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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, 0 insertions, 448 deletions
diff --git a/vendor/golang.org/x/text/internal/number/ftoa.go b/vendor/golang.org/x/text/internal/number/ftoa.go deleted file mode 100644 index 073182ece..000000000 --- a/vendor/golang.org/x/text/internal/number/ftoa.go +++ /dev/null @@ -1,448 +0,0 @@ -// 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 -} |