Copyright 2004, 2005, 2006, 2007, 2008, 2009, 2010 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 3 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.LESSER. If not, see
http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
#include "mpfr-impl.h"
unsigned long
__gmpfr_isqrt (unsigned long n)
{
unsigned long i, s;
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))));
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;
}
unsigned long
__gmpfr_cuberoot (unsigned long n)
{
unsigned long i, s;
i = n;
s = 1;
while (i >= 4)
{
i >>= 3;
s <<= 1;
}
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;
}
