2.5-18.1

1 files changed, 401 insertions, 0 deletions

diff --git a/stdlib/mul_n.c b/stdlib/mul_n.c
new file mode 100644
index 0000000..b478c76
--- /dev/null
+++ b/stdlib/mul_n.c
@@ -0,0 +1,401 @@
+/* mpn_mul_n -- Multiply two natural numbers of length n.
+
+Copyright (C) 1991, 1992, 1993, 1994, 1996 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 2.1 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; see the file COPYING.LIB.  If not, write to
+the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA. */
+
+#include <gmp.h>
+#include "gmp-impl.h"
+
+/* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
+   both with SIZE limbs, and store the result at PRODP.  2 * SIZE limbs are
+   always stored.  Return the most significant limb.
+
+   Argument constraints:
+   1. PRODP != UP and PRODP != VP, i.e. the destination
+      must be distinct from the multiplier and the multiplicand.  */
+
+/* If KARATSUBA_THRESHOLD is not already defined, define it to a
+   value which is good on most machines.  */
+#ifndef KARATSUBA_THRESHOLD
+#define KARATSUBA_THRESHOLD 32
+#endif
+
+/* The code can't handle KARATSUBA_THRESHOLD smaller than 2.  */
+#if KARATSUBA_THRESHOLD < 2
+#undef KARATSUBA_THRESHOLD
+#define KARATSUBA_THRESHOLD 2
+#endif
+
+/* Handle simple cases with traditional multiplication.
+
+   This is the most critical code of multiplication.  All multiplies rely
+   on this, both small and huge.  Small ones arrive here immediately.  Huge
+   ones arrive here as this is the base case for Karatsuba's recursive
+   algorithm below.  */
+
+void
+#if __STDC__
+impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
+#else
+impn_mul_n_basecase (prodp, up, vp, size)
+     mp_ptr prodp;
+     mp_srcptr up;
+     mp_srcptr vp;
+     mp_size_t size;
+#endif
+{
+  mp_size_t i;
+  mp_limb_t cy_limb;
+  mp_limb_t v_limb;
+
+  /* Multiply by the first limb in V separately, as the result can be
+     stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+  v_limb = vp[0];
+  if (v_limb <= 1)
+    {
+      if (v_limb == 1)
+	MPN_COPY (prodp, up, size);
+      else
+	MPN_ZERO (prodp, size);
+      cy_limb = 0;
+    }
+  else
+    cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
+
+  prodp[size] = cy_limb;
+  prodp++;
+
+  /* For each iteration in the outer loop, multiply one limb from
+     U with one limb from V, and add it to PROD.  */
+  for (i = 1; i < size; i++)
+    {
+      v_limb = vp[i];
+      if (v_limb <= 1)
+	{
+	  cy_limb = 0;
+	  if (v_limb == 1)
+	    cy_limb = mpn_add_n (prodp, prodp, up, size);
+	}
+      else
+	cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
+
+      prodp[size] = cy_limb;
+      prodp++;
+    }
+}
+
+void
+#if __STDC__
+impn_mul_n (mp_ptr prodp,
+	     mp_srcptr up, mp_srcptr vp, mp_size_t size, mp_ptr tspace)
+#else
+impn_mul_n (prodp, up, vp, size, tspace)
+     mp_ptr prodp;
+     mp_srcptr up;
+     mp_srcptr vp;
+     mp_size_t size;
+     mp_ptr tspace;
+#endif
+{
+  if ((size & 1) != 0)
+    {
+      /* The size is odd, the code code below doesn't handle that.
+	 Multiply the least significant (size - 1) limbs with a recursive
+	 call, and handle the most significant limb of S1 and S2
+	 separately.  */
+      /* A slightly faster way to do this would be to make the Karatsuba
+	 code below behave as if the size were even, and let it check for
+	 odd size in the end.  I.e., in essence move this code to the end.
+	 Doing so would save us a recursive call, and potentially make the
+	 stack grow a lot less.  */
+
+      mp_size_t esize = size - 1;	/* even size */
+      mp_limb_t cy_limb;
+
+      MPN_MUL_N_RECURSE (prodp, up, vp, esize, tspace);
+      cy_limb = mpn_addmul_1 (prodp + esize, up, esize, vp[esize]);
+      prodp[esize + esize] = cy_limb;
+      cy_limb = mpn_addmul_1 (prodp + esize, vp, size, up[esize]);
+
+      prodp[esize + size] = cy_limb;
+    }
+  else
+    {
+      /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
+
+	 Split U in two pieces, U1 and U0, such that
+	 U = U0 + U1*(B**n),
+	 and V in V1 and V0, such that
+	 V = V0 + V1*(B**n).
