3 * $Id: mp-arith.c,v 1.1 1999/11/17 18:02:16 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 1.1 1999/11/17 18:02:16 mdw
34 * New multiprecision integer arithmetic suite.
38 /*----- Header files ------------------------------------------------------*/
42 /*----- Main code ---------------------------------------------------------*/
46 * Arguments: @mp *a@ = source
48 * Returns: Result, @a@ converted to two's complement notation.
51 mp
*mp_2c(mp
*d
, mp
*a
)
56 MP_MODIFY(d
, MP_LEN(a
));
57 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
58 d
->f
= a
->f
& MP_BURN
;
65 * Arguments: @mp *d@ = destination
68 * Returns: Result, @a@ converted to the native signed-magnitude
72 mp
*mp_sm(mp
*d
, mp
*a
)
74 if (!MP_LEN(a
) || a
->vl
[-1] < MPW_MAX
/ 2)
77 MP_MODIFY(d
, MP_LEN(a
));
78 mpx_2c(d
->v
, d
->vl
, a
->v
, a
->vl
);
79 d
->f
= (a
->f
& (MP_BURN
| MP_NEG
)) ^ MP_NEG
;
86 * Arguments: @mp *d@ = destination
87 * @const mp *a@ = source
88 * @size_t n@ = number of bits to move
90 * Returns: Result, @a@ shifted left by @n@.
93 mp
*mp_lsl(mp
*d
, const mp
*a
, size_t n
)
95 MP_MODIFY(d
, MP_LEN(a
) + (n
+ MPW_BITS
- 1) / MPW_BITS
);
96 mpx_lsl(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
97 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
102 /* --- @mp_lsr@ --- *
104 * Arguments: @mp *d@ = destination
105 * @const mp *a@ = source
106 * @size_t n@ = number of bits to move
108 * Returns: Result, @a@ shifted left by @n@.
111 mp
*mp_lsr(mp
*d
, const mp
*a
, size_t n
)
113 MP_MODIFY(d
, MP_LEN(a
));
114 mpx_lsr(d
->v
, d
->vl
, a
->v
, a
->vl
, n
);
115 d
->f
= a
->f
& (MP_NEG
| MP_BURN
);
120 /* --- @mp_cmp@ --- *
122 * Arguments: @const mp *a, *b@ = two numbers
124 * Returns: Less than, equal to or greater than zero, according to
125 * whether @a@ is less than, equal to or greater than @b@.
128 int mp_cmp(const mp
*a
, const mp
*b
)
130 if (!((a
->f
^ b
->f
) & MP_NEG
))
131 return (mpx_ucmp(a
->v
, a
->vl
, b
->v
, b
->vl
));
132 else if (a
->f
& MP_NEG
)
138 /* --- @mp_add@ --- *
140 * Arguments: @mp *d@ = destination
141 * @const mp *a, *b@ = sources
143 * Returns: Result, @a@ added to @b@.
146 mp
*mp_add(mp
*d
, const mp
*a
, const mp
*b
)
148 MP_MODIFY(d
, (MP_LEN(a
) > MP_LEN(b
) ?
MP_LEN(a
) : MP_LEN(b
)) + 1);
149 if (!((a
->f
^ b
->f
) & MP_NEG
))
150 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
152 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
153 const mp
*t
= a
; a
= b
; b
= t
;
155 mpx_usub(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
157 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (a
->f
& MP_NEG
);
162 /* --- @mp_sub@ --- *
164 * Arguments: @mp *d@ = destination
165 * @const mp *a, *b@ = sources
167 * Returns: Result, @b@ subtracted from @a@.
170 mp
*mp_sub(mp
*d
, const mp
*a
, const mp
*b
)
173 MP_MODIFY(d
, (MP_LEN(a
) > MP_LEN(b
) ?
MP_LEN(a
) : MP_LEN(b
)) + 1);
174 if ((a
->f
^ b
->f
) & MP_NEG
)
175 mpx_uadd(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
177 if (MPX_UCMP(a
->v
, a
->vl
, <, b
->v
, b
->vl
)) {
178 const 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
^ sgn
) & MP_NEG
);
188 /* --- @mp_mul@ --- *
190 * Arguments: @mp *d@ = destination
191 * @const mp *a, *b@ = sources
193 * Returns: Result, @a@ multiplied by @b@.
196 mp
*mp_mul(mp
*d
, const mp
*a
, const mp
*b
)
198 if (d
== a
|| d
== b
)
200 MP_MODIFY(d
, MP_LEN(a
) + MP_LEN(b
));
201 mpx_umul(d
->v
, d
->vl
, a
->v
, a
->vl
, b
->v
, b
->vl
);
202 d
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
207 /* --- @mp_sqr@ --- *
209 * Arguments: @mp *d@ = destination
210 * @const mp *a@ = source
212 * Returns: Result, @a@ squared.
215 mp
*mp_sqr(mp
*d
, const mp
*a
)
219 MP_MODIFY(d
, 2 * MP_LEN(a
));
220 mpx_usqr(d
->v
, d
->vl
, a
->v
, a
->vl
);
221 d
->f
= a
->f
& MP_BURN
;
226 /* --- @mp_div@ --- *
228 * Arguments: @mp **qq, **rr@ = destination, quotient and remainder
229 * @const mp *a, *b@ = sources
231 * Use: Calculates the quotient and remainder when @a@ is divided by
232 * @b@. The destinations @*qq@ and @*rr@ must be distinct.
