view src/video/e_pow.h @ 1551:02e19471a694

Fixed bug #4 [Note: I'm applying this patch since it's a cleaner version of what's already implemented, and supports this controller on older kernels. I'll ask to make sure this doesn't break on the new kernels where it's no longer necessary] Date: Mon, 21 Mar 2005 09:41:11 -0500 From: Chris Nelson Subject: SDL Patch Hey, Ryan. I submitted the following patch about a year ago. It's just a simple patch for the linux port, to make multiple joysticks each appear to SDL as their own device, if they are on the same USB port (specifically, these guys <http://www.consoleplus.co.uk/product_info.php?pName=super-joybox-5-quad-joypad-converter>, which allow 4 Playstation2 controllers to be accessed via a single USB port). Without this patch, SDL pretty much drops the ball, and reports that there are 4 joysticks available when less than that number are plugged in. My work built upon the work of another person with the same device. When I submitted the patch to the list, he tested it, but it didn't work for him, so the patch was never accepted. Maybe about 3 times in the past year, I've tried to email the guy, to see if he couldn't run my new version, complete with debug code to diagnose the problem he was having. He never got back to me. So, I'm attaching the patch. I wish I knew why it didn't work for him, but I've been using it for the last year with no problems. Let me know if you need any more information, or have any ideas as to how I could test it. I'd like to see it in the tree, but I want to make sure it works. -Chris
author Sam Lantinga <slouken@libsdl.org>
date Sun, 19 Mar 2006 06:31:34 +0000
parents 7a610f25c12f
children 782fd950bd46 c121d94672cb
line wrap: on
line source

/* @(#)e_pow.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_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $";
#endif

/* __ieee754_pow(x,y) return x**y
 *
 *		      n
 * Method:  Let x =  2   * (1+f)
 *	1. Compute and return log2(x) in two pieces:
 *		log2(x) = w1 + w2,
 *	   where w1 has 53-24 = 29 bit trailing zeros.
 *	2. Perform y*log2(x) = n+y' by simulating muti-precision
 *	   arithmetic, where |y'|<=0.5.
 *	3. Return x**y = 2**n*exp(y'*log2)
 *
 * Special cases:
 *	1.  (anything) ** 0  is 1
 *	2.  (anything) ** 1  is itself
 *	3.  (anything) ** NAN is NAN
 *	4.  NAN ** (anything except 0) is NAN
 *	5.  +-(|x| > 1) **  +INF is +INF
 *	6.  +-(|x| > 1) **  -INF is +0
 *	7.  +-(|x| < 1) **  +INF is +0
 *	8.  +-(|x| < 1) **  -INF is +INF
 *	9.  +-1         ** +-INF is NAN
 *	10. +0 ** (+anything except 0, NAN)               is +0
 *	11. -0 ** (+anything except 0, NAN, odd integer)  is +0
 *	12. +0 ** (-anything except 0, NAN)               is +INF
 *	13. -0 ** (-anything except 0, NAN, odd integer)  is +INF
 *	14. -0 ** (odd integer) = -( +0 ** (odd integer) )
 *	15. +INF ** (+anything except 0,NAN) is +INF
 *	16. +INF ** (-anything except 0,NAN) is +0
 *	17. -INF ** (anything)  = -0 ** (-anything)
 *	18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer)
 *	19. (-anything except 0 and inf) ** (non-integer) is NAN
 *
 * Accuracy:
 *	pow(x,y) returns x**y nearly rounded. In particular
 *			pow(integer,integer)
 *	always returns the correct integer provided it is
 *	representable.
 *
 * 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
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */
dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */
	/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1  =  5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */
L2  =  4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */
L3  =  3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */
L4  =  2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */
L5  =  2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */
L6  =  2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */
P1   =  1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */
P2   = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */
P3   =  6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */
P4   = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */
P5   =  4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */
lg2  =  6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */
lg2_h  =  6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */
lg2_l  = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */
ovt =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp    =  9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h  =  9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l  = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

