| // 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 implements conversions to and from string representations |
| // of basic data types. |
| 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 |
| } |
| |
| 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) (f float64, err error) { |
| if bitSize == 32 { |
| f1, err1 := atof32(s) |
| return float64(f1), err1 |
| } |
| f1, err1 := atof64(s) |
| return f1, err1 |
| } |