3 * $Id: mp-arith.c,v 1.2 1999/12/10 23:18:39 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 1.2 1999/12/10 23:18:39 mdw
34 * Change interface for suggested destinations.
36 * Revision 1.1 1999/11/17 18:02:16 mdw
37 * New multiprecision integer arithmetic suite.
41 /*----- Header files ------------------------------------------------------*/
45 /*----- Macros ------------------------------------------------------------*/
47 #define MAX(x, y) ((x) >= (y) ? (x) : (y))
49 /*----- Main code ---------------------------------------------------------*/
53 * Arguments: @mp *a@ = source
55 * Returns: Result, @a@ converted to two's complement notation.
58 mp
*mp_2c(mp
*d
, mp
*a
)
63 MP_MODIFY(d
, MP_LEN(a
));
64 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
65 d
->f
= a
->f
& MP_BURN
;
72 * Arguments: @mp *d@ = destination
75 * Returns: Result, @a@ converted to the native signed-magnitude
79 mp
*mp_sm(mp
*d
, mp
*a
)
81 if (!MP_LEN(a
) || a
->vl
[-1] < MPW_MAX
/ 2)
84 MP_MODIFY(d
, MP_LEN(a
));
85 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
86 d
->f
= (a
->f
& (MP_BURN
| MP_NEG
)) ^ MP_NEG
;
93 * Arguments: @mp *d@ = destination
95 * @size_t n@ = number of bits to move
97 * Returns: Result, @a@ shifted left by @n@.
100 mp
*mp_lsl(mp
*d
, mp
*a
, size_t n
)
102 MP_MODIFY(d
, MP_LEN(a
) + (n
+ MPW_BITS
- 1) / MPW_BITS
);
103 mpx_lsl(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
104 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
109 /* --- @mp_lsr@ --- *
111 * Arguments: @mp *d@ = destination
113 * @size_t n@ = number of bits to move
115 * Returns: Result, @a@ shifted left by @n@.
118 mp
*mp_lsr(mp
*d
, mp
*a
, size_t n
)
120 MP_MODIFY(d
, MP_LEN(a
));
121 mpx_lsr(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
122 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
127 /* --- @mp_cmp@ --- *
129 * Arguments: @const mp *a, *b@ = two numbers
131 * Returns: Less than, equal to or greater than zero, according to
132 * whether @a@ is less than, equal to or greater than @b@.
135 int mp_cmp(const mp
*a
, const mp
*b
)
137 if (!((a
->f
^ b
->f
) & MP_NEG
))
138 return (mpx_ucmp(a
->v
, a
->vl
, b
->v
, b
->vl
));
139 else if (a
->f
& MP_NEG
)
145 /* --- @mp_add@ --- *
147 * Arguments: @mp *d@ = destination
148 * @mp *a, *b@ = sources
150 * Returns: Result, @a@ added to @b@.
153 mp
*mp_add(mp
*d
, mp
*a
, mp
*b
)
155 MP_MODIFY(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1);
156 if (!((a
->f
^ b
->f
) & MP_NEG
))
157 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
159 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
160 mp
*t
= a
; a
= b
; b
= t
;
162 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
164 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (a
->f
& MP_NEG
);
169 /* --- @mp_sub@ --- *
171 * Arguments: @mp *d@ = destination
172 * @mp *a, *b@ = sources
174 * Returns: Result, @b@ subtracted from @a@.
177 mp
*mp_sub(mp
*d
, mp
*a
, mp
*b
)
180 MP_MODIFY(d
, MAX(MP_LEN(a
), MP_LEN(b
)) + 1);
181 if ((a
->f
^ b
->f
) & MP_NEG
)
182 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
184 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
185 mp
*t
= a
; a
= b
; b
= t
;
188 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
190 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ sgn
) & MP_NEG
);
195 /* --- @mp_mul@ --- *
197 * Arguments: @mp *d@ = destination
198 * @mp *a, *b@ = sources
200 * Returns: Result, @a@ multiplied by @b@.
203 mp
*mp_mul(mp
*d
, mp
*a
, mp
*b
)
208 MP_MODIFY(d
, MP_LEN(a
) + MP_LEN(b
));
209 if (MP_LEN(a
) <= KARATSUBA_CUTOFF
|| MP_LEN(b
) <= KARATSUBA_CUTOFF
)
210 mpx_umul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
212 size_t m
= MAX(MP_LEN(a
), MP_LEN(b
)) * 2 + KARATSUBA_SLOP
;
216 mpx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
, s
, s
+ m
);
220 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
227 /* --- @mp_sqr@ --- *
229 * Arguments: @mp *d@ = destination
232 * Returns: Result, @a@ squared.
