale by powers of two until in range [0.5, 1.0)
  	exp = 0
  	for d.dp > 0 {
  		var n int
  		if d.dp >= len(powtab) {
  			n = 27
  		} else {
  			n = powtab[d.dp]
  		}
  		d.Shift(-n)
  		exp += n
  	}
  	for d.dp < 0 || d.dp == 0 && d.d[0] < '5' {
  		var n int
  		if -d.dp >= len(powtab) {
  			n = 27
  		} else {
  			n = powtab[-d.dp]
  		}
  		d.Shift(n)
  		exp -= n
  	}
  
  	// Our range is [0.5,1) but floating point range is [1,2).
  	exp--
  
  	// Minimum representable exponent is flt.bias+1.
  	// If the exponent is smaller, move it up and
  	// adjust d accordingly.
  	if exp < flt.bias+1 {
  		n := flt.bias + 1 - exp
  		d.Shift(-n)
  		exp += n
  	}
  
  	if exp-flt.bias >= 1<<flt.expbits-1 {
  		goto overflow
  	}
  
  	// Extract 1+flt.mantbits bits.
  	d.Shift(int(1 + flt.mantbits))
  	mant = d.RoundedInteger()
  
  	// Rounding might have added a bit; shift down.
  	if mant == 2<<flt.mantbits {
  		mant >>= 1
  		exp++
  		if exp-flt.bias >= 1<<flt.expbits-1 {
  			goto overflow
  		}
  	}
  
  	// Denormalized?
  	if mant&(1<<flt.mantbits) == 0 {
  		exp = flt.bias
  	}
  	goto out
  
  overflow:
  	// ±Inf
  	mant = 0
  	exp = 1<<flt.expbits - 1 + flt.bias
  	overflow = true
  
  out:
  	// Assemble bits.
  	bits := mant & (uint64(1)<<flt.mantbits - 1)
  	bits |= uint64((exp-flt.bias)&(1<<flt.expbits-1)) << flt.mantbits
  	if d.neg {
  		bits |= 1 << flt.mantbits << flt.expbits
  	}
  	return bits, overflow
  }
  
  // Exact powers of 10.
  var float64pow10 = []float64{
  	1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
  	1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19,
  	1e20, 1e21, 1e22,
  }
  var float32pow10 = []float32{1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10}
  
  // If possible to convert decimal representation to 64-bit float f exactly,
  // entirely in floating-point math, do so, avoiding the expense of decimalToFloatBits.
  // Three common cases:
  //	value is exact integer
  //	value is exact integer * exact power of ten
  //	value is exact integer / exact power of ten
  // These all produce potentially inexact but correctly rounded answers.
  func atof64exact(mantissa uint64, exp int, neg bool) (f float64, ok bool) {
  	if mantissa>>float64info.mantbits != 0 {
  		return
  	}
  	f = float64(mantissa)
  	if neg {
  		f = -f
  	}
  	switch {
  	case exp == 0:
  		// an integer.
  		return f, true
  	// Exact integers are <= 10^15.
  	// Exact powers of ten are <= 10^22.
  	case exp > 0 && exp <= 15+22: // int * 10^k
  		// If exponent is big but number of digits is not,
  		// can move a few zeros into the integer part.
  		if exp > 22 {
  			f *= float64pow10[exp-22]
  			exp = 22
  		}
  		if f > 1e15 || f < -1e15 {
  			// the exponent was really too large.
  			return
  		}
  		return f * float64pow10[exp], true
  	case exp < 0 && exp >= -22: // int / 10^k
  		return f / float64pow10[-exp], true
  	}
  	return
  }
  
