usr/src/lib/libast/common/uwin/expm1.c

   1 #include "FEATURE/uwin"
   2
   3 #if !_UWIN || _lib_expm1
   4
   5 void _STUB_expm1(){}
   6
   7 #else
   8
   9 /*
  10  * Copyright (c) 1985, 1993
  11  *      The Regents of the University of California.  All rights reserved.
  12  *
  13  * Redistribution and use in source and binary forms, with or without
  14  * modification, are permitted provided that the following conditions
  15  * are met:
  16  * 1. Redistributions of source code must retain the above copyright
  17  *    notice, this list of conditions and the following disclaimer.
  18  * 2. Redistributions in binary form must reproduce the above copyright
  19  *    notice, this list of conditions and the following disclaimer in the
  20  *    documentation and/or other materials provided with the distribution.
  21  * 3. Neither the name of the University nor the names of its contributors
  22  *    may be used to endorse or promote products derived from this software
  23  *    without specific prior written permission.
  24  *
  25  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  26  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  27  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  28  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  29  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  30  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  31  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  32  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  33  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  34  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  35  * SUCH DAMAGE.
  36  */
  37
  38 static char sccsid[] = "@(#)expm1.c     8.1 (Berkeley) 6/4/93";
  39
  40 /* EXPM1(X)
  41  * RETURN THE EXPONENTIAL OF X MINUS ONE
  42  * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
  43  * CODED IN C BY K.C. NG, 1/19/85;
  44  * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
  45  *
  46  * Required system supported functions:
  47  *      scalb(x,n)
  48  *      copysign(x,y)
  49  *      finite(x)
  50  *
  51  * Kernel function:
  52  *      exp__E(x,c)
  53  *
  54  * Method:
  55  *      1. Argument Reduction: given the input x, find r and integer k such
  56  *         that
  57  *                         x = k*ln2 + r,  |r| <= 0.5*ln2 .
  58  *         r will be represented as r := z+c for better accuracy.
  59  *
  60  *      2. Compute EXPM1(r)=exp(r)-1 by
  61  *
  62  *                      EXPM1(r=z+c) := z + exp__E(z,c)
  63  *
  64  *      3. EXPM1(x) =  2^k * ( EXPM1(r) + 1-2^-k ).
  65  *
  66  *      Remarks:
  67  *         1. When k=1 and z < -0.25, we use the following formula for
  68  *            better accuracy:
  69  *                      EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
  70  *         2. To avoid rounding error in 1-2^-k where k is large, we use
  71  *                      EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
  72  *            when k>56.
  73  *
  74  * Special cases:
  75  *      EXPM1(INF) is INF, EXPM1(NaN) is NaN;
  76  *      EXPM1(-INF)= -1;
  77  *      for finite argument, only EXPM1(0)=0 is exact.
  78  *
  79  * Accuracy:
  80  *      EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
  81  *      1,166,000 random arguments on a VAX, the maximum observed error was
  82  *      .872 ulps (units of the last place).
  83  *
  84  * Constants:
  85  * The hexadecimal values are the intended ones for the following constants.
  86  * The decimal values may be used, provided that the compiler will convert
  87  * from decimal to binary accurately enough to produce the hexadecimal values
  88  * shown.
  89  */
  90
  91 #include "mathimpl.h"
  92
  93 vc(ln2hi,  6.9314718055829871446E-1  ,7217,4031,0000,f7d0,   0, .B17217F7D00000)
  94 vc(ln2lo,  1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC)
  95 vc(lnhuge, 9.4961163736712506989E1   ,ec1d,43bd,9010,a73e,   7, .BDEC1DA73E9010)
  96 vc(invln2, 1.4426950408889634148E0   ,aa3b,40b8,17f1,295c,   1, .B8AA3B295C17F1)
  97
  98 ic(ln2hi,  6.9314718036912381649E-1,   -1, 1.62E42FEE00000)
  99 ic(ln2lo,  1.9082149292705877000E-10, -33, 1.A39EF35793C76)
 100 ic(lnhuge, 7.1602103751842355450E2,     9, 1.6602B15B7ECF2)
 101 ic(invln2, 1.4426950408889633870E0,     0, 1.71547652B82FE)
 102
 103 #ifdef vccast
 104 #define ln2hi   vccast(ln2hi)
 105 #define ln2lo   vccast(ln2lo)
 106 #define lnhuge  vccast(lnhuge)
 107 #define invln2  vccast(invln2)
 108 #endif
 109
 110 extern double expm1(x)
 111 double x;
 112 {
 113         const static double one=1.0, half=1.0/2.0;
 114         double  z,hi,lo,c;
 115         int k;
 116 #if defined(vax)||defined(tahoe)
 117         static prec=56;
 118 #else   /* defined(vax)||defined(tahoe) */
 119         static prec=53;
 120 #endif  /* defined(vax)||defined(tahoe) */
 121
 122 #if !defined(vax)&&!defined(tahoe)
 123         if(x!=x) return(x);     /* x is NaN */
 124 #endif  /* !defined(vax)&&!defined(tahoe) */
 125
 126         if( x <= lnhuge ) {
 127                 if( x >= -40.0 ) {
 128
 129                     /* argument reduction : x - k*ln2 */
 130                         k= (int)(invln2*x)+copysign(0.5,x);     /* k=NINT(x/ln2) */
 131                         hi=x-k*ln2hi ;
 132                         z=hi-(lo=k*ln2lo);
 133                         c=(hi-z)-lo;
 134
 135                         if(k==0) return(z+__exp__E(z,c));
 136                         if(k==1)
 137                             if(z< -0.25)
 138                                 {x=z+half;x +=__exp__E(z,c); return(x+x);}
 139                             else
 140                                 {z+=__exp__E(z,c); x=half+z; return(x+x);}
 141                     /* end of k=1 */
 142
 143                         else {
 144                             if(k<=prec)
 145                               { x=one-scalb(one,-k); z += __exp__E(z,c);}
 146                             else if(k<100)
 147                               { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
 148                             else
 149                               { x = __exp__E(z,c)+z; z=one;}
 150
 151                             return (scalb(x+z,k));
 152                         }
 153                 }
 154                 /* end of x > lnunfl */
 155
 156                 else
 157                      /* expm1(-big#) rounded to -1 (inexact) */
 158                      if(finite(x))
 159                          { ln2hi+ln2lo; return(-one);}
 160
 161                      /* expm1(-INF) is -1 */
 162                      else return(-one);
 163         }
 164         /* end of x < lnhuge */
 165
 166         else
 167         /*  expm1(INF) is INF, expm1(+big#) overflows to INF */
 168             return( finite(x) ?  scalb(one,5000) : x);
 169 }
 170
 171 #endif