diff -r 2a3ec308d995 -r a98604b691c8 src/video/e_log.h --- 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: */