* mpn/toomMN_mul.c: Add scratch parameter. Do recursive multiplies

  properly.  Misc tuning.  Remove CHECK and TIMING code.
* mpn/toom2_sqr.c, mpn/toom3_sqr.c, mpn/toom4_sqr.c: New files.

1 files changed, 356 insertions, 0 deletions

diff --git a/mpn/generic/toom62_mul.c b/mpn/generic/toom62_mul.c
new file mode 100644
index 000000000..a745458b7
--- /dev/null
+++ b/mpn/generic/toom62_mul.c
@@ -0,0 +1,356 @@
+/* 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 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 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 General Public License for more
+details.
+
+You should have received a copy of the GNU 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-->
+   ___ ______ ______ ______ ______ ______
+  |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
+  vh  = (32a0+16a1+8a2+4a3+ 2a4+  a5)*(2b0+ b1) #  A(1/2)*B(1/2)    ah  <= 62  bh <= 2
+  vmh = (32a0-16a1+8a2-4a3+ 2a4-  a5)*(2b0- b1) # A(-1/2)*B(-1/2)  -20<=ah<=41 0<=bh<=1
+  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;
+  int vm1_neg, vmh_neg, bsm_neg;
+  mp_limb_t cy;
+  mp_ptr a0_a2, a1_a3;
+  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 a5  (ap + 5*n)
+#define b0  bp
+#define b1  (bp + n)
+
+  n = 1 + (an >= 3 * bn ? (an - 1) / (unsigned long) 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);
+  ash = TMP_SALLOC_LIMBS (n + 1);
+  asmh = TMP_SALLOC_LIMBS (n + 1);
+
+  bs1 = TMP_SALLOC_LIMBS (n + 1);
+  bsm1 = TMP_SALLOC_LIMBS (n);
+  bs2 = TMP_SALLOC_LIMBS (n + 1);
+  bsh = TMP_SALLOC_LIMBS (n + 1);
+  bsmh = TMP_SALLOC_LIMBS (n + 1);
+
+  a0_a2 = pp;
+  a1_a3 = pp + n + 1;
+
+  /* Compute as1 and asm1.  */
+  a0_a2[n]  = mpn_add_n (a0_a2, a0, a2, n);
+  a0_a2[n] += mpn_add_n (a0_a2, a0_a2, a4, n);
+  a1_a3[n]  = mpn_add_n (a1_a3, a1, a3, n);
+  a1_a3[n] += mpn_add (a1_a3, a1_a3, n, a5, s);
+#if HAVE_NATIVE_mpn_addsub_n
+  if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0)
+    {
+      mpn_addsub_n (as1, asm1, a1_a3, a0_a2, n + 1);
+      vm1_neg = 1;
+    }
+  else
+    {
+      mpn_addsub_n (as1, asm1, a0_a2, a1_a3, n + 1);
+      vm1_neg = 0;
+    }
+#else
+  mpn_add_n (as1, a0_a2, a1_a3, n + 1);
+  if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0)
+    {
+      mpn_sub_n (asm1, a1_a3, a0_a2, n + 1);
+      vm1_neg = 1;
+    }
+  else
+    {
+      mpn_sub_n (asm1, a0_a2, a1_a3, n + 1);
+      vm1_neg = 0;
+    }
+#endif
+
+  /* Compute as2.  */
+#if HAVE_NATIVE_mpn_addlsh1_n
+  cy  = mpn_addlsh1_n (as2, a4, a5, s);
+  if (s != n)
+    cy = mpn_add_1 (as2 + s, a4 + s, n - s, cy);
+  cy = 2 * cy + mpn_addlsh1_n (as2, a3, as2, n);
+  cy = 2 * cy + mpn_addlsh1_n (as2, a2, as2, n);
+  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, a5, s, 1);
+  cy += mpn_add_n (as2, a4, as2, s);
+  if (s != n)
+    cy = mpn_add_1 (as2 + s, a4 + s, n - s, cy);
+  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
+  cy += mpn_add_n (as2, a3, as2, n);
+  cy = 2 * cy + mpn_lshift (as2, as2, n, 1);
+  cy += mpn_add_n (as2, a2, as2, n);
+  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.  */
+#if HAVE_NATIVE_mpn_addlsh_n
+  cy  = mpn_addlsh_n (a0_a2, a2, a0, n, 2);		/* 4a0  +  a2       */
+  cy = 4 * cy + mpn_addlsh_n (a0_a2, a4, a0_a2, n, 2);	/* 16a0 + 4a2 +  a4 */
