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b58ddff026
* merged mpfr 3.0.0 and gmp 5.0.1 in buildtools trunk git-svn-id: file:///srv/svn/repos/haiku/buildtools/trunk@37378 a95241bf-73f2-0310-859d-f6bbb57e9c96
85 lines
2.4 KiB
C
85 lines
2.4 KiB
C
/* __gmpfr_isqrt && __gmpfr_cuberoot -- Integer square root and cube root
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Copyright 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc.
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Contributed by the Arenaire and Cacao projects, INRIA.
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This file is part of the GNU MPFR Library.
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The GNU MPFR Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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The GNU MPFR Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MPFR Library; see the file COPYING.LESSER. If not, see
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http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc.,
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51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */
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#include "mpfr-impl.h"
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/* returns floor(sqrt(n)) */
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unsigned long
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__gmpfr_isqrt (unsigned long n)
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{
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unsigned long i, s;
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/* First find an approximation to floor(sqrt(n)) of the form 2^k. */
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i = n;
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s = 1;
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while (i >= 2)
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{
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i >>= 2;
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s <<= 1;
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}
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do
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{
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s = (s + n / s) / 2;
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}
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while (!(s*s <= n && (s*s > s*(s+2) || n <= s*(s+2))));
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/* Short explanation: As mathematically s*(s+2) < 2*ULONG_MAX,
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the condition s*s > s*(s+2) is evaluated as true when s*(s+2)
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"overflows" but not s*s. This implies that mathematically, one
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has s*s <= n <= s*(s+2). If s*s "overflows", this means that n
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is "large" and the inequality n <= s*(s+2) cannot be satisfied. */
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return s;
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}
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/* returns floor(n^(1/3)) */
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unsigned long
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__gmpfr_cuberoot (unsigned long n)
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{
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unsigned long i, s;
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/* First find an approximation to floor(cbrt(n)) of the form 2^k. */
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i = n;
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s = 1;
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while (i >= 4)
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{
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i >>= 3;
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s <<= 1;
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}
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/* Improve the approximation (this is necessary if n is large, so that
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mathematically (s+1)*(s+1)*(s+1) isn't much larger than ULONG_MAX). */
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if (n >= 256)
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{
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s = (2 * s + n / (s * s)) / 3;
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s = (2 * s + n / (s * s)) / 3;
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s = (2 * s + n / (s * s)) / 3;
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}
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do
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{
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s = (2 * s + n / (s * s)) / 3;
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}
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while (!(s*s*s <= n && (s*s*s > (s+1)*(s+1)*(s+1) ||
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n < (s+1)*(s+1)*(s+1))));
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return s;
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}
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