3 * $Id: mp-arith.c,v 1.7 2000/06/22 19:02:53 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 1.7 2000/06/22 19:02:53 mdw
34 * New function @mp_odd@ to extract powers of two from an integer. This is
35 * common code from the Rabin-Miller test, RSA key recovery and modular
36 * square-root extraction.
38 * Revision 1.6 2000/06/17 11:45:09 mdw
39 * Major memory management overhaul. Added arena support. Use the secure
40 * arena for secret integers. Replace and improve the MP management macros
41 * (e.g., replace MP_MODIFY by MP_DEST).
43 * Revision 1.5 1999/12/22 15:54:41 mdw
44 * Adjust Karatsuba parameters. Calculate destination size better.
46 * Revision 1.4 1999/12/13 15:35:16 mdw
47 * Slightly different rules on memory allocation.
49 * Revision 1.3 1999/12/11 10:57:43 mdw
50 * Karatsuba squaring algorithm.
52 * Revision 1.2 1999/12/10 23:18:39 mdw
53 * Change interface for suggested destinations.
55 * Revision 1.1 1999/11/17 18:02:16 mdw
56 * New multiprecision integer arithmetic suite.
60 /*----- Header files ------------------------------------------------------*/
64 /*----- Macros ------------------------------------------------------------*/
66 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
68 /*----- Main code ---------------------------------------------------------*/
72 * Arguments: @mp *a@ = source
74 * Returns: Result, @a@ converted to two's complement notation.
77 mp
*mp_2c(mp
*d
, mp
*a
)
82 MP_DEST(d
, MP_LEN(a
), a
->f
);
83 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
84 d
->f
= a
->f
& MP_BURN
;
91 * Arguments: @mp *d@ = destination
94 * Returns: Result, @a@ converted to the native signed-magnitude
98 mp
*mp_sm(mp
*d
, mp
*a
)
100 if (!MP_LEN(a
) || a
->vl
[-1] < MPW_MAX
/ 2)
103 MP_DEST(d
, MP_LEN(a
), a
->f
);
104 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
105 d
->f
= (a
->f
& (MP_BURN
| MP_NEG
)) ^ MP_NEG
;
110 /* --- @mp_lsl@ --- *
112 * Arguments: @mp *d@ = destination
114 * @size_t n@ = number of bits to move
116 * Returns: Result, @a@ shifted left by @n@.
119 mp
*mp_lsl(mp
*d
, mp
*a
, size_t n
)
121 MP_DEST(d
, MP_LEN(a
) + (n
+ MPW_BITS
- 1) / MPW_BITS
, a
->f
);
122 mpx_lsl(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
123 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
128 /* --- @mp_lsr@ --- *
130 * Arguments: @mp *d@ = destination
132 * @size_t n@ = number of bits to move
134 * Returns: Result, @a@ shifted left by @n@.
137 mp
*mp_lsr(mp
*d
, mp
*a
, size_t n
)
139 MP_DEST(d
, MP_LEN(a
), a
->f
);
140 mpx_lsr(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
141 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
146 /* --- @mp_cmp@ --- *
148 * Arguments: @const mp *a, *b@ = two numbers
150 * Returns: Less than, equal to or greater than zero, according to
151 * whether @a@ is less than, equal to or greater than @b@.
154 int mp_cmp(const mp
*a
, const mp
*b
)
156 if (!((a
->f
^ b
->f
) & MP_NEG
))
157 return (mpx_ucmp(a
->v
, a
->vl
, b
->v
, b
->vl
));
158 else if (a
->f
& MP_NEG
)
164 /* --- @mp_add@ --- *
166 * Arguments: @mp *d@ = destination
167 * @mp *a, *b@ = sources
169 * Returns: Result, @a@ added to @b@.
172 mp
*mp_add(mp
*d
, mp
*a
, mp
*b
)
174 MP_DEST(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1, a
->f
| b
->f
);
175 if (!((a
->f
^ b
->f
) & MP_NEG
))
176 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
178 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
179 mp
*t
= a
; a
= b
; b
= t
;
181 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
183 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (a
->f
& MP_NEG
);
188 /* --- @mp_sub@ --- *
190 * Arguments: @mp *d@ = destination
191 * @mp *a, *b@ = sources
193 * Returns: Result, @b@ subtracted from @a@.
