diff options
Diffstat (limited to 'vendor/golang.org/x/text/internal/number/ftoa.go')
| -rw-r--r-- | vendor/golang.org/x/text/internal/number/ftoa.go | 448 |
1 files changed, 448 insertions, 0 deletions
diff --git a/vendor/golang.org/x/text/internal/number/ftoa.go b/vendor/golang.org/x/text/internal/number/ftoa.go new file mode 100644 index 000000000..073182ece --- /dev/null +++ b/vendor/golang.org/x/text/internal/number/ftoa.go @@ -0,0 +1,448 @@ +// 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. + +// TODO: use build tags once a low-level public API has been established in +// package strconv. + +// Binary to decimal floating point conversion. +// Algorithm: +// 1) store mantissa in multiprecision decimal +// 2) shift decimal by exponent +// 3) read digits out & format + +package number + +import "math" + +var optimize = true + +// TODO: move elsewhere? +type floatInfo struct { + mantbits uint + expbits uint + bias int +} + +var float32info = floatInfo{23, 8, -127} +var float64info = floatInfo{52, 11, -1023} + +// genericFtoa converts the floating-point number f to a string, +// according to the format fmt and precision prec. It rounds the +// result assuming that the original was obtained from a floating-point +// value of bitSize bits (32 for float32, 64 for float64). +// +// The format fmt is one of +// 'b' (-ddddp±ddd, a binary exponent), +// 'e' (-d.dddde±dd, a decimal exponent), +// 'E' (-d.ddddE±dd, a decimal exponent), +// 'f' (-ddd.dddd, no exponent), +// 'g' ('e' for large exponents, 'f' otherwise), or +// 'G' ('E' for large exponents, 'f' otherwise). +// +// The precision prec controls the number of digits +// (excluding the exponent) printed by the 'e', 'E', 'f', 'g', and 'G' formats. +// For 'e', 'E', and 'f' it is the number of digits after the decimal point. +// For 'g' and 'G' it is the total number of digits. +// The special precision -1 uses the smallest number of digits +// necessary such that ParseFloat will return f exactly. +func genericFtoa(dst []byte, val float64, fmt byte, prec, bitSize int) []byte { + var bits uint64 + var flt *floatInfo + switch bitSize { + case 32: + bits = uint64(math.Float32bits(float32(val))) + flt = &float32info + case 64: + bits = math.Float64bits(val) + flt = &float64info + default: + panic("strconv: illegal AppendFloat/FormatFloat bitSize") + } + + 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 + var s string + switch { + case mant != 0: + s = "NaN" + case neg: + s = "-Inf" + default: + s = "+Inf" + } + return append(dst, s...) + + 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(dst, neg, mant, exp, flt) + } + + if !optimize { + return bigFtoa(dst, prec, fmt, neg, mant, exp, flt) + } + + var digs decimalSlice + ok := false + // Negative precision means "only as much as needed to be exact." + shortest := prec < 0 + if shortest { + // Try Grisu3 algorithm. + f := new(extFloat) + lower, upper := f.AssignComputeBounds(mant, exp, neg, flt) + var buf [32]byte + digs.d = buf[:] + ok = f.ShortestDecimal(&digs, &lower, &upper) + if !ok { + return bigFtoa(dst, prec, fmt, neg, mant, exp, flt) + } + // Precision for shortest representation mode. + switch fmt { + case 'e', 'E': + prec = max(digs.nd-1, 0) + case 'f': + prec = max(digs.nd-digs.dp, 0) + case 'g', 'G': + prec = digs.nd + } + } else if fmt != 'f' { + // Fixed number of digits. + digits := prec + switch fmt { + case 'e', 'E': + digits++ + case 'g', 'G': + if prec == 0 { + prec = 1 + } + digits = prec + } + if digits <= 15 { + // try fast algorithm when the number of digits is reasonable. + var buf [24]byte + digs.d = buf[:] + f := extFloat{mant, exp - int(flt.mantbits), neg} + ok = f.FixedDecimal(&digs, digits) + } + } + if !ok { + return bigFtoa(dst, prec, fmt, neg, mant, exp, flt) + } + return formatDigits(dst, shortest, neg, digs, prec, fmt) +} + +// bigFtoa uses multiprecision computations to format a float. +func bigFtoa(dst []byte, prec int, fmt byte, neg bool, mant uint64, exp int, flt *floatInfo) []byte { + d := new(decimal) + d.Assign(mant) + d.Shift(exp - int(flt.mantbits)) + var digs decimalSlice + shortest := prec < 0 + if shortest { + roundShortest(d, mant, exp, flt) + digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp} + // Precision for shortest representation mode. + switch fmt { + case 'e', 'E': + prec = digs.nd - 1 + case 'f': + prec = max(digs.nd-digs.dp, 0) + case 'g', 'G': + prec = digs.nd + } + } else { + // Round appropriately. + 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) + } + digs = decimalSlice{d: d.d[:], nd: d.nd, dp: d.dp} + } + return formatDigits(dst, shortest, neg, digs, prec, fmt) +} + +func formatDigits(dst []byte, shortest bool, neg bool, digs decimalSlice, prec int, fmt byte) []byte { + switch fmt { + case 'e', 'E': + return fmtE(dst, neg, digs, prec, fmt) + case 'f': + return fmtF(dst, neg, digs, prec) + case 'g', 'G': + // trailing fractional zeros in 'e' form will be trimmed. + eprec := prec + if eprec > digs.nd && digs.nd >= digs.dp { + eprec = digs.