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 /*----- Header files ------------------------------------------------------*/
37 #include <mLib/bits.h>
43 /*----- Loading and storing -----------------------------------------------*/
45 /* --- @mpx_storel@ --- *
47 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
48 * @void *pp@ = pointer to octet array
49 * @size_t sz@ = size of octet array
53 * Use: Stores an MP in an octet array, least significant octet
54 * first. High-end octets are silently discarded if there
55 * isn't enough space for them.
58 void mpx_storel(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
61 octet
*p
= pp
, *q
= p
+ sz
;
71 *p
++ = U8(w
| n
<< bits
);
83 /* --- @mpx_loadl@ --- *
85 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
86 * @const void *pp@ = pointer to octet array
87 * @size_t sz@ = size of octet array
91 * Use: Loads an MP in an octet array, least significant octet
92 * first. High-end octets are ignored if there isn't enough
96 void mpx_loadl(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
100 const octet
*p
= pp
, *q
= p
+ sz
;
109 if (bits
>= MPW_BITS
) {
111 w
= n
>> (MPW_BITS
- bits
+ 8);
121 /* --- @mpx_storeb@ --- *
123 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
124 * @void *pp@ = pointer to octet array
125 * @size_t sz@ = size of octet array
129 * Use: Stores an MP in an octet array, most significant octet
130 * first. High-end octets are silently discarded if there
131 * isn't enough space for them.
134 void mpx_storeb(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
137 octet
*p
= pp
, *q
= p
+ sz
;
147 *--q
= U8(w
| n
<< bits
);
149 bits
+= MPW_BITS
- 8;
159 /* --- @mpx_loadb@ --- *
161 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
162 * @const void *pp@ = pointer to octet array
163 * @size_t sz@ = size of octet array
167 * Use: Loads an MP in an octet array, most significant octet
168 * first. High-end octets are ignored if there isn't enough
172 void mpx_loadb(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
176 const octet
*p
= pp
, *q
= p
+ sz
;
185 if (bits
>= MPW_BITS
) {
187 w
= n
>> (MPW_BITS
- bits
+ 8);
197 /* --- @mpx_storel2cn@ --- *
199 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
200 * @void *pp@ = pointer to octet array
201 * @size_t sz@ = size of octet array
205 * Use: Stores a negative MP in an octet array, least significant
206 * octet first, as two's complement. High-end octets are
207 * silently discarded if there isn't enough space for them.
208 * This obviously makes the output bad.
211 void mpx_storel2cn(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
216 octet
*p
= pp
, *q
= p
+ sz
;
228 bits
+= MPW_BITS
- 8;
246 /* --- @mpx_loadl2cn@ --- *
248 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
249 * @const void *pp@ = pointer to octet array
250 * @size_t sz@ = size of octet array
254 * Use: Loads a negative MP in an octet array, least significant
255 * octet first, as two's complement. High-end octets are
256 * ignored if there isn't enough space for them. This probably
257 * means you made the wrong choice coming here.
260 void mpx_loadl2cn(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
265 const octet
*p
= pp
, *q
= p
+ sz
;
275 if (bits
>= MPW_BITS
) {
277 w
= n
>> (MPW_BITS
- bits
+ 8);
287 /* --- @mpx_storeb2cn@ --- *
289 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
290 * @void *pp@ = pointer to octet array
291 * @size_t sz@ = size of octet array
295 * Use: Stores a negative MP in an octet array, most significant
296 * octet first, as two's complement. High-end octets are
297 * silently discarded if there isn't enough space for them,
298 * which probably isn't what you meant.
301 void mpx_storeb2cn(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
306 octet
*p
= pp
, *q
= p
+ sz
;
318 bits
+= MPW_BITS
- 8;
330 c
= c
&& !(b
& 0xff);
336 /* --- @mpx_loadb2cn@ --- *
338 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
339 * @const void *pp@ = pointer to octet array
340 * @size_t sz@ = size of octet array
344 * Use: Loads a negative MP in an octet array, most significant octet
345 * first as two's complement. High-end octets are ignored if
346 * there isn't enough space for them. This probably means you
347 * chose this function wrongly.