233 * Either of @qq@ or @rr@ may be null to indicate that the
234 * result is irrelevant. (Discarding both results is silly.)
235 * There is a performance advantage if @a == *rr@.
237 * The behaviour when @a@ and @b@ have the same sign is
238 * straightforward. When the signs differ, this implementation
239 * chooses @r@ to have the same sign as @b@, rather than the
240 * more normal choice that the remainder has the same sign as
241 * the dividend. This makes modular arithmetic a little more
245 void mp_div(mp
**qq
, mp
**rr
, const mp
*a
, const mp
*b
)
247 mp
*r
= rr ?
*rr
: MP_NEW
;
248 mp
*q
= qq ?
*qq
: MP_NEW
;
251 /* --- Set up some temporary workspace --- */
254 size_t rq
= MP_LEN(b
) + 1;
259 /* --- Set the remainder up right --- *
261 * Just in case the divisor is larger, be able to cope with this. It's not
262 * important in @mpx_udiv@, but it is here because of the sign correction.
266 size_t rq
= MP_LEN(a
) + 2;
272 MP_ENSURE(r
, MP_LEN(r
) + 2);
276 MP_MODIFY(r
, MP_LEN(a
) + 2);
277 memcpy(r
->v
, a
->v
, MPWS(MP_LEN(a
)));
278 memset(r
->v
+ MP_LEN(a
), 0, MPWS(2));
282 /* --- Fix up the quotient too --- */
284 if (q
== a
|| q
== b
)
286 MP_MODIFY(q
, MP_LEN(a
));
288 /* --- Perform the calculation --- */
290 mpx_udiv(q
->v
, q
->vl
, r
->v
, r
->vl
, b
->v
, b
->vl
, sv
, svl
);
292 /* --- Sort out the sign of the results --- *
294 * If the signs of the arguments differ, and the remainder is nonzero, I
295 * must add one to the absolute value of the quotient and subtract the
296 * remainder from @b@.
299 q
->f
= ((a
->f
| b
->f
) & MP_BURN
) | ((a
->f
^ b
->f
) & MP_NEG
);
304 MPX_UADDN(q
->v
, q
->vl
, 1);
305 mpx_usub(r
->v
, r
->vl
, b
->v
, b
->vl
, r
->v
, r
->vl
);
311 r
->f
= ((a
->f
| b
->f
) & MP_BURN
) | (b
->f
& MP_NEG
);
313 /* --- Store the return values --- */
332 /*----- Test rig ----------------------------------------------------------*/
336 static int verify(const char *op
, mp
*expect
, mp
*result
, mp
*a
, mp
*b
)
338 if (MP_CMP(expect
, !=, result
)) {
339 fprintf(stderr
, "\n*** %s failed", op
);
340 fputs("\n*** a = ", stderr
); mp_writefile(a
, stderr
, 10);
341 fputs("\n*** b = ", stderr
); mp_writefile(b
, stderr
, 10);
342 fputs("\n*** result = ", stderr
); mp_writefile(result
, stderr
, 10);
343 fputs("\n*** expect = ", stderr
); mp_writefile(expect
, stderr
, 10);
350 #define RIG(name, op) \
351 static int t ## name(dstr *v) \
353 mp *a = *(mp **)v[0].buf; \
354 mpw n = *(int *)v[1].buf; \
356 mp *r = *(mp **)v[2].buf; \
357 mp *c = op(MP_NEW, a, n); \
359 mp_build(&b, &n, &n + 1); \
360 ok = verify(#name, r, c, a, &b); \
361 mp_drop(a); mp_drop(c); mp_drop(r); \
370 #define RIG(name, op) \
371 static int t ## name(dstr *v) \
373 mp *a = *(mp **)v[0].buf; \
374 mp *b = *(mp **)v[1].buf; \
375 mp *r = *(mp **)v[2].buf; \
376 mp *c = op(MP_NEW, a, b); \
377 int ok = verify(#name, r, c, a, b); \
378 mp_drop(a); mp_drop(b); mp_drop(c); mp_drop(r); \
388 static int tdiv(dstr
*v
)
390 mp
*a
= *(mp
**)v
[0].buf
;
391 mp
*b
= *(mp
**)v
[1].buf
;
392 mp
*q
= *(mp
**)v
[2].buf
;
393 mp
*r
= *(mp
**)v
[3].buf
;
394 mp
*c
= MP_NEW
, *d
= MP_NEW
;
396 mp_div(&c
, &d
, a
, b
);
397 ok
&= verify("div(quotient)", q
, c
, a
, b
);
398 ok
&= verify("div(remainder)", r
, d
, a
, b
);
399 mp_drop(a
); mp_drop(b
); mp_drop(c
); mp_drop(d
); mp_drop(r
); mp_drop(q
);
403 static test_chunk tests
[] = {
404 { "lsl", tlsl
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
405 { "lsr", tlsr
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
406 { "add", tadd
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
407 { "sub", tsub
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
408 { "mul", tmul
, { &type_mp
, &type_mp
, &type_mp
, 0 } },
409 { "div", tdiv
, { &type_mp
, &type_mp
, &type_mp
, &type_mp
, 0 } },
413 int main(int argc
, char *argv
[])
416 test_run(argc
, argv
, tests
, SRCDIR
"/tests/mp");
422 /*----- That's all, folks -------------------------------------------------*/