/* log.c - math routines *//* Copyright 1992-1993 Wind River Systems, Inc. *//*modification history--------------------01f,05feb93,jdi  doc changes based on kdl review.01e,02dec92,jdi  doc tweaks.01d,28oct92,jdi  documentation cleanup.01c,13oct92,jdi  mangen fixes.01b,20sep92,smb  documentation additions01a,08jul92,smb  documentation*//*DESCRIPTION* 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 X3.159-1989NOMANUAL*/#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) *//********************************************************************************* log - compute a natural logarithm (ANSI)** This routine returns the natural logarithm of <x>* in double precision (IEEE double, 53 bits).** A domain error occurs if the argument is negative.  A range error may occur* if the argument is zero.** INTERNAL:* Method:* (1) Argument Reduction: find <k> and <f> such that:**         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)...)))** (3) Finally:**         log(x) = k*ln2 + log(1+f)**     (Here n*ln2 will be stored*     in two floating-point numbers: n*ln2hi + n*ln2lo; n*ln2hi is exact*     since the last 20 bits of ln2hi is 0.)** INCLUDE FILES: math.h** RETURNS: The double-precision natural logarithm of <x>.** Special cases:*     If <x> < 0 (including -INF), it returns NaN with signal.*     If <x> is +INF, it returns <x> with no signal.*     If <x> is 0, it returns -INF with signal.*     If <x> is NaN it returns <x> with no signal.** SEE ALSO: mathALib** INTERNAL* Coded in C by K.C. Ng, 1/19/85;* Revised by K.C. Ng on 2/7/85, 3/7/85, 3/24/85, 4/16/85.*/double log    (    double x	/* value to compute the natural logarithm of */    )    {	static double zero=0.0, negone= -1.0, half=1.0/2.0;	double logb(),scalb(),copysign(),log__L(),s,z,t;	int k,n,finite();#if !defined(vax)&&!defined(tahoe)	if(x!=x) return(x);	/* x is NaN */#endif	/* !defined(vax)&&!defined(tahoe) */	if(finite(x)) {	   if( x > zero ) {	   /* argument reduction */	      k=logb(x);   x=scalb(x,-k);	      if(k == -1022) /* subnormal no. */		   {n=logb(x); x=scalb(x,-n); k+=n;}	      if(x >= sqrt2 ) {k += 1; x *= half;}	      x += negone ;	   /* compute log(1+x)  */              s=x/(2+x); t=x*x*half;	      z=k*ln2lo+s*(t+log__L(s*s));	      x += (z - t) ;	      return(k*ln2hi+x);	   }	/* end of if (x > zero) */	   else {#if defined(vax)||defined(tahoe)		extern double infnan();		if ( x == zero )		    return (infnan(-ERANGE));	/* -INF */		else		    return (infnan(EDOM));	/* NaN */#else	/* defined(vax)||defined(tahoe) */		/* zero argument, return -INF with signal */		if ( x == zero )		    return( negone/zero );		/* negative argument, return NaN with signal */		else		    return ( zero / zero );#endif	/* defined(vax)||defined(tahoe) */	    }	}    /* end of if (finite(x)) */    /* NOTREACHED if defined(vax)||defined(tahoe) */    /* log(-INF) is NaN with signal */	else if (x<0)	    return(zero/zero);    /* log(+INF) is +INF */	else return(x);    }