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. + if shortest { + eprec = 6 + } + exp := digs.dp - 1 + if exp < -4 || exp >= eprec { + if prec > digs.nd { + prec = digs.nd + } + return fmtE(dst, neg, digs, prec-1, fmt+'e'-'g') + } + if prec > digs.dp { + prec = digs.nd + } + return fmtF(dst, neg, digs, max(prec-digs.dp, 0)) + } + + // unknown format + return append(dst, '%', fmt) +} + +// roundShortest rounds d (= mant * 2^exp) to the shortest number of digits +// that will let the original floating point value be precisely reconstructed. +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 + } + + // Compute upper and lower such that any decimal number + // between upper and lower (possibly inclusive) + // will round to the original floating point number. + + // We may see at once that the number is already shortest. + // + // Suppose d is not denormal, so that 2^exp <= d < 10^dp. + // The closest shorter number is at least 10^(dp-nd) away. + // The lower/upper bounds computed below are at distance + // at most 2^(exp-mantbits). + // + // So the number is already shortest if 10^(dp-nd) > 2^(exp-mantbits), + // or equivalently log2(10)*(dp-nd) > exp-mantbits. + // It is true if 332/100*(dp-nd) >= exp-mantbits (log2(10) > 3.32). + minexp := flt.bias + 1 // minimum possible exponent + if exp > minexp && 332*(d.dp-d.nd) >= 100*(exp-int(flt.mantbits)) { + // The number is already shortest. + return + } + + // d = mant << (exp - mantbits) + // Next highest floating point number is mant+1 << exp-mantbits. + // Our upper bound is halfway between, mant*2+1 << exp-mantbits-1. + upper := new(decimal) + upper.Assign(mant*2 + 1) + upper.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 between, mantlo*2+1 << explo-mantbits-1. + 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 := new(decimal) + lower.Assign(mantlo*2 + 1) + lower.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++ { + l := byte('0') // lower digit + if i < lower.nd { + l = lower.d[i] + } + m := d.d[i] // middle digit + u := byte('0') // upper digit + if i < upper.nd { + u = upper.d[i] + } + + // Okay to round down (truncate) if lower has a different digit + // or if lower is inclusive and is exactly the result of rounding + // down (i.e., and we have reached the final digit of lower). + okdown := l != m || inclusive && 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 || m+1 < u || 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 + } + } +} + +type decimalSlice struct { + d []byte + nd, dp int + neg bool +} + +// %e: -d.ddddde±dd +func fmtE(dst []byte, neg bool, d decimalSlice, prec int, fmt byte) []byte { + // sign + if neg { + dst = append(dst, '-') + } + + // first digit + ch := byte('0') + if d.nd != 0 { + ch = d.d[0] + } + dst = append(dst, ch) + + // .moredigits + if prec > 0 { + dst = append(dst, '.') + i := 1 + m := min(d.nd, prec+1) + if i < m { + dst = append(dst, d.d[i:m]...) + i = m + } + for ; i <= prec; i++ { + dst = append(dst, '0') + } + } + + // e± + dst = append(dst, fmt) + exp := d.dp - 1 + if d.nd == 0 { // special case: 0 has exponent 0 + exp = 0 + } + if exp < 0 { + ch = '-' + exp = -exp + } else { + ch = '+' + } + dst = append(dst, ch) + + // dd or ddd + switch { + case exp < 10: + dst = append(dst, '0', byte(exp)+'0') + case exp < 100: + dst = append(dst, byte(exp/10)+'0', byte(exp%10)+'0') + default: + dst = append(dst, byte(exp/100)+'0', byte(exp/10)%10+'0', byte(exp%10)+'0') + } + + return dst +} + +// %f: -ddddddd.ddddd +func fmtF(dst []byte, neg bool, d decimalSlice, prec int) []byte { + // sign + if neg { + dst = append(dst, '-') + } + + // integer, padded with zeros as needed. + if d.dp > 0 { + m := min(d.nd, d.dp) + dst = append(dst, d.d[:m]...) + for ; m < d.dp; m++ { + dst = append(dst, '0') + } + } else { + dst = append(dst, '0') + } + + // fraction + if prec > 0 { + dst = append(dst, '.') + for i := 0; i < prec; i++ { + ch := byte('0') + if j := d.dp + i; 0 <= j && j < d.nd { + ch = d.d[j] + } + dst = append(dst, ch) + } + } + + return dst +} + +// %b: -ddddddddp±ddd +func fmtB(dst []byte, neg bool, mant uint64, exp int, flt *floatInfo) []byte { + // sign + if neg { + dst = append(dst, '-') + } + + // mantissa + dst, _ = formatBits(dst, mant, 10, false, true) + + // p + dst = append(dst, 'p') + + // ±exponent + exp -= int(flt.mantbits) + if exp >= 0 { + dst = append(dst, '+') + } + dst, _ = formatBits(dst, uint64(exp), 10, exp < 0, true) + + return dst +} + +func min(a, b int) int { + if a < b { + return a + } + return b +} + +func max(a, b int) int { + if a > b { + return a + } + return b +} |