3 * $Id: mpreduce.c,v 1.2 2004/04/08 01:36:15 mdw Exp $
5 * Efficient reduction modulo nice primes
7 * (c) 2004 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Header files ------------------------------------------------------*/
32 #include <mLib/darray.h>
33 #include <mLib/macros.h>
37 #include "mpreduce-exp.h"
39 /*----- Data structures ---------------------------------------------------*/
41 DA_DECL(instr_v
, mpreduce_instr
);
43 /*----- Main code ---------------------------------------------------------*/
45 /* --- @mpreduce_create@ --- *
47 * Arguments: @gfreduce *r@ = structure to fill in
48 * @mp *x@ = an integer
52 * Use: Initializes a context structure for reduction.
55 void mpreduce_create(mpreduce
*r
, mp
*p
)
58 enum { Z
= 0, Z1
= 2, X
= 4, X0
= 6 };
65 /* --- Fill in the easy stuff --- */
75 /* --- Stash a new instruction --- */
77 #define INSTR(op_, argx_, argy_) do { \
79 DA(&iv)[DA_LEN(&iv)].op = (op_); \
80 DA(&iv)[DA_LEN(&iv)].argx = (argx_); \
81 DA(&iv)[DA_LEN(&iv)].argy = (argy_); \
85 /* --- Main loop --- *
87 * A simple state machine decomposes @p@ conveniently into positive and
88 * negative powers of 2. The pure form of the state machine is left below
89 * for reference (and in case I need inspiration for a NAF exponentiator).
93 for (i
= 0, mp_scan(&sc
, p
); mp_step(&sc
); i
++) {
94 switch (st
| mp_bit(&sc
)) {
95 case Z
| 1: st
= Z1
; break;
96 case Z1
| 0: st
= Z
; printf("+ %lu\n", i
- 1); break;
97 case Z1
| 1: st
= X
; printf("- %lu\n", i
- 1); break;
98 case X
| 0: st
= X0
; break;
99 case X0
| 1: st
= X
; printf("- %lu\n", i
- 1); break;
100 case X0
| 0: st
= Z
; printf("+ %lu\n", i
- 1); break;
103 if (st
>= X
) printf("+ %lu\n", i
);
106 for (i
= 0, mp_scan(&sc
, p
); i
< d
- 1 && mp_step(&sc
); i
++) {
107 switch (st
| mp_bit(&sc
)) {
108 case Z
| 1: st
= Z1
; break;
109 case Z1
| 0: st
= Z
; op
= MPRI_SUB
; goto instr
;
110 case Z1
| 1: st
= X
; op
= MPRI_ADD
; goto instr
;
111 case X
| 0: st
= X0
; break;
112 case X0
| 1: st
= X
; op
= MPRI_ADD
; goto instr
;
113 case X0
| 0: st
= Z
; op
= MPRI_SUB
; goto instr
;
115 w
= (d
- i
)/MPW_BITS
+ 1;
116 b
= (MPW_BITS
+ i
- d
- 1)%MPW_BITS
;
117 INSTR(op
| !!b
, w
, b
);
120 if ((DA(&iv
)[DA_LEN(&iv
) - 1].op
& ~1u) == MPRI_SUB
) {
122 "mpreduce can't handle moduli of the form 2^m + x\n");
128 /* --- Wrap up --- */
132 r
->iv
= xmalloc(r
->in
* sizeof(mpreduce_instr
));
133 memcpy(r
->iv
, DA(&iv
), r
->in
* sizeof(mpreduce_instr
));
135 r
->iv
= xmalloc(r
->in
* 2 * sizeof(mpreduce_instr
));
136 for (i
= 0; i
< r
->in
; i
++) {
137 r
->iv
[i
] = DA(&iv
)[i
];
138 op
= r
->iv
[i
].op
& ~1u;
147 r
->iv
[i
+ r
->in
].op
= op
;
148 r
->iv
[i
+ r
->in
].argx
= w
;
149 r
->iv
[i
+ r
->in
].argy
= b
;
155 /* --- @mpreduce_destroy@ --- *
157 * Arguments: @mpreduce *r@ = structure to free
161 * Use: Reclaims the resources from a reduction context.
164 void mpreduce_destroy(mpreduce
*r
)
170 /* --- @mpreduce_dump@ --- *
172 * Arguments: @mpreduce *r@ = structure to dump
173 * @FILE *fp@ = file to dump on
177 * Use: Dumps a reduction context.
180 void mpreduce_dump(mpreduce
*r
, FILE *fp
)
183 static const char *opname
[] = { "add", "addshift", "sub", "subshift" };
185 fprintf(fp
, "mod = "); mp_writefile(r
->p
, fp
, 16);
186 fprintf(fp
, "\n lim = %lu; s = %d\n", (unsigned long)r
->lim
, r
->s
);
187 for (i
= 0; i
< r
->in
; i
++) {
188 assert(r
->iv
[i
].op
< N(opname
));
189 fprintf(fp
, " %s %lu %lu\n",
191 (unsigned long)r
->iv
[i
].argx
,
192 (unsigned long)r
->iv
[i
].argy
);
195 fprintf(fp
, "tail end charlie\n");
196 for (i
= r
->in
; i
< 2 * r
->in
; i
++) {
197 assert(r
->iv
[i
].op
< N(opname
));
198 fprintf(fp
, " %s %lu %lu\n",
200 (unsigned long)r
->iv
[i
].argx
,
201 (unsigned long)r
->iv
[i
].argy
);
206 /* --- @mpreduce_do@ --- *
208 * Arguments: @mpreduce *r@ = reduction context
209 * @mp *d@ = destination
212 * Returns: Destination, @x@ reduced modulo the reduction poly.
