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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.
package gc
import (
"cmd/compile/internal/big"
"fmt"
"math"
)
// implements float arithmetic
const (
// Maximum size in bits for Mpints before signalling
// overflow and also mantissa precision for Mpflts.
Mpprec = 512
// Turn on for constant arithmetic debugging output.
Mpdebug = false
)
// Mpflt represents a floating-point constant.
type Mpflt struct {
Val big.Float
}
// Mpcplx represents a complex constant.
type Mpcplx struct {
Real Mpflt
Imag Mpflt
}
func newMpflt() *Mpflt {
var a Mpflt
a.Val.SetPrec(Mpprec)
return &a
}
func (a *Mpflt) SetInt(b *Mpint) {
if b.Ovf {
// sign doesn't really matter but copy anyway
a.Val.SetInf(b.Val.Sign() < 0)
return
}
a.Val.SetInt(&b.Val)
}
func (a *Mpflt) Set(b *Mpflt) {
a.Val.Set(&b.Val)
}
func (a *Mpflt) Add(b *Mpflt) {
if Mpdebug {
fmt.Printf("\n%v + %v", a, b)
}
a.Val.Add(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) AddFloat64(c float64) {
var b Mpflt
b.SetFloat64(c)
a.Add(&b)
}
func (a *Mpflt) Sub(b *Mpflt) {
if Mpdebug {
fmt.Printf("\n%v - %v", a, b)
}
a.Val.Sub(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) Mul(b *Mpflt) {
if Mpdebug {
fmt.Printf("%v\n * %v\n", a, b)
}
a.Val.Mul(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) MulFloat64(c float64) {
var b Mpflt
b.SetFloat64(c)
a.Mul(&b)
}
func (a *Mpflt) Quo(b *Mpflt) {
if Mpdebug {
fmt.Printf("%v\n / %v\n", a, b)
}
a.Val.Quo(&a.Val, &b.Val)
if Mpdebug {
fmt.Printf(" = %v\n\n", a)
}
}
func (a *Mpflt) Cmp(b *Mpflt) int {
return a.Val.Cmp(&b.Val)
}
func (a *Mpflt) CmpFloat64(c float64) int {
if c == 0 {
return a.Val.Sign() // common case shortcut
}
return a.Val.Cmp(big.NewFloat(c))
}
func (a *Mpflt) Float64() float64 {
x, _ := a.Val.Float64()
// check for overflow
if math.IsInf(x, 0) && nsavederrors+nerrors == 0 {
yyerror("ovf in Mpflt Float64")
}
return x + 0 // avoid -0 (should not be needed, but be conservative)
}
func (a *Mpflt) Float32() float64 {
x32, _ := a.Val.Float32()
x := float64(x32)
// check for overflow
if math.IsInf(x, 0) && nsavederrors+nerrors == 0 {
yyerror("ovf in Mpflt Float32")
}
return x + 0 // avoid -0 (should not be needed, but be conservative)
}
func (a *Mpflt) SetFloat64(c float64) {
if Mpdebug {
fmt.Printf("\nconst %g", c)
}
// convert -0 to 0
if c == 0 {
c = 0
}
a.Val.SetFloat64(c)
if Mpdebug {
fmt.Printf(" = %v\n", a)
}
}
func (a *Mpflt) Neg() {
// avoid -0
if a.Val.Sign() != 0 {
a.Val.Neg(&a.Val)
}
}
//
// floating point input
// required syntax is [+-]d*[.]d*[e[+-]d*] or [+-]0xH*[e[+-]d*]
//
func (a *Mpflt) SetString(as string) {
for len(as) > 0 && (as[0] == ' ' || as[0] == '\t') {
as = as[1:]
}
f, ok := a.Val.SetString(as)
if !ok {
// At the moment we lose precise error cause;
// the old code additionally distinguished between:
// - malformed hex constant
// - decimal point in hex constant
// - constant exponent out of range
// - decimal point and binary point in constant
// TODO(gri) use different conversion function or check separately
yyerror("malformed constant: %s", as)
a.Val.SetFloat64(0)
return
}
if f.IsInf() {
yyerror("constant too large: %s", as)
a.Val.SetFloat64(0)
return
}
// -0 becomes 0
if f.Sign() == 0 && f.Signbit() {
a.Val.SetFloat64(0)
}
}
func (f *Mpflt) String() string {
return fconv(f, 0)
}
func fconv(fvp *Mpflt, flag FmtFlag) string {
if flag&FmtSharp == 0 {
return fvp.Val.Text('b', 0)
}
// use decimal format for error messages
// determine sign
f := &fvp.Val
var sign string
if f.Sign() < 0 {
sign = "-"
f = new(big.Float).Abs(f)
} else if flag&FmtSign != 0 {
sign = "+"
}
// Don't try to convert infinities (will not terminate).
if f.IsInf() {
return sign + "Inf"
}
// Use exact fmt formatting if in float64 range (common case):
// proceed if f doesn't underflow to 0 or overflow to inf.
if x, _ := f.Float64(); f.Sign() == 0 == (x == 0) && !math.IsInf(x, 0) {
return fmt.Sprintf("%s%.6g", sign, x)
}
// Out of float64 range. Do approximate manual to decimal
// conversion to avoid precise but possibly slow Float
// formatting.
// f = mant * 2**exp
var mant big.Float
exp := f.MantExp(&mant) // 0.5 <= mant < 1.0
// approximate float64 mantissa m and decimal exponent d
// f ~ m * 10**d
m, _ := mant.Float64() // 0.5 <= m < 1.0
d := float64(exp) * (math.Ln2 / math.Ln10) // log_10(2)
// adjust m for truncated (integer) decimal exponent e
e := int64(d)
m *= math.Pow(10, d-float64(e))
// ensure 1 <= m < 10
switch {
case m < 1-0.5e-6:
// The %.6g format below rounds m to 5 digits after the
// decimal point. Make sure that m*10 < 10 even after
// rounding up: m*10 + 0.5e-5 < 10 => m < 1 - 0.5e6.
m *= 10
e--
case m >= 10:
m /= 10
e++
}
return fmt.Sprintf("%s%.6ge%+d", sign, m, e)
}