+
+	 UV is then computed recursively using the identity
+
+		2n   n          n                     n
+	 UV = (B  + B )U V  +  B (U -U )(V -V )  +  (B + 1)U V
+			1 1        1  0   0  1              0 0
+
+	 Where B = 2**BITS_PER_MP_LIMB.  */
+
+      mp_size_t hsize = size >> 1;
+      mp_limb_t cy;
+      int negflg;
+
+      /*** Product H.	 ________________  ________________
+			|_____U1 x V1____||____U0 x V0_____|  */
+      /* Put result in upper part of PROD and pass low part of TSPACE
+	 as new TSPACE.  */
+      MPN_MUL_N_RECURSE (prodp + size, up + hsize, vp + hsize, hsize, tspace);
+
+      /*** Product M.	 ________________
+			|_(U1-U0)(V0-V1)_|  */
+      if (mpn_cmp (up + hsize, up, hsize) >= 0)
+	{
+	  mpn_sub_n (prodp, up + hsize, up, hsize);
+	  negflg = 0;
+	}
+      else
+	{
+	  mpn_sub_n (prodp, up, up + hsize, hsize);
+	  negflg = 1;
+	}
+      if (mpn_cmp (vp + hsize, vp, hsize) >= 0)
+	{
+	  mpn_sub_n (prodp + hsize, vp + hsize, vp, hsize);
+	  negflg ^= 1;
+	}
+      else
+	{
+	  mpn_sub_n (prodp + hsize, vp, vp + hsize, hsize);
+	  /* No change of NEGFLG.  */
+	}
+      /* Read temporary operands from low part of PROD.
+	 Put result in low part of TSPACE using upper part of TSPACE
+	 as new TSPACE.  */
+      MPN_MUL_N_RECURSE (tspace, prodp, prodp + hsize, hsize, tspace + size);
+
+      /*** Add/copy product H.  */
+      MPN_COPY (prodp + hsize, prodp + size, hsize);
+      cy = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize);
+
+      /*** Add product M (if NEGFLG M is a negative number).  */
+      if (negflg)
+	cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size);
+      else
+	cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
+
+      /*** Product L.	 ________________  ________________
+			|________________||____U0 x V0_____|  */
+      /* Read temporary operands from low part of PROD.
+	 Put result in low part of TSPACE using upper part of TSPACE
+	 as new TSPACE.  */
+      MPN_MUL_N_RECURSE (tspace, up, vp, hsize, tspace + size);
+
+      /*** Add/copy Product L (twice).  */
+
+      cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
+      if (cy)
+	mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy);
+
+      MPN_COPY (prodp, tspace, hsize);
+      cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
+      if (cy)
+	mpn_add_1 (prodp + size, prodp + size, size, 1);
+    }
+}
+
+void
+#if __STDC__
+impn_sqr_n_basecase (mp_ptr prodp, mp_srcptr up, mp_size_t size)
+#else
+impn_sqr_n_basecase (prodp, up, size)
+     mp_ptr prodp;
+     mp_srcptr up;
+     mp_size_t size;
+#endif
+{
+  mp_size_t i;
+  mp_limb_t cy_limb;
+  mp_limb_t v_limb;
+
+  /* Multiply by the first limb in V separately, as the result can be
+     stored (not added) to PROD.  We also avoid a loop for zeroing.  */
+  v_limb = up[0];
+  if (v_limb <= 1)
+    {
+      if (v_limb == 1)
+	MPN_COPY (prodp, up, size);
+      else
+	MPN_ZERO (prodp, size);
+      cy_limb = 0;
+    }
+  else
+    cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
+
+  prodp[size] = cy_limb;
+  prodp++;
+
+  /* For each iteration in the outer loop, multiply one limb from
+     U with one limb from V, and add it to PROD.  */
+  for (i = 1; i < size; i++)
+    {
+      v_limb = up[i];
+      if (v_limb <= 1)
+	{
+	  cy_limb = 0;
+	  if (v_limb == 1)
+	    cy_limb = mpn_add_n (prodp, prodp, up, size);
+	}
+      else
+	cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
+
+      prodp[size] = cy_limb;
+      prodp++;
+    }
+}
+
+void
+#if __STDC__
+impn_sqr_n (mp_ptr prodp,
+	     mp_srcptr up, mp_size_t size, mp_ptr tspace)
+#else
+impn_sqr_n (prodp, up, size, tspace)
+     mp_ptr prodp;
+     mp_srcptr up;
+     mp_size_t size;
+     mp_ptr tspace;
+#endif
+{
+  if ((size & 1) != 0)
+    {
+      /* The size is odd, the code code below doesn't handle that.
