usr/src/lib/libm/common/LD/sinhl.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 __sinhl = sinhl
  31
  32 #include "libm.h"
  33 #include "longdouble.h"
  34
  35 /* SINH(X)
  36  * RETURN THE HYPERBOLIC SINE OF X
  37  *
  38  * Method :
  39  *      1. reduce x to non-negative by SINH(-x) = - SINH(x).
  40  *      2.
  41  *
  42  *                                            EXPM1(x) + EXPM1(x)/(EXPM1(x)+1)
  43  *          0 <= x <= lnovft     : SINH(x) := --------------------------------
  44  *                                                            2
  45  *
  46  *     lnovft <= x <  INF        : SINH(x) := EXP(x-MEP1*ln2)*2**ME
  47  *
  48  * here
  49  *      lnovft          logarithm of the overflow threshold
  50  *                      = MEP1*ln2 chopped to machine precision.
  51  *      ME              maximum exponent
  52  *      MEP1            maximum exponent plus 1
  53  *
  54  * Special cases:
  55  *      SINH(x) is x if x is +INF, -INF, or NaN.
  56  *      only SINH(0)=0 is exact for finite argument.
  57  *
  58  */
  59
  60 static const long double C[] = {
  61         0.5L,
  62         1.0L,
  63         1.135652340629414394879149e+04L,
  64         7.004447686242549087858985e-16L
  65 };
  66
  67 #define half    C[0]
  68 #define one     C[1]
  69 #define lnovft  C[2]
  70 #define lnovlo  C[3]
  71
  72 long double
  73 sinhl(long double x)
  74 {
  75         long double     r, t;
  76
  77         if (!finitel(x))
  78                 return (x + x); /* x is INF or NaN */
  79         r = fabsl(x);
  80         if (r < lnovft) {
  81                 t = expm1l(r);
  82                 r = copysignl((t + t / (one + t)) * half, x);
  83         } else {
  84                 r = copysignl(expl((r - lnovft) - lnovlo), x);
  85                 r = scalbnl(r, 16383);
  86         }
  87         return (r);
  88 }