Initial revision

From-SVN: r26263

libjava/java/lang/e_log.c

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+
+/* @(#)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.
+ * ====================================================
+ */
+
+/* __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 "fdlibm.h"
+
+#ifndef _DOUBLE_IS_32BITS
+
+#ifdef __STDC__
+static const double
+#else
+static double
+#endif
+ln2_hi  =  6.93147180369123816490e-01,	/* 3fe62e42 fee00000 */
+ln2_lo  =  1.90821492927058770002e-10,	/* 3dea39ef 35793c76 */
+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 __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;
+	__uint32_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);
+	}
+}
+
+#endif /* defined(_DOUBLE_IS_32BITS) */