e_log.c

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Author : Pierre-Loup A. Griffais
Date : 2014-09-11 19:24:42
Hash : 24c86b55
Message : [X11] Reconcile logical keyboard state with physical state on FocusIn since the window system doesn't do it for us like other platforms. This prevents sticky keys and missed keys when going in and out of focus, for example Alt would appear to stick if switching away from an SDL app with Alt-Tab and had to be pressed again. CR: Sam
src/libm/e_log.c
/* @(#)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 const 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_libm.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 */
    two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */
    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__
static const double zero = 0.0;
#else
static double zero = 0.0;
#endif

#ifdef __STDC__
double attribute_hidden
__ieee754_log(double x)
#else
double attribute_hidden
__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);
    }
}
kc3-lang/SDL/src/libm/e_log.c

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kc3-lang/SDL /src/libm/e_log.c
