| /* mpn_toom32_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 1.5 |
| times as large as bn. Or more accurately, bn < an < 3bn. |
| |
| Contributed to the GNU project by Torbjorn Granlund. |
| |
| The idea of applying toom to unbalanced multiplication is due to by Marco |
| Bodrato and Alberto Zanoni. |
| |
| 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 allocation. |
| |
| 2. Apply optimizations also to mul_toom42.c. |
| */ |
| |
| #include "gmp.h" |
| #include "gmp-impl.h" |
| |
| /* Evaluate in: -1, 0, +1, +inf |
| |
| <-s-><--n--><--n--> |
| ___ ______ ______ |
| |a2_|___a1_|___a0_| |
| |_b1_|___b0_| |
| <-t--><--n--> |
| |
| v0 = a0 * b0 # A(0)*B(0) |
| v1 = (a0+ a1+ a2)*(b0+ b1) # A(1)*B(1) ah <= 2 bh <= 1 |
| vm1 = (a0- a1+ a2)*(b0- b1) # A(-1)*B(-1) |ah| <= 1 bh = 0 |
| vinf= a2 * b1 # A(inf)*B(inf) |
| */ |
| |
| #if TUNE_PROGRAM_BUILD |
| #define MAYBE_mul_toom22 1 |
| #else |
| #define MAYBE_mul_toom22 \ |
| (MUL_TOOM33_THRESHOLD >= 2 * MUL_TOOM22_THRESHOLD) |
| #endif |
| |
| #define TOOM22_MUL_N_REC(p, a, b, n, ws) \ |
| do { \ |
| if (! MAYBE_mul_toom22 \ |
| || BELOW_THRESHOLD (n, MUL_KARATSUBA_THRESHOLD)) \ |
| mpn_mul_basecase (p, a, n, b, n); \ |
| else \ |
| mpn_toom22_mul (p, a, n, b, n, ws); \ |
| } while (0) |
| |
| void |
| mpn_toom32_mul (mp_ptr pp, |
| mp_srcptr ap, mp_size_t an, |
| mp_srcptr bp, mp_size_t bn, |
| mp_ptr scratch) |
| { |
| mp_size_t n, s, t; |
| int vm1_neg; |
| #if HAVE_NATIVE_mpn_add_nc |
| mp_limb_t cy; |
| #else |
| mp_limb_t cy, cy2; |
| #endif |
| mp_ptr a0_a2; |
| mp_ptr as1, asm1; |
| mp_ptr bs1, bsm1; |
| TMP_DECL; |
| |
| #define a0 ap |
| #define a1 (ap + n) |
| #define a2 (ap + 2 * n) |
| #define b0 bp |
| #define b1 (bp + n) |
| |
| n = 1 + (2 * an >= 3 * bn ? (an - 1) / (size_t) 3 : (bn - 1) >> 1); |
| |
| s = an - 2 * n; |
| t = bn - n; |
| |
| ASSERT (0 < s && s <= n); |
| ASSERT (0 < t && t <= n); |
| |
| TMP_MARK; |
| |
| as1 = TMP_SALLOC_LIMBS (n + 1); |
| asm1 = TMP_SALLOC_LIMBS (n + 1); |
| |
| bs1 = TMP_SALLOC_LIMBS (n + 1); |
| bsm1 = TMP_SALLOC_LIMBS (n); |
| |
| a0_a2 = pp; |
| |
| /* Compute as1 and asm1. */ |
| a0_a2[n] = mpn_add (a0_a2, a0, n, a2, s); |
| #if HAVE_NATIVE_mpn_addsub_n |
| if (a0_a2[n] == 0 && mpn_cmp (a0_a2, a1, n) < 0) |
| { |
| cy = mpn_addsub_n (as1, asm1, a1, a0_a2, n); |
| as1[n] = cy >> 1; |
| asm1[n] = 0; |
| vm1_neg = 1; |
| } |
| else |
| { |
| cy = mpn_addsub_n (as1, asm1, a0_a2, a1, n); |
| as1[n] = a0_a2[n] + (cy >> 1); |
| asm1[n] = a0_a2[n] - (cy & 1); |
| vm1_neg = 0; |
| } |
| #else |
| as1[n] = a0_a2[n] + mpn_add_n (as1, a0_a2, a1, n); |
| if (a0_a2[n] == 0 && mpn_cmp (a0_a2, a1, n) < 0) |
| { |
| mpn_sub_n (asm1, a1, a0_a2, n); |
| asm1[n] = 0; |
| vm1_neg = 1; |
| } |
| else |
| { |
| cy = mpn_sub_n (asm1, a0_a2, a1, n); |
| asm1[n] = a0_a2[n] - cy; |
| vm1_neg = 0; |
| } |
| #endif |
| |
| /* Compute bs1 and bsm1. */ |
| if (t == n) |
| { |
| #if HAVE_NATIVE_mpn_addsub_n |
| if (mpn_cmp (b0, b1, n) < 0) |
| { |
| cy = mpn_addsub_n (bs1, bsm1, b1, b0, n); |
| vm1_neg ^= 1; |
| } |
| else |
| { |
| cy = mpn_addsub_n (bs1, bsm1, b0, b1, n); |
| } |
| bs1[n] = cy >> 1; |
| #else |
| bs1[n] = mpn_add_n (bs1, b0, b1, n); |
| |
| if (mpn_cmp (b0, b1, n) < 0) |
| { |