350 void mpx_loadb2cn(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
355 const octet
*p
= pp
, *q
= p
+ sz
;
365 if (bits
>= MPW_BITS
) {
367 w
= n
>> (MPW_BITS
- bits
+ 8);
377 /*----- Logical shifting --------------------------------------------------*/
379 /* --- @mpx_lsl@ --- *
381 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
382 * @const mpw *av, *avl@ = source vector base and limit
383 * @size_t n@ = number of bit positions to shift by
387 * Use: Performs a logical shift left operation on an integer.
390 void mpx_lsl(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
395 /* --- Trivial special case --- */
398 MPX_COPY(dv
, dvl
, av
, avl
);
400 /* --- Single bit shifting --- */
409 *dv
++ = MPW((t
<< 1) | w
);
410 w
= t
>> (MPW_BITS
- 1);
419 /* --- Break out word and bit shifts for more sophisticated work --- */
424 /* --- Handle a shift by a multiple of the word size --- */
430 MPX_COPY(dv
+ nw
, dvl
, av
, avl
);
431 memset(dv
, 0, MPWS(nw
));
435 /* --- And finally the difficult case --- *
437 * This is a little convoluted, because I have to start from the end and
438 * work backwards to avoid overwriting the source, if they're both the same
444 size_t nr
= MPW_BITS
- nb
;
445 size_t dvn
= dvl
- dv
;
446 size_t avn
= avl
- av
;
453 if (dvn
> avn
+ nw
) {
454 size_t off
= avn
+ nw
+ 1;
455 MPX_ZERO(dv
+ off
, dvl
);
465 *--dvl
= (t
>> nr
) | w
;
476 /* --- @mpx_lslc@ --- *
478 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
479 * @const mpw *av, *avl@ = source vector base and limit
480 * @size_t n@ = number of bit positions to shift by
484 * Use: Performs a logical shift left operation on an integer, only
485 * it fills in the bits with ones instead of zeroes.
488 void mpx_lslc(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
493 /* --- Trivial special case --- */
496 MPX_COPY(dv
, dvl
, av
, avl
);
498 /* --- Single bit shifting --- */
507 *dv
++ = MPW((t
<< 1) | w
);
508 w
= t
>> (MPW_BITS
- 1);
517 /* --- Break out word and bit shifts for more sophisticated work --- */
522 /* --- Handle a shift by a multiple of the word size --- */
528 MPX_COPY(dv
+ nw
, dvl
, av
, avl
);
529 MPX_ONE(dv
, dv
+ nw
);
533 /* --- And finally the difficult case --- *
535 * This is a little convoluted, because I have to start from the end and
536 * work backwards to avoid overwriting the source, if they're both the same
542 size_t nr
= MPW_BITS
- nb
;
543 size_t dvn
= dvl
- dv
;
544 size_t avn
= avl
- av
;
551 if (dvn
> avn
+ nw
) {
552 size_t off
= avn
+ nw
+ 1;
553 MPX_ZERO(dv
+ off
, dvl
);
563 *--dvl
= (t
>> nr
) | w
;
567 *--dvl
= (MPW_MAX
>> nr
) | w
;
574 /* --- @mpx_lsr@ --- *
576 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
577 * @const mpw *av, *avl@ = source vector base and limit
578 * @size_t n@ = number of bit positions to shift by
582 * Use: Performs a logical shift right operation on an integer.
585 void mpx_lsr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
590 /* --- Trivial special case --- */
593 MPX_COPY(dv
, dvl
, av
, avl
);
595 /* --- Single bit shifting --- */
598 mpw w
= av
< avl ?
*av
++ >> 1 : 0;
604 *dv
++ = MPW((t
<< (MPW_BITS
- 1)) | w
);
614 /* --- Break out word and bit shifts for more sophisticated work --- */
619 /* --- Handle a shift by a multiple of the word size --- */
625 MPX_COPY(dv
, dvl
, av
+ nw
, avl
);
628 /* --- And finally the difficult case --- */
632 size_t nr
= MPW_BITS
- nb
;
635 w
= av
< avl ?