235 mp
*mp_sqr(mp
*d
, mp
*a
)
237 size_t m
= MP_LEN(a
);
241 if (m
> KARATSUBA_CUTOFF
) {
243 m
= 2 * (m
+ 1) + 32;
245 mpx_kmul(d
->v
, d
->vl
, a
->v
, a
->vl
, a
->v
, a
->vl
, s
, s
+ m
);
248 mpx_usqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
249 d
->f
= a
->f
& MP_BURN
;
255 /* --- @mp_div@ --- *
257 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
258 * @mp *a, *b@ = sources
260 * Use: Calculates the quotient and remainder when @a@ is divided by
261 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
262 * Either of @qq@ or @rr@ may be null to indicate that the
263 * result is irrelevant. (Discarding both results is silly.)
264 * There is a performance advantage if @a == *rr@.
266 * The behaviour when @a@ and @b@ have the same sign is
267 * straightforward. When the signs differ, this implementation
268 * chooses @r@ to have the same sign as @b@, rather than the
269 * more normal choice that the remainder has the same sign as
270 * the dividend. This makes modular arithmetic a little more
274 void mp_div(mp
**qq
, mp
**rr
, mp
*a
, mp
*b
)
276 mp
*r
= rr ?
*rr
: MP_NEW
;
277 mp
*q
= qq ?
*qq
: MP_NEW
;
280 /* --- Set up some temporary workspace --- */
283 size_t rq
= MP_LEN(b
) + 1;
288 /* --- Set the remainder up right --- *
290 * Just in case the divisor is larger, be able to cope with this. It's not
291 * important in @mpx_udiv@, but it is here because of the sign correction.
295 size_t rq
= MP_LEN(a
) + 2;
303 MP_ENSURE(r
, MP_LEN(r
) + 2);
306 MP_MODIFY(r
, MP_LEN(a
) + 2);
307 memcpy(r
->v
, a
->v
, MPWS(MP_LEN(a
)));
308 memset(r
->v
+ MP_LEN(a
), 0, MPWS(2));
312 /* --- Fix up the quotient too --- */
314 MP_MODIFY(q
, MP_LEN(a
));
316 /* --- Perform the calculation --- */
318 mpx_udiv(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
, sv
, svl
);
320 /* --- Sort out the sign of the results --- *
322 * If the signs of the arguments differ, and the remainder is nonzero, I
323 * must add one to the absolute value of the quotient and subtract the
324 * remainder from @b@.
327 q
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
330 for (v
= r
->v
; v
< r
->vl
; v
++) {
332 MPX_UADDN(q
->v
, q
->vl
, 1);
333 mpx_usub(r
->v
, r
->vl
, b
->v
, b
->vl
, r
->v
, r
->vl
);
339 r
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (b
->f
& MP_NEG
);
341 /* --- Store the return values --- */
362 /*----- Test rig ----------------------------------------------------------*/
366 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
368 if (MP_CMP(expect
, !=, result
)) {
369 fprintf(stderr
, "\n*** %s failed", op
);
370 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
371 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 10);
372 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 10);
373 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 10);
380 #define RIG(name, op) \
381 static int t##name(dstr *v) \
383 mp *a = *(mp **)v[0].buf; \
384 mpw n = *(int *)v[1].buf; \
386 mp *r = *(mp **)v[2].buf; \
387 mp *c = op(MP_NEW, a, n); \
389 mp_build(&b, &n, &n + 1); \
390 ok = verify(#name, r, c, a, &b); \
391 mp_drop(a); mp_drop(c); mp_drop(r); \
392 assert(mparena_count(MPARENA_GLOBAL) == 0); \
401 #define RIG(name, op) \
402 static int t##name(dstr *v) \
404 mp *a = *(mp **)v[0].buf; \
405 mp *b = *(mp **)v[1].buf; \
406 mp *r = *(mp **)v[2].buf; \
407 mp *c = op(MP_NEW, a, b); \
408 int ok = verify(#name, r, c, a, b); \
409 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
410 assert(mparena_count(MPARENA_GLOBAL) == 0); \
420 static int tdiv(dstr
*v
)
422 mp
*a
= *(mp
**)v
[0].buf
;
423 mp
*b
= *(mp
**)v
[1].buf
;
424 mp
*q
= *(mp
**)v
[2].buf
;
425 mp
*r
= *(mp
**)v
[3].buf
;
426 mp
*c
= MP_NEW
, *d
= MP_NEW
;
428 mp_div(&c
, &d
, a
, b
);
429 ok
&= verify("div(quotient)", q
, c
, a
, b
);
430 ok
&= verify("div(remainder)", r
, d
, a
, b
);
431 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
432 assert(mparena_count(MPARENA_GLOBAL
) == 0);
436 static test_chunk tests
[] = {
437 { "lsl", tlsl
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
438 { "lsr", tlsr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
439 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
440 { "sub", tsub
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
441 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
442 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
446 int main(int argc
, char *argv
[])
449 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
455 /*----- That's all, folks -------------------------------------------------*/