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Diffstat (limited to 'src/math/cmplx/sin.go')
| -rw-r--r-- | src/math/cmplx/sin.go | 184 |
1 files changed, 184 insertions, 0 deletions
diff --git a/src/math/cmplx/sin.go b/src/math/cmplx/sin.go new file mode 100644 index 0000000..51cf405 --- /dev/null +++ b/src/math/cmplx/sin.go @@ -0,0 +1,184 @@ +// 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 cmplx + +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 { + switch re, im := real(x), imag(x); { + case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)): + return complex(math.NaN(), im) + case math.IsInf(im, 0): + switch { + case re == 0: + return x + case math.IsInf(re, 0) || math.IsNaN(re): + return complex(math.NaN(), im) + } + case re == 0 && math.IsNaN(im): + return x + } + s, c := math.Sincos(real(x)) + sh, ch := sinhcosh(imag(x)) + return complex(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 { + switch re, im := real(x), imag(x); { + case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)): + return complex(re, math.NaN()) + case math.IsInf(re, 0): + switch { + case im == 0: + return complex(re, im) + case math.IsInf(im, 0) || math.IsNaN(im): + return complex(re, math.NaN()) + } + case im == 0 && math.IsNaN(re): + return complex(math.NaN(), im) + } + s, c := math.Sincos(imag(x)) + sh, ch := sinhcosh(real(x)) + return complex(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 { + switch re, im := real(x), imag(x); { + case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)): + return complex(math.NaN(), -im*math.Copysign(0, re)) + case math.IsInf(im, 0): + switch { + case re == 0: + return complex(math.Inf(1), -re*math.Copysign(0, im)) + case math.IsInf(re, 0) || math.IsNaN(re): + return complex(math.Inf(1), math.NaN()) + } + case re == 0 && math.IsNaN(im): + return complex(math.NaN(), 0) + } + s, c := math.Sincos(real(x)) + sh, ch := sinhcosh(imag(x)) + return complex(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 { + switch re, im := real(x), imag(x); { + case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)): + return complex(math.NaN(), re*math.Copysign(0, im)) + case math.IsInf(re, 0): + switch { + case im == 0: + return complex(math.Inf(1), im*math.Copysign(0, re)) + case math.IsInf(im, 0) || math.IsNaN(im): + return complex(math.Inf(1), math.NaN()) + } + case im == 0 && math.IsNaN(re): + return complex(math.NaN(), im) + } + s, c := math.Sincos(imag(x)) + sh, ch := sinhcosh(real(x)) + return complex(c*ch, s*sh) +} + +// calculate sinh and cosh. +func sinhcosh(x float64) (sh, ch float64) { + if math.Abs(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 +} |