src/complex/csinh.c

   1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
   2 /*-
   3  * Copyright (c) 2005 Bruce D. Evans and Steven G. Kargl
   4  * All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice unmodified, this list of conditions, and the following
  11  *    disclaimer.
  12  * 2. Redistributions in binary form must reproduce the above copyright
  13  *    notice, this list of conditions and the following disclaimer in the
  14  *    documentation and/or other materials provided with the distribution.
  15  *
  16  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
  17  * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
  18  * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
  19  * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
  20  * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
  21  * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
  22  * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
  23  * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
  24  * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
  25  * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  26  */
  27 /*
  28  * Hyperbolic sine of a complex argument z = x + i y.
  29  *
  30  * sinh(z) = sinh(x+iy)
  31  *         = sinh(x) cos(y) + i cosh(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 #include "complex_impl.h"
  38
  39 static const double huge = 0x1p1023;
  40
  41 double complex csinh(double complex z)
  42 {
  43         double x, y, h;
  44         int32_t hx, hy, ix, iy, lx, ly;
  45
  46         x = creal(z);
  47         y = cimag(z);
  48
  49         EXTRACT_WORDS(hx, lx, x);
  50         EXTRACT_WORDS(hy, ly, y);
  51
  52         ix = 0x7fffffff & hx;
  53         iy = 0x7fffffff & hy;
  54
  55         /* Handle the nearly-non-exceptional cases where x and y are finite. */
  56         if (ix < 0x7ff00000 && iy < 0x7ff00000) {
  57                 if ((iy | ly) == 0)
  58                         return CMPLX(sinh(x), y);
  59                 if (ix < 0x40360000)    /* small x: normal case */
  60                         return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y));
  61
  62                 /* |x| >= 22, so cosh(x) ~= exp(|x|) */
  63                 if (ix < 0x40862e42) {
  64                         /* x < 710: exp(|x|) won't overflow */
  65                         h = exp(fabs(x)) * 0.5;
  66                         return CMPLX(copysign(h, x) * cos(y), h * sin(y));
  67                 } else if (ix < 0x4096bbaa) {
  68                         /* x < 1455: scale to avoid overflow */
  69                         z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
  70                         return CMPLX(creal(z) * copysign(1, x), cimag(z));
  71                 } else {
  72                         /* x >= 1455: the result always overflows */
  73                         h = huge * x;
  74                         return CMPLX(h * cos(y), h * h * sin(y));
  75                 }
  76         }
  77
  78         /*
  79          * sinh(+-0 +- I Inf) = sign(d(+-0, dNaN))0 + I dNaN.
  80          * The sign of 0 in the result is unspecified.  Choice = normally
  81          * the same as dNaN.  Raise the invalid floating-point exception.
  82          *
  83          * sinh(+-0 +- I NaN) = sign(d(+-0, NaN))0 + I d(NaN).
  84          * The sign of 0 in the result is unspecified.  Choice = normally
  85          * the same as d(NaN).
  86          */
  87         if ((ix | lx) == 0 && iy >= 0x7ff00000)
  88                 return CMPLX(copysign(0, x * (y - y)), y - y);
  89
  90         /*
  91          * sinh(+-Inf +- I 0) = +-Inf + I +-0.
  92          *
  93          * sinh(NaN +- I 0)   = d(NaN) + I +-0.
  94          */
  95         if ((iy | ly) == 0 && ix >= 0x7ff00000) {
  96                 if (((hx & 0xfffff) | lx) == 0)
  97                         return CMPLX(x, y);
  98                 return CMPLX(x, copysign(0, y));
  99         }
 100
 101         /*
 102          * sinh(x +- I Inf) = dNaN + I dNaN.
 103          * Raise the invalid floating-point exception for finite nonzero x.
 104          *
 105          * sinh(x + I NaN) = d(NaN) + I d(NaN).
 106          * Optionally raises the invalid floating-point exception for finite
 107          * nonzero x.  Choice = don't raise (except for signaling NaNs).
 108          */
 109         if (ix < 0x7ff00000 && iy >= 0x7ff00000)
 110                 return CMPLX(y - y, x * (y - y));
 111
 112         /*
 113          * sinh(+-Inf + I NaN)  = +-Inf + I d(NaN).
 114          * The sign of Inf in the result is unspecified.  Choice = normally
 115          * the same as d(NaN).
 116          *
 117          * sinh(+-Inf +- I Inf) = +Inf + I dNaN.
 118          * The sign of Inf in the result is unspecified.  Choice = always +.
 119          * Raise the invalid floating-point exception.
 120          *
 121          * sinh(+-Inf + I y)   = +-Inf cos(y) + I Inf sin(y)
 122          */
 123         if (ix >= 0x7ff00000 && ((hx & 0xfffff) | lx) == 0) {
 124                 if (iy >= 0x7ff00000)
 125                         return CMPLX(x * x, x * (y - y));
 126                 return CMPLX(x * cos(y), INFINITY * sin(y));
 127         }
 128
 129         /*
 130          * sinh(NaN + I NaN)  = d(NaN) + I d(NaN).
 131          *
 132          * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
 133          * Optionally raises the invalid floating-point exception.
 134          * Choice = raise.
 135          *
 136          * sinh(NaN + I y)    = d(NaN) + I d(NaN).
 137          * Optionally raises the invalid floating-point exception for finite
 138          * nonzero y.  Choice = don't raise (except for signaling NaNs).
 139          */
 140         return CMPLX((x * x) * (y - y), (x + x) * (y - y));
 141 }