usr/src/lib/libm/common/complex/ctanhl.c

   1 /*
   2  * CDDL HEADER START
   3  *
   4  * The contents of this file are subject to the terms of the
   5  * Common Development and Distribution License (the "License").
   6  * You may not use this file except in compliance with the License.
   7  *
   8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
   9  * or http://www.opensolaris.org/os/licensing.
  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29
  30 #pragma weak __ctanhl = ctanhl
  31
  32 #include "libm.h"       /* expl/expm1l/fabsl/isinfl/isnanl/sincosl/sinl/tanhl */
  33 #include "complex_wrapper.h"
  34 #include "longdouble.h"
  35
  36 /* INDENT OFF */
  37 static const long double four = 4.0L, two = 2.0L, one = 1.0L, zero = 0.0L;
  38 /* INDENT ON */
  39
  40 ldcomplex
  41 ctanhl(ldcomplex z) {
  42         long double r, u, v, t, x, y, S, C;
  43         int hx, ix, hy, iy;
  44         ldcomplex ans;
  45
  46         x = LD_RE(z);
  47         y = LD_IM(z);
  48         hx = HI_XWORD(x);
  49         ix = hx & 0x7fffffff;
  50         hy = HI_XWORD(y);
  51         iy = hy & 0x7fffffff;
  52         x = fabsl(x);
  53         y = fabsl(y);
  54
  55         if (y == zero) {        /* ctanh(x,0) = (x,0) for x = 0 or NaN */
  56                 LD_RE(ans) = tanhl(x);
  57                 LD_IM(ans) = zero;
  58         } else if (iy >= 0x7fff0000) {  /* y is inf or NaN */
  59                 if (ix < 0x7fff0000)    /* catanh(finite x,inf/nan) is nan */
  60                         LD_RE(ans) = LD_IM(ans) = y - y;
  61                 else if (isinfl(x)) {   /* x is inf */
  62                         LD_RE(ans) = one;
  63                         LD_IM(ans) = zero;
  64                 } else {
  65                         LD_RE(ans) = x + y;
  66                         LD_IM(ans) = y - y;
  67                 }
  68         } else if (ix >= 0x4004e000) {
  69                 /* INDENT OFF */
  70                 /*
  71                  * |x| > 60 = prec/2 (14,28,34,60)
  72                  * ctanh z ~ 1 + i (sin2y)/(exp(2x))
  73                  */
  74                 /* INDENT ON */
  75                 LD_RE(ans) = one;
  76                 if (iy < 0x7ffe0000)    /* t = sin(2y) */
  77                         S = sinl(y + y);
  78                 else {
  79                         (void) sincosl(y, &S, &C);
  80                         S = (S + S) * C;
  81                 }
  82                 if (ix >= 0x7ffe0000) { /* |x| > max/2 */
  83                         if (ix >= 0x7fff0000) { /* |x| is inf or NaN */
  84                                 if (isnanl(x))  /* x is NaN */
  85                                         LD_RE(ans) = LD_IM(ans) = x + y;
  86                                 else
  87                                         LD_IM(ans) = zero * S;  /* x is inf */
  88                         } else
  89                                 LD_IM(ans) = S * expl(-x);      /* underflow */
  90                 } else
  91                         LD_IM(ans) = (S + S) * expl(-(x + x));
  92                                                         /* 2 sin 2y / exp(2x) */
  93         } else {
  94                 /* INDENT OFF */
  95                 /*
  96                  *                        t*t+2t
  97                  *    ctanh z = ---------------------------
  98                  *               t*t+[4(t+1)(cos y)](cos y)
  99                  *
 100                  *                  [4(t+1)(cos y)]*(sin y)
 101                  *              i --------------------------
 102                  *                t*t+[4(t+1)(cos y)](cos y)
 103                  */
 104                 /* INDENT ON */
 105                 sincosl(y, &S, &C);
 106                 t = expm1l(x + x);
 107                 r = (four * C) * (t + one);
 108                 u = t * t;
 109                 v = one / (u + r * C);
 110                 LD_RE(ans) = (u + two * t) * v;
 111                 LD_IM(ans) = (r * S) * v;
 112         }
 113         if (hx < 0)
 114                 LD_RE(ans) = -LD_RE(ans);
 115         if (hy < 0)
 116                 LD_IM(ans) = -LD_IM(ans);
 117         return (ans);
 118 }