Add Chromium-only Blender WebEngine parity work

blender-5.2.0/extern/gmp-source/mpn/generic/mode1o.c

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+/* mpn_modexact_1c_odd -- mpn by limb exact division style remainder.
+
+   THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
+   CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
+   FUTURE GNU MP RELEASES.
+
+Copyright 2000-2004 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 "gmp-impl.h"
+#include "longlong.h"
+
+
+/* Calculate an r satisfying
+
+           r*B^k + a - c == q*d
+
+   where B=2^GMP_LIMB_BITS, a is {src,size}, k is either size or size-1
+   (the caller won't know which), and q is the quotient (discarded).  d must
+   be odd, c can be any limb value.
+
+   If c<d then r will be in the range 0<=r<d, or if c>=d then 0<=r<=d.
+
+   This slightly strange function suits the initial Nx1 reduction for GCDs
+   or Jacobi symbols since the factors of 2 in B^k can be ignored, leaving
+   -r == a mod d (by passing c=0).  For a GCD the factor of -1 on r can be
+   ignored, or for the Jacobi symbol it can be accounted for.  The function
+   also suits divisibility and congruence testing since if r=0 (or r=d) is
+   obtained then a==c mod d.
+
+
+   r is a bit like the remainder returned by mpn_divexact_by3c, and is the
+   sort of remainder mpn_divexact_1 might return.  Like mpn_divexact_by3c, r
+   represents a borrow, since effectively quotient limbs are chosen so that
+   subtracting that multiple of d from src at each step will produce a zero
+   limb.
+
+   A long calculation can be done piece by piece from low to high by passing
+   the return value from one part as the carry parameter to the next part.
+   The effective final k becomes anything between size and size-n, if n
+   pieces are used.
+
+
+   A similar sort of routine could be constructed based on adding multiples
+   of d at each limb, much like redc in mpz_powm does.  Subtracting however
+   has a small advantage that when subtracting to cancel out l there's never
+   a borrow into h, whereas using an addition would put a carry into h
+   depending whether l==0 or l!=0.
+
+
+   In terms of efficiency, this function is similar to a mul-by-inverse
+   mpn_mod_1.  Both are essentially two multiplies and are best suited to
+   CPUs with low latency multipliers (in comparison to a divide instruction
+   at least.)  But modexact has a few less supplementary operations, only
+   needs low part and high part multiplies, and has fewer working quantities
+   (helping CPUs with few registers).
+
+
+   In the main loop it will be noted that the new carry (call it r) is the
+   sum of the high product h and any borrow from l=s-c.  If c<d then we will
+   have r<d too, for the following reasons.  Let q=l*inverse be the quotient
+   limb, so that q*d = B*h + l, where B=2^GMP_NUMB_BITS.  Now if h=d-1 then
+
+       l = q*d - B*(d-1) <= (B-1)*d - B*(d-1) = B-d
+
+   But if l=s-c produces a borrow when c<d, then l>=B-d+1 and hence will
+   never have h=d-1 and so r=h+borrow <= d-1.
+
+   When c>=d, on the other hand, h=d-1 can certainly occur together with a
+   borrow, thereby giving only r<=d, as per the function definition above.
+
+   As a design decision it's left to the caller to check for r=d if it might
+   be passing c>=d.  Several applications have c<d initially so the extra
+   test is often unnecessary, for example the GCDs or a plain divisibility
+   d|a test will pass c=0.
+
+
+   The special case for size==1 is so that it can be assumed c<=d in the
+   high<=divisor test at the end.  c<=d is only guaranteed after at least
+   one iteration of the main loop.  There's also a decent chance one % is
+   faster than a binvert_limb, though that will depend on the processor.
+
+   A CPU specific implementation might want to omit the size==1 code or the
+   high<divisor test.  mpn/x86/k6/mode1o.asm for instance finds neither
+   useful.  */
+
+
+mp_limb_t
+mpn_modexact_1c_odd (mp_srcptr src, mp_size_t size, mp_limb_t d,
+                     mp_limb_t orig_c)
+{
+  mp_limb_t  s, h, l, inverse, dummy, dmul, ret;
+  mp_limb_t  c = orig_c;
+  mp_size_t  i;
+
+  ASSERT (size >= 1);
+  ASSERT (d & 1);
+  ASSERT_MPN (src, size);
+  ASSERT_LIMB (d);
+  ASSERT_LIMB (c);
+
+  if (size == 1)
+    {
+      s = src[0];
+      if (s > c)
+	{
+	  l = s-c;
+	  h = l % d;
+	  if (h != 0)
+	    h = d - h;
+	}
+      else
+	{
+	  l = c-s;
+	  h = l % d;
+	}
+      return h;
+    }
+
+
+  binvert_limb (inverse, d);
+  dmul = d << GMP_NAIL_BITS;
+
+  i = 0;
+  do
+    {
+      s = src[i];
+      SUBC_LIMB (c, l, s, c);
+      l = (l * inverse) & GMP_NUMB_MASK;
+      umul_ppmm (h, dummy, l, dmul);
+      c += h;
+    }
+  while (++i < size-1);
+
+
+  s = src[i];
+  if (s <= d)
+    {
+      /* With high<=d the final step can be a subtract and addback.  If c==0
+	 then the addback will restore to l>=0.  If c==d then will get l==d
+	 if s==0, but that's ok per the function definition.  */
+
+      l = c - s;
+      if (c < s)
+	l += d;
+
+      ret = l;
+    }
+  else
+    {
+      /* Can't skip a divide, just do the loop code once more. */
+
+      SUBC_LIMB (c, l, s, c);
+      l = (l * inverse) & GMP_NUMB_MASK;
+      umul_ppmm (h, dummy, l, dmul);
+      c += h;
+      ret = c;
+    }
+
+  ASSERT (orig_c < d ? ret < d : ret <= d);
+  return ret;
+}
+
+
+
+#if 0
+
+/* The following is an alternate form that might shave one cycle on a
+   superscalar processor since it takes c+=h off the dependent chain,
+   leaving just a low product, high product, and a subtract.
+
+   This is for CPU specific implementations to consider.  A special case for
+   high<divisor and/or size==1 can be added if desired.
+
+   Notice that c is only ever 0 or 1, since if s-c produces a borrow then
+   x=0xFF..FF and x-h cannot produce a borrow.  The c=(x>s) could become
+   c=(x==0xFF..FF) too, if that helped.  */
+
+mp_limb_t
+mpn_modexact_1c_odd (mp_srcptr src, mp_size_t size, mp_limb_t d, mp_limb_t h)
+{
+  mp_limb_t  s, x, y, inverse, dummy, dmul, c1, c2;
+  mp_limb_t  c = 0;
+  mp_size_t  i;
+
+  ASSERT (size >= 1);
+  ASSERT (d & 1);
+
+  binvert_limb (inverse, d);
+  dmul = d << GMP_NAIL_BITS;
+
+  for (i = 0; i < size; i++)
+    {
+      ASSERT (c==0 || c==1);
+
+      s = src[i];
+      SUBC_LIMB (c1, x, s, c);
+
+      SUBC_LIMB (c2, y, x, h);
+      c = c1 + c2;
+
+      y = (y * inverse) & GMP_NUMB_MASK;
+      umul_ppmm (h, dummy, y, dmul);
+    }
+
+  h += c;
+  return h;
+}
+
+#endif