1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
3 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
6 * Redistribution and use in source and binary forms, with or without
7 * modification, are permitted provided that the following conditions
9 * 1. Redistributions of source code must retain the above copyright
10 * notice unmodified, this list of conditions, and the following
12 * 2. Redistributions in binary form must reproduce the above copyright
13 * notice, this list of conditions and the following disclaimer in the
14 * documentation and/or other materials provided with the distribution.
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
17 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
18 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
19 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
20 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
21 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
25 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
28 * Hyperbolic sine of a complex argument z = x + i y.
30 * sinh(z) = sinh(x+iy)
31 * = sinh(x) cos(y) + i cosh(x) sin(y).
33 * Exceptional values are noted in the comments within the source code.
34 * These values and the return value were taken from n1124.pdf.
37 #include "complex_impl.h"
39 static const double huge
= 0x1p
1023;
41 double complex csinh(double complex z
)
44 int32_t hx
, hy
, ix
, iy
, lx
, ly
;
49 EXTRACT_WORDS(hx
, lx
, x
);
50 EXTRACT_WORDS(hy
, ly
, y
);
55 /* Handle the nearly-non-exceptional cases where x and y are finite. */
56 if (ix
< 0x7ff00000 && iy
< 0x7ff00000) {
58 return CMPLX(sinh(x
), y
);
59 if (ix
< 0x40360000) /* small x: normal case */
60 return CMPLX(sinh(x
) * cos(y
), cosh(x
) * sin(y
));
62 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
63 if (ix
< 0x40862e42) {
64 /* x < 710: exp(|x|) won't overflow */
65 h
= exp(fabs(x
)) * 0.5;
66 return CMPLX(copysign(h
, x
) * cos(y
), h
* sin(y
));
67 } else if (ix
< 0x4096bbaa) {
68 /* x < 1455: scale to avoid overflow */
69 z
= __ldexp_cexp(CMPLX(fabs(x
), y
), -1);
70 return CMPLX(creal(z
) * copysign(1, x
), cimag(z
));
72 /* x >= 1455: the result always overflows */
74 return CMPLX(h
* cos(y
), h
* h
* sin(y
));
79 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
80 * The sign of 0 in the result is unspecified. Choice = normally
81 * the same as dNaN. Raise the invalid floating-point exception.
83 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
84 * The sign of 0 in the result is unspecified. Choice = normally
87 if ((ix
| lx
) == 0 && iy
>= 0x7ff00000)
88 return CMPLX(copysign(0, x
* (y
- y
)), y
- y
);
91 * sinh(+-Inf +- I 0) = +-Inf + I +-0.
93 * sinh(NaN +- I 0) = d(NaN) + I +-0.
95 if ((iy
| ly
) == 0 && ix
>= 0x7ff00000) {
96 if (((hx
& 0xfffff) | lx
) == 0)
98 return CMPLX(x
, copysign(0, y
));
102 * sinh(x +- I Inf) = dNaN + I dNaN.
103 * Raise the invalid floating-point exception for finite nonzero x.
105 * sinh(x + I NaN) = d(NaN) + I d(NaN).
106 * Optionally raises the invalid floating-point exception for finite
107 * nonzero x. Choice = don't raise (except for signaling NaNs).
109 if (ix
< 0x7ff00000 && iy
>= 0x7ff00000)
110 return CMPLX(y
- y
, x
* (y
- y
));
113 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
114 * The sign of Inf in the result is unspecified. Choice = normally
115 * the same as d(NaN).
117 * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
118 * The sign of Inf in the result is unspecified. Choice = always +.
119 * Raise the invalid floating-point exception.
121 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
123 if (ix
>= 0x7ff00000 && ((hx
& 0xfffff) | lx
) == 0) {
124 if (iy
>= 0x7ff00000)
125 return CMPLX(x
* x
, x
* (y
- y
));
126 return CMPLX(x
* cos(y
), INFINITY
* sin(y
));
130 * sinh(NaN + I NaN) = d(NaN) + I d(NaN).
132 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
133 * Optionally raises the invalid floating-point exception.
136 * sinh(NaN + I y) = d(NaN) + I d(NaN).
137 * Optionally raises the invalid floating-point exception for finite
138 * nonzero y. Choice = don't raise (except for signaling NaNs).
140 return CMPLX((x
* x
) * (y
- y
), (x
+ x
) * (y
- y
));