409 lines
9.1 KiB
Go
409 lines
9.1 KiB
Go
// Copyright 2009 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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// Binary to decimal floating point conversion.
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// Algorithm:
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// 1) store mantissa in multiprecision decimal
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// 2) shift decimal by exponent
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// 3) read digits out & format
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package strconv
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import "math"
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// TODO: move elsewhere?
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type floatInfo struct {
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mantbits uint
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expbits uint
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bias int
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}
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var float32info = floatInfo{23, 8, -127}
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var float64info = floatInfo{52, 11, -1023}
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// Ftoa32 converts the 32-bit floating-point number f to a string,
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// according to the format fmt and precision prec.
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//
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// The format fmt is one of
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// 'b' (-ddddp±ddd, a binary exponent),
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// 'e' (-d.dddde±dd, a decimal exponent),
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// 'E' (-d.ddddE±dd, a decimal exponent),
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// 'f' (-ddd.dddd, no exponent),
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// 'g' ('e' for large exponents, 'f' otherwise), or
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// 'G' ('E' for large exponents, 'f' otherwise).
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//
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// The precision prec controls the number of digits
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// (excluding the exponent) printed by the 'e', 'E', 'f', 'g', and 'G' formats.
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// For 'e', 'E', and 'f' it is the number of digits after the decimal point.
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// For 'g' and 'G' it is the total number of digits.
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// The special precision -1 uses the smallest number of digits
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// necessary such that Atof32 will return f exactly.
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//
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// Ftoa32(f) is not the same as Ftoa64(float32(f)),
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// because correct rounding and the number of digits
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// needed to identify f depend on the precision of the representation.
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func Ftoa32(f float32, fmt byte, prec int) string {
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return genericFtoa(uint64(math.Float32bits(f)), fmt, prec, &float32info)
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}
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// Ftoa64 is like Ftoa32 but converts a 64-bit floating-point number.
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func Ftoa64(f float64, fmt byte, prec int) string {
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return genericFtoa(math.Float64bits(f), fmt, prec, &float64info)
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}
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// FtoaN converts the 64-bit floating-point number f to a string,
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// according to the format fmt and precision prec, but it rounds the
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// result assuming that it was obtained from a floating-point value
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// of n bits (32 or 64).
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func FtoaN(f float64, fmt byte, prec int, n int) string {
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if n == 32 {
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return Ftoa32(float32(f), fmt, prec)
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}
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return Ftoa64(f, fmt, prec)
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}
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func genericFtoa(bits uint64, fmt byte, prec int, flt *floatInfo) string {
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neg := bits>>(flt.expbits+flt.mantbits) != 0
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exp := int(bits>>flt.mantbits) & (1<<flt.expbits - 1)
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mant := bits & (uint64(1)<<flt.mantbits - 1)
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switch exp {
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case 1<<flt.expbits - 1:
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// Inf, NaN
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if mant != 0 {
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return "NaN"
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}
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if neg {
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return "-Inf"
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}
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return "+Inf"
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case 0:
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// denormalized
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exp++
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default:
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// add implicit top bit
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mant |= uint64(1) << flt.mantbits
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}
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exp += flt.bias
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// Pick off easy binary format.
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if fmt == 'b' {
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return fmtB(neg, mant, exp, flt)
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}
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// Create exact decimal representation.
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// The shift is exp - flt.mantbits because mant is a 1-bit integer
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// followed by a flt.mantbits fraction, and we are treating it as
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// a 1+flt.mantbits-bit integer.
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d := newDecimal(mant)
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d.Shift(exp - int(flt.mantbits))
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// Round appropriately.
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// Negative precision means "only as much as needed to be exact."
