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
