--- /dev/null
+/* mpn_toom53_mul -- Multiply {ap,an} and {bp,bn} where an is nominally 5/3
+ times as large as bn. Or more accurately, (4/3)bn < an < (5/2)bn.
+
+ Contributed to the GNU project by Torbjorn Granlund and Marco Bodrato.
+
+ 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.
+*/
+
+#include "gmp.h"
+#include "gmp-impl.h"
+
+/* Evaluate in: -1, -1/2, 0, +1/2, +1, +2, +inf
+
+ <-s-><--n--><--n--><--n--><--n-->
+ ___ ______ ______ ______ ______
+ |a4_|___a3_|___a2_|___a1_|___a0_|
+ |__b2|___b1_|___b0_|
+ <-t--><--n--><--n-->
+
+ v0 = a0 * b0 # A(0)*B(0)
+ v1 = ( a0+ a1+ a2+ a3+ a4)*( b0+ b1+ b2) # A(1)*B(1) ah <= 4 bh <= 2
+ vm1 = ( a0- a1+ a2- a3+ a4)*( b0- b1+ b2) # A(-1)*B(-1) |ah| <= 2 bh <= 1
+ v2 = ( a0+2a1+4a2+8a3+16a4)*( b0+2b1+4b2) # A(2)*B(2) ah <= 30 bh <= 6
+ vh = (16a0+8a1+4a2+2a3+ a4)*(4b0+2b1+ b2) # A(1/2)*B(1/2) ah <= 30 bh <= 6
+ vmh = (16a0-8a1+4a2-2a3+ a4)*(4b0-2b1+ b2) # A(-1/2)*B(-1/2) -9<=ah<=20 -1<=bh<=4
+ vinf= a4 * b2 # A(inf)*B(inf)
+*/
+
+void
+mpn_toom53_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, vmh_neg;
+ mp_limb_t cy;
+ mp_ptr gp, hp;
+ mp_ptr as1, asm1, as2, ash, asmh;
+ mp_ptr bs1, bsm1, bs2, bsh, bsmh;
+ enum toom4_flags flags;
+ 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 b0 bp
+#define b1 (bp + n)
+#define b2 (bp + 2*n)
+
+ n = 1 + (3 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 3);
+
+ s = an - 4 * n;
+ t = bn - 2 * 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);
+ ash = TMP_SALLOC_LIMBS (n + 1);
+ asmh = TMP_SALLOC_LIMBS (n + 1);
+
+ bs1 = TMP_SALLOC_LIMBS (n + 1);
+ bsm1 = TMP_SALLOC_LIMBS (n + 1);
+ bs2 = TMP_SALLOC_LIMBS (n + 1);
+ bsh = TMP_SALLOC_LIMBS (n + 1);
+ bsmh = TMP_SALLOC_LIMBS (n + 1);
+
+ gp = pp;
+ hp = pp + n + 1;
+
+ /* Compute as1 and asm1. */
+ gp[n] = mpn_add_n (gp, a0, a2, n);
+ gp[n] += mpn_add (gp, gp, n, a4, s);
+ hp[n] = mpn_add_n (hp, a1, a3, n);
+#if HAVE_NATIVE_mpn_addsub_n
+ if (mpn_cmp (gp, hp, n + 1) < 0)
+ {
+ mpn_addsub_n (as1, asm1, hp, gp, n + 1);
+ vm1_neg = 1;
+ }
+ else
+ {
+ mpn_addsub_n (as1, asm1, gp, hp, n + 1);
+ vm1_neg = 0;
+ }
+#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);
+ vm1_neg = 1;
+ }
+ else
+ {
+ mpn_sub_n (asm1, gp, hp, n + 1);
+ vm1_neg = 0;
+ }
+#endif
+
+ /* Compute as2. */
+#if !HAVE_NATIVE_mpn_addlsh_n
+ ash[n] = mpn_lshift (ash, a2, n, 2); /* 4a2 */
+#endif
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy = mpn_addlsh1_n (as2, a3, a4, s);
+ if (s != n)
+ cy = mpn_add_1 (as2 + s, a3 + s, n - s, cy);
+ cy = 2 * cy + mpn_addlsh1_n (as2, a2, as2, n);
