3 * $Id: mp-arith.c,v 1.4 1999/12/13 15:35:16 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 1.4 1999/12/13 15:35:16 mdw
34 * Slightly different rules on memory allocation.
36 * Revision 1.3 1999/12/11 10:57:43 mdw
37 * Karatsuba squaring algorithm.
39 * Revision 1.2 1999/12/10 23:18:39 mdw
40 * Change interface for suggested destinations.
42 * Revision 1.1 1999/11/17 18:02:16 mdw
43 * New multiprecision integer arithmetic suite.
47 /*----- Header files ------------------------------------------------------*/
51 /*----- Macros ------------------------------------------------------------*/
53 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
55 /*----- Main code ---------------------------------------------------------*/
59 * Arguments: @mp *a@ = source
61 * Returns: Result, @a@ converted to two's complement notation.
64 mp
*mp_2c(mp
*d
, mp
*a
)
69 MP_MODIFY(d
, MP_LEN(a
));
70 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
71 d
->f
= a
->f
& MP_BURN
;
78 * Arguments: @mp *d@ = destination
81 * Returns: Result, @a@ converted to the native signed-magnitude
85 mp
*mp_sm(mp
*d
, mp
*a
)
87 if (!MP_LEN(a
) || a
->vl
[-1] < MPW_MAX
/ 2)
90 MP_MODIFY(d
, MP_LEN(a
));
91 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
92 d
->f
= (a
->f
& (MP_BURN
| MP_NEG
)) ^ MP_NEG
;
99 * Arguments: @mp *d@ = destination
101 * @size_t n@ = number of bits to move
103 * Returns: Result, @a@ shifted left by @n@.
106 mp
*mp_lsl(mp
*d
, mp
*a
, size_t n
)
108 MP_MODIFY(d
, MP_LEN(a
) + (n
+ MPW_BITS
- 1) / MPW_BITS
);
109 mpx_lsl(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
110 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
115 /* --- @mp_lsr@ --- *
117 * Arguments: @mp *d@ = destination
119 * @size_t n@ = number of bits to move
121 * Returns: Result, @a@ shifted left by @n@.
124 mp
*mp_lsr(mp
*d
, mp
*a
, size_t n
)
126 MP_MODIFY(d
, MP_LEN(a
));
127 mpx_lsr(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
128 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
133 /* --- @mp_cmp@ --- *
135 * Arguments: @const mp *a, *b@ = two numbers
137 * Returns: Less than, equal to or greater than zero, according to
138 * whether @a@ is less than, equal to or greater than @b@.
141 int mp_cmp(const mp
*a
, const mp
*b
)
143 if (!((a
->f
^ b
->f
) & MP_NEG
))
144 return (mpx_ucmp(a
->v
, a
->vl
, b
->v
, b
->vl
));
145 else if (a
->f
& MP_NEG
)
151 /* --- @mp_add@ --- *
153 * Arguments: @mp *d@ = destination
154 * @mp *a, *b@ = sources
156 * Returns: Result, @a@ added to @b@.
159 mp
*mp_add(mp
*d
, mp
*a
, mp
*b
)
161 MP_MODIFY(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1);
162 if (!((a
->f
^ b
->f
) & MP_NEG
))
163 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
165 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
166 mp
*t
= a
; a
= b
; b
= t
;
168 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
170 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (a
->f
& MP_NEG
);
175 /* --- @mp_sub@ --- *
177 * Arguments: @mp *d@ = destination
178 * @mp *a, *b@ = sources
180 * Returns: Result, @b@ subtracted from @a@.
183 mp
*mp_sub(mp
*d
, mp
*a
, mp
*b
)
186 MP_MODIFY(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1);
187 if ((a
->f
^ b
->f
) & MP_NEG
)
188 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
190 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
191 mp
*t
= a
; a
= b
; b
= t
;
194 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
196 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ sgn
) & MP_NEG
);
201 /* --- @mp_mul@ --- *
203 * Arguments: @mp *d@ = destination
204 * @mp *a, *b@ = sources
206 * Returns: Result, @a@ multiplied by @b@.
209 mp
*mp_mul(mp
*d
, mp
*a
, mp
*b
)
211 size_t m
= MAX(MP_LEN(a
), MP_LEN(b
)) * 2 + KARATSUBA_SLOP
;
216 if (MP_LEN(a
) <= KARATSUBA_CUTOFF
|| MP_LEN(b
) <= KARATSUBA_CUTOFF
) {
217 MP_MODIFY(d
, MP_LEN(a
) + MP_LEN(b
));
218 mpx_umul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
223 MP_MODIFY(d
, 2 * m
+ 2);
224 mpx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
, s
, s
+ m
);
228 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
235 /* --- @mp_sqr@ --- *
237 * Arguments: @mp *d@ = destination
240 * Returns: Result, @a@ squared.
