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-rw-r--r--src/strconv/ftoa.go475
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diff --git a/src/strconv/ftoa.go b/src/strconv/ftoa.go
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+// 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}
+
+// FormatFloat 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 FormatFloat(f float64, fmt byte, prec, bitSize int) string {
+ return string(genericFtoa(make([]byte, 0, max(prec+4, 24)), f, fmt, prec, bitSize))
+}
+
+// AppendFloat appends the string form of the floating-point number f,
+// as generated by FormatFloat, to dst and returns the extended buffer.
+func AppendFloat(dst []byte, f float64, fmt byte, prec int, bitSize int) []byte {
+ return genericFtoa(dst, f, fmt, prec, bitSize)
+}
+
+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 = digs.nd - 1
+ 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)
+}
+
+// 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
+ }
+
+ // 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++ {
+ 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 || 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 := d.nd + prec + 1 - max(d.nd, prec+1)
+ for i < m {
+ dst = append(dst, d.d[i])
+ i++
+ }
+ for i <= prec {
+ dst = append(dst, '0')
+ i++
+ }
+ }
+
+ // 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)
+
+ // dddd
+ var buf [3]byte
+ i := len(buf)
+ for exp >= 10 {
+ i--
+ buf[i] = byte(exp%10 + '0')
+ exp /= 10
+ }
+ // exp < 10
+ i--
+ buf[i] = byte(exp + '0')
+
+ switch i {
+ case 0:
+ dst = append(dst, buf[0], buf[1], buf[2])
+ case 1:
+ dst = append(dst, buf[1], buf[2])
+ case 2:
+ // leading zeroes
+ dst = append(dst, '0', buf[2])
+ }
+ 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 {
+ var i int
+ for i = 0; i < d.dp && i < d.nd; i++ {
+ dst = append(dst, d.d[i])
+ }
+ for ; i < d.dp; i++ {
+ 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 {
+ 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 append(dst, buf[w:]...)
+}
+
+func max(a, b int) int {
+ if a > b {
+ return a
+ }
+ return b
+}
generated by cgit v1.2.3 (git 2.39.1) at 2025-05-02 07:12:38 +0000