src/video/e_log.h
 author Edgar Simo Sun, 06 Jul 2008 17:06:37 +0000 branch gsoc2008_force_feedback changeset 2498 ab567bd667bf parent 1895 c121d94672cb permissions -rw-r--r--
Fixed various mistakes in the doxygen.
```     1 /* @(#)e_log.c 5.1 93/09/24 */
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```     2 /*
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```     3  * ====================================================
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```     4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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```     5  *
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```     6  * Developed at SunPro, a Sun Microsystems, Inc. business.
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```     7  * Permission to use, copy, modify, and distribute this
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```     8  * software is freely granted, provided that this notice
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```     9  * is preserved.
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```    10  * ====================================================
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```    11  */
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```    12
```
```    13 #if defined(LIBM_SCCS) && !defined(lint)
```
```    14 static char rcsid[] = "\$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp \$";
```
```    15 #endif
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```    16
```
```    17 /* __ieee754_log(x)
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```    18  * Return the logrithm of x
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```    19  *
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```    20  * Method :
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```    21  *   1. Argument Reduction: find k and f such that
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```    22  *			x = 2^k * (1+f),
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```    23  *	   where  sqrt(2)/2 < 1+f < sqrt(2) .
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```    24  *
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```    25  *   2. Approximation of log(1+f).
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```    26  *	Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s)
```
```    27  *		 = 2s + 2/3 s**3 + 2/5 s**5 + .....,
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```    28  *	     	 = 2s + s*R
```
```    29  *      We use a special Reme algorithm on [0,0.1716] to generate
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```    30  * 	a polynomial of degree 14 to approximate R The maximum error
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```    31  *	of this polynomial approximation is bounded by 2**-58.45. In
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```    32  *	other words,
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```    33  *		        2      4      6      8      10      12      14
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```    34  *	    R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s  +Lg6*s  +Lg7*s
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```    35  *  	(the values of Lg1 to Lg7 are listed in the program)
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```    36  *	and
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```    37  *	    |      2          14          |     -58.45
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```    38  *	    | Lg1*s +...+Lg7*s    -  R(z) | <= 2
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```    39  *	    |                             |
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```    40  *	Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2.
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```    41  *	In order to guarantee error in log below 1ulp, we compute log
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```    42  *	by
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```    43  *		log(1+f) = f - s*(f - R)	(if f is not too large)
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```    44  *		log(1+f) = f - (hfsq - s*(hfsq+R)).	(better accuracy)
```
```    45  *
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```    46  *	3. Finally,  log(x) = k*ln2 + log(1+f).
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```    47  *			    = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo)))
```
```    48  *	   Here ln2 is split into two floating point number:
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```    49  *			ln2_hi + ln2_lo,
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```    50  *	   where n*ln2_hi is always exact for |n| < 2000.
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```    51  *
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```    52  * Special cases:
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```    53  *	log(x) is NaN with signal if x < 0 (including -INF) ;
```
```    54  *	log(+INF) is +INF; log(0) is -INF with signal;
```
```    55  *	log(NaN) is that NaN with no signal.
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```    56  *
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```    57  * Accuracy:
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```    58  *	according to an error analysis, the error is always less than
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```    59  *	1 ulp (unit in the last place).
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```    60  *
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```    61  * Constants:
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```    62  * The hexadecimal values are the intended ones for the following
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```    63  * constants. The decimal values may be used, provided that the
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```    64  * compiler will convert from decimal to binary accurately enough
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```    65  * to produce the hexadecimal values shown.
