--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/libm/e_log.c	Mon Sep 15 06:33:23 2008 +0000
@@ -0,0 +1,166 @@
+/* @(#)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 */
+    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 attribute_hidden
+__ieee754_log(double x)
+#else
+double attribute_hidden
+__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);
+    }
+}