| /* mpn_toom4_sqr -- Square {ap,an}. |
| |
| Contributed to the GNU project by Torbjorn Granlund 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 2006, 2007, 2008 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/. */ |
| |
| |
| /* |
| Things to work on: |
| |
| 1. Trim allocation. The allocations for as1, asm1, bs1, and bsm1 could be |
| avoided by instead reusing the pp area and the scratch area. |
| 2. Use new toom functions for the recursive calls. |
| */ |
| |
| #include "gmp.h" |
| #include "gmp-impl.h" |
| |
| /* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf |
| |
| <-s--><--n--><--n--><--n--> |
| ____ ______ ______ ______ |
| |_a3_|___a2_|___a1_|___a0_| |
| |b3_|___b2_|___b1_|___b0_| |
| <-t-><--n--><--n--><--n--> |
| |
| v0 = a0 * b0 # A(0)*B(0) |
| v1 = ( a0+ a1+ a2+ a3)*( b0+ b1+ b2+ b3) # A(1)*B(1) ah <= 3 bh <= 3 |
| vm1 = ( a0- a1+ a2- a3)*( b0- b1+ b2- b3) # A(-1)*B(-1) |ah| <= 1 |bh| <= 1 |
| v2 = ( a0+2a1+4a2+8a3)*( b0+2b1+4b2+8b3) # A(2)*B(2) ah <= 14 bh <= 14 |
| vh = (8a0+4a1+2a2+ a3)*(8b0+4b1+2b2+ b3) # A(1/2)*B(1/2) ah <= 14 bh <= 14 |
| vmh = (8a0-4a1+2a2- a3)*(8b0-4b1+2b2- b3) # A(-1/2)*B(-1/2) -4<=ah<=9 -4<=bh<=9 |
| vinf= a3 * b2 # A(inf)*B(inf) |
| */ |
| |
| #if TUNE_PROGRAM_BUILD |
| #define MAYBE_sqr_basecase 1 |
| #define MAYBE_sqr_toom2 1 |
| #define MAYBE_sqr_toom4 1 |
| #else |
| #define MAYBE_sqr_basecase \ |
| (SQR_TOOM4_THRESHOLD < 4 * SQR_KARATSUBA_THRESHOLD) |
| #define MAYBE_sqr_toom2 \ |
| (SQR_TOOM4_THRESHOLD < 4 * SQR_TOOM3_THRESHOLD) |
| #define MAYBE_sqr_toom4 \ |
| (SQR_FFT_THRESHOLD >= 4 * SQR_TOOM4_THRESHOLD) |
| #endif |
| |
| #define TOOM4_SQR_N_REC(p, a, n, ws) \ |
| do { \ |
| if (MAYBE_sqr_basecase \ |
| && BELOW_THRESHOLD (n, SQR_KARATSUBA_THRESHOLD)) \ |
| mpn_sqr_basecase (p, a, n); \ |
| else if (MAYBE_sqr_toom2 \ |
| && BELOW_THRESHOLD (n, SQR_TOOM3_THRESHOLD)) \ |
| mpn_kara_sqr_n (p, a, n, ws); \ |
| else if (! MAYBE_sqr_toom4 \ |
| || BELOW_THRESHOLD (n, SQR_TOOM4_THRESHOLD)) \ |
| mpn_toom3_sqr_n (p, a, n, ws); \ |
| else \ |
| mpn_toom4_sqr (p, a, n, ws); \ |
| } while (0) |
| |
| void |
| mpn_toom4_sqr (mp_ptr pp, |
| mp_srcptr ap, mp_size_t an, |
| mp_ptr scratch) |
| { |
| mp_size_t n, s; |
| mp_limb_t cy; |
| mp_ptr gp, hp; |
| mp_ptr as1, asm1, as2, ash, asmh; |
| TMP_DECL; |
| |
| #define a0 ap |
| #define a1 (ap + n) |
| #define a2 (ap + 2*n) |
| #define a3 (ap + 3*n) |
| |
| n = (an + 3) >> 2; |
| |
| s = an - 3 * n; |
| |
| ASSERT (0 < s && s <= n); |
| |
| TMP_MARK; |
| |
| as1 = TMP_SALLOC_LIMBS (n + 1); |
| asm1 = TMP_SALLOC_LIMBS (n + 1); |
| as2 = TMP_SALLOC_LIMBS (n + 1); |
| ash = TMP_SALLOC_LIMBS (n + 1); |
| asmh = TMP_SALLOC_LIMBS (n + 1); |
| |
| gp = pp; |
| hp = pp + n + 1; |
| |
| /* Compute as1 and asm1. */ |
| gp[n] = mpn_add_n (gp, a0, a2, n); |
| hp[n] = mpn_add (hp, a1, n, a3, s); |
| #if HAVE_NATIVE_mpn_addsub_n |
| if (mpn_cmp (gp, hp, n + 1) < 0) |
