| /* mpn_toom62_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 3 times |
| as large as bn. Or more accurately, (5/2)bn < an < 6bn. |
| |
| Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato. |
| |
| The idea of applying toom to unbalanced multiplication is due to 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 2006-2008, 2012 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 either: |
| |
| * 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. |
| |
| or |
| |
| * the GNU General Public License as published by the Free Software |
| Foundation; either version 2 of the License, or (at your option) any |
| later version. |
| |
| or both in parallel, as here. |
| |
| 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 General Public License |
| for more details. |
| |
| You should have received copies of the GNU General Public License and the |
| GNU Lesser General Public License along with the GNU MP Library. If not, |
| see https://www.gnu.org/licenses/. */ |
| |
| |
| #include "gmp-impl.h" |
| |
| /* Evaluate in: |
| 0, +1, -1, +2, -2, 1/2, +inf |
| |
| <-s-><--n--><--n--><--n--><--n--><--n--> |
| ___ ______ ______ ______ ______ ______ |
| |a5_|___a4_|___a3_|___a2_|___a1_|___a0_| |
| |_b1_|___b0_| |
| <-t--><--n--> |
| |
| v0 = a0 * b0 # A(0)*B(0) |
| v1 = ( a0+ a1+ a2+ a3+ a4+ a5)*( b0+ b1) # A(1)*B(1) ah <= 5 bh <= 1 |
| vm1 = ( a0- a1+ a2- a3+ a4- a5)*( b0- b1) # A(-1)*B(-1) |ah| <= 2 bh = 0 |
| v2 = ( a0+ 2a1+4a2+8a3+16a4+32a5)*( b0+2b1) # A(2)*B(2) ah <= 62 bh <= 2 |
| vm2 = ( a0- 2a1+4a2-8a3+16a4-32a5)*( b0-2b1) # A(-2)*B(-2) -41<=ah<=20 -1<=bh<=0 |
| vh = (32a0+16a1+8a2+4a3+ 2a4+ a5)*(2b0+ b1) # A(1/2)*B(1/2) ah <= 62 bh <= 2 |
| vinf= a5 * b1 # A(inf)*B(inf) |
| */ |
| |
| void |
| mpn_toom62_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; |
| mp_limb_t cy; |
| mp_ptr as1, asm1, as2, asm2, ash; |
| mp_ptr bs1, bsm1, bs2, bsm2, bsh; |
| mp_ptr gp; |
| enum toom7_flags aflags, bflags; |
| TMP_DECL; |
| |
| #define a0 ap |
| #define a1 (ap + n) |
| #define a2 (ap + 2*n) |
| #define a3 (ap + 3*n) |
| #define a4 (ap + 4*n) |
| #define a5 (ap + 5*n) |
| #define b0 bp |
| #define b1 (bp + n) |
| |
| n = 1 + (an >= 3 * bn ? (an - 1) / (size_t) 6 : (bn - 1) >> 1); |
| |
| s = an - 5 * 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); |
| as2 = TMP_SALLOC_LIMBS (n + 1); |
| asm2 = TMP_SALLOC_LIMBS (n + 1); |
| ash = TMP_SALLOC_LIMBS (n + 1); |
| |
| bs1 = TMP_SALLOC_LIMBS (n + 1); |
| bsm1 = TMP_SALLOC_LIMBS (n); |
| bs2 = TMP_SALLOC_LIMBS (n + 1); |
| bsm2 = TMP_SALLOC_LIMBS (n + 1); |
| bsh = TMP_SALLOC_LIMBS (n + 1); |
| |
| gp = pp; |
| |
| /* Compute as1 and asm1. */ |
| aflags = (enum toom7_flags) (toom7_w3_neg & mpn_toom_eval_pm1 (as1, asm1, 5, ap, n, s, gp)); |
| |
| /* Compute as2 and asm2. */ |
| aflags = (enum toom7_flags) (aflags | (toom7_w1_neg & mpn_toom_eval_pm2 (as2, asm2, 5, ap, n, s, gp))); |
| |
| /* Compute ash = 32 a0 + 16 a1 + 8 a2 + 4 a3 + 2 a4 + a5 |
| = 2*(2*(2*(2*(2*a0 + a1) + a2) + a3) + a4) + a5 */ |
| |
| #if HAVE_NATIVE_mpn_addlsh1_n |
| cy = mpn_addlsh1_n (ash, a1, a0, n); |
| cy = 2*cy + mpn_addlsh1_n (ash, a2, ash, n); |
| cy = 2*cy + mpn_addlsh1_n (ash, a3, ash, n); |
| cy = 2*cy + mpn_addlsh1_n (ash, a4, ash, n); |
| if (s < n) |
| { |
| mp_limb_t cy2; |
| cy2 = mpn_addlsh1_n (ash, a5, ash, s); |
| ash[n] = 2*cy + mpn_lshift (ash + s, ash + s, n - s, 1); |
| MPN_INCR_U (ash + s, n+1-s, cy2); |
| } |
| else |
| ash[n] = 2*cy + mpn_addlsh1_n (ash, a5, ash, n); |
| #else |
| cy = mpn_lshift (ash, a0, n, 1); |
| cy += mpn_add_n (ash, ash, a1, n); |
| cy = 2*cy + mpn_lshift (ash, ash, n, 1); |
| cy += mpn_add_n (ash, ash, a2, n); |
| cy = 2*cy + mpn_lshift (ash, ash, n, 1); |
| cy += mpn_add_n (ash, ash, a3, n); |
| cy = 2*cy + mpn_lshift (ash, ash, n, 1); |
