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1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */ | 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */ |
2 /*- | 2 /*- |
3 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl | 3 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl |
4 * All rights reserved. | 4 * All rights reserved. |
5 * | 5 * |
6 * Redistribution and use in source and binary forms, with or without | 6 * Redistribution and use in source and binary forms, with or without |
7 * modification, are permitted provided that the following conditions | 7 * modification, are permitted provided that the following conditions |
8 * are met: | 8 * are met: |
9 * 1. Redistributions of source code must retain the above copyright | 9 * 1. Redistributions of source code must retain the above copyright |
10 * notice unmodified, this list of conditions, and the following | 10 * notice unmodified, this list of conditions, and the following |
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31 * = sinh(x) cos(y) + i cosh(x) sin(y). | 31 * = sinh(x) cos(y) + i cosh(x) sin(y). |
32 * | 32 * |
33 * Exceptional values are noted in the comments within the source code. | 33 * Exceptional values are noted in the comments within the source code. |
34 * These values and the return value were taken from n1124.pdf. | 34 * These values and the return value were taken from n1124.pdf. |
35 */ | 35 */ |
36 | 36 |
37 #include "libm.h" | 37 #include "libm.h" |
38 | 38 |
39 static const double huge = 0x1p1023; | 39 static const double huge = 0x1p1023; |
40 | 40 |
41 double complex csinh(double complex z) | 41 double complex csinh(double complex z) { |
42 { | 42 double x, y, h; |
43 » double x, y, h; | 43 int32_t hx, hy, ix, iy, lx, ly; |
44 » int32_t hx, hy, ix, iy, lx, ly; | |
45 | 44 |
46 » x = creal(z); | 45 x = creal(z); |
47 » y = cimag(z); | 46 y = cimag(z); |
48 | 47 |
49 » EXTRACT_WORDS(hx, lx, x); | 48 EXTRACT_WORDS(hx, lx, x); |
50 » EXTRACT_WORDS(hy, ly, y); | 49 EXTRACT_WORDS(hy, ly, y); |
51 | 50 |
52 » ix = 0x7fffffff & hx; | 51 ix = 0x7fffffff & hx; |
53 » iy = 0x7fffffff & hy; | 52 iy = 0x7fffffff & hy; |
54 | 53 |
55 » /* Handle the nearly-non-exceptional cases where x and y are finite. */ | 54 /* Handle the nearly-non-exceptional cases where x and y are finite. */ |
56 » if (ix < 0x7ff00000 && iy < 0x7ff00000) { | 55 if (ix < 0x7ff00000 && iy < 0x7ff00000) { |
57 » » if ((iy | ly) == 0) | 56 if ((iy | ly) == 0) |
58 » » » return CMPLX(sinh(x), y); | 57 return CMPLX(sinh(x), y); |
59 » » if (ix < 0x40360000) /* small x: normal case */ | 58 if (ix < 0x40360000) /* small x: normal case */ |
60 » » » return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)); | 59 return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)); |
61 | 60 |
62 » » /* |x| >= 22, so cosh(x) ~= exp(|x|) */ | 61 /* |x| >= 22, so cosh(x) ~= exp(|x|) */ |
63 » » if (ix < 0x40862e42) { | 62 if (ix < 0x40862e42) { |
64 » » » /* x < 710: exp(|x|) won't overflow */ | 63 /* x < 710: exp(|x|) won't overflow */ |
65 » » » h = exp(fabs(x)) * 0.5; | 64 h = exp(fabs(x)) * 0.5; |
66 » » » return CMPLX(copysign(h, x) * cos(y), h * sin(y)); | 65 return CMPLX(copysign(h, x) * cos(y), h * sin(y)); |
67 » » } else if (ix < 0x4096bbaa) { | 66 } else if (ix < 0x4096bbaa) { |
68 » » » /* x < 1455: scale to avoid overflow */ | 67 /* x < 1455: scale to avoid overflow */ |
69 » » » z = __ldexp_cexp(CMPLX(fabs(x), y), -1); | 68 z = __ldexp_cexp(CMPLX(fabs(x), y), -1); |
70 » » » return CMPLX(creal(z) * copysign(1, x), cimag(z)); | 69 return CMPLX(creal(z) * copysign(1, x), cimag(z)); |
71 » » } else { | 70 } else { |
72 » » » /* x >= 1455: the result always overflows */ | 71 /* x >= 1455: the result always overflows */ |
73 » » » h = huge * x; | 72 h = huge * x; |
74 » » » return CMPLX(h * cos(y), h * h * sin(y)); | 73 return CMPLX(h * cos(y), h * h * sin(y)); |
75 » » } | 74 } |
76 » } | 75 } |
77 | 76 |
78 » /* | 77 /* |
79 » * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. | 78 * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN. |
80 » * The sign of 0 in the result is unspecified. Choice = normally | 79 * The sign of 0 in the result is unspecified. Choice = normally |
81 » * the same as dNaN. Raise the invalid floating-point exception. | 80 * the same as dNaN. Raise the invalid floating-point exception. |
