# Source file src/math/cmplx/sin.go

2  // Use of this source code is governed by a BSD-style
4
5  package cmplx
6
7  import "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.
53  func Sin(x complex128) complex128 {
54  	switch re, im := real(x), imag(x); {
55  	case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
56  		return complex(math.NaN(), im)
57  	case math.IsInf(im, 0):
58  		switch {
59  		case re == 0:
60  			return x
61  		case math.IsInf(re, 0) || math.IsNaN(re):
62  			return complex(math.NaN(), im)
63  		}
64  	case re == 0 && math.IsNaN(im):
65  		return x
66  	}
67  	s, c := math.Sincos(real(x))
68  	sh, ch := sinhcosh(imag(x))
69  	return complex(s*ch, c*sh)
70  }
71
72  // Complex hyperbolic sine
73  //
74  // DESCRIPTION:
75  //
76  // csinh z = (cexp(z) - cexp(-z))/2
77  //         = sinh x * cos y  +  i cosh x * sin y .
78  //
79  // ACCURACY:
80  //
81  //                      Relative error:
82  // arithmetic   domain     # trials      peak         rms
83  //    IEEE      -10,+10     30000       3.1e-16     8.2e-17
84
85  // Sinh returns the hyperbolic sine of x.
86  func Sinh(x complex128) complex128 {
87  	switch re, im := real(x), imag(x); {
88  	case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
89  		return complex(re, math.NaN())
90  	case math.IsInf(re, 0):
91  		switch {
92  		case im == 0:
93  			return complex(re, im)
94  		case math.IsInf(im, 0) || math.IsNaN(im):
95  			return complex(re, math.NaN())
96  		}
97  	case im == 0 && math.IsNaN(re):
98  		return complex(math.NaN(), im)
99  	}
100  	s, c := math.Sincos(imag(x))
101  	sh, ch := sinhcosh(real(x))
102  	return complex(c*sh, s*ch)
103  }
104
105  // Complex circular cosine
106  //
107  // DESCRIPTION:
108  //
109  // If
110  //     z = x + iy,
111  //
112  // then
113  //
114  //     w = cos x  cosh y  -  i sin x sinh y.
115  //
116  // ACCURACY:
117  //
118  //                      Relative error:
119  // arithmetic   domain     # trials      peak         rms
120  //    DEC       -10,+10      8400       4.5e-17     1.3e-17
121  //    IEEE      -10,+10     30000       3.8e-16     1.0e-16
122
123  // Cos returns the cosine of x.
124  func Cos(x complex128) complex128 {
125  	switch re, im := real(x), imag(x); {
126  	case im == 0 && (math.IsInf(re, 0) || math.IsNaN(re)):
127  		return complex(math.NaN(), -im*math.Copysign(0, re))
128  	case math.IsInf(im, 0):
129  		switch {
130  		case re == 0:
131  			return complex(math.Inf(1), -re*math.Copysign(0, im))
132  		case math.IsInf(re, 0) || math.IsNaN(re):
133  			return complex(math.Inf(1), math.NaN())
134  		}
135  	case re == 0 && math.IsNaN(im):
136  		return complex(math.NaN(), 0)
137  	}
138  	s, c := math.Sincos(real(x))
139  	sh, ch := sinhcosh(imag(x))
140  	return complex(c*ch, -s*sh)
141  }
142
143  // Complex hyperbolic cosine
144  //
145  // DESCRIPTION:
146  //
147  // ccosh(z) = cosh x  cos y + i sinh x sin y .
148  //
149  // ACCURACY:
150  //
151  //                      Relative error:
152  // arithmetic   domain     # trials      peak         rms
153  //    IEEE      -10,+10     30000       2.9e-16     8.1e-17
154
155  // Cosh returns the hyperbolic cosine of x.
156  func Cosh(x complex128) complex128 {
157  	switch re, im := real(x), imag(x); {
158  	case re == 0 && (math.IsInf(im, 0) || math.IsNaN(im)):
159  		return complex(math.NaN(), re*math.Copysign(0, im))
160  	case math.IsInf(re, 0):
161  		switch {
162  		case im == 0:
163  			return complex(math.Inf(1), im*math.Copysign(0, re))
164  		case math.IsInf(im, 0) || math.IsNaN(im):
165  			return complex(math.Inf(1), math.NaN())
166  		}
167  	case im == 0 && math.IsNaN(re):
168  		return complex(math.NaN(), im)
169  	}
170  	s, c := math.Sincos(imag(x))
171  	sh, ch := sinhcosh(real(x))
172  	return complex(c*ch, s*sh)
173  }
174
175  // calculate sinh and cosh
176  func sinhcosh(x float64) (sh, ch float64) {
177  	if math.Abs(x) <= 0.5 {
178  		return math.Sinh(x), math.Cosh(x)
179  	}
180  	e := math.Exp(x)
181  	ei := 0.5 / e
182  	e *= 0.5
183  	return e - ei, e + ei
184  }
185

View as plain text