+	 Multiply the least significant (size - 1) limbs with a recursive
+	 call, and handle the most significant limb of S1 and S2
+	 separately.  */
+      /* A slightly faster way to do this would be to make the Karatsuba
+	 code below behave as if the size were even, and let it check for
+	 odd size in the end.  I.e., in essence move this code to the end.
+	 Doing so would save us a recursive call, and potentially make the
+	 stack grow a lot less.  */
+
+      mp_size_t esize = size - 1;	/* even size */
+      mp_limb_t cy_limb;
+
+      MPN_SQR_N_RECURSE (prodp, up, esize, tspace);
+      cy_limb = mpn_addmul_1 (prodp + esize, up, esize, up[esize]);
+      prodp[esize + esize] = cy_limb;
+      cy_limb = mpn_addmul_1 (prodp + esize, up, size, up[esize]);
+
+      prodp[esize + size] = cy_limb;
+    }
+  else
+    {
+      mp_size_t hsize = size >> 1;
+      mp_limb_t cy;
+
+      /*** Product H.	 ________________  ________________
+			|_____U1 x U1____||____U0 x U0_____|  */
+      /* Put result in upper part of PROD and pass low part of TSPACE
+	 as new TSPACE.  */
+      MPN_SQR_N_RECURSE (prodp + size, up + hsize, hsize, tspace);
+
+      /*** Product M.	 ________________
+			|_(U1-U0)(U0-U1)_|  */
+      if (mpn_cmp (up + hsize, up, hsize) >= 0)
+	{
+	  mpn_sub_n (prodp, up + hsize, up, hsize);
+	}
+      else
+	{
+	  mpn_sub_n (prodp, up, up + hsize, hsize);
+	}
+
+      /* Read temporary operands from low part of PROD.
+	 Put result in low part of TSPACE using upper part of TSPACE
+	 as new TSPACE.  */
+      MPN_SQR_N_RECURSE (tspace, prodp, hsize, tspace + size);
+
+      /*** Add/copy product H.  */
+      MPN_COPY (prodp + hsize, prodp + size, hsize);
+      cy = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize);
+
+      /*** Add product M (if NEGFLG M is a negative number).  */
+      cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size);
+
+      /*** Product L.	 ________________  ________________
+			|________________||____U0 x U0_____|  */
+      /* Read temporary operands from low part of PROD.
+	 Put result in low part of TSPACE using upper part of TSPACE
+	 as new TSPACE.  */
+      MPN_SQR_N_RECURSE (tspace, up, hsize, tspace + size);
+
+      /*** Add/copy Product L (twice).  */
+
+      cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
+      if (cy)
+	mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy);
+
+      MPN_COPY (prodp, tspace, hsize);
+      cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
+      if (cy)
+	mpn_add_1 (prodp + size, prodp + size, size, 1);
+    }
+}
+
+/* This should be made into an inline function in gmp.h.  */
+void
+#if __STDC__
+mpn_mul_n (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
+#else
+mpn_mul_n (prodp, up, vp, size)
+     mp_ptr prodp;
+     mp_srcptr up;
+     mp_srcptr vp;
+     mp_size_t size;
+#endif
+{
+  TMP_DECL (marker);
+  TMP_MARK (marker);
+  if (up == vp)
+    {
+      if (size < KARATSUBA_THRESHOLD)
+	{
+	  impn_sqr_n_basecase (prodp, up, size);
+	}
+      else
+	{
+	  mp_ptr tspace;
+	  tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB);
+	  impn_sqr_n (prodp, up, size, tspace);
+	}
+    }
+  else
+    {
+      if (size < KARATSUBA_THRESHOLD)
+	{
+	  impn_mul_n_basecase (prodp, up, vp, size);
+	}
+      else
+	{
+	  mp_ptr tspace;
+	  tspace = (mp_ptr) TMP_ALLOC (2 * size * BYTES_PER_MP_LIMB);
+	  impn_mul_n (prodp, up, vp, size, tspace);
+	}
+    }
+  TMP_FREE (marker);
+}