usr/src/lib/libm/common/complex/ctanhf.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 __ctanhf = ctanhf
  31
  32 #include "libm.h"               /* expf/expm1f/fabsf/sincosf/sinf/tanhf */
  33 #include "complex_wrapper.h"
  34
  35 /* INDENT OFF */
  36 static const float four = 4.0F, two = 2.0F, one = 1.0F, zero = 0.0F;
  37 /* INDENT ON */
  38
  39 fcomplex
  40 ctanhf(fcomplex z) {
  41         float r, u, v, t, x, y, S, C;
  42         int hx, ix, hy, iy;
  43         fcomplex ans;
  44
  45         x = F_RE(z);
  46         y = F_IM(z);
  47         hx = THE_WORD(x);
  48         ix = hx & 0x7fffffff;
  49         hy = THE_WORD(y);
  50         iy = hy & 0x7fffffff;
  51         x = fabsf(x);
  52         y = fabsf(y);
  53
  54         if (iy == 0) {          /* ctanh(x,0) = (x,0) for x = 0 or NaN */
  55                 F_RE(ans) = tanhf(x);
  56                 F_IM(ans) = zero;
  57         } else if (iy >= 0x7f800000) {  /* y is inf or NaN */
  58                 if (ix < 0x7f800000)    /* catanh(finite x,inf/nan) is nan */
  59                         F_RE(ans) = F_IM(ans) = y - y;
  60                 else if (ix == 0x7f800000) {    /* x is inf */
  61                         F_RE(ans) = one;
  62                         F_IM(ans) = zero;
  63                 } else {
  64                         F_RE(ans) = x + y;
  65                         F_IM(ans) = y - y;
  66                 }
  67         } else if (ix >= 0x41600000) {
  68                 /*
  69                  * |x| > 14 = prec/2 (14,28,34,60)
  70                  * ctanh z ~ 1 + i (sin2y)/(exp(2x))
  71                  */
  72                 F_RE(ans) = one;
  73                 if (iy < 0x7f000000)    /* t = sin(2y) */
  74                         S = sinf(y + y);
  75                 else {
  76                         (void) sincosf(y, &S, &C);
  77                         S = (S + S) * C;
  78                 }
  79                 if (ix >= 0x7f000000) { /* |x| > max/2 */
  80                         if (ix >= 0x7f800000) { /* |x| is inf or NaN */
  81                                 if (ix > 0x7f800000)    /* x is NaN */
  82                                         F_RE(ans) = F_IM(ans) = x + y;
  83                                 else
  84                                         F_IM(ans) = zero * S;   /* x is inf */
  85                         } else
  86                                 F_IM(ans) = S * expf(-x);       /* underflow */
  87                 } else
  88                         F_IM(ans) = (S + S) * expf(-(x + x));
  89                                                         /* 2 sin 2y / exp(2x) */
  90         } else {
  91                 /* INDENT OFF */
  92                 /*
  93                  *                        t*t+2t
  94                  *    ctanh z = ---------------------------
  95                  *               t*t+[4(t+1)(cos y)](cos y)
  96                  *
  97                  *                  [4(t+1)(cos y)]*(sin y)
  98                  *              i --------------------------
  99                  *                t*t+[4(t+1)(cos y)](cos y)
 100                  */
 101                 /* INDENT ON */
 102                 (void) sincosf(y, &S, &C);
 103                 t = expm1f(x + x);
 104                 r = (four * C) * (t + one);
 105                 u = t * t;
 106                 v = one / (u + r * C);
 107                 F_RE(ans) = (u + two * t) * v;
 108                 F_IM(ans) = (r * S) * v;
 109         }
 110         if (hx < 0)
 111                 F_RE(ans) = -F_RE(ans);
 112         if (hy < 0)
 113                 F_IM(ans) = -F_IM(ans);
 114         return (ans);
 115 }