From 11da511c784eca003deb90c23570f0873954e0de Mon Sep 17 00:00:00 2001 From: Duncan Wilkie Date: Sat, 18 Nov 2023 06:11:09 -0600 Subject: Initial commit. --- gmp-6.3.0/mpf/sqrt.c | 112 +++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 112 insertions(+) create mode 100644 gmp-6.3.0/mpf/sqrt.c (limited to 'gmp-6.3.0/mpf/sqrt.c') diff --git a/gmp-6.3.0/mpf/sqrt.c b/gmp-6.3.0/mpf/sqrt.c new file mode 100644 index 0000000..ffb7c10 --- /dev/null +++ b/gmp-6.3.0/mpf/sqrt.c @@ -0,0 +1,112 @@ +/* mpf_sqrt -- Compute the square root of a float. + +Copyright 1993, 1994, 1996, 2000, 2001, 2004, 2005, 2012 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 either: + + * 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. + +or + + * the GNU General Public License as published by the Free Software + Foundation; either version 2 of the License, or (at your option) any + later version. + +or both in parallel, as here. + +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 General Public License +for more details. + +You should have received copies of the GNU General Public License and the +GNU Lesser General Public License along with the GNU MP Library. If not, +see https://www.gnu.org/licenses/. */ + +#include /* for NULL */ +#include "gmp-impl.h" + + +/* As usual, the aim is to produce PREC(r) limbs of result, with the high + limb non-zero. This is accomplished by applying mpn_sqrtrem to either + 2*prec or 2*prec-1 limbs, both such sizes resulting in prec limbs. + + The choice between 2*prec or 2*prec-1 limbs is based on the input + exponent. With b=2^GMP_NUMB_BITS the limb base then we can think of + effectively taking out a factor b^(2k), for suitable k, to get to an + integer input of the desired size ready for mpn_sqrtrem. It must be an + even power taken out, ie. an even number of limbs, so the square root + gives factor b^k and the radix point is still on a limb boundary. So if + EXP(r) is even we'll get an even number of input limbs 2*prec, or if + EXP(r) is odd we get an odd number 2*prec-1. + + Further limbs below the 2*prec or 2*prec-1 used don't affect the result + and are simply truncated. This can be seen by considering an integer x, + with s=floor(sqrt(x)). s is the unique integer satisfying s^2 <= x < + (s+1)^2. Notice that adding a fraction part to x (ie. some further bits) + doesn't change the inequality, s remains the unique solution. Working + suitable factors of 2 into this argument lets it apply to an intended + precision at any position for any x, not just the integer binary point. + + If the input is smaller than 2*prec or 2*prec-1, then we just pad with + zeros, that of course being our usual interpretation of short inputs. + The effect is to extend the root beyond the size of the input (for + instance into fractional limbs if u is an integer). */ + +void +mpf_sqrt (mpf_ptr r, mpf_srcptr u) +{ + mp_size_t usize; + mp_ptr up, tp; + mp_size_t prec, tsize; + mp_exp_t uexp, expodd; + TMP_DECL; + + usize = u->_mp_size; + if (UNLIKELY (usize <= 0)) + { + if (usize < 0) + SQRT_OF_NEGATIVE; + r->_mp_size = 0; + r->_mp_exp = 0; + return; + } + + TMP_MARK; + + uexp = u->_mp_exp; + prec = r->_mp_prec; + up = u->_mp_d; + + expodd = (uexp & 1); + tsize = 2 * prec - expodd; + r->_mp_size = prec; + r->_mp_exp = (uexp + expodd) / 2; /* ceil(uexp/2) */ + + /* root size is ceil(tsize/2), this will be our desired "prec" limbs */ + ASSERT ((tsize + 1) / 2 == prec); + + tp = TMP_ALLOC_LIMBS (tsize); + + if (usize > tsize) + { + up += usize - tsize; + usize = tsize; + MPN_COPY (tp, up, tsize); + } + else + { + MPN_ZERO (tp, tsize - usize); + MPN_COPY (tp + (tsize - usize), up, usize); + } + + mpn_sqrtrem (r->_mp_d, NULL, tp, tsize); + + TMP_FREE; +} -- cgit v1.2.3