/* expm1.c - math routines *//* Copyright 1992 Wind River Systems, Inc. *//*modification history--------------------01c,20sep92,smb  documentation additions.01b,30jul92,kdl  marked routine NOMANUAL.01a,08jul92,smb  documentation.*//*DESCRIPTION** This file includes a support routine (expm1()) which is used by* other portions of the UCB ANSI C library.** Copyright (c) 1985 Regents of the University of California.* All rights reserved.** Redistribution and use in source and binary forms are permitted* provided that the above copyright notice and this paragraph are* duplicated in all such forms and that any documentation,* advertising materials, and other materials related to such* distribution and use acknowledge that the software was developed* by the University of California, Berkeley.  The name of the* University may not be used to endorse or promote products derived* from this software without specific prior written permission.* THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR* IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED* WARRANTIES OF MERCHANTIBILITY AND FITNESS FOR A PARTICULAR PURPOSE.** All recipients should regard themselves as participants in an ongoing* research project and hence should feel obligated to report their* experiences (good or bad) with these elementary function codes, using* the sendbug(8) program, to the authors.** SEE ALSO: American National Standard X3.159-1989** NOMANUAL*/#include "vxWorks.h"#include "math.h"#if defined(vax)||defined(tahoe)	/* VAX D format */#ifdef vax#define _0x(A,B)	0x/**/A/**/B#else	/* vax */#define _0x(A,B)	0x/**/B/**/A#endif	/* vax *//* static double *//* ln2hi  =  6.9314718055829871446E-1    , Hex  2^  0   *  .B17217F7D00000 *//* ln2lo  =  1.6465949582897081279E-12   , Hex  2^-39   *  .E7BCD5E4F1D9CC *//* lnhuge =  9.4961163736712506989E1     , Hex  2^  7   *  .BDEC1DA73E9010 *//* invln2 =  1.4426950408889634148E0     ; Hex  2^  1   *  .B8AA3B295C17F1 */static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};static long    lnhugex[] = { _0x(ec1d,43bd), _0x(9010,a73e)};static long    invln2x[] = { _0x(aa3b,40b8), _0x(17f1,295c)};#define    ln2hi    (*(double*)ln2hix)#define    ln2lo    (*(double*)ln2lox)#define   lnhuge    (*(double*)lnhugex)#define   invln2    (*(double*)invln2x)#else	/* defined(vax)||defined(tahoe) */static doubleln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */lnhuge =  7.1602103751842355450E2     , /*Hex  2^  9   *  1.6602B15B7ECF2 */invln2 =  1.4426950408889633870E0     ; /*Hex  2^  0   *  1.71547652B82FE */#endif	/* defined(vax)||defined(tahoe) *//****************************************************************************** expm1 -** EXPM1(X)* RETURN THE EXPONENTIAL OF X MINUS ONE* DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS)* CODED IN C BY K.C. NG, 1/19/85;* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85.** Required system supported functions:*	scalb(x,n)*	copysign(x,y)*	finite(x)** Kernel function:*	exp__E(x,c)** Method:*	1. Argument Reduction: given the input x, find r and integer k such*	   that*	                   x = k*ln2 + r,  |r| <= 0.5*ln2 .*	   r will be represented as r := z+c for better accuracy.**	2. Compute EXPM1(r)=exp(r)-1 by**			EXPM1(r=z+c) := z + exp__E(z,c)**	3. EXPM1(x) =  2^k * ( EXPM1(r) + 1-2^-k ).** 	Remarks:*	   1. When k=1 and z < -0.25, we use the following formula for*	      better accuracy:*			EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) )*	   2. To avoid rounding error in 1-2^-k where k is large, we use*			EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 }*	      when k>56.** Special cases:*	EXPM1(INF) is INF, EXPM1(NaN) is NaN;*	EXPM1(-INF)= -1;*	for finite argument, only EXPM1(0)=0 is exact.** Accuracy:*	EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with*	1,166,000 random arguments on a VAX, the maximum observed error was*	.872 ulps (units of the last place).** Constants:* The hexadecimal values are the intended ones for the following constants.* The decimal values may be used, provided that the compiler will convert* from decimal to binary accurately enough to produce the hexadecimal values* shown.** NOMANUAL*/double expm1(x)double x;{	static double one=1.0, half=1.0/2.0;	double scalb(), copysign(), exp__E(), z,hi,lo,c;	int k,finite();#if defined(vax)||defined(tahoe)	static prec=56;#else	/* defined(vax)||defined(tahoe) */	static prec=53;#endif	/* defined(vax)||defined(tahoe) */#if !defined(vax)&&!defined(tahoe)	if(x!=x) return(x);	/* x is NaN */#endif	/* !defined(vax)&&!defined(tahoe) */	if( x <= lnhuge ) {		if( x >= -40.0 ) {		    /* argument reduction : x - k*ln2 */			k= invln2 *x+copysign(0.5,x);	/* k=NINT(x/ln2) */			hi=x-k*ln2hi ;			z=hi-(lo=k*ln2lo);			c=(hi-z)-lo;			if(k==0) return(z+exp__E(z,c));			if(k==1)			    if(z< -0.25)				{x=z+half;x +=exp__E(z,c); return(x+x);}			    else				{z+=exp__E(z,c); x=half+z; return(x+x);}		    /* end of k=1 */			else {			    if(k<=prec)			      { x=one-scalb(one,-k); z += exp__E(z,c);}			    else if(k<100)			      { x = exp__E(z,c)-scalb(one,-k); x+=z; z=one;}			    else			      { x = exp__E(z,c)+z; z=one;}			    return (scalb(x+z,k));			}		}		/* end of x > lnunfl */		else		     /* expm1(-big#) rounded to -1 (inexact) */		     if(finite(x))			 { ln2hi+ln2lo; return(-one);}		     /* expm1(-INF) is -1 */		     else return(-one);	}	/* end of x < lnhuge */	else	/*  expm1(INF) is INF, expm1(+big#) overflows to INF */	    return( finite(x) ?  scalb(one,5000) : x);}