3 * $Id: mp-arith.c,v 1.6 2000/06/17 11:45:09 mdw Exp $
5 * Basic arithmetic on multiprecision integers
7 * (c) 1999 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 /*----- Revision history --------------------------------------------------*
32 * $Log: mp-arith.c,v $
33 * Revision 1.6 2000/06/17 11:45:09 mdw
34 * Major memory management overhaul. Added arena support. Use the secure
35 * arena for secret integers. Replace and improve the MP management macros
36 * (e.g., replace MP_MODIFY by MP_DEST).
38 * Revision 1.5 1999/12/22 15:54:41 mdw
39 * Adjust Karatsuba parameters. Calculate destination size better.
41 * Revision 1.4 1999/12/13 15:35:16 mdw
42 * Slightly different rules on memory allocation.
44 * Revision 1.3 1999/12/11 10:57:43 mdw
45 * Karatsuba squaring algorithm.
47 * Revision 1.2 1999/12/10 23:18:39 mdw
48 * Change interface for suggested destinations.
50 * Revision 1.1 1999/11/17 18:02:16 mdw
51 * New multiprecision integer arithmetic suite.
55 /*----- Header files ------------------------------------------------------*/
59 /*----- Macros ------------------------------------------------------------*/
61 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
63 /*----- Main code ---------------------------------------------------------*/
67 * Arguments: @mp *a@ = source
69 * Returns: Result, @a@ converted to two's complement notation.
72 mp
*mp_2c(mp
*d
, mp
*a
)
77 MP_DEST(d
, MP_LEN(a
), a
->f
);
78 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
79 d
->f
= a
->f
& MP_BURN
;
86 * Arguments: @mp *d@ = destination
89 * Returns: Result, @a@ converted to the native signed-magnitude
93 mp
*mp_sm(mp
*d
, mp
*a
)
95 if (!MP_LEN(a
) || a
->vl
[-1] < MPW_MAX
/ 2)
98 MP_DEST(d
, MP_LEN(a
), a
->f
);
99 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
100 d
->f
= (a
->f
& (MP_BURN
| MP_NEG
)) ^ MP_NEG
;
105 /* --- @mp_lsl@ --- *
107 * Arguments: @mp *d@ = destination
109 * @size_t n@ = number of bits to move
111 * Returns: Result, @a@ shifted left by @n@.
114 mp
*mp_lsl(mp
*d
, mp
*a
, size_t n
)
116 MP_DEST(d
, MP_LEN(a
) + (n
+ MPW_BITS
- 1) / MPW_BITS
, a
->f
);
117 mpx_lsl(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
118 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
123 /* --- @mp_lsr@ --- *
125 * Arguments: @mp *d@ = destination
127 * @size_t n@ = number of bits to move
129 * Returns: Result, @a@ shifted left by @n@.
132 mp
*mp_lsr(mp
*d
, mp
*a
, size_t n
)
134 MP_DEST(d
, MP_LEN(a
), a
->f
);
135 mpx_lsr(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
136 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
141 /* --- @mp_cmp@ --- *
143 * Arguments: @const mp *a, *b@ = two numbers
145 * Returns: Less than, equal to or greater than zero, according to
146 * whether @a@ is less than, equal to or greater than @b@.
149 int mp_cmp(const mp
*a
, const mp
*b
)
151 if (!((a
->f
^ b
->f
) & MP_NEG
))
152 return (mpx_ucmp(a
->v
, a
->vl
, b
->v
, b
->vl
));
153 else if (a
->f
& MP_NEG
)
159 /* --- @mp_add@ --- *
161 * Arguments: @mp *d@ = destination
162 * @mp *a, *b@ = sources
164 * Returns: Result, @a@ added to @b@.
167 mp
*mp_add(mp
*d
, mp
*a
, mp
*b
)
169 MP_DEST(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1, a
->f
| b
->f
);
170 if (!((a
->f
^ b
->f
) & MP_NEG
))
171 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
173 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
174 mp
*t
= a
; a
= b
; b
= t
;
176 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
178 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (a
->f
& MP_NEG
);
183 /* --- @mp_sub@ --- *
185 * Arguments: @mp *d@ = destination
186 * @mp *a, *b@ = sources
188 * Returns: Result, @b@ subtracted from @a@.
191 mp
*mp_sub(mp
*d
, mp
*a
, mp
*b
)
194 MP_DEST(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1, a
->f
| b
->f
);
195 if ((a
->f
^ b
->f
) & MP_NEG
)
196 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
198 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
199 mp
*t
= a
; a
= b
; b
= t
;
202 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
204 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ sgn
) & MP_NEG
);
209 /* --- @mp_mul@ --- *
211 * Arguments: @mp *d@ = destination
212 * @mp *a, *b@ = sources
214 * Returns: Result, @a@ multiplied by @b@.
217 mp
*mp_mul(mp
*d
, mp
*a
, mp
*b
)
222 if (MP_LEN(a
) <= KARATSUBA_CUTOFF
|| MP_LEN(b
) <= KARATSUBA_CUTOFF
) {
223 MP_DEST(d
, MP_LEN(a
) + MP_LEN(b
), a
->f
| b
->f
| MP_UNDEF
);
224 mpx_umul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
226 size_t m
= 2 * MAX(MP_LEN(a
), MP_LEN(b
)) + 2;
228 MP_DEST(d
, m
, a
->f
| b
->f
| MP_UNDEF
);
230 s
= mpalloc(d
->a
, m
);
231 mpx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
, s
, s
+ m
);
235 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
242 /* --- @mp_sqr@ --- *
244 * Arguments: @mp *d@ = destination
247 * Returns: Result, @a@ squared.