| mpn_sub_n (bsm1, b1, b0, n); |
| vm1_neg ^= 1; |
| } |
| else |
| { |
| mpn_sub_n (bsm1, b0, b1, n); |
| } |
| #endif |
| } |
| else |
| { |
| bs1[n] = mpn_add (bs1, b0, n, b1, t); |
| |
| if (mpn_zero_p (b0 + t, n - t) && mpn_cmp (b0, b1, t) < 0) |
| { |
| mpn_sub_n (bsm1, b1, b0, t); |
| MPN_ZERO (bsm1 + t, n - t); |
| vm1_neg ^= 1; |
| } |
| else |
| { |
| mpn_sub (bsm1, b0, n, b1, t); |
| } |
| } |
| |
| ASSERT (as1[n] <= 2); |
| ASSERT (bs1[n] <= 1); |
| ASSERT (asm1[n] <= 1); |
| /*ASSERT (bsm1[n] == 0); */ |
| |
| #define v0 pp /* 2n */ |
| #define v1 (scratch) /* 2n+1 */ |
| #define vinf (pp + 3 * n) /* s+t */ |
| #define vm1 (scratch + 2 * n + 1) /* 2n+1 */ |
| #define scratch_out scratch + 4 * n + 2 |
| |
| /* vm1, 2n+1 limbs */ |
| TOOM22_MUL_N_REC (vm1, asm1, bsm1, n, scratch_out); |
| cy = 0; |
| if (asm1[n] != 0) |
| cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n); |
| vm1[2 * n] = cy; |
| |
| /* vinf, s+t limbs */ |
| if (s > t) mpn_mul (vinf, a2, s, b1, t); |
| else mpn_mul (vinf, b1, t, a2, s); |
| |
| /* v1, 2n+1 limbs */ |
| TOOM22_MUL_N_REC (v1, as1, bs1, n, scratch_out); |
| if (as1[n] == 1) |
| { |
| cy = bs1[n] + mpn_add_n (v1 + n, v1 + n, bs1, n); |
| } |
| else if (as1[n] == 2) |
| { |
| #if HAVE_NATIVE_mpn_addlsh1_n |
| cy = 2 * bs1[n] + mpn_addlsh1_n (v1 + n, v1 + n, bs1, n); |
| #else |
| cy = 2 * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, CNST_LIMB(2)); |
| #endif |
| } |
| else |
| cy = 0; |
| if (bs1[n] != 0) |
| cy += mpn_add_n (v1 + n, v1 + n, as1, n); |
| v1[2 * n] = cy; |
| |
| mpn_mul_n (v0, ap, bp, n); /* v0, 2n limbs */ |
| |
| /* Interpolate */ |
| |
| if (vm1_neg) |
| { |
| #if HAVE_NATIVE_mpn_rsh1add_n |
| mpn_rsh1add_n (vm1, v1, vm1, 2 * n + 1); |
| #else |
| mpn_add_n (vm1, v1, vm1, 2 * n + 1); |
| mpn_rshift (vm1, vm1, 2 * n + 1, 1); |
| #endif |
| } |
| else |
| { |
| #if HAVE_NATIVE_mpn_rsh1sub_n |
| mpn_rsh1sub_n (vm1, v1, vm1, 2 * n + 1); |
| #else |
| mpn_sub_n (vm1, v1, vm1, 2 * n + 1); |
| mpn_rshift (vm1, vm1, 2 * n + 1, 1); |
| #endif |
| } |
| |
| mpn_sub_n (v1, v1, vm1, 2 * n + 1); |
| v1[2 * n] -= mpn_sub_n (v1, v1, v0, 2 * n); |
| |
| /* |
| pp[] prior to operations: |
| |_H vinf|_L vinf|_______|_______|_______| |
| |
| summation scheme for remaining operations: |
| |_______|_______|_______|_______|_______| |
| |_Hvinf_|_Lvinf_| |_H v0__|_L v0__| |
| | H vm1 | L vm1 | |
| |-H vinf|-L vinf| |
| | H v1 | L v1 | |
| */ |
| |
| mpn_sub (vm1, vm1, 2 * n + 1, vinf, s + t); |
| #if HAVE_NATIVE_mpn_add_nc |
| cy = mpn_add_n (pp + n, pp + n, vm1, n); |
| cy = mpn_add_nc (pp + 2 * n, v1, vm1 + n, n, cy); |
| cy = mpn_add_nc (pp + 3 * n, pp + 3 * n, v1 + n, n, cy); |
| mpn_incr_u (pp + 3 * n, vm1[2 * n]); |
| if (LIKELY (n != s + t)) /* FIXME: Limit operand range to avoid condition */ |
| mpn_incr_u (pp + 4 * n, cy + v1[2 * n]); |
| #else |
| cy2 = mpn_add_n (pp + n, pp + n, vm1, n); |
| cy = mpn_add_n (pp + 2 * n, v1, vm1 + n, n); |
| mpn_incr_u (pp + 2 * n, cy2); |
| mpn_incr_u (pp + 3 * n, cy + vm1[2 * n]); |
| cy = mpn_add_n (pp + 3 * n, pp + 3 * n, v1 + n, n); |
| if (LIKELY (n != s + t)) /* FIXME: Limit operand range to avoid condition */ |
| mpn_incr_u (pp + 4 * n, cy + v1[2 * n]); |
| #endif |
| |
| TMP_FREE; |
| } |