compiler/stdc/math/s_ccosh.c

   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 cosine of a complex argument z = x + i y.
  29  *
  30  * cosh(z) = cosh(x+iy)
  31  *         = cosh(x) cos(y) + i sinh(x) sin(y).
  32  *
  33  * Exceptional values are noted in the comments within the source code.
  34  * These values and the return value were taken from n1124.pdf.
  35  */
  36
  37 //__FBSDID("$FreeBSD: src/lib/msun/src/s_ccosh.c,v 1.2 2011/10/21 06:29:32 das Exp $");
  38
  39 #include <float.h>
  40 #include <complex.h>
  41 #include "math.h"
  42
  43 #include "math_private.h"
  44
  45 static const double huge = 0x1p1023;
  46
  47 double complex
  48 ccosh(double complex z)
  49 {
  50         double x, y, h;
  51         int32_t hx, hy, ix, iy, lx, ly;
  52
  53         x = creal(z);
  54         y = cimag(z);
  55
  56         EXTRACT_WORDS(hx, lx, x);
  57         EXTRACT_WORDS(hy, ly, y);
  58
  59         ix = 0x7fffffff & hx;
  60         iy = 0x7fffffff & hy;
  61
  62         /* Handle the nearly-non-exceptional cases where x and y are finite. */
  63         if (ix < 0x7ff00000 && iy < 0x7ff00000) {
  64                 if ((iy | ly) == 0)
  65                         return (CMPLX(cosh(x), x * y));
  66                 if (ix < 0x40360000)    /* |x| < 22: normal case */
  67                         return (CMPLX(cosh(x) * cos(y), sinh(x) * sin(y)));
  68
  69                 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
  70                 if (ix < 0x40862e42) {
  71                         /* x < 710: exp(|x|) won't overflow */
  72                         h = exp(fabs(x)) * 0.5;
  73                         return (CMPLX(h * cos(y), copysign(h, x) * sin(y)));
  74                 } else if (ix < 0x4096bbaa) {
  75                         /* x < 1455: scale to avoid overflow */
  76                         z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
  77                         return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
  78                 } else {
  79                         /* x >= 1455: the result always overflows */
  80                         h = huge * x;
  81                         return (CMPLX(h * h * cos(y), h * sin(y)));
  82                 }
  83         }
  84
  85         /*
  86          * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
  87          * The sign of 0 in the result is unspecified.  Choice = product
  88          * of the signs of the argument.  Raise the invalid floating-point
  89          * exception.
  90          *
  91          * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
  92          * The sign of 0 in the result is unspecified.  Choice = product
  93          * of the signs of the argument.
  94          */
  95         if ((ix | lx) == 0)             /* && iy >= 0x7ff00000 */
  96                 return (CMPLX(y - y, x * copysign(0, y)));
  97
  98         /*
  99          * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
 100          *
 101          * cosh(NaN +- I 0)   = d(NaN) + I (+-)(+-)0.
 102          * The sign of 0 in the result is unspecified.  Choice = product
 103          * of the signs of the argument.
 104          */
 105         if ((iy | ly) == 0)             /* && ix >= 0x7ff00000 */
 106                         return (CMPLX(x * x, copysign(0, x) * y));
 107
 108         /*
 109          * cosh(x +- I Inf) = dNaN + I dNaN.
 110          * Raise the invalid floating-point exception for finite nonzero x.
 111          *
 112          * cosh(x + I NaN) = d(NaN) + I d(NaN).
 113          * Optionally raises the invalid floating-point exception for finite
 114          * nonzero x.  Choice = don't raise (except for signaling NaNs).
 115          */
 116         if (ix < 0x7ff00000)            /* && iy >= 0x7ff00000 */
 117                 return (CMPLX(y - y, x * (y - y)));
 118
 119         /*
 120          * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
 121          *
 122          * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
 123          * The sign of Inf in the result is unspecified.  Choice = always +.
 124          * Raise the invalid floating-point exception.
 125          *
 126          * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
 127          */
 128         if (ix == 0x7ff00000 && lx == 0) {
 129                 if (iy >= 0x7ff00000)
 130                         return (CMPLX(INFINITY, x * (y - y)));
 131                 return (CMPLX(INFINITY * cos(y), x * sin(y)));
 132         }
 133
 134         /*
 135          * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
 136          *
 137          * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
 138          * Optionally raises the invalid floating-point exception.
 139          * Choice = raise.
 140          *
 141          * cosh(NaN + I y)    = d(NaN) + I d(NaN).
 142          * Optionally raises the invalid floating-point exception for finite
 143          * nonzero y.  Choice = don't raise (except for signaling NaNs).
 144          */
 145         return (CMPLX((x * x) * (y - y), (x + x) * (y - y)));
 146 }
 147
 148 #if     LDBL_MANT_DIG == DBL_MANT_DIG
 149 AROS_MAKE_ASM_SYM(typeof(ccoshl), ccoshl, AROS_CSYM_FROM_ASM_NAME(ccoshl), AROS_CSYM_FROM_ASM_NAME(ccosh));
 150 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(ccoshl));
 151 #endif