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shortest := false
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if prec < 0 {
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shortest = true
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roundShortest(d, mant, exp, flt)
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switch fmt {
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case 'e', 'E':
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prec = d.nd - 1
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case 'f':
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prec = max(d.nd-d.dp, 0)
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case 'g', 'G':
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prec = d.nd
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}
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} else {
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switch fmt {
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case 'e', 'E':
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d.Round(prec + 1)
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case 'f':
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d.Round(d.dp + prec)
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case 'g', 'G':
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if prec == 0 {
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prec = 1
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}
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d.Round(prec)
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}
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}
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switch fmt {
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case 'e', 'E':
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return fmtE(neg, d, prec, fmt)
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case 'f':
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return fmtF(neg, d, prec)
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case 'g', 'G':
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// trailing fractional zeros in 'e' form will be trimmed.
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eprec := prec
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if eprec > d.nd && d.nd >= d.dp {
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eprec = d.nd
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}
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// %e is used if the exponent from the conversion
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// is less than -4 or greater than or equal to the precision.
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// if precision was the shortest possible, use precision 6 for this decision.
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if shortest {
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eprec = 6
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}
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exp := d.dp - 1
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if exp < -4 || exp >= eprec {
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if prec > d.nd {
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prec = d.nd
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}
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return fmtE(neg, d, prec-1, fmt+'e'-'g')
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}
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if prec > d.dp {
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prec = d.nd
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}
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return fmtF(neg, d, max(prec-d.dp, 0))
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}
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return "%" + string(fmt)
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}
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// Round d (= mant * 2^exp) to the shortest number of digits
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// that will let the original floating point value be precisely
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// reconstructed. Size is original floating point size (64 or 32).
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func roundShortest(d *decimal, mant uint64, exp int, flt *floatInfo) {
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// If mantissa is zero, the number is zero; stop now.
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if mant == 0 {
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d.nd = 0
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return
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}
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// TODO(rsc): Unless exp == minexp, if the number of digits in d
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// is less than 17, it seems likely that it would be
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// the shortest possible number already. So maybe we can
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// bail out without doing the extra multiprecision math here.
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// Compute upper and lower such that any decimal number
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// between upper and lower (possibly inclusive)
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// will round to the original floating point number.
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// d = mant << (exp - mantbits)
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// Next highest floating point number is mant+1 << exp-mantbits.
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// Our upper bound is halfway inbetween, mant*2+1 << exp-mantbits-1.
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upper := newDecimal(mant*2 + 1)
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upper.Shift(exp - int(flt.mantbits) - 1)
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// d = mant << (exp - mantbits)
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// Next lowest floating point number is mant-1 << exp-mantbits,
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// unless mant-1 drops the significant bit and exp is not the minimum exp,
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// in which case the next lowest is mant*2-1 << exp-mantbits-1.
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// Either way, call it mantlo << explo-mantbits.
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// Our lower bound is halfway inbetween, mantlo*2+1 << explo-mantbits-1.
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minexp := flt.bias + 1 // minimum possible exponent
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var mantlo uint64
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var explo int
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if mant > 1<<flt.mantbits || exp == minexp {
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mantlo = mant - 1
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explo = exp
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} else {
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mantlo = mant*2 - 1
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explo = exp - 1
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}
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lower := newDecimal(mantlo*2 + 1)
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lower.Shift(explo - int(flt.mantbits) - 1)
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// The upper and lower bounds are possible outputs only if
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// the original mantissa is even, so that IEEE round-to-even
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// would round to the original mantissa and not the neighbors.
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inclusive := mant%2 == 0
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// Now we can figure out the minimum number of digits required.
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// Walk along until d has distinguished itself from upper and lower.
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for i := 0; i < d.nd; i++ {
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var l, m, u byte // lower, middle, upper digits
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if i < lower.nd {
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l = lower.d[i]
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} else {
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l = '0'
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}
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m = d.d[i]
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if i < upper.nd {
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u = upper.d[i]
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} else {
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u = '0'
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}
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// Okay to round down (truncate) if lower has a different digit
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// or if lower is inclusive and is exactly the result of rounding down.
