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