| // 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. |
| |
| // Binary to decimal floating point conversion. |
| // Algorithm: |
| // 1) store mantissa in multiprecision decimal |
| // 2) shift decimal by exponent |
| // 3) read digits out & format |
| |
| package strconv |
| |
| import "math" |
| |
| // TODO: move elsewhere? |
| type floatInfo struct { |
| mantbits uint |
| expbits uint |
| bias int |
| } |
| |
| var float32info = floatInfo{23, 8, -127} |
| var float64info = floatInfo{52, 11, -1023} |
| |
| func floatsize() int { |
| // Figure out whether float is float32 or float64. |
| // 1e-35 is representable in both, but 1e-70 |
| // is too small for a float32. |
| var f float = 1e-35 |
| if f*f == 0 { |
| return 32 |
| } |
| return 64 |
| } |
| |
| // Floatsize gives the size of the float type, either 32 or 64. |
| var FloatSize = floatsize() |
| |
| // Ftoa32 converts the 32-bit floating-point number f to a string, |
| // according to the format fmt and precision prec. |
| // |
| // The format fmt is one of |
| // 'b' (-ddddp±ddd, a binary exponent), |
| // 'e' (-d.dddde±dd, a decimal exponent), |
| // 'f' (-ddd.dddd, no exponent), or |
| // 'g' ('e' for large exponents, 'f' otherwise). |
| // |
| // The precision prec controls the number of digits |
| // (excluding the exponent) printed by the 'e', 'f', and 'g' formats. |
| // For 'e' and 'f' it is the number of digits after the decimal point. |
| // For 'g' it is the total number of digits. |
| // The special precision -1 uses the smallest number of digits |
| // necessary such that Atof32 will return f exactly. |
| // |
| // Ftoa32(f) is not the same as Ftoa64(float32(f)), |
| // because correct rounding and the number of digits |
| // needed to identify f depend on the precision of the representation. |
| func Ftoa32(f float32, fmt byte, prec int) string { |
| return genericFtoa(uint64(math.Float32bits(f)), fmt, prec, &float32info) |
| } |
| |
| // Ftoa64 is like Ftoa32 but converts a 64-bit floating-point number. |
| func Ftoa64(f float64, fmt byte, prec int) string { |
| return genericFtoa(math.Float64bits(f), fmt, prec, &float64info) |
| } |
| |
| // Ftoa behaves as Ftoa32 or Ftoa64, depending on the size of the float type. |
| func Ftoa(f float, fmt byte, prec int) string { |
| if FloatSize == 32 { |
| return Ftoa32(float32(f), fmt, prec) |
| } |
| return Ftoa64(float64(f), fmt, prec) |
| } |
| |
| func genericFtoa(bits uint64, fmt byte, prec int, flt *floatInfo) string { |
| neg := bits>>flt.expbits>>flt.mantbits != 0 |
| exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1) |
| mant := bits & (uint64(1)<<flt.mantbits - 1) |
| |
| switch exp { |
| case 1<<flt.expbits - 1: |
| // Inf, NaN |
| if mant != 0 { |
| return "NaN" |
| } |
| if neg { |
| return "-Inf" |
| } |
| return "+Inf" |
| |
| case 0: |
| // denormalized |
| exp++ |
| |
| default: |
| // add implicit top bit |
| mant |= uint64(1) << flt.mantbits |
| } |
| exp += flt.bias |
| |
| // Pick off easy binary format. |
| if fmt == 'b' { |
| return fmtB(neg, mant, exp, flt) |
| } |
| |
| // Create exact decimal representation. |
| // The shift is exp - flt.mantbits because mant is a 1-bit integer |
| // followed by a flt.mantbits fraction, and we are treating it as |
| // a 1+flt.mantbits-bit integer. |
| d := newDecimal(mant).Shift(exp - int(flt.mantbits)) |
| |
| // Round appropriately. |
