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authorUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
committerUlrich Drepper <drepper@redhat.com>1999-07-14 00:54:57 +0000
commitabfbdde177c3a7155070dda1b2cdc8292054cc26 (patch)
treee021306b596381fbf8311d2b7eb294e918ff17c8 /sysdeps/libm-ieee754/s_log2.c
parent86421aa57ecfd70963ae66848bd6a6dd3b8e0fe6 (diff)
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-/* Adapted for log2 by Ulrich Drepper <drepper@cygnus.com>.  */
-/*
- * ====================================================
- * 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.
- * ====================================================
- */
-
-/* __log2(x)
- * Return the logarithm to base 2 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 + log(1+f).
- *			    = k+(f-(hfsq-(s*(hfsq+R))))
- *
- * Special cases:
- *	log2(x) is NaN with signal if x < 0 (including -INF) ;
- *	log2(+INF) is +INF; log(0) is -INF with signal;
- *	log2(NaN) is that NaN with no signal.
- *
- * 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 = 0.69314718055994530942,
-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 __log2(double x)
-#else
-	double __log2(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/(x-x);		/* log(+-0)=-inf */
-	    if (hx<0) return (x-x)/(x-x);	/* 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);
-	dk = (double) k;
-	f = x-1.0;
-	if((0x000fffff&(2+hx))<3) {	/* |f| < 2**-20 */
-	    if(f==zero) return dk;
-	    R = f*f*(0.5-0.33333333333333333*f);
-	    return dk-(R-f)/ln2;
-	}
- 	s = f/(2.0+f);
-	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;
-	    return dk-((hfsq-(s*(hfsq+R)))-f)/ln2;
-	} else {
-	    return dk-((s*(f-R))-f)/ln2;
-	}
-}
-
-weak_alias (__log2, log2)
-#ifdef NO_LONG_DOUBLE
-strong_alias (__log2, __log2l)
-weak_alias (__log2, log2l)
-#endif