src/video/e_log.h
changeset 2756 a98604b691c8
parent 2755 2a3ec308d995
child 2757 0581f49c9294
--- a/src/video/e_log.h	Mon Sep 15 05:14:11 2008 +0000
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,161 +0,0 @@
-/* @(#)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: */