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+
+/* @(#)z_sqrt.c 1.0 98/08/13 */
+/*****************************************************************
+ * The following routines are coded directly from the algorithms
+ * and coefficients given in "Software Manual for the Elementary
+ * Functions" by William J. Cody, Jr. and William Waite, Prentice
+ * Hall, 1980.
+ *****************************************************************/
+
+/*
+FUNCTION
+ <<sqrt>>, <<sqrtf>>---positive square root
+
+INDEX
+ sqrt
+INDEX
+ sqrtf
+
+ANSI_SYNOPSIS
+ #include <math.h>
+ double sqrt(double <[x]>);
+ float sqrtf(float <[x]>);
+
+TRAD_SYNOPSIS
+ #include <math.h>
+ double sqrt(<[x]>);
+ float sqrtf(<[x]>);
+
+DESCRIPTION
+ <<sqrt>> computes the positive square root of the argument.
+
+RETURNS
+ On success, the square root is returned. If <[x]> is real and
+ positive, then the result is positive. If <[x]> is real and
+ negative, the global value <<errno>> is set to <<EDOM>> (domain error).
+
+
+PORTABILITY
+ <<sqrt>> is ANSI C. <<sqrtf>> is an extension.
+*/
+
+/******************************************************************
+ * Square Root
+ *
+ * Input:
+ * x - floating point value
+ *
+ * Output:
+ * square-root of x
+ *
+ * Description:
+ * This routine performs floating point square root.
+ *
+ * The initial approximation is computed as
+ * y0 = 0.41731 + 0.59016 * f
+ * where f is a fraction such that x = f * 2^exp.
+ *
+ * Three Newton iterations in the form of Heron's formula
+ * are then performed to obtain the final value:
+ * y[i] = (y[i-1] + f / y[i-1]) / 2, i = 1, 2, 3.
+ *
+ *****************************************************************/
+
+#include "fdlibm.h"
+#include "zmath.h"
+
+#ifndef _DOUBLE_IS_32BITS
+
+double
+_DEFUN (sqrt, (double),
+ double x)
+{
+ double f, y;
+ int exp, i, odd;
+
+ /* Check for special values. */
+ switch (numtest (x))
+ {
+ case NAN:
+ errno = EDOM;
+ return (x);
+ case INF:
+ if (ispos (x))
+ {
+ errno = EDOM;
+ return (z_notanum.d);
+ }
+ else
+ {
+ errno = ERANGE;
+ return (z_infinity.d);
+ }
+ }
+
+ /* Initial checks are performed here. */
+ if (x == 0.0)
+ return (0.0);
+ if (x < 0)
+ {
+ errno = EDOM;
+ return (z_notanum.d);
+ }
+
+ /* Find the exponent and mantissa for the form x = f * 2^exp. */
+ f = frexp (x, &exp);
+
+ odd = exp & 1;
+
+ /* Get the initial approximation. */
+ y = 0.41731 + 0.59016 * f;
+
+ f /= 2.0;
+ /* Calculate the remaining iterations. */
+ for (i = 0; i < 3; ++i)
+ y = y / 2.0 + f / y;
+
+ /* Calculate the final value. */
+ if (odd)
+ {
+ y *= __SQRT_HALF;
+ exp++;
+ }
+ exp >>= 1;
+ y = ldexp (y, exp);
+
+ return (y);
+}
+
+#endif /* _DOUBLE_IS_32BITS */