  // If possible to compute mantissa*10^exp to 32-bit float f exactly,
  // entirely in floating-point math, do so, avoiding the machinery above.
  func atof32exact(mantissa uint64, exp int, neg bool) (f float32, ok bool) {
  	if mantissa>>float32info.mantbits != 0 {
  		return
  	}
  	f = float32(mantissa)
  	if neg {
  		f = -f
  	}
  	switch {
  	case exp == 0:
  		return f, true
  	// Exact integers are <= 10^7.
  	// Exact powers of ten are <= 10^10.
  	case exp > 0 && exp <= 7+10: // int * 10^k
  		// If exponent is big but number of digits is not,
  		// can move a few zeros into the integer part.
  		if exp > 10 {
  			f *= float32pow10[exp-10]
  			exp = 10
  		}
  		if f > 1e7 || f < -1e7 {
  			// the exponent was really too large.
  			return
  		}
  		return f * float32pow10[exp], true
  	case exp < 0 && exp >= -10: // int / 10^k
  		return f / float32pow10[-exp], true
  	}
  	return
  }
  
  const fnParseFloat = "ParseFloat"
  
  func atof32(s string) (f float32, err error) {
  	if val, ok := special(s); ok {
  		return float32(val), nil
  	}
  
  	if optimize {
  		// Parse mantissa and exponent.
  		mantissa, exp, neg, trunc, ok := readFloat(s)
  		if ok {
  			// Try pure floating-point arithmetic conversion.
  			if !trunc {
  				if f, ok := atof32exact(mantissa, exp, neg); ok {
  					return f, nil
  				}
  			}
  			// Try another fast path.
  			ext := new(extFloat)
  			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float32info); ok {
  				b, ovf := ext.floatBits(&float32info)
  				f = math.Float32frombits(uint32(b))
  				if ovf {
  					err = rangeError(fnParseFloat, s)
  				}
  				return f, err
  			}
  		}
  	}
  	var d decimal
  	if !d.set(s) {
  		return 0, syntaxError(fnParseFloat, s)
  	}
  	b, ovf := d.floatBits(&float32info)
  	f = math.Float32frombits(uint32(b))
  	if ovf {
  		err = rangeError(fnParseFloat, s)
  	}
  	return f, err
  }
  
  func atof64(s string) (f float64, err error) {
  	if val, ok := special(s); ok {
  		return val, nil
  	}
  
  	if optimize {
  		// Parse mantissa and exponent.
  		mantissa, exp, neg, trunc, ok := readFloat(s)
  		if ok {
  			// Try pure floating-point arithmetic conversion.
  			if !trunc {
  				if f, ok := atof64exact(mantissa, exp, neg); ok {
  					return f, nil
  				}
  			}
  			// Try another fast path.
  			ext := new(extFloat)
  			if ok := ext.AssignDecimal(mantissa, exp, neg, trunc, &float64info); ok {
  				b, ovf := ext.floatBits(&float64info)
  				f = math.Float64frombits(b)
  				if ovf {
  					err = rangeError(fnParseFloat, s)
  				}
  				return f, err
  			}
  		}
  	}
  	var d decimal
  	if !d.set(s) {
  		return 0, syntaxError(fnParseFloat, s)
  	}
  	b, ovf := d.floatBits(&float64info)
  	f = math.Float64frombits(b)
  	if ovf {
  		err = rangeError(fnParseFloat, s)
  	}
  	return f, err
  }
  
  // ParseFloat converts the string s to a floating-point number
  // with the precision specified by bitSize: 32 for float32, or 64 for float64.
  // When bitSize=32, the result still has type float64, but it will be
  // convertible to float32 without changing its value.
  //
  // If s is well-formed and near a valid floating point number,
  // ParseFloat returns the nearest floating point number rounded
  // using IEEE754 unbiased rounding.
  //
  // The errors that ParseFloat returns have concrete type *NumError
  // and include err.Num = s.
  //
  // If s is not syntactically well-formed, ParseFloat returns err.Err = ErrSyntax.
  //
  // If s is syntactically well-formed but is more than 1/2 ULP
  // away from the largest floating point number of the given size,
  // ParseFloat returns f = ±Inf, err.Err = ErrRange.
  func ParseFloat(s string, bitSize int) (float64, error) {
  	if bitSize == 32 {
  		f, err := atof32(s)
  		return float64(f), err
  	}
  	return atof64(s)
  }
  

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