*av
++ : 0;
641 *dv
++ = MPW((w
>> nb
) | (t
<< nr
));
645 *dv
++ = MPW(w
>> nb
);
653 /*----- Bitwise operations ------------------------------------------------*/
655 /* --- @mpx_bitop@ --- *
657 * Arguments: @mpw *dv, *dvl@ = destination vector
658 * @const mpw *av, *avl@ = first source vector
659 * @const mpw *bv, *bvl@ = second source vector
663 * Use; Provides the dyadic boolean functions.
666 #define MPX_BITBINOP(string) \
668 void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \
669 const mpw *bv, const mpw *bvl) \
671 MPX_SHRINK(av, avl); \
672 MPX_SHRINK(bv, bvl); \
676 a = (av < avl) ? *av++ : 0; \
677 b = (bv < bvl) ? *bv++ : 0; \
678 *dv++ = B##string(a, b); \
682 MPX_DOBIN(MPX_BITBINOP
)
684 void mpx_not(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
)
690 a
= (av
< avl
) ?
*av
++ : 0;
695 /*----- Unsigned arithmetic -----------------------------------------------*/
697 /* --- @mpx_2c@ --- *
699 * Arguments: @mpw *dv, *dvl@ = destination vector
700 * @const mpw *v, *vl@ = source vector
704 * Use: Calculates the two's complement of @v@.
707 void mpx_2c(mpw
*dv
, mpw
*dvl
, const mpw
*v
, const mpw
*vl
)
710 while (dv
< dvl
&& v
< vl
)
711 *dv
++ = c
= MPW(~*v
++);
718 MPX_UADDN(dv
, dvl
, 1);
721 /* --- @mpx_ueq@ --- *
723 * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
724 * @const mpw *bv, *bvl@ = second argument vector base and limit
726 * Returns: Nonzero if the two vectors are equal.
728 * Use: Performs an unsigned integer test for equality.
731 int mpx_ueq(const mpw
*av
, const mpw
*avl
, const mpw
*bv
, const mpw
*bvl
)
735 if (avl
- av
!= bvl
- bv
)
744 /* --- @mpx_ucmp@ --- *
746 * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
747 * @const mpw *bv, *bvl@ = second argument vector base and limit
749 * Returns: Less than, equal to, or greater than zero depending on
750 * whether @a@ is less than, equal to or greater than @b@,
753 * Use: Performs an unsigned integer comparison.
756 int mpx_ucmp(const mpw
*av
, const mpw
*avl
, const mpw
*bv
, const mpw
*bvl
)
761 if (avl
- av
> bvl
- bv
)
763 else if (avl
- av
< bvl
- bv
)
765 else while (avl
> av
) {
766 mpw a
= *--avl
, b
= *--bvl
;
775 /* --- @mpx_uadd@ --- *
777 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
778 * @const mpw *av, *avl@ = first addend vector base and limit
779 * @const mpw *bv, *bvl@ = second addend vector base and limit
783 * Use: Performs unsigned integer addition. If the result overflows
784 * the destination vector, high-order bits are discarded. This
785 * means that two's complement addition happens more or less for
786 * free, although that's more a side-effect than anything else.
787 * The result vector may be equal to either or both source
788 * vectors, but may not otherwise overlap them.
791 void mpx_uadd(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
792 const mpw
*bv
, const mpw
*bvl
)
796 while (av
< avl
|| bv
< bvl
) {
801 a
= (av
< avl
) ?
*av
++ : 0;
802 b
= (bv
< bvl
) ?
*bv
++ : 0;
803 x
= (mpd
)a
+ (mpd
)b
+ c
;
813 /* --- @mpx_uaddn@ --- *
815 * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
816 * @mpw n@ = other addend
820 * Use: Adds a small integer to a multiprecision number.
823 void mpx_uaddn(mpw
*dv
, mpw
*dvl
, mpw n
) { MPX_UADDN(dv
, dvl
, n
); }
825 /* --- @mpx_uaddnlsl@ --- *
827 * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
828 * @mpw a@ = second argument
829 * @unsigned o@ = offset in bits
833 * Use: Computes %$d + 2^o a$%. If the result overflows then
834 * high-order bits are discarded, as usual. We must have
835 * @0 < o < MPW_BITS@.
