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authorJakub Jelinek <jakub@redhat.com>2007-07-12 18:26:36 +0000
committerJakub Jelinek <jakub@redhat.com>2007-07-12 18:26:36 +0000
commit0ecb606cb6cf65de1d9fc8a919bceb4be476c602 (patch)
tree2ea1f8305970753e4a657acb2ccc15ca3eec8e2c /sysdeps/generic/mul_n.c
parent7d58530341304d403a6626d7f7a1913165fe2f32 (diff)
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2.5-18.1
Diffstat (limited to 'sysdeps/generic/mul_n.c')
-rw-r--r--sysdeps/generic/mul_n.c401
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diff --git a/sysdeps/generic/mul_n.c b/sysdeps/generic/mul_n.c
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--- a/sysdeps/generic/mul_n.c
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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);
-}