+ cy = 2 * cy + mpn_addlsh1_n (as2, a1, as2, n);
+ as2[n] = 2 * cy + mpn_addlsh1_n (as2, a0, as2, n);
+#else
+ cy = mpn_lshift (as2, a4, s, 1);
+ cy += mpn_add_n (as2, a3, as2, s);
+ if (s != n)
+ cy = mpn_add_1 (as2 + s, a3 + s, n - s, cy);
+ cy = 4 * cy + mpn_lshift (as2, as2, n, 2);
+ cy += mpn_add_n (as2, a1, as2, n);
+ cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
+ as2[n] = cy + mpn_add_n (as2, a0, as2, n);
+ mpn_add_n (as2, ash, as2, n + 1);
+#endif
+
+ /* Compute ash and asmh. */
+#if HAVE_NATIVE_mpn_addlsh_n
+ cy = mpn_addlsh_n (gp, a2, a0, n, 2); /* 4a0 + a2 */
+ cy = 4 * cy + mpn_addlsh_n (gp, a4, gp, n, 2); /* 16a0 + 4a2 + a4 */ /* FIXME s */
+ gp[n] = cy;
+ cy = mpn_addlsh_n (hp, a3, a1, n, 2); /* 4a1 + a3 */
+ cy = 2 * cy + mpn_lshift (hp, hp, n, 1); /* 8a1 + 2a3 */
+ hp[n] = cy;
+#else
+ gp[n] = mpn_lshift (gp, a0, n, 4); /* 16a0 */
+ mpn_add (gp, gp, n + 1, a4, s); /* 16a0 + a4 */
+ mpn_add_n (gp, ash, gp, n+1); /* 16a0 + 4a2 + a4 */
+ cy = mpn_lshift (hp, a1, n, 3); /* 8a1 */
+ cy += mpn_lshift (ash, a3, n, 1); /* 2a3 */
+ cy += mpn_add_n (hp, ash, hp, n); /* 8a1 + 2a3 */
+ hp[n] = cy;
+#endif
+#if HAVE_NATIVE_mpn_addsub_n
+ if (mpn_cmp (gp, hp, n + 1) < 0)
+ {
+ mpn_addsub_n (ash, asmh, hp, gp, n + 1);
+ vmh_neg = 1;
+ }
+ else
+ {
+ mpn_addsub_n (ash, asmh, gp, hp, n + 1);
+ vmh_neg = 0;
+ }
+#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);
+ vmh_neg = 1;
+ }
+ else
+ {
+ mpn_sub_n (asmh, gp, hp, n + 1);
+ vmh_neg = 0;
+ }
+#endif
+
+ /* Compute bs1 and bsm1. */
+ bs1[n] = mpn_add (bs1, b0, n, b2, t); /* b0 + b2 */
+#if HAVE_NATIVE_mpn_addsub_n
+ if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
+ {
+ bs1[n] = mpn_addsub_n (bs1, bsm1, b1, bs1, n) >> 1;
+ bsm1[n] = 0;
+ vm1_neg ^= 1;
+ }
+ else
+ {
+ cy = mpn_addsub_n (bs1, bsm1, bs1, b1, n);
+ bsm1[n] = bs1[n] - (cy & 1);
+ bs1[n] += (cy >> 1);
+ }
+#else
+ if (bs1[n] == 0 && mpn_cmp (bs1, b1, n) < 0)
+ {
+ mpn_sub_n (bsm1, b1, bs1, n);
+ bsm1[n] = 0;
+ vm1_neg ^= 1;
+ }
+ else
+ {
+ bsm1[n] = bs1[n] - mpn_sub_n (bsm1, bs1, b1, n);
+ }
+ bs1[n] += mpn_add_n (bs1, bs1, b1, n); /* b0+b1+b2 */
+#endif
+
+ /* Compute bs2 */
+ hp[n] = mpn_lshift (hp, b1, n, 1); /* 2b1 */
+
+#ifdef HAVE_NATIVE_mpn_addlsh1_n
+ cy = mpn_addlsh1_n (bs2, b1, b2, t);
+ if (t != n)
+ cy = mpn_add_1 (bs2 + t, b1 + t, n - t, cy);
+ bs2[n] = 2 * cy + mpn_addlsh1_n (bs2, b0, bs2, n);
+#else
+ bs2[t] = mpn_lshift (bs2, b2, t, 2);
+ mpn_add (bs2, hp, n + 1, bs2, t + 1);
+ bs2[n] += mpn_add_n (bs2, bs2, b0, n);
+#endif
+
+ /* Compute bsh and bsmh. */