| { |
| mpn_addsub_n (as1, asm1, hp, gp, n + 1); |
| } |
| else |
| { |
| mpn_addsub_n (as1, asm1, gp, hp, n + 1); |
| } |
| #else |
| mpn_add_n (as1, gp, hp, n + 1); |
| if (mpn_cmp (gp, hp, n + 1) < 0) |
| { |
| mpn_sub_n (asm1, hp, gp, n + 1); |
| } |
| else |
| { |
| mpn_sub_n (asm1, gp, hp, n + 1); |
| } |
| #endif |
| |
| /* Compute as2. */ |
| #if HAVE_NATIVE_mpn_addlsh1_n |
| cy = mpn_addlsh1_n (as2, a2, a3, s); |
| if (s != n) |
| cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy); |
| cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n); |
| cy = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n); |
| #else |
| cy = mpn_lshift (as2, a3, s, 1); |
| cy += mpn_add_n (as2, a2, as2, s); |
| if (s != n) |
| cy = mpn_add_1 (as2 + s, a2 + s, n - s, cy); |
| cy = 2 * cy + mpn_lshift (as2, as2, n, 1); |
| cy += mpn_add_n (as2, a1, as2, n); |
| cy = 2 * cy + mpn_lshift (as2, as2, n, 1); |
| cy += mpn_add_n (as2, a0, as2, n); |
| #endif |
| as2[n] = cy; |
| |
| /* Compute ash and asmh. */ |
| cy = mpn_lshift (gp, a0, n, 3); /* 8a0 */ |
| #if HAVE_NATIVE_mpn_addlsh1_n |
| gp[n] = cy + mpn_addlsh1_n (gp, gp, a2, n); /* 8a0 + 2a2 */ |
| #else |
| cy += mpn_lshift (hp, a2, n, 1); /* 2a2 */ |
| gp[n] = cy + mpn_add_n (gp, gp, hp, n); /* 8a0 + 2a2 */ |
| #endif |
| cy = mpn_lshift (hp, a1, n, 2); /* 4a1 */ |
| hp[n] = cy + mpn_add (hp, hp, n, a3, s); /* 4a1 + a3 */ |
| #if HAVE_NATIVE_mpn_addsub_n |
| if (mpn_cmp (gp, hp, n + 1) < 0) |
| { |
| mpn_addsub_n (ash, asmh, hp, gp, n + 1); |
| } |
| else |
| { |
| mpn_addsub_n (ash, asmh, gp, hp, n + 1); |
| } |
| #else |
| mpn_add_n (ash, gp, hp, n + 1); |
| if (mpn_cmp (gp, hp, n + 1) < 0) |
| { |
| mpn_sub_n (asmh, hp, gp, n + 1); |
| } |
| else |
| { |
| mpn_sub_n (asmh, gp, hp, n + 1); |
| } |
| #endif |
| |
| ASSERT (as1[n] <= 3); |
| ASSERT (asm1[n] <= 1); |
| ASSERT (as2[n] <= 14); |
| ASSERT (ash[n] <= 14); |
| ASSERT (asmh[n] <= 9); |
| |
| #define v0 pp /* 2n */ |
| #define v1 (scratch + 6 * n + 6) /* 2n+1 */ |
| #define vm1 scratch /* 2n+1 */ |
| #define v2 (scratch + 2 * n + 2) /* 2n+1 */ |
| #define vinf (pp + 6 * n) /* s+t */ |
| #define vh (pp + 2 * n) /* 2n+1 */ |
| #define vmh (scratch + 4 * n + 4) |
| #define scratch_out (scratch + 8 * n + 8) |
| |
| /* vm1, 2n+1 limbs */ |
| TOOM4_SQR_N_REC (vm1, asm1, n + 1, scratch_out); /* vm1, 2n+1 limbs */ |
| |
| TOOM4_SQR_N_REC (v2 , as2 , n + 1, scratch_out); /* v2, 2n+1 limbs */ |
| |
| TOOM4_SQR_N_REC (vinf, a3 , s, scratch_out); /* vinf, 2s limbs */ |
| |
| TOOM4_SQR_N_REC (v1 , as1 , n + 1, scratch_out); /* v1, 2n+1 limbs */ |
| |
| TOOM4_SQR_N_REC (vh , ash , n + 1, scratch_out); |
| |
| TOOM4_SQR_N_REC (vmh, asmh, n + 1, scratch_out); |
| |
| TOOM4_SQR_N_REC (v0 , ap , n , scratch_out); /* v0, 2n limbs */ |
| |
| mpn_toom_interpolate_7pts (pp, n, 0, vmh, vm1, v1, v2, s + s, scratch_out); |
| |
| TMP_FREE; |
| } |
