view src/video/e_log.h @ 1982:3b4ce57c6215

First shot at new audio data types (int32 and float32). Notable changes: - Converters between types are autogenerated. Instead of making multiple passes over the data with seperate filters for endianess, size, signedness, etc, converting between data types is always one specialized filter. This simplifies SDL_BuildAudioCVT(), which otherwise had a million edge cases with the new types, and makes the actually conversions more CPU cache friendly. Left a stub for adding specific optimized versions of these routines (SSE/MMX/Altivec, assembler, etc) - Autogenerated converters are built by SDL/src/audio/sdlgenaudiocvt.pl. This does not need to be run unless tweaking the code, and thus doesn't need integration into the build system. - Went through all the drivers and tried to weed out all the "Uint16" references that are better specified with the new SDL_AudioFormat typedef. - Cleaned out a bunch of hardcoded bitwise magic numbers and replaced them with new SDL_AUDIO_* macros. - Added initial float32 and int32 support code. Theoretically, existing drivers will push these through converters to get the data they want to feed to the hardware. Still TODO: - Optimize and debug new converters. - Update the CoreAudio backend to accept float32 data directly. - Other backends, too? - SDL_LoadWAV() needs to be updated to support int32 and float32 .wav files (both of which exist and can be generated by 'sox' for testing purposes). - Update the mixer to handle new datatypes. - Optionally update SDL_sound and SDL_mixer, etc.
author Ryan C. Gordon <icculus@icculus.org>
date Thu, 24 Aug 2006 12:10:46 +0000
parents c121d94672cb
children
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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);
    }
}

/* vi: set ts=4 sw=4 expandtab: */