| // Copyright 2010 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 cmath |
| |
| import "math" |
| |
| // The original C code, the long comment, and the constants |
| // below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c. |
| // The go code is a simplified version of the original C. |
| // |
| // Cephes Math Library Release 2.8: June, 2000 |
| // Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier |
| // |
| // The readme file at http://netlib.sandia.gov/cephes/ says: |
| // Some software in this archive may be from the book _Methods and |
| // Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster |
| // International, 1989) or from the Cephes Mathematical Library, a |
| // commercial product. In either event, it is copyrighted by the author. |
| // What you see here may be used freely but it comes with no support or |
| // guarantee. |
| // |
| // The two known misprints in the book are repaired here in the |
| // source listings for the gamma function and the incomplete beta |
| // integral. |
| // |
| // Stephen L. Moshier |
| // moshier@na-net.ornl.gov |
| |
| // Complex circular sine |
| // |
| // DESCRIPTION: |
| // |
| // If |
| // z = x + iy, |
| // |
| // then |
| // |
| // w = sin x cosh y + i cos x sinh y. |
| // |
| // csin(z) = -i csinh(iz). |
| // |
| // ACCURACY: |
| // |
| // Relative error: |
| // arithmetic domain # trials peak rms |
| // DEC -10,+10 8400 5.3e-17 1.3e-17 |
| // IEEE -10,+10 30000 3.8e-16 1.0e-16 |
| // Also tested by csin(casin(z)) = z. |
| |
| // Sin returns the sine of x. |
| func Sin(x complex128) complex128 { |
| s, c := math.Sincos(real(x)) |
| sh, ch := sinhcosh(imag(x)) |
| return cmplx(s*ch, c*sh) |
| } |
| |
| // Complex hyperbolic sine |
| // |
| // DESCRIPTION: |
| // |
| // csinh z = (cexp(z) - cexp(-z))/2 |
| // = sinh x * cos y + i cosh x * sin y . |
| // |
| // ACCURACY: |
| // |
| // Relative error: |
| // arithmetic domain # trials peak rms |
| // IEEE -10,+10 30000 3.1e-16 8.2e-17 |
| |
| // Sinh returns the hyperbolic sine of x. |
| func Sinh(x complex128) complex128 { |
| s, c := math.Sincos(imag(x)) |
| sh, ch := sinhcosh(real(x)) |
| return cmplx(c*sh, s*ch) |
| } |
| |
| // Complex circular cosine |
| // |
| // DESCRIPTION: |
| // |
| // If |
| // z = x + iy, |
| // |
| // then |
| // |
| // w = cos x cosh y - i sin x sinh y. |
| // |
| // ACCURACY: |
| // |
| // Relative error: |
| // arithmetic domain # trials peak rms |
| // DEC -10,+10 8400 4.5e-17 1.3e-17 |
| // IEEE -10,+10 30000 3.8e-16 1.0e-16 |
| |
| // Cos returns the cosine of x. |
| func Cos(x complex128) complex128 { |
| s, c := math.Sincos(real(x)) |
| sh, ch := sinhcosh(imag(x)) |
| return cmplx(c*ch, -s*sh) |
| } |
| |
| // Complex hyperbolic cosine |
| // |
| // DESCRIPTION: |
| // |
| // ccosh(z) = cosh x cos y + i sinh x sin y . |
| // |
| // ACCURACY: |
| // |
| // Relative error: |
| // arithmetic domain # trials peak rms |
| // IEEE -10,+10 30000 2.9e-16 8.1e-17 |
| |
| // Cosh returns the hyperbolic cosine of x. |
| func Cosh(x complex128) complex128 { |
| s, c := math.Sincos(imag(x)) |
| sh, ch := sinhcosh(real(x)) |
| return cmplx(c*ch, s*sh) |
| } |
| |
| // calculate sinh and cosh |
| func sinhcosh(x float64) (sh, ch float64) { |
| if math.Fabs(x) <= 0.5 { |
| return math.Sinh(x), math.Cosh(x) |
| } |
| e := math.Exp(x) |
| ei := 0.5 / e |
| e *= 0.5 |
| return e - ei, e + ei |
| } |