250 mp
*mp_sqr(mp
*d
, mp
*a
)
252 size_t m
= MP_LEN(a
);
255 MP_DEST(d
, 2 * m
+ 2, a
->f
| MP_UNDEF
);
256 if (m
> KARATSUBA_CUTOFF
) {
258 m
= 2 * (m
+ 1) + KARATSUBA_SLOP
;
259 s
= mpalloc(d
->a
, m
);
260 mpx_ksqr(d
->v
, d
->vl
, a
->v
, a
->vl
, s
, s
+ m
);
263 mpx_usqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
264 d
->f
= a
->f
& MP_BURN
;
270 /* --- @mp_div@ --- *
272 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
273 * @mp *a, *b@ = sources
275 * Use: Calculates the quotient and remainder when @a@ is divided by
276 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
277 * Either of @qq@ or @rr@ may be null to indicate that the
278 * result is irrelevant. (Discarding both results is silly.)
279 * There is a performance advantage if @a == *rr@.
281 * The behaviour when @a@ and @b@ have the same sign is
282 * straightforward. When the signs differ, this implementation
283 * chooses @r@ to have the same sign as @b@, rather than the
284 * more normal choice that the remainder has the same sign as
285 * the dividend. This makes modular arithmetic a little more
289 void mp_div(mp
**qq
, mp
**rr
, mp
*a
, mp
*b
)
291 mp
*r
= rr ?
*rr
: MP_NEW
;
292 mp
*q
= qq ?
*qq
: MP_NEW
;
295 /* --- Set the remainder up right --- *
297 * Just in case the divisor is larger, be able to cope with this. It's not
298 * important in @mpx_udiv@, but it is here because of the sign correction.
306 MP_DEST(r
, MP_LEN(a
) + 2, a
->f
| b
->f
);
308 /* --- Fix up the quotient too --- */
311 MP_DEST(q
, MP_LEN(r
), r
->f
| MP_UNDEF
);
314 /* --- Set up some temporary workspace --- */
317 size_t rq
= MP_LEN(b
) + 1;
318 sv
= mpalloc(r
->a
, rq
);
322 /* --- Perform the calculation --- */
324 mpx_udiv(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
, sv
, svl
);
326 /* --- Sort out the sign of the results --- *
328 * If the signs of the arguments differ, and the remainder is nonzero, I
329 * must add one to the absolute value of the quotient and subtract the
330 * remainder from @b@.
333 q
->f
= ((r
->f
| b
->f
) & MP_BURN
) | ((r
->f
^ b
->f
) & MP_NEG
);
336 for (v
= r
->v
; v
< r
->vl
; v
++) {
338 MPX_UADDN(q
->v
, q
->vl
, 1);
339 mpx_usub(r
->v
, r
->vl
, b
->v
, b
->vl
, r
->v
, r
->vl
);
345 r
->f
= ((r
->f
| b
->f
) & MP_BURN
) | (b
->f
& MP_NEG
);
347 /* --- Store the return values --- */
367 /*----- Test rig ----------------------------------------------------------*/
371 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
373 if (MP_CMP(expect
, !=, result
)) {
374 fprintf(stderr
, "\n*** %s failed", op
);
375 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
376 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 10);
377 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 10);
378 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 10);
385 #define RIG(name, op) \
386 static int t##name(dstr *v) \
388 mp *a = *(mp **)v[0].buf; \
389 mpw n = *(int *)v[1].buf; \
391 mp *r = *(mp **)v[2].buf; \
392 mp *c = op(MP_NEW, a, n); \
394 mp_build(&b, &n, &n + 1); \
395 ok = verify(#name, r, c, a, &b); \
396 mp_drop(a); mp_drop(c); mp_drop(r); \
397 assert(mparena_count(MPARENA_GLOBAL) == 0); \
406 #define RIG(name, op) \
407 static int t##name(dstr *v) \
409 mp *a = *(mp **)v[0].buf; \
410 mp *b = *(mp **)v[1].buf; \
411 mp *r = *(mp **)v[2].buf; \
412 mp *c = op(MP_NEW, a, b); \
413 int ok = verify(#name, r, c, a, b); \
414 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
415 assert(mparena_count(MPARENA_GLOBAL) == 0); \
425 static int tdiv(dstr
*v
)
427 mp
*a
= *(mp
**)v
[0].buf
;
428 mp
*b
= *(mp
**)v
[1].buf
;
429 mp
*q
= *(mp
**)v
[2].buf
;
430 mp
*r
= *(mp
**)v
[3].buf
;
431 mp
*c
= MP_NEW
, *d
= MP_NEW
;
433 mp_div(&c
, &d
, a
, b
);
434 ok
&= verify("div(quotient)", q
, c
, a
, b
);
435 ok
&= verify("div(remainder)", r
, d
, a
, b
);
436 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
437 assert(mparena_count(MPARENA_GLOBAL
) == 0);
441 static test_chunk tests
[] = {
442 { "lsl", tlsl
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
443 { "lsr", tlsr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
444 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
445 { "sub", tsub
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
446 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
447 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
451 int main(int argc
, char *argv
[])
454 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
460 /*----- That's all, folks -------------------------------------------------*/