3 * $Id: mpx.c,v 1.2 1999/11/13 01:50:59 mdw Exp $
5 * Low-level multiprecision arithmetic
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 --------------------------------------------------*
33 * Revision 1.2 1999/11/13 01:50:59 mdw
34 * Multiprecision routines finished and tested.
36 * Revision 1.1 1999/09/03 08:41:12 mdw
41 /*----- Header files ------------------------------------------------------*/
48 #include <mLib/bits.h>
53 /*----- Loading and storing -----------------------------------------------*/
55 /* --- @mpx_storel@ --- *
57 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
58 * @void *pp@ = pointer to octet array
59 * @size_t sz@ = size of octet array
63 * Use: Stores an MP in an octet array, least significant octet
64 * first. High-end octets are silently discarded if there
65 * isn't enough space for them.
68 void mpx_storel(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
71 octet
*p
= pp
, *q
= p
+ sz
;
81 *p
++ = U8(w
| n
<< bits
);
93 /* --- @mpx_loadl@ --- *
95 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
96 * @const void *pp@ = pointer to octet array
97 * @size_t sz@ = size of octet array
101 * Use: Loads an MP in an octet array, least significant octet
102 * first. High-end octets are ignored if there isn't enough
106 void mpx_loadl(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
110 const octet
*p
= pp
, *q
= p
+ sz
;
119 if (bits
>= MPW_BITS
) {
121 w
= n
>> (MPW_BITS
- bits
+ 8);
131 /* --- @mpx_storeb@ --- *
133 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
134 * @void *pp@ = pointer to octet array
135 * @size_t sz@ = size of octet array
139 * Use: Stores an MP in an octet array, most significant octet
140 * first. High-end octets are silently discarded if there
141 * isn't enough space for them.
144 void mpx_storeb(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
147 octet
*p
= pp
, *q
= p
+ sz
;
157 *--q
= U8(w
| n
<< bits
);
159 bits
+= MPW_BITS
- 8;
169 /* --- @mpx_loadb@ --- *
171 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
172 * @const void *pp@ = pointer to octet array
173 * @size_t sz@ = size of octet array
177 * Use: Loads an MP in an octet array, most significant octet
178 * first. High-end octets are ignored if there isn't enough
182 void mpx_loadb(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
186 const octet
*p
= pp
, *q
= p
+ sz
;
195 if (bits
>= MPW_BITS
) {
197 w
= n
>> (MPW_BITS
- bits
+ 8);
207 /*----- Logical shifting --------------------------------------------------*/
209 /* --- @mpx_lsl@ --- *
211 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
212 * @const mpw *av, *avl@ = source vector base and limit
213 * @size_t n@ = number of bit positions to shift by
217 * Use: Performs a logical shift left operation on an integer.
220 void mpx_lsl(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
225 /* --- Trivial special case --- */
228 MPX_COPY(dv
, dvl
, av
, avl
);
230 /* --- Single bit shifting --- */
239 *dv
++ = MPW((t
<< 1) | w
);
240 w
= t
>> (MPW_BITS
- 1);
249 /* --- Break out word and bit shifts for more sophisticated work --- */
254 /* --- Handle a shift by a multiple of the word size --- */
257 MPX_COPY(dv
+ nw
, dvl
, av
, avl
);
258 memset(dv
, 0, MPWS(nw
));
261 /* --- And finally the difficult case --- *
263 * This is a little convoluted, because I have to start from the end and
264 * work backwards to avoid overwriting the source, if they're both the same
270 size_t nr
= MPW_BITS
- nb
;
271 size_t dvn
= dvl
- dv
;
272 size_t avn
= avl
- av
;
279 if (dvn
> avn
+ nw
) {
280 size_t off
= avn
+ nw
+ 1;
281 MPX_ZERO(dv
+ off
, dvl
);
291 *--dvl
= (t
>> nr
) | w
;
302 /* --- @mpx_lsr@ --- *
304 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
305 * @const mpw *av, *avl@ = source vector base and limit
306 * @size_t n@ = number of bit positions to shift by
310 * Use: Performs a logical shift right operation on an integer.
