148 lines
4.8 KiB
C
148 lines
4.8 KiB
C
/* mpn_divexact_by3c -- mpn exact division by 3.
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Copyright 2000, 2001, 2002, 2003, 2006 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or (at your
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option) any later version.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library; see the file COPYING.LIB. If not, write to
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the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
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MA 02110-1301, USA. */
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#include "gmp.h"
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#include "gmp-impl.h"
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#if 1
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/* The algorithm here is basically the same as mpn_divexact_1, as described
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in the manual. Namely at each step q = (src[i]-c)*inverse, and new c =
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borrow(src[i]-c) + high(divisor*q). But because the divisor is just 3,
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high(divisor*q) can be determined with two comparisons instead of a
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multiply.
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The "c += ..."s add the high limb of 3*l to c. That high limb will be 0,
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1 or 2. Doing two separate "+="s seems to give better code on gcc (as of
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2.95.2 at least).
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It will be noted that the new c is formed by adding three values each 0
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or 1. But the total is only 0, 1 or 2. When the subtraction src[i]-c
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causes a borrow, that leaves a limb value of either 0xFF...FF or
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0xFF...FE. The multiply by MODLIMB_INVERSE_3 gives 0x55...55 or
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0xAA...AA respectively, and in those cases high(3*q) is only 0 or 1
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respectively, hence a total of no more than 2.
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Alternatives:
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This implementation has each multiply on the dependent chain, due to
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"l=s-c". See below for alternative code which avoids that. */
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mp_limb_t
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mpn_divexact_by3c (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_limb_t c)
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{
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mp_limb_t l, q, s;
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mp_size_t i;
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ASSERT (un >= 1);
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ASSERT (c == 0 || c == 1 || c == 2);
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ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
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i = 0;
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do
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{
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s = up[i];
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SUBC_LIMB (c, l, s, c);
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q = (l * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
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rp[i] = q;
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c += (q >= GMP_NUMB_CEIL_MAX_DIV3);
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c += (q >= GMP_NUMB_CEIL_2MAX_DIV3);
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}
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while (++i < un);
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ASSERT (c == 0 || c == 1 || c == 2);
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return c;
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}
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#else
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/* The following alternative code re-arranges the quotient calculation from
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(src[i]-c)*inverse to instead
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q = src[i]*inverse - c*inverse
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thereby allowing src[i]*inverse to be scheduled back as far as desired,
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making full use of multiplier throughput and leaving just some carry
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handing on the dependent chain.
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The carry handling consists of determining the c for the next iteration.
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This is the same as described above, namely look for any borrow from
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src[i]-c, and at the high of 3*q.
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high(3*q) is done with two comparisons as above (in c2 and c3). The
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borrow from src[i]-c is incorporated into those by noting that if there's
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a carry then then we have src[i]-c == 0xFF..FF or 0xFF..FE, in turn
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giving q = 0x55..55 or 0xAA..AA. Adding 1 to either of those q values is
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enough to make high(3*q) come out 1 bigger, as required.
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l = -c*inverse is calculated at the same time as c, since for most chips
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it can be more conveniently derived from separate c1/c2/c3 values than
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from a combined c equal to 0, 1 or 2.
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The net effect is that with good pipelining this loop should be able to
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run at perhaps 4 cycles/limb, depending on available execute resources
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etc.
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Usage:
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This code is not used by default, since we really can't rely on the
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compiler generating a good software pipeline, nor on such an approach
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even being worthwhile on all CPUs.
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Itanium is one chip where this algorithm helps though, see
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mpn/ia64/diveby3.asm. */
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mp_limb_t
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mpn_divexact_by3c (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_limb_t cy)
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{
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mp_limb_t s, sm, cl, q, qx, c2, c3;
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mp_size_t i;
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ASSERT (un >= 1);
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ASSERT (cy == 0 || cy == 1 || cy == 2);
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ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
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cl = cy == 0 ? 0 : cy == 1 ? -MODLIMB_INVERSE_3 : -2*MODLIMB_INVERSE_3;
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for (i = 0; i < un; i++)
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{
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s = up[i];
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sm = (s * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
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q = (cl + sm) & GMP_NUMB_MASK;
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rp[i] = q;
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qx = q + (s < cy);
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c2 = qx >= GMP_NUMB_CEIL_MAX_DIV3;
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c3 = qx >= GMP_NUMB_CEIL_2MAX_DIV3 ;
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cy = c2 + c3;
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cl = (-c2 & -MODLIMB_INVERSE_3) + (-c3 & -MODLIMB_INVERSE_3);
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}
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return cy;
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}
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#endif
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