1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
|
/* mpn_mul -- Multiply two natural numbers.
Copyright (C) 1991-2013 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, see
<http://www.gnu.org/licenses/>. */
#include <gmp.h>
#include "gmp-impl.h"
/* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
and v (pointed to by VP, with VSIZE limbs), and store the result at
PRODP. USIZE + VSIZE limbs are always stored, but if the input
operands are normalized. Return the most significant limb of the
result.
NOTE: The space pointed to by PRODP is overwritten before finished
with U and V, so overlap is an error.
Argument constraints:
1. USIZE >= VSIZE.
2. 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
mp_limb_t
#if __STDC__
mpn_mul (mp_ptr prodp,
mp_srcptr up, mp_size_t usize,
mp_srcptr vp, mp_size_t vsize)
#else
mpn_mul (prodp, up, usize, vp, vsize)
mp_ptr prodp;
mp_srcptr up;
mp_size_t usize;
mp_srcptr vp;
mp_size_t vsize;
#endif
{
mp_ptr prod_endp = prodp + usize + vsize - 1;
mp_limb_t cy;
mp_ptr tspace;
TMP_DECL (marker);
if (vsize < KARATSUBA_THRESHOLD)
{
/* Handle simple cases with traditional multiplication.
This is the most critical code of the entire function. 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. */
mp_size_t i;
mp_limb_t cy_limb;
mp_limb_t v_limb;
if (vsize == 0)
return 0;
/* 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, usize);
else
MPN_ZERO (prodp, usize);
cy_limb = 0;
}
else
cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
prodp[usize] = 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 < vsize; i++)
{
v_limb = vp[i];
if (v_limb <= 1)
{
cy_limb = 0;
if (v_limb == 1)
cy_limb = mpn_add_n (prodp, prodp, up, usize);
}
else
cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
prodp[usize] = cy_limb;
prodp++;
}
return cy_limb;
}
TMP_MARK (marker);
tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
prodp += vsize;
up += vsize;
usize -= vsize;
if (usize >= vsize)
{
mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
do
{
MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
cy = mpn_add_n (prodp, prodp, tp, vsize);
mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
prodp += vsize;
up += vsize;
usize -= vsize;
}
while (usize >= vsize);
}
/* True: usize < vsize. */
/* Make life simple: Recurse. */
if (usize != 0)
{
mpn_mul (tspace, vp, vsize, up, usize);
cy = mpn_add_n (prodp, prodp, tspace, vsize);
mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
}
TMP_FREE (marker);
return *prod_endp;
}
|
