189 lines
5.7 KiB
C
189 lines
5.7 KiB
C
/* expm1.c - math routines */
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/* Copyright 1992 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01c,20sep92,smb documentation additions.
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01b,30jul92,kdl marked routine NOMANUAL.
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01a,08jul92,smb documentation.
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*/
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/*
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DESCRIPTION
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*
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* This file includes a support routine (expm1()) which is used by
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* other portions of the UCB ANSI C library.
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*
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* Copyright (c) 1985 Regents of the University of California.
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms are permitted
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* provided that the above copyright notice and this paragraph are
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* duplicated in all such forms and that any documentation,
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* advertising materials, and other materials related to such
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* distribution and use acknowledge that the software was developed
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* by the University of California, Berkeley. The name of the
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* University may not be used to endorse or promote products derived
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* from this software without specific prior written permission.
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* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED
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* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.
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*
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* All recipients should regard themselves as participants in an ongoing
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* research project and hence should feel obligated to report their
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* experiences (good or bad) with these elementary function codes, using
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* the sendbug(8) program, to the authors.
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*
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* SEE ALSO: American National Standard X3.159-1989
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*
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* NOMANUAL
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*/
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#include "vxWorks.h"
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#include "math.h"
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#if defined(vax)||defined(tahoe) /* VAX D format */
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#ifdef vax
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#define _0x(A,B) 0x/**/A/**/B
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#else /* vax */
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#define _0x(A,B) 0x/**/B/**/A
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#endif /* vax */
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/* static double */
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/* ln2hi = 6.9314718055829871446E-1 , Hex 2^ 0 * .B17217F7D00000 */
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/* ln2lo = 1.6465949582897081279E-12 , Hex 2^-39 * .E7BCD5E4F1D9CC */
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/* lnhuge = 9.4961163736712506989E1 , Hex 2^ 7 * .BDEC1DA73E9010 */
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/* invln2 = 1.4426950408889634148E0 ; Hex 2^ 1 * .B8AA3B295C17F1 */
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static long ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};
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static long ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};
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static long lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};
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static long invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#define lnhuge (*(double*)lnhugex)
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#define invln2 (*(double*)invln2x)
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#else /* defined(vax)||defined(tahoe) */
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static double
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ln2hi = 6.9314718036912381649E-1 , /*Hex 2^ -1 * 1.62E42FEE00000 */
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ln2lo = 1.9082149292705877000E-10 , /*Hex 2^-33 * 1.A39EF35793C76 */
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lnhuge = 7.1602103751842355450E2 , /*Hex 2^ 9 * 1.6602B15B7ECF2 */
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invln2 = 1.4426950408889633870E0 ; /*Hex 2^ 0 * 1.71547652B82FE */
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#endif /* defined(vax)||defined(tahoe) */
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/*****************************************************************************
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* expm1 -
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*
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* EXPM1(X)
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* RETURN THE EXPONENTIAL OF X MINUS ONE
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* DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)
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* CODED IN C BY K.C. NG, 1/19/85;
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* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.
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*
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* Required system supported functions:
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* scalb(x,n)
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* copysign(x,y)
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* finite(x)
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*
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* Kernel function:
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* exp__E(x,c)
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*
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* Method:
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* 1. Argument Reduction: given the input x, find r and integer k such
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* that
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* x = k*ln2 + r, |r| <= 0.5*ln2 .
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* r will be represented as r := z+c for better accuracy.
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*
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* 2. Compute EXPM1(r)=exp(r)-1 by
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*
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* EXPM1(r=z+c) := z + exp__E(z,c)
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*
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* 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ).
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*
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* Remarks:
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* 1. When k=1 and z < -0.25, we use the following formula for
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* better accuracy:
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* EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )
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* 2. To avoid rounding error in 1-2^-k where k is large, we use
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* EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }
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* when k>56.
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*
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* Special cases:
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* EXPM1(INF) is INF, EXPM1(NaN) is NaN;
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* EXPM1(-INF)= -1;
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* for finite argument, only EXPM1(0)=0 is exact.
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*
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* Accuracy:
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* EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with
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* 1,166,000 random arguments on a VAX, the maximum observed error was
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* .872 ulps (units of the last place).
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*
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* Constants:
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* The hexadecimal values are the intended ones for the following constants.
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* The decimal values may be used, provided that the compiler will convert
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* from decimal to binary accurately enough to produce the hexadecimal values
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* shown.
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*
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* NOMANUAL
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*/
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double expm1(x)
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double x;
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{
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static double one=1.0, half=1.0/2.0;
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double scalb(), copysign(), exp__E(), z,hi,lo,c;
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int k,finite();
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#if defined(vax)||defined(tahoe)
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static prec=56;
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#else /* defined(vax)||defined(tahoe) */
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static prec=53;
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#endif /* defined(vax)||defined(tahoe) */
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#if !defined(vax)&&!defined(tahoe)
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if(x!=x) return(x); /* x is NaN */
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#endif /* !defined(vax)&&!defined(tahoe) */
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if( x <= lnhuge ) {
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if( x >= -40.0 ) {
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/* argument reduction : x - k*ln2 */
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k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */
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hi=x-k*ln2hi ;
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z=hi-(lo=k*ln2lo);
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c=(hi-z)-lo;
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if(k==0) return(z+exp__E(z,c));
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if(k==1)
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if(z< -0.25)
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{x=z+half;x +=exp__E(z,c); return(x+x);}
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else
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{z+=exp__E(z,c); x=half+z; return(x+x);}
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/* end of k=1 */
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else {
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if(k<=prec)
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{ x=one-scalb(one,-k); z += exp__E(z,c);}
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else if(k<100)
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{ x = exp__E(z,c)-scalb(one,-k); x+=z; z=one;}
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else
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{ x = exp__E(z,c)+z; z=one;}
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return (scalb(x+z,k));
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}
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}
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/* end of x > lnunfl */
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else
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/* expm1(-big#) rounded to -1 (inexact) */
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if(finite(x))
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{ ln2hi+ln2lo; return(-one);}
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/* expm1(-INF) is -1 */
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else return(-one);
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}
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/* end of x < lnhuge */
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else
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/* expm1(INF) is INF, expm1(+big#) overflows to INF */
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return( finite(x) ? scalb(one,5000) : x);
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}
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