compiler/stdc/math/s_ctanh.c

   1 /*-
   2  * Copyright (c) 2011 David Schultz
   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 tangent of a complex argument z = x + i y.
  29  *
  30  * The algorithm is from:
  31  *
  32  *   W. Kahan.  Branch Cuts for Complex Elementary Functions or Much
  33  *   Ado About Nothing's Sign Bit.  In The State of the Art in
  34  *   Numerical Analysis, pp. 165 ff.  Iserles and Powell, eds., 1987.
  35  *
  36  * Method:
  37  *
  38  *   Let t    = tan(x)
  39  *       beta = 1/cos^2(y)
  40  *       s    = sinh(x)
  41  *       rho  = cosh(x)
  42  *
  43  *   We have:
  44  *
  45  *   tanh(z) = sinh(z) / cosh(z)
  46  *
  47  *             sinh(x) cos(y) + i cosh(x) sin(y)
  48  *           = ---------------------------------
  49  *             cosh(x) cos(y) + i sinh(x) sin(y)
  50  *
  51  *             cosh(x) sinh(x) / cos^2(y) + i tan(y)
  52  *           = -------------------------------------
  53  *                    1 + sinh^2(x) / cos^2(y)
  54  *
  55  *             beta rho s + i t
  56  *           = ----------------
  57  *               1 + beta s^2
  58  *
  59  * Modifications:
  60  *
  61  *   I omitted the original algorithm's handling of overflow in tan(x) after
  62  *   verifying with nearpi.c that this can't happen in IEEE single or double
  63  *   precision.  I also handle large x differently.
  64  */
  65
  66 //__FBSDID("$FreeBSD: src/lib/msun/src/s_ctanh.c,v 1.2 2011/10/21 06:30:16 das Exp $");
  67
  68 #include <float.h>
  69 #include <complex.h>
  70 #include "math.h"
  71
  72 #include "math_private.h"
  73
  74 double complex
  75 ctanh(double complex z)
  76 {
  77         double x, y;
  78         double t, beta, s, rho, denom;
  79         uint32_t hx, ix, lx;
  80
  81         x = creal(z);
  82         y = cimag(z);
  83
  84         EXTRACT_WORDS(hx, lx, x);
  85         ix = hx & 0x7fffffff;
  86
  87         /*
  88          * ctanh(NaN +- I 0) = d(NaN) +- I 0
  89          *
  90          * ctanh(NaN + I y) = d(NaN,y) + I d(NaN,y)     for y != 0
  91          *
  92          * The imaginary part has the sign of x*sin(2*y), but there's no
  93          * special effort to get this right.
  94          *
  95          * ctanh(+-Inf +- I Inf) = +-1 +- I 0
  96          *
  97          * ctanh(+-Inf + I y) = +-1 + I 0 sin(2y)       for y finite
  98          *
  99          * The imaginary part of the sign is unspecified.  This special
 100          * case is only needed to avoid a spurious invalid exception when
 101          * y is infinite.
 102          */
 103         if (ix >= 0x7ff00000) {
 104                 if ((ix & 0xfffff) | lx)        /* x is NaN */
 105                         return (CMPLX((x + 0) * (y + 0),
 106                             y == 0 ? y : (x + 0) * (y + 0)));
 107                 SET_HIGH_WORD(x, hx - 0x40000000);      /* x = copysign(1, x) */
 108                 return (CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y))));
 109         }
 110
 111         /*
 112          * ctanh(x + I NaN) = d(NaN) + I d(NaN)
 113          * ctanh(x +- I Inf) = dNaN + I dNaN
 114          */
 115         if (!isfinite(y))
 116                 return (CMPLX(y - y, y - y));
 117
 118         /*
 119          * ctanh(+-huge +- I y) ~= +-1 +- I 2sin(2y)/exp(2x), using the
 120          * approximation sinh^2(huge) ~= exp(2*huge) / 4.
 121          * We use a modified formula to avoid spurious overflow.
 122          */
 123         if (ix >= 0x40360000) { /* |x| >= 22 */
 124                 double exp_mx = exp(-fabs(x));
 125                 return (CMPLX(copysign(1, x),
 126                     4 * sin(y) * cos(y) * exp_mx * exp_mx));
 127         }
 128
 129         /* Kahan's algorithm */
 130         t = tan(y);
 131         beta = 1.0 + t * t;     /* = 1 / cos^2(y) */
 132         s = sinh(x);
 133         rho = sqrt(1 + s * s);  /* = cosh(x) */
 134         denom = 1 + beta * s * s;
 135         return (CMPLX((beta * rho * s) / denom, t / denom));
 136 }
 137
 138 #if     LDBL_MANT_DIG == DBL_MANT_DIG
 139 AROS_MAKE_ASM_SYM(typeof(ctanhl), ctanhl, AROS_CSYM_FROM_ASM_NAME(ctanhl), AROS_CSYM_FROM_ASM_NAME(ctanh));
 140 AROS_EXPORT_ASM_SYM(AROS_CSYM_FROM_ASM_NAME(ctanhl));
 141 #endif  /* LDBL_MANT_DIG == DBL_MANT_DIG */