#ifdef __STDC__
	double __ieee754_pow(double x, double y)
#else
	double __ieee754_pow(x,y)
	double x, y;
#endif
{
	double z,ax,z_h,z_l,p_h,p_l;
	double y1,t1,t2,r,s,t,u,v,w;
	int32_t i,j,k,yisint,n;
	int32_t hx,hy,ix,iy;
	u_int32_t lx,ly;

	EXTRACT_WORDS(hx,lx,x);
	EXTRACT_WORDS(hy,ly,y);
	ix = hx&0x7fffffff;  iy = hy&0x7fffffff;

    /* y==zero: x**0 = 1 */
	if((iy|ly)==0) return one;

    /* +-NaN return x+y */
	if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) ||
	   iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0)))
		return x+y;

    /* determine if y is an odd int when x < 0
     * yisint = 0	... y is not an integer
     * yisint = 1	... y is an odd int
     * yisint = 2	... y is an even int
     */
	yisint  = 0;
	if(hx<0) {
	    if(iy>=0x43400000) yisint = 2; /* even integer y */
	    else if(iy>=0x3ff00000) {
		k = (iy>>20)-0x3ff;	   /* exponent */
		if(k>20) {
		    j = ly>>(52-k);
		    if((u_int32_t)(j<<(52-k))==ly) yisint = 2-(j&1);
		} else if(ly==0) {
		    j = iy>>(20-k);
		    if((j<<(20-k))==iy) yisint = 2-(j&1);
		}
	    }
	}

    /* special value of y */
	if(ly==0) {
	    if (iy==0x7ff00000) {	/* y is +-inf */
	        if(((ix-0x3ff00000)|lx)==0)
		    return  y - y;	/* inf**+-1 is NaN */
	        else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
		    return (hy>=0)? y: zero;
	        else			/* (|x|<1)**-,+inf = inf,0 */
		    return (hy<0)?-y: zero;
	    }
	    if(iy==0x3ff00000) {	/* y is  +-1 */
		if(hy<0) return one/x; else return x;
	    }
	    if(hy==0x40000000) return x*x; /* y is  2 */
	    if(hy==0x3fe00000) {	/* y is  0.5 */
		if(hx>=0)	/* x >= +0 */
		return __ieee754_sqrt(x);
	    }
	}

	ax   = x < 0 ? -x : x; /*fabs(x);*/
    /* special value of x */
	if(lx==0) {
	    if(ix==0x7ff00000||ix==0||ix==0x3ff00000){
		z = ax;			/*x is +-0,+-inf,+-1*/
		if(hy<0) z = one/z;	/* z = (1/|x|) */
		if(hx<0) {
		    if(((ix-0x3ff00000)|yisint)==0) {
			z = (z-z)/(z-z); /* (-1)**non-int is NaN */
		    } else if(yisint==1)
			z = -z;		/* (x<0)**odd = -(|x|**odd) */
		}
		return z;
	    }
	}

    /* (x<0)**(non-int) is NaN */
	if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x);

    /* |y| is huge */
	if(iy>0x41e00000) { /* if |y| > 2**31 */
	    if(iy>0x43f00000){	/* if |y| > 2**64, must o/uflow */
		if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
		if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
	    }
	/* over/underflow if x is not close to one */
	    if(ix<0x3fefffff) return (hy<0)? huge*huge:tiny*tiny;
	    if(ix>0x3ff00000) return (hy>0)? huge*huge:tiny*tiny;
	/* now |1-x| is tiny <= 2**-20, suffice to compute
	   log(x) by x-x^2/2+x^3/3-x^4/4 */
	    t = x-1;		/* t has 20 trailing zeros */
	    w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25));
	    u = ivln2_h*t;	/* ivln2_h has 21 sig. bits */
	    v = t*ivln2_l-w*ivln2;
	    t1 = u+v;
	    SET_LOW_WORD(t1,0);
	    t2 = v-(t1-u);
	} else {
	    double s2,s_h,s_l,t_h,t_l;
	    n = 0;
	/* take care subnormal number */
	    if(ix<0x00100000)
		{ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); }
	    n  += ((ix)>>20)-0x3ff;
	    j  = ix&0x000fffff;
	/* determine interval */
	    ix = j|0x3ff00000;		/* normalize ix */
	    if(j<=0x3988E) k=0;		/* |x|<sqrt(3/2) */
	    else if(j<0xBB67A) k=1;	/* |x|<sqrt(3)   */
	    else {k=0;n+=1;ix -= 0x00100000;}
	    SET_HIGH_WORD(ax,ix);