196 mp
*mp_sub(mp
*d
, mp
*a
, mp
*b
)
199 MP_DEST(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1, a
->f
| b
->f
);
200 if ((a
->f
^ b
->f
) & MP_NEG
)
201 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
203 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
204 mp
*t
= a
; a
= b
; b
= t
;
207 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
209 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ sgn
) & MP_NEG
);
214 /* --- @mp_mul@ --- *
216 * Arguments: @mp *d@ = destination
217 * @mp *a, *b@ = sources
219 * Returns: Result, @a@ multiplied by @b@.
222 mp
*mp_mul(mp
*d
, mp
*a
, mp
*b
)
227 if (MP_LEN(a
) <= KARATSUBA_CUTOFF
|| MP_LEN(b
) <= KARATSUBA_CUTOFF
) {
228 MP_DEST(d
, MP_LEN(a
) + MP_LEN(b
), a
->f
| b
->f
| MP_UNDEF
);
229 mpx_umul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
231 size_t m
= 2 * MAX(MP_LEN(a
), MP_LEN(b
)) + 2;
233 MP_DEST(d
, m
, a
->f
| b
->f
| MP_UNDEF
);
235 s
= mpalloc(d
->a
, m
);
236 mpx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
, s
, s
+ m
);
240 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
247 /* --- @mp_sqr@ --- *
249 * Arguments: @mp *d@ = destination
252 * Returns: Result, @a@ squared.
255 mp
*mp_sqr(mp
*d
, mp
*a
)
257 size_t m
= MP_LEN(a
);
260 MP_DEST(d
, 2 * m
+ 2, a
->f
| MP_UNDEF
);
261 if (m
> KARATSUBA_CUTOFF
) {
263 m
= 2 * (m
+ 1) + KARATSUBA_SLOP
;
264 s
= mpalloc(d
->a
, m
);
265 mpx_ksqr(d
->v
, d
->vl
, a
->v
, a
->vl
, s
, s
+ m
);
268 mpx_usqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
269 d
->f
= a
->f
& MP_BURN
;
275 /* --- @mp_div@ --- *
277 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
278 * @mp *a, *b@ = sources
280 * Use: Calculates the quotient and remainder when @a@ is divided by
281 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
282 * Either of @qq@ or @rr@ may be null to indicate that the
283 * result is irrelevant. (Discarding both results is silly.)
284 * There is a performance advantage if @a == *rr@.
286 * The behaviour when @a@ and @b@ have the same sign is
287 * straightforward. When the signs differ, this implementation
288 * chooses @r@ to have the same sign as @b@, rather than the
289 * more normal choice that the remainder has the same sign as
290 * the dividend. This makes modular arithmetic a little more
294 void mp_div(mp
**qq
, mp
**rr
, mp
*a
, mp
*b
)
296 mp
*r
= rr ?
*rr
: MP_NEW
;
297 mp
*q
= qq ?
*qq
: MP_NEW
;
300 /* --- Set the remainder up right --- *
302 * Just in case the divisor is larger, be able to cope with this. It's not
303 * important in @mpx_udiv@, but it is here because of the sign correction.
311 MP_DEST(r
, MP_LEN(a
) + 2, a
->f
| b
->f
);
313 /* --- Fix up the quotient too --- */
316 MP_DEST(q
, MP_LEN(r
), r
->f
| MP_UNDEF
);
319 /* --- Set up some temporary workspace --- */
322 size_t rq
= MP_LEN(b
) + 1;
323 sv
= mpalloc(r
->a
, rq
);
327 /* --- Perform the calculation --- */
329 mpx_udiv(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
, sv
, svl
);
331 /* --- Sort out the sign of the results --- *
333 * If the signs of the arguments differ, and the remainder is nonzero, I
334 * must add one to the absolute value of the quotient and subtract the
335 * remainder from @b@.
