summaryrefslogtreecommitdiff
path: root/Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c
diff options
context:
space:
mode:
Diffstat (limited to 'Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c')
-rw-r--r--Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c113
1 files changed, 113 insertions, 0 deletions
diff --git a/Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c b/Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c
new file mode 100644
index 00000000000..44502244e24
--- /dev/null
+++ b/Build/source/libs/gmp/gmp-6.0.0/mpf/sqrt.c
@@ -0,0 +1,113 @@
+/* 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 <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. 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;
+}