view src/libm/e_log.c @ 3415:1756b9569141

Adam Strzelecki to SDL Actually after my patch commited in r4928 MinGW configure seems to generate broken Makefile due MSYS bash bug. (Attaching cure/patch below) The problem is that: TEST=`echo 'one\\ two\\ three\\'` echo "$TEST" Should echo: one\ two\ three\ Does it on Linux, Mac.. all UNIX but not on MSYS (MinGW) which outputs: one\two\three\ (new lines removed, probably it doesn't like backslashes) Probably this bug should be submitted to MSYS team, but not waiting till MSYS gets it fixed (they have very slow release cycles) here goes simple cure... My patch simply replaces single quoted SED rules where we needed newlien injection with double quoted ones. Tested on Mac, Linux & MinGW. Please review it ASAP coz this may be showstopper for everybody compiling with MinGW.
author Sam Lantinga <slouken@libsdl.org>
date Wed, 28 Oct 2009 04:27:50 +0000
parents dc1eb82ffdaa
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 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.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);
    }
}