| // Negative precision means "only as much as needed to be exact." |
| shortest := false |
| if prec < 0 { |
| shortest = true |
| roundShortest(d, mant, exp, flt) |
| switch fmt { |
| case 'e', 'E': |
| prec = d.nd - 1 |
| case 'f': |
| prec = max(d.nd-d.dp, 0) |
| case 'g', 'G': |
| prec = d.nd |
| } |
| } else { |
| switch fmt { |
| case 'e', 'E': |
| d.Round(prec + 1) |
| case 'f': |
| d.Round(d.dp + prec) |
| case 'g', 'G': |
| if prec == 0 { |
| prec = 1 |
| } |
| d.Round(prec) |
| } |
| } |
| |
| switch fmt { |
| case 'e', 'E': |
| return fmtE(neg, d, prec, fmt) |
| case 'f': |
| return fmtF(neg, d, prec) |
| case 'g', 'G': |
| // trailing zeros are removed. |
| if prec > d.nd { |
| prec = d.nd |
| } |
| // %e is used if the exponent from the conversion |
| // is less than -4 or greater than or equal to the precision. |
| // if precision was the shortest possible, use precision 6 for this decision. |
| eprec := prec |
| if shortest { |
| eprec = 6 |
| } |
| exp := d.dp - 1 |
| if exp < -4 || exp >= eprec { |
| return fmtE(neg, d, prec-1, fmt+'e'-'g') |
| } |
| return fmtF(neg, d, max(prec-d.dp, 0)) |
| } |
| |
| return "%" + string(fmt) |
| } |
| |
| // Round d (= mant * 2^exp) to the shortest number of digits |
| // that will let the original floating point value be precisely |
| // reconstructed. Size is original floating point size (64 or 32). |
| func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) { |
| // If mantissa is zero, the number is zero; stop now. |
| if mant == 0 { |
| d.nd = 0 |
| return |
| } |
| |
| // TODO(rsc): Unless exp == minexp, if the number of digits in d |
| // is less than 17, it seems likely that it would be |
| // the shortest possible number already. So maybe we can |
| // bail out without doing the extra multiprecision math here. |
| |
| // Compute upper and lower such that any decimal number |
| // between upper and lower (possibly inclusive) |
| // will round to the original floating point number. |
| |
| // d = mant << (exp - mantbits) |
| // Next highest floating point number is mant+1 << exp-mantbits. |
| // Our upper bound is halfway inbetween, mant*2+1 << exp-mantbits-1. |
| upper := newDecimal(mant*2 + 1).Shift(exp - int(flt.mantbits) - 1) |
| |
| // d = mant << (exp - mantbits) |
| // Next lowest floating point number is mant-1 << exp-mantbits, |
| // unless mant-1 drops the significant bit and exp is not the minimum exp, |
| // in which case the next lowest is mant*2-1 << exp-mantbits-1. |
| // Either way, call it mantlo << explo-mantbits. |
| // Our lower bound is halfway inbetween, mantlo*2+1 << explo-mantbits-1. |
| minexp := flt.bias + 1 // minimum possible exponent |
| var mantlo uint64 |
| var explo int |
| if mant > 1<<flt.mantbits || exp == minexp { |
| mantlo = mant - 1 |
| explo = exp |
| } else { |
| mantlo = mant*2 - 1 |
| explo = exp - 1 |
| } |
| lower := newDecimal(mantlo*2 + 1).Shift(explo - int(flt.mantbits) - 1) |
| |
| // The upper and lower bounds are possible outputs only if |
| // the original mantissa is even, so that IEEE round-to-even |
| // would round to the original mantissa and not the neighbors. |
| inclusive := mant%2 == 0 |
| |
| // Now we can figure out the minimum number of digits required. |
| // Walk along until d has distinguished itself from upper and lower. |
| for i := 0; i < d.nd; i++ { |
| var l, m, u byte // lower, middle, upper digits |