313 void mpx_lsr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
318 /* --- Trivial special case --- */
321 MPX_COPY(dv
, dvl
, av
, avl
);
323 /* --- Single bit shifting --- */
332 *dv
++ = MPW((t
<< (MPW_BITS
- 1)) | w
);
342 /* --- Break out word and bit shifts for more sophisticated work --- */
347 /* --- Handle a shift by a multiple of the word size --- */
350 MPX_COPY(dv
, dvl
, av
+ nw
, avl
);
352 /* --- And finally the difficult case --- */
356 size_t nr
= MPW_BITS
- nb
;
365 *dv
++ = MPW((w
>> nb
) | (t
<< nr
));
369 *dv
++ = MPW(w
>> nb
);
377 /*----- Unsigned arithmetic -----------------------------------------------*/
379 /* --- @mpx_ucmp@ --- *
381 * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
382 * @const mpw *bv, *bvl@ = second argument vector base and limit
384 * Returns: Less than, equal to, or greater than zero depending on
385 * whether @a@ is less than, equal to or greater than @b@,
388 * Use: Performs an unsigned integer comparison.
391 int mpx_ucmp(const mpw
*av
, const mpw
*avl
, const mpw
*bv
, const mpw
*bvl
)
396 if (avl
- av
> bvl
- bv
)
398 else if (avl
- av
< bvl
- bv
)
400 else while (avl
> av
) {
401 mpw a
= *--avl
, b
= *--bvl
;
410 /* --- @mpx_uadd@ --- *
412 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
413 * @const mpw *av, *avl@ = first addend vector base and limit
414 * @const mpw *bv, *bvl@ = second addend vector base and limit
418 * Use: Performs unsigned integer addition. If the result overflows
419 * the destination vector, high-order bits are discarded. This
420 * means that two's complement addition happens more or less for
421 * free, although that's more a side-effect than anything else.
422 * The result vector may be equal to either or both source
423 * vectors, but may not otherwise overlap them.
426 void mpx_uadd(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
427 const mpw
*bv
, const mpw
*bvl
)
431 while (av
< avl
|| bv
< bvl
) {
436 a
= (av
< avl
) ?
*av
++ : 0;
437 b
= (bv
< bvl
) ?
*bv
++ : 0;
438 x
= (mpd
)a
+ (mpd
)b
+ c
;
448 /* --- @mpx_usub@ --- *
450 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
451 * @const mpw *av, *avl@ = first argument vector base and limit
452 * @const mpw *bv, *bvl@ = second argument vector base and limit
456 * Use: Performs unsigned integer subtraction. If the result
457 * overflows the destination vector, high-order bits are
458 * discarded. This means that two's complement subtraction
459 * happens more or less for free, althuogh that's more a side-
460 * effect than anything else. The result vector may be equal to
461 * either or both source vectors, but may not otherwise overlap
465 void mpx_usub(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
466 const mpw
*bv
, const mpw
*bvl
)
470 while (av
< avl
|| bv
< bvl
) {
475 a
= (av
< avl
) ?
*av
++ : 0;
476 b
= (bv
< bvl
) ?
*bv
++ : 0;
477 x
= (mpd
)a
- (mpd
)b
- c
;
490 /* --- @mpx_umul@ --- *
492 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
493 * @const mpw *av, *avl@ = multiplicand vector base and limit
494 * @const mpw *bv, *bvl@ = multiplier vector base and limit
498 * Use: Performs unsigned integer multiplication. If the result
499 * overflows the desination vector, high-order bits are
500 * discarded. The result vector may not overlap the argument
501 * vectors in any way.
504 void mpx_umul(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
505 const mpw
*bv
, const mpw
*bvl
)
507 /* --- This is probably worthwhile on a multiply --- */
512 /* --- Deal with a multiply by zero --- */
519 /* --- Do the initial multiply and initialize the accumulator --- */
521 MPX_UMULN(dv
, dvl
, av
, avl
, *bv
++);
523 /* --- Do the remaining multiply/accumulates --- */
525 while (dv
< dvl
&& bv
< bvl
) {
535 x
= (mpd
)*dvv
+ (mpd
)m
* (mpd
)*avv
++ + c
;
539 MPX_UADDN(dvv
, dvl
, c
);
544 /* --- @mpx_usqr@ --- *
546 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
547 * @const mpw *av, *av@ = source vector base and limit
551 * Use: Performs unsigned integer squaring. The result vector must
552 * not overlap the source vector in any way.
