DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

#### Mercurial (d38398e5144e)

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100
``````
``````/* @(#)e_log.c 1.3 95/01/18 */
``````/*
`````` * ====================================================
`````` * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
`````` *
`````` * Developed at SunSoft, a Sun Microsystems, Inc. business.
`````` * Permission to use, copy, modify, and distribute this
`````` * software is freely granted, provided that this notice
`````` * is preserved.
`````` * ====================================================
`````` */
``````
``````//#include <sys/cdefs.h>
``````//__FBSDID("\$FreeBSD\$");
``````
``````/*
`````` * k_log1p(f):
`````` * Return log(1+f) - f for 1+f in ~[sqrt(2)/2, sqrt(2)].
`````` *
`````` * The following describes the overall strategy for computing
`````` * logarithms in base e.  The argument reduction and adding the final
`````` * term of the polynomial are done by the caller for increased accuracy
`````` * when different bases are used.
`````` *
`````` * 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.
`````` */
``````
``````static const double
``````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 */
``````
``````/*
`````` * We always inline k_log1p(), since doing so produces a
`````` * substantial performance improvement (~40% on amd64).
`````` */
``````static inline double
``````k_log1p(double f)
``````{
``````	double hfsq,s,z,R,w,t1,t2;
``````
`````` 	s = f/(2.0+f);
``````	z = s*s;
``````	w = z*z;
``````	t1= w*(Lg2+w*(Lg4+w*Lg6));
``````	t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7)));
``````	R = t2+t1;
``````	hfsq=0.5*f*f;
``````	return s*(hfsq+R);
``````}
``````