| cy += mpn_add_n (ash, ash, a4, n); |
| cy = 2*cy + mpn_lshift (ash, ash, n, 1); |
| ash[n] = cy + mpn_add (ash, ash, n, a5, s); |
| #endif |
| |
| /* Compute bs1 and bsm1. */ |
| if (t == n) |
| { |
| #if HAVE_NATIVE_mpn_add_n_sub_n |
| if (mpn_cmp (b0, b1, n) < 0) |
| { |
| cy = mpn_add_n_sub_n (bs1, bsm1, b1, b0, n); |
| bflags = toom7_w3_neg; |
| } |
| else |
| { |
| cy = mpn_add_n_sub_n (bs1, bsm1, b0, b1, n); |
| bflags = (enum toom7_flags) 0; |
| } |
| 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); |
| bflags = toom7_w3_neg; |
| } |
| else |
| { |
| mpn_sub_n (bsm1, b0, b1, n); |
| bflags = (enum toom7_flags) 0; |
| } |
| #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); |
| bflags = toom7_w3_neg; |
| } |
| else |
| { |
| mpn_sub (bsm1, b0, n, b1, t); |
| bflags = (enum toom7_flags) 0; |
| } |
| } |
| |
| /* Compute bs2 and bsm2. Recycling bs1 and bsm1; bs2=bs1+b1, bsm2 = |
| bsm1 - b1 */ |
| mpn_add (bs2, bs1, n + 1, b1, t); |
| if (bflags & toom7_w3_neg) |
| { |
| bsm2[n] = mpn_add (bsm2, bsm1, n, b1, t); |
| bflags = (enum toom7_flags) (bflags | toom7_w1_neg); |
| } |
| else |
| { |
| /* FIXME: Simplify this logic? */ |
| if (t < n) |
| { |
| if (mpn_zero_p (bsm1 + t, n - t) && mpn_cmp (bsm1, b1, t) < 0) |
| { |
| ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, t)); |
| MPN_ZERO (bsm2 + t, n + 1 - t); |
| bflags = (enum toom7_flags) (bflags | toom7_w1_neg); |
| } |
| else |
| { |
| ASSERT_NOCARRY (mpn_sub (bsm2, bsm1, n, b1, t)); |
| bsm2[n] = 0; |
| } |
| } |
| else |
| { |
| if (mpn_cmp (bsm1, b1, n) < 0) |
| { |
| ASSERT_NOCARRY (mpn_sub_n (bsm2, b1, bsm1, n)); |
| bflags = (enum toom7_flags) (bflags | toom7_w1_neg); |
| } |
| else |
| { |
| ASSERT_NOCARRY (mpn_sub_n (bsm2, bsm1, b1, n)); |
| } |
| bsm2[n] = 0; |
| } |
| } |
| |
| /* Compute bsh, recycling bs1. bsh=bs1+b0; */ |
| bsh[n] = bs1[n] + mpn_add_n (bsh, bs1, b0, n); |
| |
| ASSERT (as1[n] <= 5); |
| ASSERT (bs1[n] <= 1); |
| ASSERT (asm1[n] <= 2); |
| ASSERT (as2[n] <= 62); |
| ASSERT (bs2[n] <= 2); |
| ASSERT (asm2[n] <= 41); |
| ASSERT (bsm2[n] <= 1); |
| ASSERT (ash[n] <= 62); |
| ASSERT (bsh[n] <= 2); |
| |
| #define v0 pp /* 2n */ |
| #define v1 (pp + 2 * n) /* 2n+1 */ |
| #define vinf (pp + 6 * n) /* s+t */ |
| #define v2 scratch /* 2n+1 */ |
| #define vm2 (scratch + 2 * n + 1) /* 2n+1 */ |
| #define vh (scratch + 4 * n + 2) /* 2n+1 */ |
| #define vm1 (scratch + 6 * n + 3) /* 2n+1 */ |
| #define scratch_out (scratch + 8 * n + 4) /* 2n+1 */ |
| /* Total scratch need: 10*n+5 */ |
| |
| /* Must be in allocation order, as they overwrite one limb beyond |
| * 2n+1. */ |
| mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */ |
| mpn_mul_n (vm2, asm2, bsm2, n + 1); /* vm2, 2n+1 limbs */ |
| mpn_mul_n (vh, ash, bsh, n + 1); /* vh, 2n+1 limbs */ |
| |
| /* vm1, 2n+1 limbs */ |
| mpn_mul_n (vm1, asm1, bsm1, n); |
| cy = 0; |
| if (asm1[n] == 1) |
| { |
| cy = mpn_add_n (vm1 + n, vm1 + n, bsm1, n); |
| } |
| else if (asm1[n] == 2) |
| { |
| #if HAVE_NATIVE_mpn_addlsh1_n |
| cy = mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n); |
| #else |
| cy = mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2)); |
| #endif |
| } |
| vm1[2 * n] = cy; |
| |
| /* v1, 2n+1 limbs */ |
| mpn_mul_n (v1, as1, bs1, n); |
| 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 if (as1[n] != 0) |
| { |
| cy = as1[n] * bs1[n] + mpn_addmul_1 (v1 + n, bs1, n, as1[n]); |
| } |
| 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, a0, b0, n); /* v0, 2n limbs */ |
| |
| /* vinf, s+t limbs */ |
| if (s > t) mpn_mul (vinf, a5, s, b1, t); |
| else mpn_mul (vinf, b1, t, a5, s); |
| |
| mpn_toom_interpolate_7pts (pp, n, (enum toom7_flags) (aflags ^ bflags), |
| vm2, vm1, v2, vh, s + t, scratch_out); |
| |
| TMP_FREE; |
| } |