| if i < lower.nd { |
| l = lower.d[i] |
| } else { |
| l = '0' |
| } |
| m = d.d[i] |
| if i < upper.nd { |
| u = upper.d[i] |
| } else { |
| u = '0' |
| } |
| |
| // Okay to round down (truncate) if lower has a different digit |
| // or if lower is inclusive and is exactly the result of rounding down. |
| okdown := l != m || (inclusive && l == m && i+1 == lower.nd) |
| |
| // Okay to round up if upper has a different digit and |
| // either upper is inclusive or upper is bigger than the result of rounding up. |
| okup := m != u && (inclusive || i+1 < upper.nd) |
| |
| // If it's okay to do either, then round to the nearest one. |
| // If it's okay to do only one, do it. |
| switch { |
| case okdown && okup: |
| d.Round(i + 1) |
| return |
| case okdown: |
| d.RoundDown(i + 1) |
| return |
| case okup: |
| d.RoundUp(i + 1) |
| return |
| } |
| } |
| } |
| |
| // %e: -d.ddddde±dd |
| func fmtE(neg bool, d *decimal, prec int, fmt byte) string { |
| buf := make([]byte, 3+max(prec, 0)+30) // "-0." + prec digits + exp |
| w := 0 // write index |
| |
| // sign |
| if neg { |
| buf[w] = '-' |
| w++ |
| } |
| |
| // first digit |
| if d.nd == 0 { |
| buf[w] = '0' |
| } else { |
| buf[w] = d.d[0] |
| } |
| w++ |
| |
| // .moredigits |
| if prec > 0 { |
| buf[w] = '.' |
| w++ |
| for i := 0; i < prec; i++ { |
| if 1+i < d.nd { |
| buf[w] = d.d[1+i] |
| } else { |
| buf[w] = '0' |
| } |
| w++ |
| } |
| } |
| |
| // e± |
| buf[w] = fmt |
| w++ |
| exp := d.dp - 1 |
| if d.nd == 0 { // special case: 0 has exponent 0 |
| exp = 0 |
| } |
| if exp < 0 { |
| buf[w] = '-' |
| exp = -exp |
| } else { |
| buf[w] = '+' |
| } |
| w++ |
| |
| // dddd |
| // count digits |
| n := 0 |
| for e := exp; e > 0; e /= 10 { |
| n++ |
| } |
| // leading zeros |
| for i := n; i < 2; i++ { |
| buf[w] = '0' |
| w++ |
| } |
| // digits |
| w += n |
| n = 0 |
| for e := exp; e > 0; e /= 10 { |
| n++ |
| buf[w-n] = byte(e%10 + '0') |
| } |
| |
| return string(buf[0:w]) |
| } |
| |
| // %f: -ddddddd.ddddd |
| func fmtF(neg bool, d *decimal, prec int) string { |
| buf := make([]byte, 1+max(d.dp, 1)+1+max(prec, 0)) |
| w := 0 |
| |
| // sign |
| if neg { |
| buf[w] = '-' |
| w++ |
| } |
| |
| // integer, padded with zeros as needed. |
| if d.dp > 0 { |
| var i int |
| for i = 0; i < d.dp && i < d.nd; i++ { |
| buf[w] = d.d[i] |
| w++ |
| } |
| for ; i < d.dp; i++ { |
| buf[w] = '0' |
| w++ |
| } |
| } else { |
| buf[w] = '0' |
| w++ |
| } |
| |
| // fraction |
| if prec > 0 { |
| buf[w] = '.' |
| w++ |
| for i := 0; i < prec; i++ { |
| if d.dp+i < 0 || d.dp+i >= d.nd { |
| buf[w] = '0' |
| } else { |
| buf[w] = d.d[d.dp+i] |
| } |
| w++ |
| } |
| } |
| |
| return string(buf[0:w]) |
| } |
| |
| // %b: -ddddddddp+ddd |
| func fmtB(neg bool, mant uint64, exp int, flt *floatInfo) string { |
| var buf [50]byte |
| w := len(buf) |
| exp -= int(flt.mantbits) |
| esign := byte('+') |
| if exp < 0 { |
| esign = '-' |
| exp = -exp |
| } |
| n := 0 |
| for exp > 0 || n < 1 { |
| n++ |
| w-- |
| buf[w] = byte(exp%10 + '0') |
| exp /= 10 |
| } |
| w-- |
| buf[w] = esign |
| w-- |
| buf[w] = 'p' |
| n = 0 |
| for mant > 0 || n < 1 { |
| n++ |
| w-- |
| buf[w] = byte(mant%10 + '0') |
| mant /= 10 |
| } |
| if neg { |
| w-- |
| buf[w] = '-' |
| } |
| return string(buf[w:]) |
| } |
| |
| func max(a, b int) int { |
| if a > b { |
| return a |
| } |
| return b |
| } |