	/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
	    u = ax-bp[k];		/* bp[0]=1.0, bp[1]=1.5 */
	    v = one/(ax+bp[k]);
	    s = u*v;
	    s_h = s;
	    SET_LOW_WORD(s_h,0);
	/* t_h=ax+bp[k] High */
	    t_h = zero;
	    SET_HIGH_WORD(t_h,((ix>>1)|0x20000000)+0x00080000+(k<<18));
	    t_l = ax - (t_h-bp[k]);
	    s_l = v*((u-s_h*t_h)-s_h*t_l);
	/* compute log(ax) */
	    s2 = s*s;
	    r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
	    r += s_l*(s_h+s);
	    s2  = s_h*s_h;
	    t_h = 3.0+s2+r;
	    SET_LOW_WORD(t_h,0);
	    t_l = r-((t_h-3.0)-s2);
	/* u+v = s*(1+...) */
	    u = s_h*t_h;
	    v = s_l*t_h+t_l*s;
	/* 2/(3log2)*(s+...) */
	    p_h = u+v;
	    SET_LOW_WORD(p_h,0);
	    p_l = v-(p_h-u);
	    z_h = cp_h*p_h;		/* cp_h+cp_l = 2/(3*log2) */
	    z_l = cp_l*p_h+p_l*cp+dp_l[k];
	/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
	    t = (double)n;
	    t1 = (((z_h+z_l)+dp_h[k])+t);
	    SET_LOW_WORD(t1,0);
	    t2 = z_l-(((t1-t)-dp_h[k])-z_h);
	}

	s = one; /* s (sign of result -ve**odd) = -1 else = 1 */
	if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0)
	    s = -one;/* (-ve)**(odd int) */

    /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
	y1  = y;
	SET_LOW_WORD(y1,0);
	p_l = (y-y1)*t1+y*t2;
	p_h = y1*t1;
	z = p_l+p_h;
	EXTRACT_WORDS(j,i,z);
	if (j>=0x40900000) {				/* z >= 1024 */
	    if(((j-0x40900000)|i)!=0)			/* if z > 1024 */
		return s*huge*huge;			/* overflow */
	    else {
		if(p_l+ovt>z-p_h) return s*huge*huge;	/* overflow */
	    }
	} else if((j&0x7fffffff)>=0x4090cc00 ) {	/* z <= -1075 */
	    if(((j-0xc090cc00)|i)!=0) 		/* z < -1075 */
		return s*tiny*tiny;		/* underflow */
	    else {
		if(p_l<=z-p_h) return s*tiny*tiny;	/* underflow */
	    }
	}
    /*
     * compute 2**(p_h+p_l)
     */
	i = j&0x7fffffff;
	k = (i>>20)-0x3ff;
	n = 0;
	if(i>0x3fe00000) {		/* if |z| > 0.5, set n = [z+0.5] */
	    n = j+(0x00100000>>(k+1));
	    k = ((n&0x7fffffff)>>20)-0x3ff;	/* new k for n */
	    t = zero;
	    SET_HIGH_WORD(t,n&~(0x000fffff>>k));
	    n = ((n&0x000fffff)|0x00100000)>>(20-k);
	    if(j<0) n = -n;
	    p_h -= t;
	}
	t = p_l+p_h;
	SET_LOW_WORD(t,0);
	u = t*lg2_h;
	v = (p_l-(t-p_h))*lg2+t*lg2_l;
	z = u+v;
	w = v-(z-u);
	t  = z*z;
	t1  = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
	r  = (z*t1)/(t1-two)-(w+z*w);
	z  = one-(r-z);
	GET_HIGH_WORD(j,z);
	j += (n<<20);
	if((j>>20)<=0) z = SDL_NAME(scalbn)(z,n);	/* subnormal output */
	else SET_HIGH_WORD(z,j);
	return s*z;
}