1 /* mpn_mul_n -- Multiply two natural numbers of length n.
2
3 Copyright (C) 1991, 1992, 1993, 1994, 1996 Free Software Foundation, Inc.
4
5 This file is part of the GNU MP Library.
6
7 The GNU MP Library is free software; you can redistribute it and/or modify
8 it under the terms of the GNU Lesser General Public License as published by
9 the Free Software Foundation; either version 2.1 of the License, or (at your
10 option) any later version.
11
12 The GNU MP Library is distributed in the hope that it will be useful, but
13 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
14 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
15 License for more details.
16
17 You should have received a copy of the GNU Lesser General Public License
18 along with the GNU MP Library; see the file COPYING.LIB. If not, write to
19 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
20 MA 02111-1307, USA. */
21
22 #include <config.h>
23 #include "gmp-impl.h"
24
25 /* Multiply the natural numbers u (pointed to by UP) and v (pointed to by VP),
26 both with SIZE limbs, and store the result at PRODP. 2 * SIZE limbs are
27 always stored. Return the most significant limb.
28
29 Argument constraints:
30 1. PRODP != UP and PRODP != VP, i.e. the destination
31 must be distinct from the multiplier and the multiplicand. */
32
33 /* If KARATSUBA_THRESHOLD is not already defined, define it to a
34 value which is good on most machines. */
35 #ifndef KARATSUBA_THRESHOLD
36 #define KARATSUBA_THRESHOLD 32
37 #endif
38
39 /* The code can't handle KARATSUBA_THRESHOLD smaller than 2. */
40 #if KARATSUBA_THRESHOLD < 2
41 #undef KARATSUBA_THRESHOLD
42 #define KARATSUBA_THRESHOLD 2
43 #endif
44
45 /* Handle simple cases with traditional multiplication.
46
47 This is the most critical code of multiplication. All multiplies rely
48 on this, both small and huge. Small ones arrive here immediately. Huge
49 ones arrive here as this is the base case for Karatsuba's recursive
50 algorithm below. */
51
52 void
53 #if __STDC__
54 impn_mul_n_basecase (mp_ptr prodp, mp_srcptr up, mp_srcptr vp, mp_size_t size)
55 #else
56 impn_mul_n_basecase (prodp, up, vp, size)
57 mp_ptr prodp;
58 mp_srcptr up;
59 mp_srcptr vp;
60 mp_size_t size;
61 #endif
62 {
63 mp_size_t i;
64 mp_limb_t cy_limb;
65 mp_limb_t v_limb;
66
67 /* Multiply by the first limb in V separately, as the result can be
68 stored (not added) to PROD. We also avoid a loop for zeroing. */
69 v_limb = vp[0];
70 if (v_limb <= 1)
71 {
72 if (v_limb == 1)
73 MPN_COPY (prodp, up, size);
74 else
75 MPN_ZERO (prodp, size);
76 cy_limb = 0;
77 }
78 else
79 cy_limb = mpn_mul_1 (prodp, up, size, v_limb);
80
81 prodp[size] = cy_limb;
82 prodp++;
83
84 /* For each iteration in the outer loop, multiply one limb from
85 U with one limb from V, and add it to PROD. */
86 for (i = 1; i < size; i++)
87 {
88 v_limb = vp[i];
89 if (v_limb <= 1)
90 {
91 cy_limb = 0;
92 if (v_limb == 1)
93 cy_limb = mpn_add_n (prodp, prodp, up, size);
94 }
95 else
96 cy_limb = mpn_addmul_1 (prodp, up, size, v_limb);
97
98 prodp[size] = cy_limb;
99 prodp++;
100 }
101 }
102
103 void
104 #if __STDC__
105 impn_mul_n (mp_ptr prodp,
106 mp_srcptr up, mp_srcptr vp, mp_size_t size, mp_ptr tspace)
107 #else
108 impn_mul_n (prodp, up, vp, size, tspace)
109 mp_ptr prodp;
110 mp_srcptr up;
111 mp_srcptr vp;
112 mp_size_t size;
113 mp_ptr tspace;
114 #endif
115 {
116 if ((size & 1) != 0)
117 {
118 /* The size is odd, the code code below doesn't handle that.
