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+/*
+ * IBM Accurate Mathematical Library
+ * written by International Business Machines Corp.
+ * Copyright (C) 2001, 2004, 2006 Free Software Foundation
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU Lesser General Public License as published by
+ * the Free Software Foundation; either version 2.1 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+ */
+/*********************************************************************/
+/* MODULE_NAME: uroot.c */
+/* */
+/* FUNCTION: usqrt */
+/* */
+/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
+/* uroot.tbl */
+/* */
+/* An ultimate sqrt routine. Given an IEEE double machine number x */
+/* it computes the correctly rounded (to nearest) value of square */
+/* root of x. */
+/* Assumption: Machine arithmetic operations are performed in */
+/* round to nearest mode of IEEE 754 standard. */
+/* */
+/*********************************************************************/
+
+#include <math_private.h>
+
+typedef unsigned int int4;
+typedef union {int4 i[4]; long double x; double d[2]; } mynumber;
+
+static const mynumber
+ t512 = {{0x5ff00000, 0x00000000, 0x00000000, 0x00000000 }}, /* 2^512 */
+ tm256 = {{0x2ff00000, 0x00000000, 0x00000000, 0x00000000 }}; /* 2^-256 */
+static const double
+two54 = 1.80143985094819840000e+16, /* 0x4350000000000000 */
+twom54 = 5.55111512312578270212e-17; /* 0x3C90000000000000 */
+
+/*********************************************************************/
+/* An ultimate sqrt routine. Given an IEEE double machine number x */
+/* it computes the correctly rounded (to nearest) value of square */
+/* root of x. */
+/*********************************************************************/
+long double __ieee754_sqrtl(long double x)
+{
+ static const long double big = 134217728.0, big1 = 134217729.0;
+ long double t,s,i;
+ mynumber a,c;
+ int4 k, l, m;
+ int n;
+ double d;
+
+ a.x=x;
+ k=a.i[0] & 0x7fffffff;
+ /*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
+ if (k>0x000fffff && k<0x7ff00000) {
+ if (x < 0) return (big1-big1)/(big-big);
+ l = (k&0x001fffff)|0x3fe00000;
+ if (((a.i[2] & 0x7fffffff) | a.i[3]) != 0) {
+ n = (int) ((l - k) * 2) >> 21;
+ m = (a.i[2] >> 20) & 0x7ff;
+ if (m == 0) {
+ a.d[1] *= two54;
+ m = ((a.i[2] >> 20) & 0x7ff) - 54;
+ }
+ m += n;
+ if (m > 0)
+ a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
+ else if (m <= -54) {
+ a.i[2] &= 0x80000000;
+ a.i[3] = 0;
+ } else {
+ m += 54;
+ a.i[2] = (a.i[2] & 0x800fffff) | (m << 20);
+ a.d[1] *= twom54;
+ }
+ }
+ a.i[0] = l;
+ s = a.x;
+ d = __ieee754_sqrt (a.d[0]);
+ c.i[0] = 0x20000000+((k&0x7fe00000)>>1);
+ c.i[1] = 0;
+ c.i[2] = 0;
+ c.i[3] = 0;
+ i = d;
+ t = 0.5L * (i + s / i);
+ i = 0.5L * (t + s / t);
+ return c.x * i;
+ }
+ else {
+ if (k>=0x7ff00000) {
+ if (a.i[0] == 0xfff00000 && a.i[1] == 0)
+ return (big1-big1)/(big-big); /* sqrt (-Inf) = NaN. */
+ return x; /* sqrt (NaN) = NaN, sqrt (+Inf) = +Inf. */
+ }
+ if (x == 0) return x;
+ if (x < 0) return (big1-big1)/(big-big);
+ return tm256.x*__ieee754_sqrtl(x*t512.x);
+ }
+}