101 lines
3.3 KiB
C
101 lines
3.3 KiB
C
/* mpf_sqrt_ui -- Compute the square root of an unsigned integer.
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Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005 Free Software Foundation,
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Inc.
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This file is part of the GNU MP Library.
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The GNU MP 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 2.1 of the License, or (at your
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option) any later version.
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The GNU MP 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 MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include <stdio.h> /* for NULL */
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#include "gmp.h"
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#include "gmp-impl.h"
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/* As usual the aim is to produce PREC(r) limbs of result with the high limb
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non-zero. That high limb will end up floor(sqrt(u)), and limbs below are
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produced by padding the input with zeros, two for each desired result
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limb, being 2*(prec-1) for a total 2*prec-1 limbs passed to mpn_sqrtrem.
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The way mpn_sqrtrem calculates floor(sqrt(x)) ensures the root is correct
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to the intended accuracy, ie. truncated to prec limbs.
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With nails, u might be two limbs, in which case a total 2*prec limbs is
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passed to mpn_sqrtrem (still giving a prec limb result). If uhigh is
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zero we adjust back to 2*prec-1, since mpn_sqrtrem requires the high
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non-zero. 2*prec limbs are always allocated, even when uhigh is zero, so
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the store of uhigh can be done without a conditional.
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u==0 is a special case so the rest of the code can assume the result is
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non-zero (ie. will have a non-zero high limb on the result).
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Not done:
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No attempt is made to identify perfect squares. It's considered this can
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be left to an application if it might occur with any frequency. As it
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stands, mpn_sqrtrem does its normal amount of work on a perfect square
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followed by zero limbs, though of course only an mpn_sqrtrem1 would be
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actually needed. We also end up leaving our mpf result with lots of low
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trailing zeros, slowing down subsequent operations.
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We're not aware of any optimizations that can be made using the fact the
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input has lots of trailing zeros (apart from the perfect square
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case). */
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/* 1 if we (might) need two limbs for u */
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#define U2 (GMP_NUMB_BITS < BITS_PER_ULONG)
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void
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mpf_sqrt_ui (mpf_ptr r, unsigned long int u)
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{
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mp_size_t rsize, zeros;
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mp_ptr tp;
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mp_size_t prec;
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TMP_DECL;
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if (UNLIKELY (u == 0))
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{
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r->_mp_size = 0;
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r->_mp_exp = 0;
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return;
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}
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TMP_MARK;
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prec = r->_mp_prec;
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zeros = 2 * prec - 2;
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rsize = zeros + 1 + U2;
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tp = (mp_ptr) TMP_ALLOC (rsize * BYTES_PER_MP_LIMB);
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MPN_ZERO (tp, zeros);
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tp[zeros] = u & GMP_NUMB_MASK;
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#if U2
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{
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mp_limb_t uhigh = u >> GMP_NUMB_BITS;
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tp[zeros + 1] = uhigh;
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rsize -= (uhigh == 0);
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}
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#endif
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mpn_sqrtrem (r->_mp_d, NULL, tp, rsize);
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r->_mp_size = prec;
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r->_mp_exp = 1;
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TMP_FREE;
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}
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