243 mp
*mp_sqr(mp
*d
, mp
*a
)
245 size_t m
= MP_LEN(a
);
248 MP_MODIFY(d
, 2 * m
+ 2);
249 if (m
> KARATSUBA_CUTOFF
) {
251 m
= 2 * (m
+ 1) + 32;
253 mpx_ksqr(d
->v
, d
->vl
, a
->v
, a
->vl
, s
, s
+ m
);
256 mpx_usqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
257 d
->f
= a
->f
& MP_BURN
;
263 /* --- @mp_div@ --- *
265 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
266 * @mp *a, *b@ = sources
268 * Use: Calculates the quotient and remainder when @a@ is divided by
269 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
270 * Either of @qq@ or @rr@ may be null to indicate that the
271 * result is irrelevant. (Discarding both results is silly.)
272 * There is a performance advantage if @a == *rr@.
274 * The behaviour when @a@ and @b@ have the same sign is
275 * straightforward. When the signs differ, this implementation
276 * chooses @r@ to have the same sign as @b@, rather than the
277 * more normal choice that the remainder has the same sign as
278 * the dividend. This makes modular arithmetic a little more
282 void mp_div(mp
**qq
, mp
**rr
, mp
*a
, mp
*b
)
284 mp
*r
= rr ?
*rr
: MP_NEW
;
285 mp
*q
= qq ?
*qq
: MP_NEW
;
288 /* --- Set up some temporary workspace --- */
291 size_t rq
= MP_LEN(b
) + 1;
296 /* --- Set the remainder up right --- *
298 * Just in case the divisor is larger, be able to cope with this. It's not
299 * important in @mpx_udiv@, but it is here because of the sign correction.
303 size_t rq
= MP_LEN(a
) + 2;
311 MP_ENSURE(r
, MP_LEN(r
) + 2);
314 MP_MODIFY(r
, MP_LEN(a
) + 2);
315 memcpy(r
->v
, a
->v
, MPWS(MP_LEN(a
)));
316 memset(r
->v
+ MP_LEN(a
), 0, MPWS(2));
320 /* --- Fix up the quotient too --- */
322 MP_MODIFY(q
, MP_LEN(a
));
324 /* --- Perform the calculation --- */
326 mpx_udiv(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
, sv
, svl
);
328 /* --- Sort out the sign of the results --- *
330 * If the signs of the arguments differ, and the remainder is nonzero, I
331 * must add one to the absolute value of the quotient and subtract the
332 * remainder from @b@.
335 q
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
338 for (v
= r
->v
; v
< r
->vl
; v
++) {
340 MPX_UADDN(q
->v
, q
->vl
, 1);
341 mpx_usub(r
->v
, r
->vl
, b
->v
, b
->vl
, r
->v
, r
->vl
);
347 r
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (b
->f
& MP_NEG
);
349 /* --- Store the return values --- */
370 /*----- Test rig ----------------------------------------------------------*/
374 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
376 if (MP_CMP(expect
, !=, result
)) {
377 fprintf(stderr
, "\n*** %s failed", op
);
378 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
379 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 10);
380 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 10);
381 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 10);
388 #define RIG(name, op) \
389 static int t##name(dstr *v) \
391 mp *a = *(mp **)v[0].buf; \
392 mpw n = *(int *)v[1].buf; \
394 mp *r = *(mp **)v[2].buf; \
395 mp *c = op(MP_NEW, a, n); \
397 mp_build(&b, &n, &n + 1); \
398 ok = verify(#name, r, c, a, &b); \
399 mp_drop(a); mp_drop(c); mp_drop(r); \
400 assert(mparena_count(MPARENA_GLOBAL) == 0); \
409 #define RIG(name, op) \
410 static int t##name(dstr *v) \
412 mp *a = *(mp **)v[0].buf; \
413 mp *b = *(mp **)v[1].buf; \
414 mp *r = *(mp **)v[2].buf; \
415 mp *c = op(MP_NEW, a, b); \
416 int ok = verify(#name, r, c, a, b); \
417 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
418 assert(mparena_count(MPARENA_GLOBAL) == 0); \
428 static int tdiv(dstr
*v
)
430 mp
*a
= *(mp
**)v
[0].buf
;
431 mp
*b
= *(mp
**)v
[1].buf
;
432 mp
*q
= *(mp
**)v
[2].buf
;
433 mp
*r
= *(mp
**)v
[3].buf
;
434 mp
*c
= MP_NEW
, *d
= MP_NEW
;
436 mp_div(&c
, &d
, a
, b
);
437 ok
&= verify("div(quotient)", q
, c
, a
, b
);
438 ok
&= verify("div(remainder)", r
, d
, a
, b
);
439 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
440 assert(mparena_count(MPARENA_GLOBAL
) == 0);
444 static test_chunk tests
[] = {
445 { "lsl", tlsl
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
446 { "lsr", tlsr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
447 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
448 { "sub", tsub
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
449 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
450 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
454 int main(int argc
, char *argv
[])
457 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
463 /*----- That's all, folks -------------------------------------------------*/