mirror of
https://github.com/golang/go
synced 2024-10-05 10:31:22 -06:00
380 lines
8.1 KiB
Go
380 lines
8.1 KiB
Go
|
// 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 "strconv"
|
||
|
|
||
|
// TODO: move elsewhere?
|
||
|
package type FloatInfo struct {
|
||
|
mantbits uint;
|
||
|
expbits uint;
|
||
|
bias int;
|
||
|
}
|
||
|
package var float32info = FloatInfo{ 23, 8, -127 }
|
||
|
package var float64info = FloatInfo{ 52, 11, -1023 }
|
||
|
|
||
|
func FmtB(neg bool, mant uint64, exp int, flt *FloatInfo) string
|
||
|
func FmtE(neg bool, d *Decimal, prec int) string
|
||
|
func FmtF(neg bool, d *Decimal, prec int) string
|
||
|
func GenericFtoa(bits uint64, fmt byte, prec int, flt *FloatInfo) string
|
||
|
func Max(a, b int) int
|
||
|
func RoundShortest(d *Decimal, mant uint64, exp int, flt *FloatInfo)
|
||
|
|
||
|
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;
|
||
|
}
|
||
|
export var floatsize = FloatSize()
|
||
|
|
||
|
export func ftoa32(f float32, fmt byte, prec int) string {
|
||
|
return GenericFtoa(uint64(sys.float32bits(f)), fmt, prec, &float32info);
|
||
|
}
|
||
|
|
||
|
export func ftoa64(f float64, fmt byte, prec int) string {
|
||
|
return GenericFtoa(sys.float64bits(f), fmt, prec, &float64info);
|
||
|
}
|
||
|
|
||
|
export 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."
|
||
|
if prec < 0 {
|
||
|
RoundShortest(d, mant, exp, flt);
|
||
|
switch fmt {
|
||
|
case 'e':
|
||
|
prec = d.nd - 1;
|
||
|
case 'f':
|
||
|
prec = Max(d.nd - d.dp, 0);
|
||
|
case 'g':
|
||
|
prec = d.nd;
|
||
|
}
|
||
|
} else {
|
||
|
switch fmt {
|
||
|
case 'e':
|
||
|
d.Round(prec+1);
|
||
|
case 'f':
|
||
|
d.Round(d.dp+prec);
|
||
|
case 'g':
|
||
|
if prec == 0 {
|
||
|
prec = 1;
|
||
|
}
|
||
|
d.Round(prec);
|
||
|
}
|
||
|
}
|
||
|
|
||
|
switch fmt {
|
||
|
case 'e':
|
||
|
return FmtE(neg, d, prec);
|
||
|
case 'f':
|
||
|
return FmtF(neg, d, prec);
|
||
|
case '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.
|
||
|
exp := d.dp - 1;
|
||
|
if exp < -4 || exp >= prec {
|
||
|
return FmtE(neg, d, prec - 1);
|
||
|
}
|
||
|
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) {
|
||
|
// TODO: Unless exp == minexp, if the number of digits in d
|
||
|
// is less than 17, it seems unlikely that it could not 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) string {
|
||
|
buf := new([]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] = 'e';
|
||
|
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 := new([]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:len(buf)]);
|
||
|
}
|
||
|
|
||
|
func Max(a, b int) int {
|
||
|
if a > b {
|
||
|
return a;
|
||
|
}
|
||
|
return b;
|
||
|
}
|
||
|
|