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s_ccosh.c (226599) s_ccosh.c (275819)
1/*-
2 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright

--- 21 unchanged lines hidden (view full) ---

30 * cosh(z) = cosh(x+iy)
31 * = cosh(x) cos(y) + i sinh(x) sin(y).
32 *
33 * Exceptional values are noted in the comments within the source code.
34 * These values and the return value were taken from n1124.pdf.
35 */
36
37#include <sys/cdefs.h>
1/*-
2 * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright

--- 21 unchanged lines hidden (view full) ---

30 * cosh(z) = cosh(x+iy)
31 * = cosh(x) cos(y) + i sinh(x) sin(y).
32 *
33 * Exceptional values are noted in the comments within the source code.
34 * These values and the return value were taken from n1124.pdf.
35 */
36
37#include <sys/cdefs.h>
38__FBSDID("$FreeBSD: head/lib/msun/src/s_ccosh.c 226599 2011-10-21 06:29:32Z das $");
38__FBSDID("$FreeBSD: head/lib/msun/src/s_ccosh.c 275819 2014-12-16 09:21:56Z ed $");
39
40#include <complex.h>
41#include <math.h>
42
43#include "math_private.h"
44
45static const double huge = 0x1p1023;
46

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57 EXTRACT_WORDS(hy, ly, y);
58
59 ix = 0x7fffffff & hx;
60 iy = 0x7fffffff & hy;
61
62 /* Handle the nearly-non-exceptional cases where x and y are finite. */
63 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
64 if ((iy | ly) == 0)
39
40#include <complex.h>
41#include <math.h>
42
43#include "math_private.h"
44
45static const double huge = 0x1p1023;
46

