1// Copyright 2010 The Go Authors. All rights reserved.
2// Use of this source code is governed by a BSD-style
3// license that can be found in the LICENSE file.
4
5package cmplx
6
7import "math"
8
9// The original C code, the long comment, and the constants
10// below are from http://netlib.sandia.gov/cephes/c9x-complex/clog.c.
11// The go code is a simplified version of the original C.
12//
13// Cephes Math Library Release 2.8:  June, 2000
14// Copyright 1984, 1987, 1989, 1992, 2000 by Stephen L. Moshier
15//
16// The readme file at http://netlib.sandia.gov/cephes/ says:
17//    Some software in this archive may be from the book _Methods and
18// Programs for Mathematical Functions_ (Prentice-Hall or Simon & Schuster
19// International, 1989) or from the Cephes Mathematical Library, a
20// commercial product. In either event, it is copyrighted by the author.
21// What you see here may be used freely but it comes with no support or
22// guarantee.
23//
24//   The two known misprints in the book are repaired here in the
25// source listings for the gamma function and the incomplete beta
26// integral.
27//
28//   Stephen L. Moshier
29//   moshier@na-net.ornl.gov
30
31// Complex circular sine
32//
33// DESCRIPTION:
34//
35// If
36//     z = x + iy,
37//
38// then
39//
40//     w = sin x  cosh y  +  i cos x sinh y.
41//
42// csin(z) = -i csinh(iz).
43//
44// ACCURACY:
45//
46//                      Relative error:
47// arithmetic   domain     # trials      peak         rms
48//    DEC       -10,+10      8400       5.3e-17     1.3e-17
49//    IEEE      -10,+10     30000       3.8e-16     1.0e-16
50// Also tested by csin(casin(z)) = z.
51
52// Sin returns the sine of x.
53func Sin(x complex128) complex128 {
54	s, c := math.Sincos(real(x))
55	sh, ch := sinhcosh(imag(x))
56	return complex(s*ch, c*sh)
57}
58
59// Complex hyperbolic sine
60//
61// DESCRIPTION:
62//
63// csinh z = (cexp(z) - cexp(-z))/2
64//         = sinh x * cos y  +  i cosh x * sin y .
65//
66// ACCURACY:
67//
68//                      Relative error:
69// arithmetic   domain     # trials      peak         rms
70//    IEEE      -10,+10     30000       3.1e-16     8.2e-17
71
72// Sinh returns the hyperbolic sine of x.
73func Sinh(x complex128) complex128 {
74	s, c := math.Sincos(imag(x))
75	sh, ch := sinhcosh(real(x))
76	return complex(c*sh, s*ch)
77}
78
79// Complex circular cosine
80//
81// DESCRIPTION:
82//
83// If
84//     z = x + iy,
85//
86// then
87//
88//     w = cos x  cosh y  -  i sin x sinh y.
89//
90// ACCURACY:
91//
92//                      Relative error:
93// arithmetic   domain     # trials      peak         rms
94//    DEC       -10,+10      8400       4.5e-17     1.3e-17
95//    IEEE      -10,+10     30000       3.8e-16     1.0e-16
96
97// Cos returns the cosine of x.
98func Cos(x complex128) complex128 {
99	s, c := math.Sincos(real(x))
100	sh, ch := sinhcosh(imag(x))
101	return complex(c*ch, -s*sh)
102}
103
104// Complex hyperbolic cosine
105//
106// DESCRIPTION:
107//
108// ccosh(z) = cosh x  cos y + i sinh x sin y .
109//
110// ACCURACY:
111//
112//                      Relative error:
113// arithmetic   domain     # trials      peak         rms
114//    IEEE      -10,+10     30000       2.9e-16     8.1e-17
115
116// Cosh returns the hyperbolic cosine of x.
117func Cosh(x complex128) complex128 {
118	s, c := math.Sincos(imag(x))
119	sh, ch := sinhcosh(real(x))
120	return complex(c*ch, s*sh)
121}
122
123// calculate sinh and cosh
124func sinhcosh(x float64) (sh, ch float64) {
125	if math.Abs(x) <= 0.5 {
126		return math.Sinh(x), math.Cosh(x)
127	}
128	e := math.Exp(x)
129	ei := 0.5 / e
130	e *= 0.5
131	return e - ei, e + ei
132}
133