838 void mpx_uaddnlsl(mpw
*dv
, mpw
*dvl
, mpw a
, unsigned o
)
842 while (x
&& dv
< dvl
) {
849 /* --- @mpx_usub@ --- *
851 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
852 * @const mpw *av, *avl@ = first argument vector base and limit
853 * @const mpw *bv, *bvl@ = second argument vector base and limit
857 * Use: Performs unsigned integer subtraction. If the result
858 * overflows the destination vector, high-order bits are
859 * discarded. This means that two's complement subtraction
860 * happens more or less for free, althuogh that's more a side-
861 * effect than anything else. The result vector may be equal to
862 * either or both source vectors, but may not otherwise overlap
866 void mpx_usub(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
867 const mpw
*bv
, const mpw
*bvl
)
871 while (av
< avl
|| bv
< bvl
) {
876 a
= (av
< avl
) ?
*av
++ : 0;
877 b
= (bv
< bvl
) ?
*bv
++ : 0;
878 x
= (mpd
)a
- (mpd
)b
- c
;
891 /* --- @mpx_usubn@ --- *
893 * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
898 * Use: Subtracts a small integer from a multiprecision number.
901 void mpx_usubn(mpw
*dv
, mpw
*dvl
, mpw n
) { MPX_USUBN(dv
, dvl
, n
); }
903 /* --- @mpx_uaddnlsl@ --- *
905 * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
906 * @mpw a@ = second argument
907 * @unsigned o@ = offset in bits
911 * Use: Computes %$d + 2^o a$%. If the result overflows then
912 * high-order bits are discarded, as usual. We must have
913 * @0 < o < MPW_BITS@.
916 void mpx_usubnlsl(mpw
*dv
, mpw
*dvl
, mpw a
, unsigned o
)
918 mpw b
= a
>> (MPW_BITS
- o
);
922 mpd x
= (mpd
)*dv
- (mpd
)a
;
926 MPX_USUBN(dv
, dvl
, b
);
930 /* --- @mpx_umul@ --- *
932 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
933 * @const mpw *av, *avl@ = multiplicand vector base and limit
934 * @const mpw *bv, *bvl@ = multiplier vector base and limit
938 * Use: Performs unsigned integer multiplication. If the result
939 * overflows the desination vector, high-order bits are
940 * discarded. The result vector may not overlap the argument
941 * vectors in any way.
944 void mpx_umul(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
945 const mpw
*bv
, const mpw
*bvl
)
947 /* --- This is probably worthwhile on a multiply --- */
952 /* --- Deal with a multiply by zero --- */
959 /* --- Do the initial multiply and initialize the accumulator --- */
961 MPX_UMULN(dv
, dvl
, av
, avl
, *bv
++);
963 /* --- Do the remaining multiply/accumulates --- */
965 while (dv
< dvl
&& bv
< bvl
) {
975 x
= (mpd
)*dvv
+ (mpd
)m
* (mpd
)*avv
++ + c
;
979 MPX_UADDN(dvv
, dvl
, c
);
984 /* --- @mpx_umuln@ --- *
986 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
987 * @const mpw *av, *avl@ = multiplicand vector base and limit
988 * @mpw m@ = multiplier
992 * Use: Multiplies a multiprecision integer by a single-word value.
993 * The destination and source may be equal. The destination
994 * is completely cleared after use.
997 void mpx_umuln(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, mpw m
)
999 MPX_UMULN(dv
, dvl
, av
, avl
, m
);
1002 /* --- @mpx_umlan@ --- *
1004 * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit
1005 * @const mpw *av, *avl@ = multiplicand vector base and limit
1006 * @mpw m@ = multiplier
1010 * Use: Multiplies a multiprecision integer by a single-word value
1011 * and adds the result to an accumulator.
1014 void mpx_umlan(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, mpw m
)
1016 MPX_UMLAN(dv
, dvl
, av
, avl
, m
);
1019 /* --- @mpx_usqr@ --- *
1021 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
1022 * @const mpw *av, *av@ = source vector base and limit
1026 * Use: Performs unsigned integer squaring. The result vector must
1027 * not overlap the source vector in any way.