--- 10 unchanged lines hidden (view full) ---

57 EXTRACT_WORDS(hy, ly, y);
58
59 ix = 0x7fffffff & hx;
60 iy = 0x7fffffff & hy;
61
62 /* Handle the nearly-non-exceptional cases where x and y are finite. */
63 if (ix < 0x7ff00000 && iy < 0x7ff00000) {
64 if ((iy | ly) == 0)
65 return (cpack(cosh(x), x * y));
65 return (CMPLX(cosh(x), x * y));
66 if (ix < 0x40360000) /* small x: normal case */
66 if (ix < 0x40360000) /* small x: normal case */
67 return (cpack(cosh(x) * cos(y), sinh(x) * sin(y)));
67 return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
68
69 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
70 if (ix < 0x40862e42) {
71 /* x < 710: exp(|x|) won't overflow */
72 h = exp(fabs(x)) * 0.5;
68
69 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
70 if (ix < 0x40862e42) {
71 /* x < 710: exp(|x|) won't overflow */
72 h = exp(fabs(x)) * 0.5;
73 return (cpack(h * cos(y), copysign(h, x) * sin(y)));
73 return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
74 } else if (ix < 0x4096bbaa) {
75 /* x < 1455: scale to avoid overflow */
74 } else if (ix < 0x4096bbaa) {
75 /* x < 1455: scale to avoid overflow */
76 z = __ldexp_cexp(cpack(fabs(x), y), -1);
77 return (cpack(creal(z), cimag(z) * copysign(1, x)));
76 z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
77 return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
78 } else {
79 /* x >= 1455: the result always overflows */
80 h = huge * x;
78 } else {
79 /* x >= 1455: the result always overflows */
80 h = huge * x;
81 return (cpack(h * h * cos(y), h * sin(y)));
81 return (CMPLX(h * h * cos(y), h * sin(y)));
82 }
83 }
84
85 /*
86 * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
87 * The sign of 0 in the result is unspecified. Choice = normally
88 * the same as dNaN. Raise the invalid floating-point exception.
89 *
90 * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
91 * The sign of 0 in the result is unspecified. Choice = normally
92 * the same as d(NaN).
93 */
94 if ((ix | lx) == 0 && iy >= 0x7ff00000)
82 }
83 }
84
85 /*
86 * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
87 * The sign of 0 in the result is unspecified. Choice = normally
88 * the same as dNaN. Raise the invalid floating-point exception.
89 *
90 * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
91 * The sign of 0 in the result is unspecified. Choice = normally
92 * the same as d(NaN).
93 */
94 if ((ix | lx) == 0 && iy >= 0x7ff00000)
95 return (cpack(y - y, copysign(0, x * (y - y))));
95 return (CMPLX(y - y, copysign(0, x * (y - y))));
96
97 /*
98 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
99 *
100 * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
101 * The sign of 0 in the result is unspecified.
102 */
103 if ((iy | ly) == 0 && ix >= 0x7ff00000) {
104 if (((hx & 0xfffff) | lx) == 0)
96
97 /*
98 * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
99 *
100 * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
101 * The sign of 0 in the result is unspecified.
102 */
103 if ((iy | ly) == 0 && ix >= 0x7ff00000) {
104 if (((hx & 0xfffff) | lx) == 0)
105 return (cpack(x * x, copysign(0, x) * y));
106 return (cpack(x * x, copysign(0, (x + x) * y)));
105 return (CMPLX(x * x, copysign(0, x) * y));
106 return (CMPLX(x * x, copysign(0, (x + x) * y)));
107 }
108
109 /*
110 * cosh(x +- I Inf) = dNaN + I dNaN.
111 * Raise the invalid floating-point exception for finite nonzero x.
112 *
113 * cosh(x + I NaN) = d(NaN) + I d(NaN).
114 * Optionally raises the invalid floating-point exception for finite
115 * nonzero x. Choice = don't raise (except for signaling NaNs).
116 */
117 if (ix < 0x7ff00000 && iy >= 0x7ff00000)
107 }
108
109 /*
110 * cosh(x +- I Inf) = dNaN + I dNaN.
111 * Raise the invalid floating-point exception for finite nonzero x.
112 *
113 * cosh(x + I NaN) = d(NaN) + I d(NaN).
114 * Optionally raises the invalid floating-point exception for finite
115 * nonzero x. Choice = don't raise (except for signaling NaNs).
116 */
117 if (ix < 0x7ff00000 && iy >= 0x7ff00000)
118 return (cpack(y - y, x * (y - y)));
118 return (CMPLX(y - y, x * (y - y)));
119
120 /*
121 * cosh(+-Inf + I NaN) = +Inf + I d(NaN).
122 *
123 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
124 * The sign of Inf in the result is unspecified. Choice = always +.
125 * Raise the invalid floating-point exception.
126 *
127 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
128 */
129 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
130 if (iy >= 0x7ff00000)
119
120 /*
121 * cosh(+-Inf + I NaN) = +Inf + I d(NaN).
122 *
123 * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
124 * The sign of Inf in the result is unspecified. Choice = always +.
125 * Raise the invalid floating-point exception.
126 *
127 * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
128 */
129 if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
130 if (iy >= 0x7ff00000)
131 return (cpack(x * x, x * (y - y)));
132 return (cpack((x * x) * cos(y), x * sin(y)));
131 return (CMPLX(x * x, x * (y - y)));
132 return (CMPLX((x * x) * cos(y), x * sin(y)));
133 }
134
135 /*
136 * cosh(NaN + I NaN) = d(NaN) + I d(NaN).
137 *
138 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
139 * Optionally raises the invalid floating-point exception.
140 * Choice = raise.
141 *
142 * cosh(NaN + I y) = d(NaN) + I d(NaN).
143 * Optionally raises the invalid floating-point exception for finite
144 * nonzero y. Choice = don't raise (except for signaling NaNs).
145 */
133 }
134
135 /*
136 * cosh(NaN + I NaN) = d(NaN) + I d(NaN).
137 *
138 * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
139 * Optionally raises the invalid floating-point exception.
140 * Choice = raise.
141 *
142 * cosh(NaN + I y) = d(NaN) + I d(NaN).
143 * Optionally raises the invalid floating-point exception for finite
144 * nonzero y. Choice = don't raise (except for signaling NaNs).
145 */
146 return (cpack((x * x) * (y - y), (x + x) * (y - y)));
146 return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
147}
148
149double complex
150ccos(double complex z)
151{
152
153 /* ccos(z) = ccosh(I * z) */
147}
148
149double complex
150ccos(double complex z)
151{
152
153 /* ccos(z) = ccosh(I * z) */
154 return (ccosh(cpack(-cimag(z), creal(z))));
154 return (ccosh(CMPLX(-cimag(z), creal(z))));
155}
155}