usr/src/lib/libm/common/LD/coshl.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 __coshl = coshl
  31
  32 #include "libm.h"
  33 #include "longdouble.h"
  34
  35 /*
  36  * COSH(X)
  37  * RETURN THE HYPERBOLIC COSINE OF X
  38  *
  39  * Method :
  40  *      1. Replace x by |x| (COSH(x) = COSH(-x)).
  41  *      2.
  42  *                                                      [ EXP(x) - 1 ]^2
  43  *          0        <= x <= 0.3465  :  COSH(x) := 1 + -------------------
  44  *                                                         2*EXP(x)
  45  *
  46  *                                                 EXP(x) +  1/EXP(x)
  47  *          0.3465   <= x <= thresh  :  COSH(x) := -------------------
  48  *                                                         2
  49  *          thresh   <= x <= lnovft  :  COSH(x) := EXP(x)/2
  50  *          lnovft   <= x <  INF     :  COSH(x) := SCALBN(EXP(x-MEP1*ln2),ME)
  51  *
  52  *
  53  * here
  54  *      0.3465          a number that is near one half of ln2.
  55  *      thresh          a number such that
  56  *                              EXP(thresh)+EXP(-thresh)=EXP(thresh)
  57  *      lnovft          logarithm of the overflow threshold
  58  *                      = MEP1*ln2 chopped to machine precision.
  59  *      ME              maximum exponent
  60  *      MEP1            maximum exponent plus 1
  61  *
  62  * Special cases:
  63  *      COSH(x) is |x| if x is +INF, -INF, or NaN.
  64  *      only COSH(0)=1 is exact for finite x.
  65  */
  66
  67 static const long double C[] = {
  68         0.5L,
  69         1.0L,
  70         0.3465L,
  71         45.0L,
  72         1.135652340629414394879149e+04L,
  73         7.004447686242549087858985e-16L,
  74         2.710505431213761085018632e-20L,                /* 2^-65 */
  75 };
  76
  77 #define half    C[0]
  78 #define one     C[1]
  79 #define thr1    C[2]
  80 #define thr2    C[3]
  81 #define lnovft  C[4]
  82 #define lnovlo  C[5]
  83 #define tinyl   C[6]
  84
  85 long double
  86 coshl(long double x) {
  87         long double w, t;
  88
  89         w = fabsl(x);
  90         if (!finitel(w))
  91                 return (w + w); /* x is INF or NaN */
  92         if (w < thr1) {
  93                 if (w < tinyl)
  94                         return (one + w);       /* inexact+directed rounding */
  95                 t = expm1l(w);
  96                 w = one + t;
  97                 w = one + (t * t) / (w + w);
  98                 return (w);
  99         }
 100         if (w < thr2) {
 101                 t = expl(w);
 102                 return (half * (t + one / t));
 103         }
 104         if (w <= lnovft)
 105                 return (half * expl(w));
 106         return (scalbnl(expl((w - lnovft) - lnovlo), 16383));
 107 }