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libc/math/log.c
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libc/math/log.c
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/* log.c - math routines */
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/* Copyright 1992-1993 Wind River Systems, Inc. */
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/*
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modification history
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--------------------
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01f,05feb93,jdi doc changes based on kdl review.
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01e,02dec92,jdi doc tweaks.
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01d,28oct92,jdi documentation cleanup.
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01c,13oct92,jdi mangen fixes.
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01b,20sep92,smb documentation additions
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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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* 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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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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#include <errno.h>
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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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/* sqrt2 = 1.4142135623730950622E0 ; Hex 2^ 1 * .B504F333F9DE65 */
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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 sqrt2x[] = { _0x(04f3,40b5), _0x(de65,33f9)};
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#define ln2hi (*(double*)ln2hix)
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#define ln2lo (*(double*)ln2lox)
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#define sqrt2 (*(double*)sqrt2x)
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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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sqrt2 = 1.4142135623730951455E0 ; /*Hex 2^ 0 * 1.6A09E667F3BCD */
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#endif /* defined(vax)||defined(tahoe) */
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/*******************************************************************************
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*
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* log - compute a natural logarithm (ANSI)
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*
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* This routine returns the natural logarithm of <x>
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* in double precision (IEEE double, 53 bits).
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*
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* A domain error occurs if the argument is negative. A range error may occur
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* if the argument is zero.
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*
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* INTERNAL:
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* Method:
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* (1) Argument Reduction: find <k> and <f> such that:
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*
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* x = 2^k * (1+f)
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*
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* where:
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*
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* sqrt(2)/2 < 1+f < sqrt(2)
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*
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* (2) Let s = f/(2+f); based on:
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*
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* log(1+f) = log(1+s) - log(1-s) = 2s + 2/3 s**3 + 2/5 s**5 + .....
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*
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* log(1+f) is computed by:
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*
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* log(1+f) = 2s + s*log__L(s*s)
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*
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* where:
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*
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* log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...)))
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*
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* (3) Finally:
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*
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* log(x) = k*ln2 + log(1+f)
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*
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* (Here n*ln2 will be stored
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* in two floating-point numbers: n*ln2hi + n*ln2lo; n*ln2hi is exact
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* since the last 20 bits of ln2hi is 0.)
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*
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* INCLUDE FILES: math.h
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*
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* RETURNS: The double-precision natural logarithm of <x>.
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*
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* Special cases:
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* If <x> < 0 (including -INF), it returns NaN with signal.
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* If <x> is +INF, it returns <x> with no signal.
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* If <x> is 0, it returns -INF with signal.
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* If <x> is NaN it returns <x> with no signal.
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*
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* SEE ALSO: mathALib
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*
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* INTERNAL
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* Coded in C by K.C. Ng, 1/19/85;
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* Revised by K.C. Ng on 2/7/85, 3/7/85, 3/24/85, 4/16/85.
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*/
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double log
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(
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double x /* value to compute the natural logarithm of */
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)
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{
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static double zero=0.0, negone= -1.0, half=1.0/2.0;
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double logb(),scalb(),copysign(),log__L(),s,z,t;
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int k,n,finite();
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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(finite(x)) {
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if( x > zero ) {
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/* argument reduction */
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k=logb(x); x=scalb(x,-k);
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if(k == -1022) /* subnormal no. */
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{n=logb(x); x=scalb(x,-n); k+=n;}
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if(x >= sqrt2 ) {k += 1; x *= half;}
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x += negone ;
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/* compute log(1+x) */
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s=x/(2+x); t=x*x*half;
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z=k*ln2lo+s*(t+log__L(s*s));
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x += (z - t) ;
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return(k*ln2hi+x);
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}
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/* end of if (x > zero) */
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else {
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#if defined(vax)||defined(tahoe)
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extern double infnan();
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if ( x == zero )
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return (infnan(-ERANGE)); /* -INF */
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else
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return (infnan(EDOM)); /* NaN */
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#else /* defined(vax)||defined(tahoe) */
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/* zero argument, return -INF with signal */
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if ( x == zero )
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return( negone/zero );
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/* negative argument, return NaN with signal */
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else
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return ( zero / zero );
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#endif /* defined(vax)||defined(tahoe) */
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}
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}
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/* end of if (finite(x)) */
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/* NOTREACHED if defined(vax)||defined(tahoe) */
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/* log(-INF) is NaN with signal */
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else if (x<0)
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return(zero/zero);
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/* log(+INF) is +INF */
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else return(x);
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}
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