+#if HAVE_NATIVE_mpn_addlsh_n
+ gp[n] = mpn_addlsh_n (gp, b2, b0, n, 2); /* 4a0 + a2 */
+#else
+ cy = mpn_lshift (gp, b0, n, 2); /* 4b0 */
+ gp[n] = cy + mpn_add (gp, gp, n, b2, t); /* 4b0 + b2 */
+#endif
+#if HAVE_NATIVE_mpn_addsub_n
+ if (mpn_cmp (gp, hp, n + 1) < 0)
+ {
+ mpn_addsub_n (bsh, bsmh, hp, gp, n + 1);
+ vmh_neg^= 1;
+ }
+ else
+ mpn_addsub_n (bsh, bsmh, gp, hp, n + 1);
+#else
+ mpn_add_n (bsh, gp, hp, n + 1); /* 4b0 + 2b1 + b2 */
+ if (mpn_cmp (gp, hp, n + 1) < 0)
+ {
+ mpn_sub_n (bsmh, hp, gp, n + 1);
+ vmh_neg ^= 1;
+ }
+ else
+ {
+ mpn_sub_n (bsmh, gp, hp, n + 1);
+ }
+#endif
+
+ ASSERT (as1[n] <= 4);
+ ASSERT (bs1[n] <= 2);
+ ASSERT (asm1[n] <= 2);
+ ASSERT (bsm1[n] <= 1);
+ ASSERT (as2[n] <= 30);
+ ASSERT (bs2[n] <= 6);
+ ASSERT (ash[n] <= 30);
+ ASSERT (bsh[n] <= 6);
+ ASSERT (asmh[n] <= 20);
+ ASSERT (bsmh[n] <= 4);
+
+#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)
+
+ /* vm1, 2n+1 limbs */
+#ifdef SMALLER_RECURSION
+ mpn_mul_n (vm1, asm1, bsm1, n);
+ if (asm1[n] == 1)
+ {
+ cy = bsm1[n] + mpn_add_n (vm1 + n, vm1 + n, bsm1, n);
+ }
+ else if (asm1[n] == 2)
+ {
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy = 2 * bsm1[n] + mpn_addlsh1_n (vm1 + n, vm1 + n, bsm1, n);
+#else
+ cy = 2 * bsm1[n] + mpn_addmul_1 (vm1 + n, bsm1, n, CNST_LIMB(2));
+#endif
+ }
+ else
+ cy = 0;
+ if (bsm1[n] != 0)
+ cy += mpn_add_n (vm1 + n, vm1 + n, asm1, n);
+ vm1[2 * n] = cy;
+#else /* SMALLER_RECURSION */
+ vm1[2 * n] = 0;
+ mpn_mul_n (vm1, asm1, bsm1, n + ((asm1[n] | bsm1[n]) != 0));
+#endif /* SMALLER_RECURSION */
+
+ mpn_mul_n (v2, as2, bs2, n + 1); /* v2, 2n+1 limbs */
+
+ /* vinf, s+t limbs */
+ if (s > t) mpn_mul (vinf, a4, s, b2, t);
+ else mpn_mul (vinf, b2, t, a4, s);
+
+ /* v1, 2n+1 limbs */
+#ifdef SMALLER_RECURSION
+ 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] == 1)
+ {
+ cy += mpn_add_n (v1 + n, v1 + n, as1, n);
+ }
+ else if (bs1[n] == 2)
+ {
+#if HAVE_NATIVE_mpn_addlsh1_n
+ cy += mpn_addlsh1_n (v1 + n, v1 + n, as1, n);
+#else
+ cy += mpn_addmul_1 (v1 + n, as1, n, CNST_LIMB(2));
+#endif
+ }
+ v1[2 * n] = cy;
+#else /* SMALLER_RECURSION */
+ v1[2 * n] = 0;
+ mpn_mul_n (v1, as1, bs1, n + ((as1[n] | bs1[n]) != 0));
+#endif /* SMALLER_RECURSION */
+
+ mpn_mul_n (vh, ash, bsh, n + 1);
+
+ mpn_mul_n (vmh, asmh, bsmh, n + 1);
+
+ mpn_mul_n (v0, ap, bp, n); /* v0, 2n limbs */
+
+ flags = vm1_neg ? toom4_w3_neg : 0;
+ flags |= vmh_neg ? toom4_w1_neg : 0;
+
+ mpn_toom_interpolate_7pts (pp, n, flags, vmh, vm1, v1, v2, s + t, scratch + 8 * n + 8);
+
+ TMP_FREE;
+}
projects / msp430-gcc.git / blobdiff