+  cy = 2 * cy + mpn_lshift (a0_a2, a0_a2, n, 1);	/* 32a0 + 8a2 + 2a4 */
+  a0_a2[n] = cy;
+  cy  = mpn_addlsh_n (a1_a3, a3, a1, n, 2);		/* 4a1              */
+  cy = 4 * cy + mpn_addlsh_n (a1_a3, a5, a1_a3, n, 2);	/* 16a1 + 4a3       */
+  a1_a3[n] = cy;
+#else
+  cy  = mpn_lshift (a0_a2, a0, n, 2);			/* 4a0              */
+  cy += mpn_add_n (a0_a2, a2, a0_a2, n);		/* 4a0  +  a2       */
+  cy = 4 * cy + mpn_lshift (a0_a2, a0_a2, n, 2);	/* 16a0 + 4a2       */
+  cy += mpn_add_n (a0_a2, a4, a0_a2, n);		/* 16a0 + 4a2 +  a4 */
+  cy = 2 * cy + mpn_lshift (a0_a2, a0_a2, n, 1);	/* 32a0 + 8a2 + 2a4 */
+  a0_a2[n] = cy;
+  cy  = mpn_lshift (a1_a3, a1, n, 2);			/* 4a1              */
+  cy += mpn_add_n (a1_a3, a3, a1_a3, n);		/* 4a1  +  a3       */
+  cy = 4 * cy + mpn_lshift (a1_a3, a1_a3, n, 2);	/* 16a1 + 4a3       */
+  cy += mpn_add (a1_a3, a1_a3, n, a5, s);		/* 16a1 + 4a3 + a5  */
+  a1_a3[n] = cy;
+#endif
+#if HAVE_NATIVE_mpn_addsub_n
+  if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0)
+    {
+      mpn_addsub_n (ash, asmh, a1_a3, a0_a2, n + 1);
+      vmh_neg = 1;
+    }
+  else
+    {
+      mpn_addsub_n (ash, asmh, a0_a2, a1_a3, n + 1);
+      vmh_neg = 0;
+    }
+#else
+  mpn_add_n (ash, a0_a2, a1_a3, n + 1);
+  if (mpn_cmp (a0_a2, a1_a3, n + 1) < 0)
+    {
+      mpn_sub_n (asmh, a1_a3, a0_a2, n + 1);
+      vmh_neg = 1;
+    }
+  else
+    {
+      mpn_sub_n (asmh, a0_a2, a1_a3, n + 1);
+      vmh_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);
+	  bsm_neg = 1;
+	}
+      else
+	{
+	  cy = mpn_addsub_n (bs1, bsm1, b0, b1, n);
+	  bsm_neg = 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);
+	  bsm_neg = 1;
+	}
+      else
+	{
+	  mpn_sub_n (bsm1, b0, b1, n);
+	  bsm_neg = 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);
+	  bsm_neg = 1;
+	}
+      else
+	{
+	  mpn_sub (bsm1, b0, n, b1, t);
+	  bsm_neg = 0;
+	}
+    }
+
+  vm1_neg ^= bsm_neg;
+
+  /* Compute bs2, recycling bs1. bs2=bs1+b1  */
+  mpn_add (bs2, bs1, n + 1, b1, t);
+
+  /* Compute bsh and bsmh, recycling bs1 and bsm1. bsh=bs1+b0; bsmh=bsmh+b0  */
+  if (bsm_neg == 1)
+    {
+      bsmh[n] = 0;
+      if (mpn_cmp (bsm1, b0, n) < 0)
+	{
+	  bsm_neg = 0;
+	  mpn_sub_n (bsmh, b0, bsm1, n);
+	}
+      else
+	mpn_sub_n (bsmh, bsm1, b0, n);
+    }
+  else
+    bsmh[n] = mpn_add_n (bsmh, bsm1, b0, n);
+  mpn_add (bsh, bs1, n + 1, b0, n);
+  vmh_neg ^= bsm_neg;
+
+
+  ASSERT (as1[n] <= 5);
+  ASSERT (bs1[n] <= 1);
+  ASSERT (asm1[n] <= 2);
+/*ASSERT (bsm1[n] == 0);*/
+  ASSERT (as2[n] <= 62);
+  ASSERT (bs2[n] <= 2);
+  ASSERT (ash[n] <= 62);
+  ASSERT (bsh[n] <= 2);
+  ASSERT (asmh[n] <= 41);
+  ASSERT (bsmh[n] <= 1);
+
+#define v0    pp				/* 2n */
+#define v1    (scratch + 6 * n + 6)		/* 2n+1 */
+#define vinf  (pp + 6 * n)			/* s+t */
+#define vm1   scratch				/* 2n+1 */
+#define v2    (scratch + 2 * n + 2)		/* 2n+1 */
+#define vh    (pp + 2 * n)			/* 2n+1 */
+#define vmh   (scratch + 4 * n + 4)
+
+  /* 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;
+
+  mpn_mul_n (v2, as2, bs2, n + 1);		/* v2, 2n+1 limbs */
+
+  /* vinf, s+t limbs */
+  if (s > t)  mpn_mul (vinf, a5, s, b1, t);
+  else        mpn_mul (vinf, b1, t, a5, s);
+
+  /* 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 (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;
+}