82 » * | 81 * |
83 » * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). | 82 * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN). |
84 » * The sign of 0 in the result is unspecified. Choice = normally | 83 * The sign of 0 in the result is unspecified. Choice = normally |
85 » * the same as d(NaN). | 84 * the same as d(NaN). |
86 » */ | 85 */ |
87 » if ((ix | lx) == 0 && iy >= 0x7ff00000) | 86 if ((ix | lx) == 0 && iy >= 0x7ff00000) |
88 » » return CMPLX(copysign(0, x * (y - y)), y - y); | 87 return CMPLX(copysign(0, x * (y - y)), y - y); |
89 | 88 |
90 » /* | 89 /* |
91 » * sinh(+-Inf +- I 0) = +-Inf + I +-0. | 90 * sinh(+-Inf +- I 0) = +-Inf + I +-0. |
92 » * | 91 * |
93 » * sinh(NaN +- I 0) = d(NaN) + I +-0. | 92 * sinh(NaN +- I 0) = d(NaN) + I +-0. |
94 » */ | 93 */ |
95 » if ((iy | ly) == 0 && ix >= 0x7ff00000) { | 94 if ((iy | ly) == 0 && ix >= 0x7ff00000) { |
96 » » if (((hx & 0xfffff) | lx) == 0) | 95 if (((hx & 0xfffff) | lx) == 0) |
97 » » » return CMPLX(x, y); | 96 return CMPLX(x, y); |
98 » » return CMPLX(x, copysign(0, y)); | 97 return CMPLX(x, copysign(0, y)); |
99 » } | 98 } |
100 | 99 |
101 » /* | 100 /* |
102 » * sinh(x +- I Inf) = dNaN + I dNaN. | 101 * sinh(x +- I Inf) = dNaN + I dNaN. |
103 » * Raise the invalid floating-point exception for finite nonzero x. | 102 * Raise the invalid floating-point exception for finite nonzero x. |
104 » * | 103 * |
105 » * sinh(x + I NaN) = d(NaN) + I d(NaN). | 104 * sinh(x + I NaN) = d(NaN) + I d(NaN). |
106 » * Optionally raises the invalid floating-point exception for finite | 105 * Optionally raises the invalid floating-point exception for finite |
107 » * nonzero x. Choice = don't raise (except for signaling NaNs). | 106 * nonzero x. Choice = don't raise (except for signaling NaNs). |
108 » */ | 107 */ |
109 » if (ix < 0x7ff00000 && iy >= 0x7ff00000) | 108 if (ix < 0x7ff00000 && iy >= 0x7ff00000) |
110 » » return CMPLX(y - y, x * (y - y)); | 109 return CMPLX(y - y, x * (y - y)); |
111 | 110 |
112 » /* | 111 /* |
113 » * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). | 112 * sinh(+-Inf + I NaN) = +-Inf + I d(NaN). |
114 » * The sign of Inf in the result is unspecified. Choice = normally | 113 * The sign of Inf in the result is unspecified. Choice = normally |
115 » * the same as d(NaN). | 114 * the same as d(NaN). |
116 » * | 115 * |
117 » * sinh(+-Inf +- I Inf) = +Inf + I dNaN. | 116 * sinh(+-Inf +- I Inf) = +Inf + I dNaN. |
118 » * The sign of Inf in the result is unspecified. Choice = always +. | 117 * The sign of Inf in the result is unspecified. Choice = always +. |
119 » * Raise the invalid floating-point exception. | 118 * Raise the invalid floating-point exception. |
120 » * | 119 * |
121 » * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) | 120 * sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y) |
122 » */ | 121 */ |
123 » if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { | 122 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) { |
124 » » if (iy >= 0x7ff00000) | 123 if (iy >= 0x7ff00000) |
125 » » » return CMPLX(x * x, x * (y - y)); | 124 return CMPLX(x * x, x * (y - y)); |
126 » » return CMPLX(x * cos(y), INFINITY * sin(y)); | 125 return CMPLX(x * cos(y), INFINITY * sin(y)); |
127 » } | 126 } |
128 | 127 |
129 » /* | 128 /* |
130 » * sinh(NaN + I NaN) = d(NaN) + I d(NaN). | 129 * sinh(NaN + I NaN) = d(NaN) + I d(NaN). |
131 » * | 130 * |
132 » * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). | 131 * sinh(NaN +- I Inf) = d(NaN) + I d(NaN). |
133 » * Optionally raises the invalid floating-point exception. | 132 * Optionally raises the invalid floating-point exception. |
134 » * Choice = raise. | 133 * Choice = raise. |
135 » * | 134 * |
136 » * sinh(NaN + I y) = d(NaN) + I d(NaN). | 135 * sinh(NaN + I y) = d(NaN) + I d(NaN). |
137 » * Optionally raises the invalid floating-point exception for finite | 136 * Optionally raises the invalid floating-point exception for finite |
138 » * nonzero y. Choice = don't raise (except for signaling NaNs). | 137 * nonzero y. Choice = don't raise (except for signaling NaNs). |
139 » */ | 138 */ |
140 » return CMPLX((x * x) * (y - y), (x + x) * (y - y)); | 139 return CMPLX((x * x) * (y - y), (x + x) * (y - y)); |
141 } | 140 } |
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