view src/libm/e_pow.c @ 4447:947201caa46e

Added automated test to Xcode project plus needed changes to SDL_RWFromFile to be OS X bundle aware. The Mac OS X project has a new target called testsdl which builds the automated test. I looked at using Xcode's native unit test support, but the impedance mismatch between the existing automated test structure and Apple's was more than I could handle. As such, the testsdl application is a full blown proper OS X application, which means it is a self-contained .app bundle. This immediately revealed some problems from the automated test. The largest problem was the assumption about the current working directory and where to find resources. (I suspect Windows may have a similar problem depending on circumstance.) To open resources, the test was looking in directories relative to the SDL source directory, but this will not work well with self-contained .app bundles and Xcode which can place its built applications almost anywhere. And for real-world situations, this is pretty useless anyway. So I modified SDL_RWFromFile to do special things on OS X. First, it will look for a file in the .app bundle. If not found, it will fallback and just call fopen as it used to do. I also had to modify the automated test itself because it had a contrieved test which called fopen directly to do read from an existing FILE pointer. In addition, there was a write test. Since a .app bundle is likely going to be read-only, I added a special case for OS X to write to NSTemporaryDirectory. I expect these changes should work for both Mac and iPhone OS (which includes iPad). I will update the iPhone Xcode project next. Finally, FYI, the X11 automated test seems to be failing. Below is my output. Pending breakpoint 4 - "-[NSException raise]" resolved Platform : All tests successful (2) SDL_RWops : All tests successful (5) Rect : All tests successful (1) SDL_Surface : All tests successful (6) Rendering with cocoa driver : All tests successful (3) Assert Failed! Blit output not the same. Test Case 'Renderer x11' Test Suite 'Rendering with x11 driver' Last SDL error '' Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorFailure: Set a breakpoint @ CGErrorBreakpoint() to catch errors as they are logged. Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetWindowBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSGetSurfaceBounds Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Sat May 8 00:30:34 iMacAL.local testsdl[71586] <Error>: kCGErrorIllegalArgument: CGSBindSurface: Invalid window 0xa150 Rendering with x11 driver : Failed 1 out of 4 testcases! Rendering with dummy driver : All tests successful (3) SDL_Audio : All tests successful (1) Tests run with SDL 1.3.0 revision 1095906 System is running Mac OS X and is little endian
author Eric Wing <ewing . public |-at-| gmail . com>
date Sat, 08 May 2010 00:54:22 -0700
parents 9ac6f0782dd6
children
line wrap: on
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/* @(#)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"

libm_hidden_proto(scalbn)
    libm_hidden_proto(fabs)
#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 */

         zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0,  /* 0x43400000, 0x00000000 */
         huge_val = 1.0e300, tiny = 1.0e-300,
         /* 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 attribute_hidden __ieee754_pow(double x, double y)
#else
     double attribute_hidden __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 ((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 = 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_val * huge_val : tiny * tiny;
                 if (ix >= 0x3ff00000)
                     return (hy > 0) ? huge_val * huge_val : tiny * tiny;
             }
             /* over/underflow if x is not close to one */
             if (ix < 0x3fefffff)
                 return (hy < 0) ? huge_val * huge_val : tiny * tiny;
             if (ix > 0x3ff00000)
                 return (hy > 0) ? huge_val * huge_val : 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_val * huge_val;        /* overflow */
             else {
                 if (p_l + ovt > z - p_h)
                     return s * huge_val * huge_val;    /* 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 = scalbn(z, n);  /* subnormal output */
         else
             SET_HIGH_WORD(z, j);
         return s * z;
     }