view src/video/e_log.h @ 1775:5572e4204f36

Date: Sun, 7 May 2006 19:22:33 -0400 From: Mike Frysinger Subject: [SDL] [patch] fix building with DirectFB-0.9.25.1 another DirectFB release, another small bit of API breakage :) this time around, DIKI_ALTGR has been removed and DIKI_ALT_R is supposed to be used ... DIKI_ALT_R is not a new define, so there shouldnt be any need for checking the DirectFB version ... it should work with older DirectFB's as well thanks to Sascha Schwarz for pointing this out on the Gentoo bugzilla: http://bugs.gentoo.org/132571 -mike
author Sam Lantinga <slouken@libsdl.org>
date Mon, 08 May 2006 02:09:34 +0000
parents 450721ad5436
children 782fd950bd46 c121d94672cb
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/* @(#)e_log.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#if defined(LIBM_SCCS) && !defined(lint)
static char rcsid[] = "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $";
#endif

/* __ieee754_log(x)
 * Return the logrithm of x
 *
 * Method :
 *   1. Argument Reduction: find k and f such that
 *			x = 2^k * (1+f),
 *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
 *
 *   2. Approximation of log(1+f).
 *	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 + .....,
 *	     	 = 2s + s*R
 *      We use a special Reme algorithm on [0,0.1716] to generate
 * 	a polynomial of degree 14 to approximate R The maximum error
 *	of this polynomial approximation is bounded by 2**-58.45. In
 *	other words,
 *		        2      4      6      8      10      12      14
 *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
 *  	(the values of Lg1 to Lg7 are listed in the program)
 *	and
 *	    |      2          14          |     -58.45
 *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2
 *	    |                             |
 *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
 *	In order to guarantee error in log below 1ulp, we compute log
 *	by
 *		log(1+f) = f - s*(f - R)	(if f is not too large)
 *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
 *
 *	3. Finally,  log(x) = k*ln2 + log(1+f).
 *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
 *	   Here ln2 is split into two floating point number:
 *			ln2_hi + ln2_lo,
 *	   where n*ln2_hi is always exact for |n| < 2000.
 *
 * Special cases:
 *	log(x) is NaN with signal if x < 0 (including -INF) ;
 *	log(+INF) is +INF; log(0) is -INF with signal;
 *	log(NaN) is that NaN with no signal.
 *
 * Accuracy:
 *	according to an error analysis, the error is always less than
 *	1 ulp (unit 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.
 */

/*#include "math.h"*/
#include "math_private.h"

#ifdef __STDC__
static const double
#else
static double
#endif
ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
Lg1 = 6.666666666666735130e-01,  /* 3FE55555 55555593 */
Lg2 = 3.999999999940941908e-01,  /* 3FD99999 9997FA04 */
Lg3 = 2.857142874366239149e-01,  /* 3FD24924 94229359 */
Lg4 = 2.222219843214978396e-01,  /* 3FCC71C5 1D8E78AF */
Lg5 = 1.818357216161805012e-01,  /* 3FC74664 96CB03DE */
Lg6 = 1.531383769920937332e-01,  /* 3FC39A09 D078C69F */
Lg7 = 1.479819860511658591e-01;  /* 3FC2F112 DF3E5244 */

#ifdef __STDC__
	double __ieee754_log(double x)
#else
	double __ieee754_log(x)
	double x;
#endif
{
	double hfsq,f,s,z,R,w,t1,t2,dk;
	int32_t k,hx,i,j;
	u_int32_t lx;

	EXTRACT_WORDS(hx,lx,x);

	k=0;
	if (hx < 0x00100000) {			/* x < 2**-1022  */
	    if (((hx&0x7fffffff)|lx)==0)
		return -two54/zero;		/* log(+-0)=-inf */
	    if (hx<0) return (x-x)/zero;	/* log(-#) = NaN */
	    k -= 54; x *= two54; /* subnormal number, scale up x */
	    GET_HIGH_WORD(hx,x);
	}
	if (hx >= 0x7ff00000) return x+x;
	k += (hx>>20)-1023;
	hx &= 0x000fffff;
	i = (hx+0x95f64)&0x100000;
	SET_HIGH_WORD(x,hx|(i^0x3ff00000));	/* normalize x or x/2 */
	k += (i>>20);
	f = x-1.0;
	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
	    if(f==zero) {if(k==0) return zero;  else {dk=(double)k;
				 return dk*ln2_hi+dk*ln2_lo;}
	    }
	    R = f*f*(0.5-0.33333333333333333*f);
	    if(k==0) return f-R; else {dk=(double)k;
	    	     return dk*ln2_hi-((R-dk*ln2_lo)-f);}
	}
 	s = f/(2.0+f);
	dk = (double)k;
	z = s*s;
	i = hx-0x6147a;
	w = z*z;
	j = 0x6b851-hx;
	t1= w*(Lg2+w*(Lg4+w*Lg6));
	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
	i |= j;
	R = t2+t1;
	if(i>0) {
	    hfsq=0.5*f*f;
	    if(k==0) return f-(hfsq-s*(hfsq+R)); else
		     return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f);
	} else {
	    if(k==0) return f-s*(f-R); else
		     return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f);
	}
}