157 lines
5.0 KiB
C
157 lines
5.0 KiB
C
/*-
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* Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice unmodified, this list of conditions, and the following
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* disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/*
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* Hyperbolic sine of a complex argument z = x + i y.
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*
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* sinh(z) = sinh(x+iy)
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* = sinh(x) cos(y) + i cosh(x) sin(y).
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*
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* Exceptional values are noted in the comments within the source code.
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* These values and the return value were taken from n1124.pdf.
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* The sign of the result for some exceptional values is unspecified but
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* must satisfy both sinh(conj(z)) == conj(sinh(z)) and sinh(-z) == -sinh(z).
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*/
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#include <sys/cdefs.h>
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__FBSDID("$FreeBSD: head/lib/msun/src/s_csinh.c 284426 2015-06-15 20:16:53Z tijl $");
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#include <complex.h>
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#include <math.h>
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#include "math_private.h"
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static const double huge = 0x1p1023;
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double complex
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csinh(double complex z)
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{
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double x, y, h;
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int32_t hx, hy, ix, iy, lx, ly;
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x = creal(z);
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y = cimag(z);
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EXTRACT_WORDS(hx, lx, x);
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EXTRACT_WORDS(hy, ly, y);
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ix = 0x7fffffff & hx;
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iy = 0x7fffffff & hy;
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/* Handle the nearly-non-exceptional cases where x and y are finite. */
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if (ix < 0x7ff00000 && iy < 0x7ff00000) {
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if ((iy | ly) == 0)
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return (CMPLX(sinh(x), y));
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if (ix < 0x40360000) /* |x| < 22: normal case */
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return (CMPLX(sinh(x) * cos(y), cosh(x) * sin(y)));
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/* |x| >= 22, so cosh(x) ~= exp(|x|) */
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if (ix < 0x40862e42) {
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/* x < 710: exp(|x|) won't overflow */
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h = exp(fabs(x)) * 0.5;
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return (CMPLX(copysign(h, x) * cos(y), h * sin(y)));
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} else if (ix < 0x4096bbaa) {
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/* x < 1455: scale to avoid overflow */
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z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
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return (CMPLX(creal(z) * copysign(1, x), cimag(z)));
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} else {
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/* x >= 1455: the result always overflows */
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h = huge * x;
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return (CMPLX(h * cos(y), h * h * sin(y)));
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}
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}
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/*
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* sinh(+-0 +- I Inf) = +-0 + I dNaN.
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* The sign of 0 in the result is unspecified. Choice = same sign
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* as the argument. Raise the invalid floating-point exception.
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*
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* sinh(+-0 +- I NaN) = +-0 + I d(NaN).
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* The sign of 0 in the result is unspecified. Choice = same sign
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* as the argument.
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*/
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if ((ix | lx) == 0) /* && iy >= 0x7ff00000 */
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return (CMPLX(x, y - y));
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/*
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* sinh(+-Inf +- I 0) = +-Inf + I +-0.
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*
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* sinh(NaN +- I 0) = d(NaN) + I +-0.
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*/
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if ((iy | ly) == 0) /* && ix >= 0x7ff00000 */
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return (CMPLX(x + x, y));
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/*
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* sinh(x +- I Inf) = dNaN + I dNaN.
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* Raise the invalid floating-point exception for finite nonzero x.
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*
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* sinh(x + I NaN) = d(NaN) + I d(NaN).
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* Optionally raises the invalid floating-point exception for finite
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* nonzero x. Choice = don't raise (except for signaling NaNs).
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*/
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if (ix < 0x7ff00000) /* && iy >= 0x7ff00000 */
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return (CMPLX(y - y, y - y));
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/*
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* sinh(+-Inf + I NaN) = +-Inf + I d(NaN).
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* The sign of Inf in the result is unspecified. Choice = same sign
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* as the argument.
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*
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* sinh(+-Inf +- I Inf) = +-Inf + I dNaN.
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* The sign of Inf in the result is unspecified. Choice = same sign
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* as the argument. Raise the invalid floating-point exception.
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*
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* sinh(+-Inf + I y) = +-Inf cos(y) + I Inf sin(y)
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*/
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if (ix == 0x7ff00000 && lx == 0) {
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if (iy >= 0x7ff00000)
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return (CMPLX(x, y - y));
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return (CMPLX(x * cos(y), INFINITY * sin(y)));
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}
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/*
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* sinh(NaN1 + I NaN2) = d(NaN1, NaN2) + I d(NaN1, NaN2).
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*
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* sinh(NaN +- I Inf) = d(NaN, dNaN) + I d(NaN, dNaN).
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* Optionally raises the invalid floating-point exception.
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* Choice = raise.
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*
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* sinh(NaN + I y) = d(NaN) + I d(NaN).
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* Optionally raises the invalid floating-point exception for finite
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* nonzero y. Choice = don't raise (except for signaling NaNs).
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*/
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return (CMPLX((x + x) * (y - y), (x * x) * (y - y)));
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}
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double complex
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csin(double complex z)
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{
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/* csin(z) = -I * csinh(I * z) = I * conj(csinh(I * conj(z))). */
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z = csinh(CMPLX(cimag(z), creal(z)));
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return (CMPLX(cimag(z), creal(z)));
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}
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