338 q
->f
= ((r
->f
| b
->f
) & MP_BURN
) | ((r
->f
^ b
->f
) & MP_NEG
);
341 for (v
= r
->v
; v
< r
->vl
; v
++) {
343 MPX_UADDN(q
->v
, q
->vl
, 1);
344 mpx_usub(r
->v
, r
->vl
, b
->v
, b
->vl
, r
->v
, r
->vl
);
350 r
->f
= ((r
->f
| b
->f
) & MP_BURN
) | (b
->f
& MP_NEG
);
352 /* --- Store the return values --- */
372 /* --- @mp_odd@ --- *
374 * Arguments: @mp *d@ = pointer to destination integer
375 * @mp *m@ = pointer to source integer
376 * @size_t *s@ = where to store the power of 2
378 * Returns: An odd integer integer %$t$% such that %$m = 2^s t$%.
380 * Use: Computes a power of two and an odd integer which, when
381 * multiplied, give a specified result. This sort of thing is
382 * useful in number theory quite often.
385 mp
*mp_odd(mp
*d
, mp
*m
, size_t *s
)
392 for (; !*v
&& v
< vl
; v
++)
399 unsigned z
= MPW_BITS
/ 2;
412 return (mp_lsr(d
, m
, ss
));
415 /*----- Test rig ----------------------------------------------------------*/
419 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
421 if (MP_CMP(expect
, !=, result
)) {
422 fprintf(stderr
, "\n*** %s failed", op
);
423 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
424 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 10);
425 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 10);
426 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 10);
433 #define RIG(name, op) \
434 static int t##name(dstr *v) \
436 mp *a = *(mp **)v[0].buf; \
437 mpw n = *(int *)v[1].buf; \
439 mp *r = *(mp **)v[2].buf; \
440 mp *c = op(MP_NEW, a, n); \
442 mp_build(&b, &n, &n + 1); \
443 ok = verify(#name, r, c, a, &b); \
444 mp_drop(a); mp_drop(c); mp_drop(r); \
445 assert(mparena_count(MPARENA_GLOBAL) == 0); \
454 #define RIG(name, op) \
455 static int t##name(dstr *v) \
457 mp *a = *(mp **)v[0].buf; \
458 mp *b = *(mp **)v[1].buf; \
459 mp *r = *(mp **)v[2].buf; \
460 mp *c = op(MP_NEW, a, b); \
461 int ok = verify(#name, r, c, a, b); \
462 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
463 assert(mparena_count(MPARENA_GLOBAL) == 0); \
473 static int tdiv(dstr
*v
)
475 mp
*a
= *(mp
**)v
[0].buf
;
476 mp
*b
= *(mp
**)v
[1].buf
;
477 mp
*q
= *(mp
**)v
[2].buf
;
478 mp
*r
= *(mp
**)v
[3].buf
;
479 mp
*c
= MP_NEW
, *d
= MP_NEW
;
481 mp_div(&c
, &d
, a
, b
);
482 ok
&= verify("div(quotient)", q
, c
, a
, b
);
483 ok
&= verify("div(remainder)", r
, d
, a
, b
);
484 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
485 assert(mparena_count(MPARENA_GLOBAL
) == 0);
489 static int todd(dstr
*v
)
491 mp
*a
= *(mp
**)v
[0].buf
;
492 size_t rs
= *(uint32
*)v
[1].buf
;
493 mp
*rt
= *(mp
**)v
[2].buf
;
497 t
= mp_odd(MP_NEW
, a
, &s
);
498 if (s
!= rs
|| MP_CMP(t
, !=, rt
)) {
500 fprintf(stderr
, "\n*** odd failed");
501 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
502 fprintf(stderr
, "\n*** s = %lu", (unsigned long)s
);
503 fputs("\n*** t = ", stderr
); mp_writefile(t
, stderr
, 10);
504 fprintf(stderr
, "\n*** rs = %lu", (unsigned long)rs
);
505 fputs("\n*** rt = ", stderr
); mp_writefile(rt
, stderr
, 10);
514 static test_chunk tests
[] = {
515 { "lsl", tlsl
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
516 { "lsr", tlsr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
517 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
518 { "sub", tsub
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
519 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
520 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
521 { "odd", todd
, { &type_mp
, &type_uint32
, &type_mp
, 0 } },
525 int main(int argc
, char *argv
[])
528 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
534 /*----- That's all, folks -------------------------------------------------*/