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+/* 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);
+}