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Code Editor : mpfloat.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. 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 } // Use newMpflt (not new(Mpflt)!) to get the correct default precision. func newMpflt() *Mpflt { var a Mpflt a.Val.SetPrec(Mpprec) return &a } // Use newMpcmplx (not new(Mpcplx)!) to get the correct default precision. 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) { f, _, err := a.Val.Parse(as, 0) 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 f.Val.Text('b', 0) } func (fvp *Mpflt) GoString() string { // determine sign sign := "" f := &fvp.Val if f.Sign() < 0 { sign = "-" f = new(big.Float).Abs(f) } // 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) } // complex multiply v *= rv // (a, b) * (c, d) = (a*c - b*d, b*c + a*d) func (v *Mpcplx) Mul(rv *Mpcplx) { var ac, ad, bc, bd Mpflt ac.Set(&v.Real) ac.Mul(&rv.Real) // ac bd.Set(&v.Imag) bd.Mul(&rv.Imag) // bd bc.Set(&v.Imag) bc.Mul(&rv.Real) // bc ad.Set(&v.Real) ad.Mul(&rv.Imag) // ad v.Real.Set(&ac) v.Real.Sub(&bd) // ac-bd v.Imag.Set(&bc) v.Imag.Add(&ad) // bc+ad } // complex divide v /= rv // (a, b) / (c, d) = ((a*c + b*d), (b*c - a*d))/(c*c + d*d) func (v *Mpcplx) Div(rv *Mpcplx) bool { if rv.Real.CmpFloat64(0) == 0 && rv.Imag.CmpFloat64(0) == 0 { return false } var ac, ad, bc, bd, cc_plus_dd Mpflt cc_plus_dd.Set(&rv.Real) cc_plus_dd.Mul(&rv.Real) // cc ac.Set(&rv.Imag) ac.Mul(&rv.Imag) // dd cc_plus_dd.Add(&ac) // cc+dd // We already checked that c and d are not both zero, but we can't // assume that c²+d² != 0 follows, because for tiny values of c // and/or d c²+d² can underflow to zero. Check that c²+d² is // nonzero, return if it's not. if cc_plus_dd.CmpFloat64(0) == 0 { return false } ac.Set(&v.Real) ac.Mul(&rv.Real) // ac bd.Set(&v.Imag) bd.Mul(&rv.Imag) // bd bc.Set(&v.Imag) bc.Mul(&rv.Real) // bc ad.Set(&v.Real) ad.Mul(&rv.Imag) // ad v.Real.Set(&ac) v.Real.Add(&bd) // ac+bd v.Real.Quo(&cc_plus_dd) // (ac+bd)/(cc+dd) v.Imag.Set(&bc) v.Imag.Sub(&ad) // bc-ad v.Imag.Quo(&cc_plus_dd) // (bc+ad)/(cc+dd) return true } func (v *Mpcplx) String() string { return fmt.Sprintf("(%s+%si)", v.Real.String(), v.Imag.String()) } func (v *Mpcplx) GoString() string { var re string sre := v.Real.CmpFloat64(0) if sre != 0 { re = v.Real.GoString() } var im string sim := v.Imag.CmpFloat64(0) if sim != 0 { im = v.Imag.GoString() } switch { case sre == 0 && sim == 0: return "0" case sre == 0: return im + "i" case sim == 0: return re case sim < 0: return fmt.Sprintf("(%s%si)", re, im) default: return fmt.Sprintf("(%s+%si)", re, im) } }
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