toom_interpolate_5pts.c
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- /* mpn_toom_interpolate_5pts -- Interpolate for toom3, 33, 42.
- Contributed to the GNU project by Robert Harley.
- Improvements by Paul Zimmermann and Marco Bodrato.
- THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE. IT IS ONLY
- SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
- GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
- Copyright 2000, 2001, 2002, 2003, 2005, 2006, 2007, 2009 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 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.
- 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 Lesser General Public License
- for more details.
- You should have received a copy of the GNU Lesser General Public License
- along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
- #include "gmp.h"
- #include "gmp-impl.h"
- void
- mpn_toom_interpolate_5pts (mp_ptr c, mp_ptr v2, mp_ptr vm1,
- mp_size_t k, mp_size_t twor, int sa,
- mp_limb_t vinf0)
- {
- mp_limb_t cy, saved;
- mp_size_t twok;
- mp_size_t kk1;
- mp_ptr c1, v1, c3, vinf;
- twok = k + k;
- kk1 = twok + 1;
- c1 = c + k;
- v1 = c1 + k;
- c3 = v1 + k;
- vinf = c3 + k;
- #define v0 (c)
- /* (1) v2 <- v2-vm1 < v2+|vm1|, (16 8 4 2 1) - (1 -1 1 -1 1) =
- thus 0 <= v2 < 50*B^(2k) < 2^6*B^(2k) (15 9 3 3 0)
- */
- if (sa)
- ASSERT_NOCARRY (mpn_add_n (v2, v2, vm1, kk1));
- else
- ASSERT_NOCARRY (mpn_sub_n (v2, v2, vm1, kk1));
- /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
- v0 v1 hi(vinf) |vm1| v2-vm1 EMPTY */
- ASSERT_NOCARRY (mpn_divexact_by3 (v2, v2, kk1)); /* v2 <- v2 / 3 */
- /* (5 3 1 1 0)*/
- /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
- v0 v1 hi(vinf) |vm1| (v2-vm1)/3 EMPTY */
- /* (2) vm1 <- tm1 := (v1 - vm1) / 2 [(1 1 1 1 1) - (1 -1 1 -1 1)] / 2 =
- tm1 >= 0 (0 1 0 1 0)
- No carry comes out from {v1, kk1} +/- {vm1, kk1},
- and the division by two is exact.
- If (sa!=0) the sign of vm1 is negative */
- if (sa)
- {
- #ifdef HAVE_NATIVE_mpn_rsh1add_n
- mpn_rsh1add_n (vm1, v1, vm1, kk1);
- #else
- ASSERT_NOCARRY (mpn_add_n (vm1, v1, vm1, kk1));
- ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
- #endif
- }
- else
- {
- #ifdef HAVE_NATIVE_mpn_rsh1sub_n
- mpn_rsh1sub_n (vm1, v1, vm1, kk1);
- #else
- ASSERT_NOCARRY (mpn_sub_n (vm1, v1, vm1, kk1));
- ASSERT_NOCARRY (mpn_rshift (vm1, vm1, kk1, 1));
- #endif
- }
- /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
- v0 v1 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
- /* (3) v1 <- t1 := v1 - v0 (1 1 1 1 1) - (0 0 0 0 1) = (1 1 1 1 0)
- t1 >= 0
- */
- vinf[0] -= mpn_sub_n (v1, v1, c, twok);
- /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
- v0 v1-v0 hi(vinf) tm1 (v2-vm1)/3 EMPTY */
- /* (4) v2 <- t2 := ((v2-vm1)/3-t1)/2 = (v2-vm1-3*t1)/6
- t2 >= 0 [(5 3 1 1 0) - (1 1 1 1 0)]/2 = (2 1 0 0 0)
- */
- #ifdef HAVE_NATIVE_mpn_rsh1sub_n
- mpn_rsh1sub_n (v2, v2, v1, kk1);
- #else
- ASSERT_NOCARRY (mpn_sub_n (v2, v2, v1, kk1));
- ASSERT_NOCARRY (mpn_rshift (v2, v2, kk1, 1));
- #endif
- /* {c,2k} {c+2k,2k+1} {c+4k+1,2r-1} {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r}
- v0 v1-v0 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */
- /* (5) v1 <- t1-tm1 (1 1 1 1 0) - (0 1 0 1 0) = (1 0 1 0 0)
- result is v1 >= 0
- */
- ASSERT_NOCARRY (mpn_sub_n (v1, v1, vm1, kk1));
- /* We do not need to read the value in vm1, so we add it in {c+k, ...} */
- cy = mpn_add_n (c1, c1, vm1, kk1);
- MPN_INCR_U (c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */
- /* Memory allocated for vm1 is now free, it can be recycled ...*/
- /* (6) v2 <- v2 - 2*vinf, (2 1 0 0 0) - 2*(1 0 0 0 0) = (0 1 0 0 0)
- result is v2 >= 0 */
- saved = vinf[0]; /* Remember v1's highest byte (will be overwritten). */
- vinf[0] = vinf0; /* Set the right value for vinf0 */
- #ifdef HAVE_NATIVE_mpn_sublsh1_n
- cy = mpn_sublsh1_n (v2, v2, vinf, twor);
- #else
- /* Overwrite unused vm1 */
- cy = mpn_lshift (vm1, vinf, twor, 1);
- cy += mpn_sub_n (v2, v2, vm1, twor);
- #endif
- MPN_DECR_U (v2 + twor, kk1 - twor, cy);
- /* Current matrix is
- [1 0 0 0 0; vinf
- 0 1 0 0 0; v2
- 1 0 1 0 0; v1
- 0 1 0 1 0; vm1
- 0 0 0 0 1] v0
- Some vaues already are in-place (we added vm1 in the correct position)
- | vinf| v1 | v0 |
- | vm1 |
- One still is in a separated area
- | +v2 |
- We have to compute v1-=vinf; vm1 -= v2,
- |-vinf|
- | -v2 |
- Carefully reordering operations we can avoid to compute twice the sum
- of the high half of v2 plus the low half of vinf.
- */
- /* Add the high half of t2 in {vinf} */
- if ( LIKELY(twor > k + 1) ) { /* This is the expected flow */
- cy = mpn_add_n (vinf, vinf, v2 + k, k + 1);
- MPN_INCR_U (c3 + kk1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */
- } else { /* triggered only by very unbalanced cases like
- (k+k+(k-2))x(k+k+1) , should be handled by toom32 */
- ASSERT_NOCARRY (mpn_add_n (vinf, vinf, v2 + k, twor));
- }
- /* (7) v1 <- v1 - vinf, (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0)
- result is >= 0 */
- /* Side effect: we also subtracted (high half) vm1 -= v2 */
- cy = mpn_sub_n (v1, v1, vinf, twor); /* vinf is at most twor long. */
- vinf0 = vinf[0]; /* Save again the right value for vinf0 */
- vinf[0] = saved;
- MPN_DECR_U (v1 + twor, kk1 - twor, cy); /* Treat the last bytes. */
- /* (8) vm1 <- vm1-v2 (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0)
- Operate only on the low half.
- */
- cy = mpn_sub_n (c1, c1, v2, k);
- MPN_DECR_U (v1, kk1, cy);
- /********************* Beginning the final phase **********************/
- /* Most of the recomposition was done */
- /* add t2 in {c+3k, ...}, but only the low half */
- cy = mpn_add_n (c3, c3, v2, k);
- vinf[0] += cy;
- ASSERT(vinf[0] >= cy); /* No carry */
- MPN_INCR_U (vinf, twor, vinf0); /* Add vinf0, propagate carry. */
- #undef v0
- }