Add Chromium-only Blender WebEngine parity work

blender-5.2.0/extern/gmp-source/mpf/sqrt.c

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+/* 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-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;
+}