[444] | 1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_ccosh.c */
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| 2 | /*-
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| 3 | * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
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| 4 | * All rights reserved.
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| 5 | *
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| 6 | * Redistribution and use in source and binary forms, with or without
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| 7 | * modification, are permitted provided that the following conditions
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| 8 | * are met:
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| 9 | * 1. Redistributions of source code must retain the above copyright
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| 10 | * notice unmodified, this list of conditions, and the following
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| 11 | * disclaimer.
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| 12 | * 2. Redistributions in binary form must reproduce the above copyright
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| 13 | * notice, this list of conditions and the following disclaimer in the
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| 14 | * documentation and/or other materials provided with the distribution.
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| 15 | *
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| 16 | * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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| 17 | * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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| 18 | * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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| 19 | * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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| 20 | * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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| 21 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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| 22 | * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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| 23 | * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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| 24 | * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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| 25 | * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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| 26 | */
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| 27 | /*
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| 28 | * Hyperbolic cosine of a complex argument z = x + i y.
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| 29 | *
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| 30 | * cosh(z) = cosh(x+iy)
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| 31 | * = cosh(x) cos(y) + i sinh(x) sin(y).
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| 32 | *
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| 33 | * Exceptional values are noted in the comments within the source code.
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| 34 | * These values and the return value were taken from n1124.pdf.
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| 35 | */
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| 36 |
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| 37 | #include "libm.h"
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| 38 |
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| 39 | static const double huge = 0x1p1023;
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| 40 |
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| 41 | double complex ccosh(double complex z)
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| 42 | {
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| 43 | double x, y, h;
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| 44 | int32_t hx, hy, ix, iy, lx, ly;
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| 45 |
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| 46 | x = creal(z);
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| 47 | y = cimag(z);
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| 48 |
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| 49 | EXTRACT_WORDS(hx, lx, x);
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| 50 | EXTRACT_WORDS(hy, ly, y);
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| 51 |
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| 52 | ix = 0x7fffffff & hx;
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| 53 | iy = 0x7fffffff & hy;
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| 54 |
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| 55 | /* Handle the nearly-non-exceptional cases where x and y are finite. */
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| 56 | if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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| 57 | if ((iy | ly) == 0)
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| 58 | return CMPLX(cosh(x), x * y);
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| 59 | if (ix < 0x40360000) /* small x: normal case */
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| 60 | return CMPLX(cosh(x) * cos(y), sinh(x) * sin(y));
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| 61 |
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| 62 | /* |x| >= 22, so cosh(x) ~= exp(|x|) */
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| 63 | if (ix < 0x40862e42) {
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| 64 | /* x < 710: exp(|x|) won't overflow */
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| 65 | h = exp(fabs(x)) * 0.5;
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| 66 | return CMPLX(h * cos(y), copysign(h, x) * sin(y));
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| 67 | } else if (ix < 0x4096bbaa) {
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| 68 | /* x < 1455: scale to avoid overflow */
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| 69 | z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
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| 70 | return CMPLX(creal(z), cimag(z) * copysign(1, x));
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| 71 | } else {
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| 72 | /* x >= 1455: the result always overflows */
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| 73 | h = huge * x;
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| 74 | return CMPLX(h * h * cos(y), h * sin(y));
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| 75 | }
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| 76 | }
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| 77 |
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| 78 | /*
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| 79 | * cosh(+-0 +- I Inf) = dNaN + I sign(d(+-0, dNaN))0.
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| 80 | * The sign of 0 in the result is unspecified. Choice = normally
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| 81 | * the same as dNaN. Raise the invalid floating-point exception.
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| 82 | *
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| 83 | * cosh(+-0 +- I NaN) = d(NaN) + I sign(d(+-0, NaN))0.
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| 84 | * The sign of 0 in the result is unspecified. Choice = normally
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| 85 | * the same as d(NaN).
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| 86 | */
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| 87 | if ((ix | lx) == 0 && iy >= 0x7ff00000)
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| 88 | return CMPLX(y - y, copysign(0, x * (y - y)));
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| 89 |
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| 90 | /*
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| 91 | * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
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| 92 | *
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| 93 | * cosh(NaN +- I 0) = d(NaN) + I sign(d(NaN, +-0))0.
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| 94 | * The sign of 0 in the result is unspecified.
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| 95 | */
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| 96 | if ((iy | ly) == 0 && ix >= 0x7ff00000) {
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| 97 | if (((hx & 0xfffff) | lx) == 0)
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| 98 | return CMPLX(x * x, copysign(0, x) * y);
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| 99 | return CMPLX(x * x, copysign(0, (x + x) * y));
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| 100 | }
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| 101 |
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| 102 | /*
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| 103 | * cosh(x +- I Inf) = dNaN + I dNaN.
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| 104 | * Raise the invalid floating-point exception for finite nonzero x.
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| 105 | *
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| 106 | * cosh(x + I NaN) = d(NaN) + I d(NaN).
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| 107 | * Optionally raises the invalid floating-point exception for finite
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| 108 | * nonzero x. Choice = don't raise (except for signaling NaNs).
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| 109 | */
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| 110 | if (ix < 0x7ff00000 && iy >= 0x7ff00000)
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| 111 | return CMPLX(y - y, x * (y - y));
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| 112 |
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| 113 | /*
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| 114 | * cosh(+-Inf + I NaN) = +Inf + I d(NaN).
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| 115 | *
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| 116 | * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
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| 117 | * The sign of Inf in the result is unspecified. Choice = always +.
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| 118 | * Raise the invalid floating-point exception.
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| 119 | *
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| 120 | * cosh(+-Inf + I y) = +Inf cos(y) +- I Inf sin(y)
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| 121 | */
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| 122 | if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
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| 123 | if (iy >= 0x7ff00000)
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| 124 | return CMPLX(x * x, x * (y - y));
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| 125 | return CMPLX((x * x) * cos(y), x * sin(y));
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| 126 | }
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| 127 |
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| 128 | /*
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| 129 | * cosh(NaN + I NaN) = d(NaN) + I d(NaN).
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| 130 | *
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| 131 | * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
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| 132 | * Optionally raises the invalid floating-point exception.
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| 133 | * Choice = raise.
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| 134 | *
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| 135 | * cosh(NaN + I y) = d(NaN) + I d(NaN).
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| 136 | * Optionally raises the invalid floating-point exception for finite
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| 137 | * nonzero y. Choice = don't raise (except for signaling NaNs).
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| 138 | */
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| 139 | return CMPLX((x * x) * (y - y), (x + x) * (y - y));
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| 140 | }
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