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okdown := l != m || (inclusive && l == m && i+1 == lower.nd)
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// Okay to round up if upper has a different digit and
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// either upper is inclusive or upper is bigger than the result of rounding up.
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okup := m != u && (inclusive || i+1 < upper.nd)
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// If it's okay to do either, then round to the nearest one.
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// If it's okay to do only one, do it.
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switch {
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case okdown && okup:
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d.Round(i + 1)
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return
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case okdown:
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d.RoundDown(i + 1)
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return
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case okup:
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d.RoundUp(i + 1)
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return
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}
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}
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}
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// %e: -d.ddddde±dd
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func fmtE(neg bool, d *decimal, prec int, fmt byte) string {
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buf := make([]byte, 3+max(prec, 0)+30) // "-0." + prec digits + exp
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w := 0 // write index
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// sign
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if neg {
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buf[w] = '-'
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w++
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}
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// first digit
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if d.nd == 0 {
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buf[w] = '0'
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} else {
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buf[w] = d.d[0]
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}
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w++
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// .moredigits
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if prec > 0 {
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buf[w] = '.'
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w++
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for i := 0; i < prec; i++ {
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if 1+i < d.nd {
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buf[w] = d.d[1+i]
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} else {
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buf[w] = '0'
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}
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w++
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}
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}
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// e±
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buf[w] = fmt
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w++
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exp := d.dp - 1
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if d.nd == 0 { // special case: 0 has exponent 0
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exp = 0
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}
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if exp < 0 {
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buf[w] = '-'
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exp = -exp
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} else {
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buf[w] = '+'
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}
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w++
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// dddd
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// count digits
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n := 0
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for e := exp; e > 0; e /= 10 {
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n++
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}
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// leading zeros
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for i := n; i < 2; i++ {
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buf[w] = '0'
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w++
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}
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// digits
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w += n
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n = 0
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for e := exp; e > 0; e /= 10 {
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n++
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buf[w-n] = byte(e%10 + '0')
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}
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return string(buf[0:w])
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}
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// %f: -ddddddd.ddddd
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func fmtF(neg bool, d *decimal, prec int) string {
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buf := make([]byte, 1+max(d.dp, 1)+1+max(prec, 0))
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w := 0
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// sign
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if neg {
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buf[w] = '-'
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w++
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}
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// integer, padded with zeros as needed.
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if d.dp > 0 {
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var i int
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for i = 0; i < d.dp && i < d.nd; i++ {
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buf[w] = d.d[i]
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w++
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}
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for ; i < d.dp; i++ {
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buf[w] = '0'
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w++
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}
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} else {
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buf[w] = '0'
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w++
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}
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// fraction
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if prec > 0 {
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buf[w] = '.'
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w++
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for i := 0; i < prec; i++ {
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if d.dp+i < 0 || d.dp+i >= d.nd {
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buf[w] = '0'
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} else {
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buf[w] = d.d[d.dp+i]
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}
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w++
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}
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}
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return string(buf[0:w])
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}
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// %b: -ddddddddp+ddd
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func fmtB(neg bool, mant uint64, exp int, flt *floatInfo) string {
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var buf [50]byte
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w := len(buf)
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exp -= int(flt.mantbits)
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esign := byte('+')
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if exp < 0 {
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esign = '-'
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exp = -exp
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}
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n := 0
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for exp > 0 || n < 1 {
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n++
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w--
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buf[w] = byte(exp%10 + '0')
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exp /= 10
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}
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w--
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buf[w] = esign
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w--
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buf[w] = 'p'
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n = 0
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for mant > 0 || n < 1 {
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n++
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w--
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buf[w] = byte(mant%10 + '0')
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mant /= 10
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}
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if neg {
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w--
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buf[w] = '-'
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}
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return string(buf[w:])
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}
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func max(a, b int) int {
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if a > b {
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return a
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}
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return b
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}
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