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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.
+ * ====================================================
+ */
+
+/* __ieee754_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>
+#include <fix-int-fp-convert-zero.h>
+
+static const double ln2 = 0.69314718055994530942;
+static const double two54 = 1.80143985094819840000e+16; /* 43500000 00000000 */
+static const double Lg1 = 6.666666666666735130e-01;     /* 3FE55555 55555593 */
+static const double Lg2 = 3.999999999940941908e-01;     /* 3FD99999 9997FA04 */
+static const double Lg3 = 2.857142874366239149e-01;     /* 3FD24924 94229359 */
+static const double Lg4 = 2.222219843214978396e-01;     /* 3FCC71C5 1D8E78AF */
+static const double Lg5 = 1.818357216161805012e-01;     /* 3FC74664 96CB03DE */
+static const double Lg6 = 1.531383769920937332e-01;     /* 3FC39A09 D078C69F */
+static const double Lg7 = 1.479819860511658591e-01;     /* 3FC2F112 DF3E5244 */
+
+static const double zero = 0.0;
+
+double
+__ieee754_log2 (double x)
+{
+  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 (__glibc_unlikely (((hx & 0x7fffffff) | lx) == 0))
+	return -two54 / __fabs (x);        /* log(+-0)=-inf */
+      if (__glibc_unlikely (hx < 0))
+	return (x - x) / (x - x);       /* log(-#) = NaN */
+      k -= 54;
+      x *= two54;               /* subnormal number, scale up x */
+      GET_HIGH_WORD (hx, x);
+    }
+  if (__glibc_unlikely (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)
+	{
+	  if (FIX_INT_FP_CONVERT_ZERO && dk == 0.0)
+	    dk = 0.0;
+	  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;
+    }
+}
+
+strong_alias (__ieee754_log2, __log2_finite)