/* log1p.c - math routines *//* Copyright 1992 Wind River Systems, Inc. *//*modification history--------------------01b,30jul92,kdl  marked routine NOMANUAL.01a,08jul92,smb  documentation.*//** DESCRIPTION** This file includes a support routine (log1p()) 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.** #ifndef lint* static char sccsid[] = "@(#)log1p.c	5.3 (Berkeley) 6/30/88";* #endif	* not lint ** * SEE ALSO: American National Standard X3.159-1989* * NOMANUAL* */#include "vxWorks.h"#include "math.h"#if defined(vax)||defined(tahoe)	/* VAX D format */#include <errno.h>#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 *//* sqrt2  =  1.4142135623730950622E0     ; Hex  2^  1   *  .B504F333F9DE65 */static long     ln2hix[] = { _0x(7217,4031), _0x(0000,f7d0)};static long     ln2lox[] = { _0x(bcd5,2ce7), _0x(d9cc,e4f1)};static long     sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};#define    ln2hi    (*(double*)ln2hix)#define    ln2lo    (*(double*)ln2lox)#define    sqrt2    (*(double*)sqrt2x)#else	/* defined(vax)||defined(tahoe) */static doubleln2hi  =  6.9314718036912381649E-1    , /*Hex  2^ -1   *  1.62E42FEE00000 */ln2lo  =  1.9082149292705877000E-10   , /*Hex  2^-33   *  1.A39EF35793C76 */sqrt2  =  1.4142135623730951455E0     ; /*Hex  2^  0   *  1.6A09E667F3BCD */#endif	/* defined(vax)||defined(tahoe) *//*************************************************************************** log1p	-** LOG1P(x)* RETURN THE LOGARITHM OF 1+x* DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS)* CODED IN C BY K.C. NG, 1/19/85;* REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85.** Required system supported functions:*	scalb(x,n)*	copysign(x,y)*	logb(x)*	finite(x)** Required kernel function:*	log__L(z)** Method :*	1. Argument Reduction: find k and f such that*			1+x  = 2^k * (1+f),*	   where  sqrt(2)/2 < 1+f < sqrt(2) .**	2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)*		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,*	   log(1+f) is computed by**	     		log(1+f) = 2s + s*log__L(s*s)*	   where*		log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))**	   See log__L() for the values of the coefficients.**	3. Finally,  log(1+x) = k*ln2 + log(1+f).**	Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers*		   n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last*		   20 bits (for VAX D format), or the last 21 bits ( for IEEE*		   double) is 0. This ensures n*ln2hi is exactly representable.*		2. In step 1, f may not be representable. A correction term c*	 	   for f is computed. It follows that the correction term for*		   f - t (the leading term of log(1+f) in step 2) is c-c*x. We*		   add this correction term to n*ln2lo to attenuate the error.*** Special cases:*	log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal;*	log1p(INF) is +INF; log1p(-1) is -INF with signal;*	only log1p(0)=0 is exact for finite argument.** Accuracy:*	log1p(x) returns the exact log(1+x) nearly rounded. In a test run*	with 1,536,000 random arguments on a VAX, the maximum observed*	error was .846 ulps (units in 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 log1p(x)double x;{	static double zero=0.0, negone= -1.0, one=1.0,		      half=1.0/2.0, small=1.0E-20;   /* 1+small == 1 */	double logb(),copysign(),scalb(),log__L(),z,s,t,c;	int k,finite();#if !defined(vax)&&!defined(tahoe)	if(x!=x) return(x);	/* x is NaN */#endif	/* !defined(vax)&&!defined(tahoe) */	if(finite(x)) {	   if( x > negone ) {	   /* argument reduction */	      if(copysign(x,one)<small) return(x);	      k=logb(one+x); z=scalb(x,-k); t=scalb(one,-k);	      if(z+t >= sqrt2 )		  { k += 1 ; z *= half; t *= half; }	      t += negone; x = z + t;	      c = (t-x)+z ;		/* correction term for x */ 	   /* compute log(1+x)  */              s = x/(2+x); t = x*x*half;	      c += (k*ln2lo-c*x);	      z = c+s*(t+log__L(s*s));	      x += (z - t) ;	      return(k*ln2hi+x);	   }	/* end of if (x > negone) */	    else {#if defined(vax)||defined(tahoe)		extern double infnan();		if ( x == negone )		    return (infnan(-ERANGE));	/* -INF */		else		    return (infnan(EDOM));	/* NaN */#else	/* defined(vax)||defined(tahoe) */		/* x = -1, return -INF with signal */		if ( x == negone ) return( negone/zero );		/* negative argument for log, return NaN with signal */	        else return ( zero / zero );#endif	/* defined(vax)||defined(tahoe) */	    }	}    /* end of if (finite(x)) */    /* log(-INF) is NaN */	else if(x<0)	     return(zero/zero);    /* log(+INF) is INF */	else return(x);}