math/k_casinh.c

   1 /* Return arc hyperbole sine for double value, with the imaginary part
   2    of the result possibly adjusted for use in computing other
   3    functions.
   4    Copyright (C) 1997-2013 Free Software Foundation, Inc.
   5    This file is part of the GNU C Library.
   6
   7    The GNU C Library is free software; you can redistribute it and/or
   8    modify it under the terms of the GNU Lesser General Public
   9    License as published by the Free Software Foundation; either
  10    version 2.1 of the License, or (at your option) any later version.
  11
  12    The GNU C Library is distributed in the hope that it will be useful,
  13    but WITHOUT ANY WARRANTY; without even the implied warranty of
  14    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  15    Lesser General Public License for more details.
  16
  17    You should have received a copy of the GNU Lesser General Public
  18    License along with the GNU C Library; if not, see
  19    <http://www.gnu.org/licenses/>.  */
  20
  21 #include <complex.h>
  22 #include <math.h>
  23 #include <math_private.h>
  24 #include <float.h>
  25
  26 /* Return the complex inverse hyperbolic sine of finite nonzero Z,
  27    with the imaginary part of the result subtracted from pi/2 if ADJ
  28    is nonzero.  */
  29
  30 __complex__ double
  31 __kernel_casinh (__complex__ double x, int adj)
  32 {
  33   __complex__ double res;
  34   double rx, ix;
  35   __complex__ double y;
  36
  37   /* Avoid cancellation by reducing to the first quadrant.  */
  38   rx = fabs (__real__ x);
  39   ix = fabs (__imag__ x);
  40
  41   if (rx >= 1.0 / DBL_EPSILON || ix >= 1.0 / DBL_EPSILON)
  42     {
  43       /* For large x in the first quadrant, x + csqrt (1 + x * x)
  44          is sufficiently close to 2 * x to make no significant
  45          difference to the result; avoid possible overflow from
  46          the squaring and addition.  */
  47       __real__ y = rx;
  48       __imag__ y = ix;
  49
  50       if (adj)
  51         {
  52           double t = __real__ y;
  53           __real__ y = __copysign (__imag__ y, __imag__ x);
  54           __imag__ y = t;
  55         }
  56
  57       res = __clog (y);
  58       __real__ res += M_LN2;
  59     }
  60   else if (rx >= 0.5 && ix < DBL_EPSILON / 8.0)
  61     {
  62       double s = __ieee754_hypot (1.0, rx);
  63
  64       __real__ res = __ieee754_log (rx + s);
  65       if (adj)
  66         __imag__ res = __ieee754_atan2 (s, __imag__ x);
  67       else
  68         __imag__ res = __ieee754_atan2 (ix, s);
  69     }
  70   else if (rx < DBL_EPSILON / 8.0 && ix >= 1.5)
  71     {
  72       double s = __ieee754_sqrt ((ix + 1.0) * (ix - 1.0));
  73
  74       __real__ res = __ieee754_log (ix + s);
  75       if (adj)
  76         __imag__ res = __ieee754_atan2 (rx, __copysign (s, __imag__ x));
  77       else
  78         __imag__ res = __ieee754_atan2 (s, rx);
  79     }
  80   else
  81     {
  82       __real__ y = (rx - ix) * (rx + ix) + 1.0;
  83       __imag__ y = 2.0 * rx * ix;
  84
  85       y = __csqrt (y);
  86
  87       __real__ y += rx;
  88       __imag__ y += ix;
  89
  90       if (adj)
  91         {
  92           double t = __real__ y;
  93           __real__ y = copysign (__imag__ y, __imag__ x);
  94           __imag__ y = t;
  95         }
  96
  97       res = __clog (y);
  98     }
  99
 100   /* Give results the correct sign for the original argument.  */
 101   __real__ res = __copysign (__real__ res, __real__ x);
 102   __imag__ res = __copysign (__imag__ res, (adj ? 1.0 : __imag__ x));
 103
 104   return res;
 105 }