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```    66  */
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```    67
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```    68 /*#include "math.h"*/
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```    69 #include "math_private.h"
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```    70
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```    71 #ifdef __STDC__
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```    72 static const double
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```    73 #else
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```    74 static double
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```    75 #endif
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```    76   ln2_hi = 6.93147180369123816490e-01,  /* 3fe62e42 fee00000 */
```
```    77     ln2_lo = 1.90821492927058770002e-10,        /* 3dea39ef 35793c76 */
```
```    78     Lg1 = 6.666666666666735130e-01,     /* 3FE55555 55555593 */
```
```    79     Lg2 = 3.999999999940941908e-01,     /* 3FD99999 9997FA04 */
```
```    80     Lg3 = 2.857142874366239149e-01,     /* 3FD24924 94229359 */
```
```    81     Lg4 = 2.222219843214978396e-01,     /* 3FCC71C5 1D8E78AF */
```
```    82     Lg5 = 1.818357216161805012e-01,     /* 3FC74664 96CB03DE */
```
```    83     Lg6 = 1.531383769920937332e-01,     /* 3FC39A09 D078C69F */
```
```    84     Lg7 = 1.479819860511658591e-01;     /* 3FC2F112 DF3E5244 */
```
```    85
```
```    86 #ifdef __STDC__
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```    87 double
```
```    88 __ieee754_log(double x)
```
```    89 #else
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```    90 double
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```    91 __ieee754_log(x)
```
```    92      double x;
```
```    93 #endif
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```    94 {
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```    95     double hfsq, f, s, z, R, w, t1, t2, dk;
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```    96     int32_t k, hx, i, j;
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```    97     u_int32_t lx;
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```    98
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```    99     EXTRACT_WORDS(hx, lx, x);
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```   100
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```   101     k = 0;
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```   102     if (hx < 0x00100000) {      /* x < 2**-1022  */
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```   103         if (((hx & 0x7fffffff) | lx) == 0)
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```   104             return -two54 / zero;       /* log(+-0)=-inf */
```
```   105         if (hx < 0)
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```   106             return (x - x) / zero;      /* log(-#) = NaN */
```
```   107         k -= 54;
```
```   108         x *= two54;             /* subnormal number, scale up x */
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```   109         GET_HIGH_WORD(hx, x);
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```   110     }
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```   111     if (hx >= 0x7ff00000)
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```   112         return x + x;
```
```   113     k += (hx >> 20) - 1023;
```
```   114     hx &= 0x000fffff;
```
```   115     i = (hx + 0x95f64) & 0x100000;
```
```   116     SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000));    /* normalize x or x/2 */
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```   117     k += (i >> 20);
```
```   118     f = x - 1.0;
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```   119     if ((0x000fffff & (2 + hx)) < 3) {  /* |f| < 2**-20 */
```
```   120         if (f == zero) {
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```   121             if (k == 0)
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```   122                 return zero;
```
```   123             else {
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```   124                 dk = (double) k;
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```   125                 return dk * ln2_hi + dk * ln2_lo;
```
```   126             }
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```   127         }
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```   128         R = f * f * (0.5 - 0.33333333333333333 * f);
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```   129         if (k == 0)
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```   130             return f - R;
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```   131         else {
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```   132             dk = (double) k;
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```   133             return dk * ln2_hi - ((R - dk * ln2_lo) - f);
```
```   134         }
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```   135     }
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```   136     s = f / (2.0 + f);
```
```   137     dk = (double) k;
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```   138     z = s * s;
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```   139     i = hx - 0x6147a;
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```   140     w = z * z;
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```   141     j = 0x6b851 - hx;
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```   142     t1 = w * (Lg2 + w * (Lg4 + w * Lg6));
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```   143     t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7)));
```
```   144     i |= j;
```
```   145     R = t2 + t1;
```
```   146     if (i > 0) {
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```   147         hfsq = 0.5 * f * f;
```
```   148         if (k == 0)
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```   149             return f - (hfsq - s * (hfsq + R));
```
```   150         else
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```   151             return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) -
```
```   152                                   f);
```
```   153     } else {
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```   154         if (k == 0)
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```   155             return f - s * (f - R);
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```   156         else
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```   157             return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f);
```
```   158     }
```
```   159 }
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```   160
```
```   161 /* vi: set ts=4 sw=4 expandtab: */
```