555 void mpx_usqr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
)
559 /* --- Main loop --- */
567 /* --- Stop if I've run out of destination --- */
572 /* --- Work out the square at this point in the proceedings --- */
576 mpd x
= (mpd
)a
* (mpd
)a
+ *dvv
;
578 c
= MPW(x
>> MPW_BITS
);
581 /* --- Now fix up the rest of the vector upwards --- */
584 while (dvv
< dvl
&& avv
< avl
) {
586 mpd x
= (mpd
)a
* (mpd
)*avv
++;
587 mpd y
= ((x
<< 1) & MPW_MAX
) + c
+ *dvv
;
588 c
= (x
>> (MPW_BITS
- 1)) + (y
>> MPW_BITS
);
591 while (dvv
< dvl
&& c
) {
597 /* --- Get ready for the next round --- */
604 /* --- @mpx_udiv@ --- *
606 * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
607 * @mpw *rv, *rvl@ = dividend/remainder vector base and limit
608 * @const mpw *dv, *dvl@ = divisor vector base and limit
609 * @mpw *sv, *svl@ = scratch workspace
613 * Use: Performs unsigned integer division. If the result overflows
614 * the quotient vector, high-order bits are discarded. (Clearly
615 * the remainder vector can't overflow.) The various vectors
616 * may not overlap in any way. Yes, I know it's a bit odd
617 * requiring the dividend to be in the result position but it
618 * does make some sense really. The remainder must have
619 * headroom for at least two extra words. The scratch space
620 * must be at least two words larger than twice the size of the
624 void mpx_udiv(mpw
*qv
, mpw
*qvl
, mpw
*rv
, mpw
*rvl
,
625 const mpw
*dv
, const mpw
*dvl
,
632 /* --- Initialize the quotient --- */
636 /* --- Perform some sanity checks --- */
639 assert(((void)"division by zero in mpx_udiv", dv
< dvl
));
641 /* --- Normalize the divisor --- *
643 * The algorithm requires that the divisor be at least two digits long.
644 * This is easy to fix.
651 for (b
= MPW_BITS
/ 2; b
; b
>>= 1) {
652 if (d
< (MPW_MAX
>> b
)) {
661 /* --- Normalize the dividend/remainder to match --- */
664 mpw
*svvl
= sv
+ (dvl
- dv
) + 1;
665 mpx_lsl(rv
, rvl
, rv
, rvl
, norm
);
666 mpx_lsl(sv
, svvl
, dv
, dvl
, norm
);
677 /* --- Work out the relative scales --- */
680 size_t rvn
= rvl
- rv
;
681 size_t dvn
= dvl
- dv
;
683 /* --- If the divisor is clearly larger, notice this --- */
686 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
693 /* --- Calculate the most significant quotient digit --- *
695 * Because the divisor has its top bit set, this can only happen once. The
696 * pointer arithmetic is a little contorted, to make sure that the
697 * behaviour is defined.
700 if (MPX_UCMP(rv
+ scale
, rvl
, >=, dv
, dvl
)) {
701 mpx_usub(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
702 if (qvl
- qv
> scale
)
706 /* --- Now for the main loop --- */
715 /* --- Get an estimate for the next quotient digit --- */
722 rh
= ((mpd
)r
<< MPW_BITS
) | rr
;
728 /* --- Refine the estimate --- */
732 mpd yl
= (mpd
)dd
* q
;
735 yh
+= yl
>> MPW_BITS
;
739 while (yh
> rh
|| (yh
== rh
&& yl
> rrr
)) {
750 /* --- Remove a chunk from the dividend --- */
757 /* --- Calculate the size of the chunk --- */
759 for (svv
= sv
, dvv
= dv
; dvv
< dvl
; svv
++, dvv
++) {
760 mpd x
= (mpd
)*dvv
* (mpd
)q
+ c
;
767 /* --- Now make sure that we can cope with the difference --- *
769 * Take advantage of the fact that subtraction works two's-
773 mpx_usub(rv
+ scale
, rvl
, rv
+ scale
, rvl
, sv
, svv
);
774 if (rvl
[-1] > MPW_MAX
/ 2) {
775 mpx_uadd(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
780 /* --- Done for another iteration --- */
782 if (qvl
- qv
> scale
)
789 /* --- Now fiddle with unnormalizing and things --- */
791 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
794 /*----- That's all, folks -------------------------------------------------*/