// 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 ( "fmt" "math" "math/big" ) // 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 newMpcmplx() *Mpcplx { var a Mpcplx a.Real = *newMpflt() a.Imag = *newMpflt() return &a } func (a *Mpflt) SetInt(b *Mpint) { if b.checkOverflow(0) { // 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 { Fatalf("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 { Fatalf("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) } } func (a *Mpflt) SetString(as string) { for len(as) > 0 && (as[0] == ' ' || as[0] == '\t') { as = as[1:] } f, _, err := a.Val.Parse(as, 10) if err != nil { yyerror("malformed constant: %s (%v)", as, err) 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) }