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Side by Side Diff: fusl/src/complex/ctanh.c

Issue 1714623002: [fusl] clang-format fusl (Closed) Base URL: git@github.com:domokit/mojo.git@master
Patch Set: headers too Created 4 years, 10 months ago
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1 /* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */ 1 /* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */
2 /*- 2 /*-
3 * Copyright (c) 2011 David Schultz 3 * Copyright (c) 2011 David Schultz
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
(...skipping 47 matching lines...) Expand 10 before | Expand all | Expand 10 after
58 * 58 *
59 * Modifications: 59 * Modifications:
60 * 60 *
61 * I omitted the original algorithm's handling of overflow in tan(x) after 61 * I omitted the original algorithm's handling of overflow in tan(x) after
62 * verifying with nearpi.c that this can't happen in IEEE single or double 62 * verifying with nearpi.c that this can't happen in IEEE single or double
63 * precision. I also handle large x differently. 63 * precision. I also handle large x differently.
64 */ 64 */
65 65
66 #include "libm.h" 66 #include "libm.h"
67 67
68 double complex ctanh(double complex z) 68 double complex ctanh(double complex z) {
69 { 69 double x, y;
70 » double x, y; 70 double t, beta, s, rho, denom;
71 » double t, beta, s, rho, denom; 71 uint32_t hx, ix, lx;
72 » uint32_t hx, ix, lx;
73 72
74 » x = creal(z); 73 x = creal(z);
75 » y = cimag(z); 74 y = cimag(z);
76 75
77 » EXTRACT_WORDS(hx, lx, x); 76 EXTRACT_WORDS(hx, lx, x);
78 » ix = hx & 0x7fffffff; 77 ix = hx & 0x7fffffff;
79 78
80 » /* 79 /*
81 » * ctanh(NaN + i 0) = NaN + i 0 80 * ctanh(NaN + i 0) = NaN + i 0
82 » * 81 *
83 » * ctanh(NaN + i y) = NaN + i NaN for y != 0 82 * ctanh(NaN + i y) = NaN + i NaN for y != 0
84 » * 83 *
85 » * The imaginary part has the sign of x*sin(2*y), but there's no 84 * The imaginary part has the sign of x*sin(2*y), but there's no
86 » * special effort to get this right. 85 * special effort to get this right.
87 » * 86 *
88 » * ctanh(+-Inf +- i Inf) = +-1 +- 0 87 * ctanh(+-Inf +- i Inf) = +-1 +- 0
89 » * 88 *
90 » * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite 89 * ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite
91 » * 90 *
92 » * The imaginary part of the sign is unspecified. This special 91 * The imaginary part of the sign is unspecified. This special
93 » * case is only needed to avoid a spurious invalid exception when 92 * case is only needed to avoid a spurious invalid exception when
94 » * y is infinite. 93 * y is infinite.
95 » */ 94 */
96 » if (ix >= 0x7ff00000) { 95 if (ix >= 0x7ff00000) {
97 » » if ((ix & 0xfffff) | lx) /* x is NaN */ 96 if ((ix & 0xfffff) | lx) /* x is NaN */
98 » » » return CMPLX(x, (y == 0 ? y : x * y)); 97 return CMPLX(x, (y == 0 ? y : x * y));
99 » » SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */ 98 SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
100 » » return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))); 99 return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
101 » } 100 }
102 101
103 » /* 102 /*
104 » * ctanh(+-0 + i NAN) = +-0 + i NaN 103 * ctanh(+-0 + i NAN) = +-0 + i NaN
105 » * ctanh(+-0 +- i Inf) = +-0 + i NaN 104 * ctanh(+-0 +- i Inf) = +-0 + i NaN
106 » * ctanh(x + i NAN) = NaN + i NaN 105 * ctanh(x + i NAN) = NaN + i NaN
107 » * ctanh(x +- i Inf) = NaN + i NaN 106 * ctanh(x +- i Inf) = NaN + i NaN
108 » */ 107 */
109 » if (!isfinite(y)) 108 if (!isfinite(y))
110 » » return CMPLX(x ? y - y : x, y - y); 109 return CMPLX(x ? y - y : x, y - y);
111 110
112 » /* 111 /*
113 » * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the 112 * ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
114 » * approximation sinh^2(huge) ~= exp(2*huge) / 4. 113 * approximation sinh^2(huge) ~= exp(2*huge) / 4.
115 » * We use a modified formula to avoid spurious overflow. 114 * We use a modified formula to avoid spurious overflow.
116 » */ 115 */
117 » if (ix >= 0x40360000) { /* x >= 22 */ 116 if (ix >= 0x40360000) { /* x >= 22 */
118 » » double exp_mx = exp(-fabs(x)); 117 double exp_mx = exp(-fabs(x));
119 » » return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_ mx); 118 return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
120 » } 119 }
121 120
122 » /* Kahan's algorithm */ 121 /* Kahan's algorithm */
123 » t = tan(y); 122 t = tan(y);
124 » beta = 1.0 + t * t; /* = 1 / cos^2(y) */ 123 beta = 1.0 + t * t; /* = 1 / cos^2(y) */
125 » s = sinh(x); 124 s = sinh(x);
126 » rho = sqrt(1 + s * s); /* = cosh(x) */ 125 rho = sqrt(1 + s * s); /* = cosh(x) */
127 » denom = 1 + beta * s * s; 126 denom = 1 + beta * s * s;
128 » return CMPLX((beta * rho * s) / denom, t / denom); 127 return CMPLX((beta * rho * s) / denom, t / denom);
129 } 128 }
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