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+/*
+ * Copyright (c) 1985 Regents of the University of California.
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms are permitted provided
+ * that: (1) source distributions retain this entire copyright notice and
+ * comment, and (2) distributions including binaries display the following
+ * acknowledgement: ``This product includes software developed by the
+ * University of California, Berkeley and its contributors'' in the
+ * documentation or other materials provided with the distribution and in
+ * all advertising materials mentioning features or use of this software.
+ * Neither the name of the University nor the names of its contributors may
+ * be used to endorse or promote products derived from this software without
+ * specific prior written permission.
+ * THIS SOFTWARE IS PROVIDED ``AS IS'' AND WITHOUT ANY EXPRESS OR IMPLIED
+ * WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
+ */
+
+#include <ansidecl.h>
+#include <errno.h>
+#include <math.h>
+
+/* Return the square root of X. */
+double
+DEFUN (sqrt, (x), double x)
+{
+ double q, s, b, r, t;
+ CONST double zero = 0.0;
+ int m, n, i;
+
+ /* sqrt (NaN) is NaN; sqrt (+-0) is +-0. */
+ if (__isnan (x) || x == zero)
+ return x;
+
+ if (x < zero)
+ return zero / zero;
+
+ /* sqrt (Inf) is Inf. */
+ if (__isinf (x))
+ return x;
+
+ /* Scale X to [1,4). */
+ n = __logb (x);
+ x = __scalb (x, -n);
+ m = __logb (x);
+ if (m != 0)
+ /* Subnormal number. */
+ x = __scalb (x, -m);
+
+ m += n;
+ n = m / 2;
+
+ if ((n + n) != m)
+ {
+ x *= 2;
+ --m;
+ n = m / 2;
+ }
+
+ /* Generate sqrt (X) bit by bit (accumulating in Q). */
+ q = 1.0;
+ s = 4.0;
+ x -= 1.0;
+ r = 1;
+ for (i = 1; i <= 51; i++)
+ {
+ t = s + 1;
+ x *= 4;
+ r /= 2;
+ if (t <= x)
+ {
+ s = t + t + 2, x -= t;
+ q += r;
+ }
+ else
+ s *= 2;
+ }
+
+ /* Generate the last bit and determine the final rounding. */
+ r /= 2;
+ x *= 4;
+ if (x == zero)
+ goto end;
+ (void) (100 + r); /* Trigger inexact flag. */
+ if (s < x)
+ {
+ q += r;
+ x -= s;
+ s += 2;
+ s *= 2;
+ x *= 4;
+ t = (x - s) - 5;
+ b = 1.0 + 3 * r / 4;
+ if (b == 1.0)
+ goto end; /* B == 1: Round to zero. */
+ b = 1.0 + r / 4;
+ if (b > 1.0)
+ t = 1; /* B > 1: Round to +Inf. */
+ if (t >= 0)
+ q += r;
+ } /* Else round to nearest. */
+ else
+ {
+ s *= 2;
+ x *= 4;
+ t = (x - s) - 1;
+ b = 1.0 + 3 * r / 4;
+ if (b == 1.0)
+ goto end;
+ b = 1.0 + r / 4;
+ if (b > 1.0)
+ t = 1;
+ if (t >= 0)
+ q += r;
+ }
+
+end:
+ return __scalb (q, n);
+}