| /* 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 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_ptr ws) |
| { |
| mp_limb_t cy, saved; |
| mp_size_t twok = k + k; |
| mp_size_t kk1 = twok + 1; |
| mp_ptr c1, v1, c3, vinf, c5; |
| mp_limb_t cout; /* final carry, should be zero at the end */ |
| |
| c1 = c + k; |
| v1 = c1 + k; |
| c3 = v1 + k; |
| vinf = c3 + k; |
| c5 = vinf + 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 <= 0) |
| mpn_add_n (v2, v2, vm1, kk1); |
| else |
| 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 - sa*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) |
| { |
| #ifdef HAVE_NATIVE_mpn_rsh1add_n |
| mpn_rsh1add_n (vm1, v1, vm1, kk1); |
| #else |
| mpn_add_n (vm1, v1, vm1, kk1); |
| mpn_rshift (vm1, vm1, kk1, 1); |
| #endif |
| } |
| else |
| { |
| #ifdef HAVE_NATIVE_mpn_rsh1sub_n |
| mpn_rsh1sub_n (vm1, v1, vm1, kk1); |
| #else |
| mpn_sub_n (vm1, v1, vm1, kk1); |
| 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 |
| mpn_sub_n (v2, v2, v1, kk1); |
| 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 |
| */ |
| mpn_sub_n (v1, v1, 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-v0-tm1 hi(vinf) tm1 (v2-vm1-3t1)/6 EMPTY */ |
| |
| /* (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 |
| cy = mpn_lshift (ws, vinf, twor, 1); |
| cy += mpn_sub_n (v2, v2, ws, twor); |
| #endif |
| MPN_DECR_U (v2 + twor, kk1 - twor, cy); |
| |
| /* (7) v1 <- v1 - vinf, (1 0 1 0 0) - (1 0 0 0 0) = (0 0 1 0 0) |
| result is >= 0 */ |
| cy = mpn_sub_n (v1, v1, vinf, twor); /* vinf is at most twor long. */ |
| vinf[0] = saved; |
| MPN_DECR_U (v1 + twor, kk1 - twor, cy); /* Treat the last bytes. */ |
| __GMPN_ADD_1 (cout, vinf, vinf, twor, vinf0); /* Add vinf0, propagate carry. */ |
| |
| /* (8) vm1 <- vm1-t2 (0 1 0 1 0) - (0 1 0 0 0) = (0 0 0 1 0) |
| vm1 >= 0 |
| */ |
| mpn_sub_n (vm1, vm1, v2, kk1); /* No overlapping here. */ |
| |
| /********************* Beginning the final phase **********************/ |
| |
| /* {c,2k} {c+2k,2k } {c+4k ,2r } {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r} |
| v0 t1 hi(t1)+vinf tm1 (v2-vm1-3t1)/6 EMPTY */ |
| |
| /* (9) add t2 in {c+3k, ...} */ |
| cy = mpn_add_n (c3, c3, v2, kk1); |
| __GMPN_ADD_1 (cout, c5 + 1, c5 + 1, twor - k - 1, cy); /* 2n-(5k+1) = 2r-k-1 */ |
| |
| /* {c,2k} {c+2k,2k } {c+4k ,2r } {t,2k+1} {t+2k+1,2k+1} {t+4k+2,2r} |
| v0 t1 hi(t1)+vinf tm1 (v2-vm1-3t1)/6 EMPTY */ |
| /* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2 |
| v0 t1 vinf tm1 t2 |
| +t2 */ |
| |
| /* add vm1 in {c+k, ...} */ |
| cy = mpn_add_n (c1, c1, vm1, kk1); |
| __GMPN_ADD_1 (cout, c3 + 1, c3 + 1, twor + k - 1, cy); /* 2n-(3k+1) = 2r+k-1 */ |
| |
| /* c c+k c+2k c+3k c+4k t t+2k+1 t+4k+2 |
| v0 t1 vinf tm1 t2 |
| +tm1 +t2 */ |
| |
| #undef v0 |
| #undef t2 |
| } |
