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