119 Multiply the least significant (size - 1) limbs with a recursive
120 call, and handle the most significant limb of S1 and S2
121 separately. */
122 /* A slightly faster way to do this would be to make the Karatsuba
123 code below behave as if the size were even, and let it check for
124 odd size in the end. I.e., in essence move this code to the end.
125 Doing so would save us a recursive call, and potentially make the
126 stack grow a lot less. */
127
128 mp_size_t esize = size - 1; /* even size */
129 mp_limb_t cy_limb;
130
131 MPN_MUL_N_RECURSE (prodp, up, vp, esize, tspace);
132 cy_limb = mpn_addmul_1 (prodp + esize, up, esize, vp[esize]);
133 prodp[esize + esize] = cy_limb;
134 cy_limb = mpn_addmul_1 (prodp + esize, vp, size, up[esize]);
135
136 prodp[esize + size] = cy_limb;
137 }
138 else
139 {
140 /* Anatolij Alekseevich Karatsuba's divide-and-conquer algorithm.
141
142 Split U in two pieces, U1 and U0, such that
143 U = U0 + U1*(B**n),
144 and V in V1 and V0, such that
145 V = V0 + V1*(B**n).
146
147 UV is then computed recursively using the identity
148
149 2n n n n
150 UV = (B + B )U V + B (U -U )(V -V ) + (B + 1)U V
151 1 1 1 0 0 1 0 0
152
153 Where B = 2**BITS_PER_MP_LIMB. */
154
155 mp_size_t hsize = size >> 1;
156 mp_limb_t cy;
157 int negflg;
158
159 /*** Product H. ________________ ________________
160 |_____U1 x V1____||____U0 x V0_____| */
161 /* Put result in upper part of PROD and pass low part of TSPACE
162 as new TSPACE. */
163 MPN_MUL_N_RECURSE (prodp + size, up + hsize, vp + hsize, hsize, tspace);
164
165 /*** Product M. ________________
166 |_(U1-U0)(V0-V1)_| */
167 if (mpn_cmp (up + hsize, up, hsize) >= 0)
168 {
169 mpn_sub_n (prodp, up + hsize, up, hsize);
170 negflg = 0;
171 }
172 else
173 {
174 mpn_sub_n (prodp, up, up + hsize, hsize);
175 negflg = 1;
176 }
177 if (mpn_cmp (vp + hsize, vp, hsize) >= 0)
178 {
179 mpn_sub_n (prodp + hsize, vp + hsize, vp, hsize);
180 negflg ^= 1;
181 }
182 else
183 {
184 mpn_sub_n (prodp + hsize, vp, vp + hsize, hsize);
185 /* No change of NEGFLG. */
186 }
187 /* Read temporary operands from low part of PROD.
188 Put result in low part of TSPACE using upper part of TSPACE
189 as new TSPACE. */
190 MPN_MUL_N_RECURSE (tspace, prodp, prodp + hsize, hsize, tspace + size);
191
192 /*** Add/copy product H. */
193 MPN_COPY (prodp + hsize, prodp + size, hsize);
194 cy = mpn_add_n (prodp + size, prodp + size, prodp + size + hsize, hsize);
195
196 /*** Add product M (if NEGFLG M is a negative number). */
197 if (negflg)
198 cy -= mpn_sub_n (prodp + hsize, prodp + hsize, tspace, size);
199 else
200 cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
201
202 /*** Product L. ________________ ________________
203 |________________||____U0 x V0_____| */
204 /* Read temporary operands from low part of PROD.
205 Put result in low part of TSPACE using upper part of TSPACE
206 as new TSPACE. */
207 MPN_MUL_N_RECURSE (tspace, up, vp, hsize, tspace + size);
208
209 /*** Add/copy Product L (twice). */
210
211 cy += mpn_add_n (prodp + hsize, prodp + hsize, tspace, size);
212 if (cy)
213 mpn_add_1 (prodp + hsize + size, prodp + hsize + size, hsize, cy);
214
215 MPN_COPY (prodp, tspace, hsize);
216 cy = mpn_add_n (prodp + hsize, prodp + hsize, tspace + hsize, hsize);
217 if (cy)
218 mpn_add_1 (prodp + size, prodp + size, size, 1);
219 }
220 }