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      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
      9  *    notice unmodified, this list of conditions, and the following
     10  *    disclaimer.
     11  * 2. Redistributions in binary form must reproduce the above copyright
     12  *    notice, this list of conditions and the following disclaimer in the
     13  *    documentation and/or other materials provided with the distribution.
     14  *
     15  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
     16  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
     17  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
     18  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
     19  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
     20  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
     21  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
     22  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
     23  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
     24  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
     25  */
     26 
     27 /*
     28  * Hyperbolic sine of a complex argument z.  See s_csinh.c for details.
     29  */
     30 
     31 #include <sys/cdefs.h>
     32 __FBSDID("$FreeBSD$");
     33 
     34 #include <complex.h>
     35 #include <math.h>
     36 
     37 #include "math_private.h"
     38 
     39 static const float huge = 0x1p127;
     40 
     41 float complex
     42 csinhf(float complex z)
     43 {
     44 	float x, y, h;
     45 	int32_t hx, hy, ix, iy;
     46 
     47 	x = crealf(z);
     48 	y = cimagf(z);
     49 
     50 	GET_FLOAT_WORD(hx, x);
     51 	GET_FLOAT_WORD(hy, y);
     52 
     53 	ix = 0x7fffffff & hx;
     54 	iy = 0x7fffffff & hy;
     55 
     56 	if (ix < 0x7f800000 && iy < 0x7f800000) {
     57 		if (iy == 0)
     58 			return (cpackf(sinhf(x), y));
     59 		if (ix < 0x41100000)	/* small x: normal case */
     60 			return (cpackf(sinhf(x) * cosf(y), coshf(x) * sinf(y)));
     61 
     62 		/* |x| >= 9, so cosh(x) ~= exp(|x|) */
     63 		if (ix < 0x42b17218) {
     64 			/* x < 88.7: expf(|x|) won't overflow */
     65 			h = expf(fabsf(x)) * 0.5f;
     66 			return (cpackf(copysignf(h, x) * cosf(y), h * sinf(y)));
     67 		} else if (ix < 0x4340b1e7) {
     68 			/* x < 192.7: scale to avoid overflow */
     69 			z = __ldexp_cexpf(cpackf(fabsf(x), y), -1);
     70 			return (cpackf(crealf(z) * copysignf(1, x), cimagf(z)));
     71 		} else {
     72 			/* x >= 192.7: the result always overflows */
     73 			h = huge * x;
     74 			return (cpackf(h * cosf(y), h * h * sinf(y)));
     75 		}
     76 	}
     77 
     78 	if (ix == 0 && iy >= 0x7f800000)
     79 		return (cpackf(copysignf(0, x * (y - y)), y - y));
     80 
     81 	if (iy == 0 && ix >= 0x7f800000) {
     82 		if ((hx & 0x7fffff) == 0)
     83 			return (cpackf(x, y));
     84 		return (cpackf(x, copysignf(0, y)));
     85 	}
     86 
     87 	if (ix < 0x7f800000 && iy >= 0x7f800000)
     88 		return (cpackf(y - y, x * (y - y)));
     89 
     90 	if (ix >= 0x7f800000 && (hx & 0x7fffff) == 0) {
     91 		if (iy >= 0x7f800000)
     92 			return (cpackf(x * x, x * (y - y)));
     93 		return (cpackf(x * cosf(y), INFINITY * sinf(y)));
     94 	}
     95 
     96 	return (cpackf((x * x) * (y - y), (x + x) * (y - y)));
     97 }
     98 
     99 float complex
    100 csinf(float complex z)
    101 {
    102 
    103 	z = csinhf(cpackf(-cimagf(z), crealf(z)));
    104 	return (cpackf(cimagf(z), -crealf(z)));
    105 }
    106