Imported gcc-4.4.3

[msp430-gcc.git] / mpfr / isqrt.c

diff --git a/mpfr/isqrt.c b/mpfr/isqrt.c
new file mode 100644 (file)
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--- /dev/null
+++ b/mpfr/isqrt.c
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+/* __gmpfr_isqrt && __gmpfr_cuberoot -- Integer square root and cube root
+
+Copyright 2004, 2005, 2006, 2007, 2008, 2009 Free Software Foundation, Inc.
+Contributed by the Arenaire and Cacao projects, INRIA.
+
+This file is part of the GNU MPFR Library.
+
+The GNU MPFR Library 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.
+
+The GNU MPFR Library 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 the GNU MPFR Library; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
+MA 02110-1301, USA. */
+
+#include "mpfr-impl.h"
+
+/* returns floor(sqrt(n)) */
+unsigned long
+__gmpfr_isqrt (unsigned long n)
+{
+  unsigned long i, s;
+
+  /* First find an approximation to floor(sqrt(n)) of the form 2^k. */
+  i = n;
+  s = 1;
+  while (i >= 2)
+    {
+      i >>= 2;
+      s <<= 1;
+    }
+
+  do
+    {
+      s = (s + n / s) / 2;
+    }
+  while (!(s*s <= n && (s*s > s*(s+2) || n <= s*(s+2))));
+  /* Short explanation: As mathematically s*(s+2) < 2*ULONG_MAX,
+     the condition s*s > s*(s+2) is evaluated as true when s*(s+2)
+     "overflows" but not s*s. This implies that mathematically, one
+     has s*s <= n <= s*(s+2). If s*s "overflows", this means that n
+     is "large" and the inequality n <= s*(s+2) cannot be satisfied. */
+  return s;
+}
+
+/* returns floor(n^(1/3)) */
+unsigned long
+__gmpfr_cuberoot (unsigned long n)
+{
+  unsigned long i, s;
+
+  /* First find an approximation to floor(cbrt(n)) of the form 2^k. */
+  i = n;
+  s = 1;
+  while (i >= 4)
+    {
+      i >>= 3;
+      s <<= 1;
+    }
+
+  /* Improve the approximation (this is necessary if n is large, so that
+     mathematically (s+1)*(s+1)*(s+1) isn't much larger than ULONG_MAX). */
+  if (n >= 256)
+    {
+      s = (2 * s + n / (s * s)) / 3;
+      s = (2 * s + n / (s * s)) / 3;
+      s = (2 * s + n / (s * s)) / 3;
+    }
+
+  do
+    {
+      s = (2 * s + n / (s * s)) / 3;
+    }
+  while (!(s*s*s <= n && (s*s*s > (s+1)*(s+1)*(s+1) ||
+                          n < (s+1)*(s+1)*(s+1))));
+  return s;
+}