sqrt_ui.c
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上传日期:2022-08-06
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- /* mpf_sqrt_ui -- Compute the square root of an unsigned integer.
- Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005 Free Software Foundation,
- Inc.
- This file is part of the GNU MP Library.
- The GNU MP 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 MP 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 MP Library. If not, see http://www.gnu.org/licenses/. */
- #include <stdio.h> /* for NULL */
- #include "gmp.h"
- #include "gmp-impl.h"
- /* As usual the aim is to produce PREC(r) limbs of result with the high limb
- non-zero. That high limb will end up floor(sqrt(u)), and limbs below are
- produced by padding the input with zeros, two for each desired result
- limb, being 2*(prec-1) for a total 2*prec-1 limbs passed to mpn_sqrtrem.
- The way mpn_sqrtrem calculates floor(sqrt(x)) ensures the root is correct
- to the intended accuracy, ie. truncated to prec limbs.
- With nails, u might be two limbs, in which case a total 2*prec limbs is
- passed to mpn_sqrtrem (still giving a prec limb result). If uhigh is
- zero we adjust back to 2*prec-1, since mpn_sqrtrem requires the high
- non-zero. 2*prec limbs are always allocated, even when uhigh is zero, so
- the store of uhigh can be done without a conditional.
- u==0 is a special case so the rest of the code can assume the result is
- non-zero (ie. will have a non-zero high limb on the result).
- Not done:
- No attempt is made to identify perfect squares. It's considered this can
- be left to an application if it might occur with any frequency. As it
- stands, mpn_sqrtrem does its normal amount of work on a perfect square
- followed by zero limbs, though of course only an mpn_sqrtrem1 would be
- actually needed. We also end up leaving our mpf result with lots of low
- trailing zeros, slowing down subsequent operations.
- We're not aware of any optimizations that can be made using the fact the
- input has lots of trailing zeros (apart from the perfect square
- case). */
- /* 1 if we (might) need two limbs for u */
- #define U2 (GMP_NUMB_BITS < BITS_PER_ULONG)
- void
- mpf_sqrt_ui (mpf_ptr r, unsigned long int u)
- {
- mp_size_t rsize, zeros;
- mp_ptr tp;
- mp_size_t prec;
- TMP_DECL;
- if (UNLIKELY (u == 0))
- {
- r->_mp_size = 0;
- r->_mp_exp = 0;
- return;
- }
- TMP_MARK;
- prec = r->_mp_prec;
- zeros = 2 * prec - 2;
- rsize = zeros + 1 + U2;
- tp = TMP_ALLOC_LIMBS (rsize);
- MPN_ZERO (tp, zeros);
- tp[zeros] = u & GMP_NUMB_MASK;
- #if U2
- {
- mp_limb_t uhigh = u >> GMP_NUMB_BITS;
- tp[zeros + 1] = uhigh;
- rsize -= (uhigh == 0);
- }
- #endif
- mpn_sqrtrem (r->_mp_d, NULL, tp, rsize);
- r->_mp_size = prec;
- r->_mp_exp = 1;
- TMP_FREE;
- }