215 static void run(const mpreduce_instr
*i
, const mpreduce_instr
*il
,
218 for (; i
< il
; i
++) {
221 mp_build(&vv
, v
- i
->argx
, v
+ 1);
222 printf(" 0x"); mp_writefile(&vv
, stdout
, 16);
223 printf(" %c (0x%lx << %u) == 0x",
224 (i
->op
& ~1u) == MPRI_ADD ?
'+' : '-',
229 case MPRI_ADD
: MPX_UADDN(v
- i
->argx
, v
+ 1, z
); break;
230 case MPRI_ADDLSL
: mpx_uaddnlsl(v
- i
->argx
, v
+ 1, z
, i
->argy
); break;
231 case MPRI_SUB
: MPX_USUBN(v
- i
->argx
, v
+ 1, z
); break;
232 case MPRI_SUBLSL
: mpx_usubnlsl(v
- i
->argx
, v
+ 1, z
, i
->argy
); break;
237 mp_build(&vv
, v
- i
->argx
, v
+ 1);
238 mp_writefile(&vv
, stdout
, 16);
244 mp
*mpreduce_do(mpreduce
*r
, mp
*d
, mp
*x
)
247 const mpreduce_instr
*il
;
251 mp
*_r
= 0, *_rr
= 0;
254 /* --- If source is negative, divide --- */
257 mp_div(0, &d
, x
, r
->p
);
261 /* --- Try to reuse the source's space --- */
265 MP_DEST(x
, MP_LEN(x
), x
->f
);
267 /* --- Do the reduction --- */
271 mp_div(0, &_r
, x
, r
->p
);
277 if (MP_LEN(x
) >= r
->lim
) {
284 run(r
->iv
, il
, vl
, z
);
287 mp_div(0, &_rr
, x
, r
->p
);
288 assert(MP_EQ(_r
, _rr
));
293 while (*vl
>> r
->s
) {
295 *vl
&= ((1 << r
->s
) - 1);
296 run(r
->iv
+ r
->in
, il
+ r
->in
, vl
, z
);
299 mp_div(0, &_rr
, x
, r
->p
);
300 assert(MP_EQ(_r
, _rr
));
306 /* --- Finishing touches --- */
309 if (MP_CMP(x
, >=, r
->p
))
310 x
= mp_sub(x
, x
, r
->p
);
315 assert(MP_EQ(_r
, x
));
322 /* --- @mpreduce_exp@ --- *
324 * Arguments: @mpreduce *mr@ = pointer to reduction context
325 * @mp *d@ = fake destination
329 * Returns: Result, %$a^e \bmod m$%.
332 mp
*mpreduce_exp(mpreduce
*mr
, mp
*d
, mp
*a
, mp
*e
)
335 mp
*spare
= (e
->f
& MP_BURN
) ? MP_NEWSEC
: MP_NEW
;
340 else if (MP_LEN(e
) < EXP_THRESH
)
349 /*----- Test rig ----------------------------------------------------------*/
354 #define MP(x) mp_readstring(MP_NEW, #x, 0, 0)
356 static int vreduce(dstr
*v
)
358 mp
*d
= *(mp
**)v
[0].buf
;
359 mp
*n
= *(mp
**)v
[1].buf
;
360 mp
*r
= *(mp
**)v
[2].buf
;
365 mpreduce_create(&rr
, d
);
366 c
= mpreduce_do(&rr
, MP_NEW
, n
);
368 fprintf(stderr
, "\n*** reduction failed\n*** ");
369 mpreduce_dump(&rr
, stderr
);
370 fprintf(stderr
, "\n*** n = "); mp_writefile(n
, stderr
, 10);
371 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 10);
372 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 10);
373 fprintf(stderr
, "\n");
376 mpreduce_destroy(&rr
);
377 mp_drop(n
); mp_drop(d
); mp_drop(r
); mp_drop(c
);
378 assert(mparena_count(MPARENA_GLOBAL
) == 0);
382 static int vmodexp(dstr
*v
)
384 mp
*p
= *(mp
**)v
[0].buf
;
385 mp
*g
= *(mp
**)v
[1].buf
;
386 mp
*x
= *(mp
**)v
[2].buf
;
387 mp
*r
= *(mp
**)v
[3].buf
;
392 mpreduce_create(&rr
, p
);
393 c
= mpreduce_exp(&rr
, MP_NEW
, g
, x
);
395 fprintf(stderr
, "\n*** modexp failed\n*** ");
396 fprintf(stderr
, "\n*** p = "); mp_writefile(p
, stderr
, 10);
397 fprintf(stderr
, "\n*** g = "); mp_writefile(g
, stderr
, 10);
398 fprintf(stderr
, "\n*** x = "); mp_writefile(x
, stderr
, 10);
399 fprintf(stderr
, "\n*** c = "); mp_writefile(c
, stderr
, 10);
400 fprintf(stderr
, "\n*** r = "); mp_writefile(r
, stderr
, 10);
401 fprintf(stderr
, "\n");
404 mpreduce_destroy(&rr
);
405 mp_drop(p
); mp_drop(g
); mp_drop(r
); mp_drop(x
); mp_drop(c
);
406 assert(mparena_count(MPARENA_GLOBAL
) == 0);
410 static test_chunk defs
[] = {
411 { "reduce", vreduce
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
412 { "modexp", vmodexp
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
416 int main(int argc
, char *argv
[])
418 test_run(argc
, argv
, defs
, SRCDIR
"/tests/mpreduce");
424 /*----- That's all, folks -------------------------------------------------*/