lib/libm/noieee_src/n_sinh.c

   1 /*      $NetBSD: n_sinh.c,v 1.7 2008/03/20 16:41:26 mhitch Exp $ */
   2 /*
   3  * Copyright (c) 1985, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * Redistribution and use in source and binary forms, with or without
   7  * modification, are permitted provided that the following conditions
   8  * are met:
   9  * 1. Redistributions of source code must retain the above copyright
  10  *    notice, this list of conditions and the following 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  * 3. Neither the name of the University nor the names of its contributors
  15  *    may be used to endorse or promote products derived from this software
  16  *    without specific prior written permission.
  17  *
  18  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  19  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  20  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  21  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  22  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  23  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  24  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  25  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  26  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  27  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  28  * SUCH DAMAGE.
  29  */
  30
  31 #ifndef lint
  32 #if 0
  33 static char sccsid[] = "@(#)sinh.c      8.1 (Berkeley) 6/4/93";
  34 #endif
  35 #endif /* not lint */
  36
  37 /* SINH(X)
  38  * RETURN THE HYPERBOLIC SINE OF X
  39  * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS)
  40  * CODED IN C BY K.C. NG, 1/8/85;
  41  * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85.
  42  *
  43  * Required system supported functions :
  44  *      copysign(x,y)
  45  *      scalb(x,N)
  46  *
  47  * Required kernel functions:
  48  *      expm1(x)        ...return exp(x)-1
  49  *
  50  * Method :
  51  *      1. reduce x to non-negative by sinh(-x) = - sinh(x).
  52  *      2.
  53  *
  54  *                                            expm1(x) + expm1(x)/(expm1(x)+1)
  55  *          0 <= x <= lnovfl     : sinh(x) := --------------------------------
  56  *                                                            2
  57  *     lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow)
  58  * lnovfl+ln2 <  x <  INF        :  overflow to INF
  59  *
  60  *
  61  * Special cases:
  62  *      sinh(x) is x if x is +INF, -INF, or NaN.
  63  *      only sinh(0)=0 is exact for finite argument.
  64  *
  65  * Accuracy:
  66  *      sinh(x) returns the exact hyperbolic sine of x nearly rounded. In
  67  *      a test run with 1,024,000 random arguments on a VAX, the maximum
  68  *      observed error was 1.93 ulps (units in the last place).
  69  *
  70  * Constants:
  71  * The hexadecimal values are the intended ones for the following constants.
  72  * The decimal values may be used, provided that the compiler will convert
  73  * from decimal to binary accurately enough to produce the hexadecimal values
  74  * shown.
  75  */
  76
  77 #define _LIBM_STATIC
  78 #include "../src/namespace.h"
  79 #include "mathimpl.h"
  80
  81 #ifdef __weak_alias
  82 __weak_alias(sinh, _sinh);
  83 __weak_alias(sinhf, _sinhf);
  84 #endif
  85
  86 vc(mln2hi, 8.8029691931113054792E1   ,0f33,43b0,2bdb,c7e2,   7, .B00F33C7E22BDB)
  87 vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A)
  88 vc(lnovfl, 8.8029691931113053016E1   ,0f33,43b0,2bda,c7e2,   7, .B00F33C7E22BDA)
  89
  90 ic(mln2hi, 7.0978271289338397310E2,    10, 1.62E42FEFA39EF)
  91 ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F)
  92 ic(lnovfl, 7.0978271289338397310E2,     9, 1.62E42FEFA39EF)
  93
  94 #ifdef vccast
  95 #define mln2hi  vccast(mln2hi)
  96 #define mln2lo  vccast(mln2lo)
  97 #define lnovfl  vccast(lnovfl)
  98 #endif
  99
 100 #if defined(__vax__)||defined(tahoe)
 101 static const int max = 126                      ;
 102 #else   /* defined(__vax__)||defined(tahoe) */
 103 static const int max = 1023                     ;
 104 #endif  /* defined(__vax__)||defined(tahoe) */
 105
 106
 107 double
 108 sinh(double x)
 109 {
 110         static const double  one=1.0, half=1.0/2.0 ;
 111         double t, sign;
 112 #if !defined(__vax__)&&!defined(tahoe)
 113         if(x!=x) return(x);     /* x is NaN */
 114 #endif  /* !defined(__vax__)&&!defined(tahoe) */
 115         sign=copysign(one,x);
 116         x=copysign(x,one);
 117         if(x<lnovfl)
 118             {t=expm1(x); return(copysign((t+t/(one+t))*half,sign));}
 119
 120         else if(x <= lnovfl+0.7)
 121                 /* subtract x by ln(2^(max+1)) and return 2^max*exp(x)
 122                         to avoid unnecessary overflow */
 123             return(copysign(scalb(one+expm1((x-mln2hi)-mln2lo),max),sign));
 124
 125         else  /* sinh(+-INF) = +-INF, sinh(+-big no.) overflow to +-INF */
 126             return( expm1(x)*sign );
 127 }
 128
 129 float
 130 sinhf(float x)
 131 {
 132         return(sinh((double)x));
 133 }