1030 void mpx_usqr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
)
1034 /* --- Main loop --- */
1037 const mpw
*avv
= av
;
1042 /* --- Stop if I've run out of destination --- */
1047 /* --- Work out the square at this point in the proceedings --- */
1050 mpd x
= (mpd
)a
* (mpd
)a
+ *dvv
;
1052 c
= MPW(x
>> MPW_BITS
);
1055 /* --- Now fix up the rest of the vector upwards --- */
1058 while (dvv
< dvl
&& avv
< avl
) {
1059 mpd x
= (mpd
)a
* (mpd
)*avv
++;
1060 mpd y
= ((x
<< 1) & MPW_MAX
) + c
+ *dvv
;
1061 c
= (x
>> (MPW_BITS
- 1)) + (y
>> MPW_BITS
);
1064 while (dvv
< dvl
&& c
) {
1070 /* --- Get ready for the next round --- */
1077 /* --- @mpx_udiv@ --- *
1079 * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
1080 * @mpw *rv, *rvl@ = dividend/remainder vector base and limit
1081 * @const mpw *dv, *dvl@ = divisor vector base and limit
1082 * @mpw *sv, *svl@ = scratch workspace
1086 * Use: Performs unsigned integer division. If the result overflows
1087 * the quotient vector, high-order bits are discarded. (Clearly
1088 * the remainder vector can't overflow.) The various vectors
1089 * may not overlap in any way. Yes, I know it's a bit odd
1090 * requiring the dividend to be in the result position but it
1091 * does make some sense really. The remainder must have
1092 * headroom for at least two extra words. The scratch space
1093 * must be at least one word larger than the divisor.
1096 void mpx_udiv(mpw
*qv
, mpw
*qvl
, mpw
*rv
, mpw
*rvl
,
1097 const mpw
*dv
, const mpw
*dvl
,
1104 /* --- Initialize the quotient --- */
1108 /* --- Perform some sanity checks --- */
1110 MPX_SHRINK(dv
, dvl
);
1111 assert(((void)"division by zero in mpx_udiv", dv
< dvl
));
1113 /* --- Normalize the divisor --- *
1115 * The algorithm requires that the divisor be at least two digits long.
1116 * This is easy to fix.
1123 for (b
= MPW_BITS
/ 2; b
; b
>>= 1) {
1124 if (d
<= (MPW_MAX
>> b
)) {
1133 /* --- Normalize the dividend/remainder to match --- */
1136 mpx_lsl(rv
, rvl
, rv
, rvl
, norm
);
1137 mpx_lsl(sv
, svl
, dv
, dvl
, norm
);
1140 MPX_SHRINK(dv
, dvl
);
1143 MPX_SHRINK(rv
, rvl
);
1147 /* --- Work out the relative scales --- */
1150 size_t rvn
= rvl
- rv
;
1151 size_t dvn
= dvl
- dv
;
1153 /* --- If the divisor is clearly larger, notice this --- */
1156 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
1163 /* --- Calculate the most significant quotient digit --- *
1165 * Because the divisor has its top bit set, this can only happen once. The
1166 * pointer arithmetic is a little contorted, to make sure that the
1167 * behaviour is defined.
1170 if (MPX_UCMP(rv
+ scale
, rvl
, >=, dv
, dvl
)) {
1171 mpx_usub(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
1172 if (qvl
- qv
> scale
)
1176 /* --- Now for the main loop --- */
1185 /* --- Get an estimate for the next quotient digit --- */
1192 rh
= ((mpd
)r
<< MPW_BITS
) | rr
;
1198 /* --- Refine the estimate --- */
1201 mpd yh
= (mpd
)d
* q
;
1202 mpd yy
= (mpd
)dd
* q
;
1206 yh
+= yy
>> MPW_BITS
;
1209 while (yh
> rh
|| (yh
== rh
&& yl
> rrr
)) {
1218 /* --- Remove a chunk from the dividend --- */
1225 /* --- Calculate the size of the chunk --- *
1227 * This does the whole job of calculating @r >> scale - qd@.
1230 for (svv
= rv
+ scale
, dvv
= dv
;
1231 dvv
< dvl
&& svv
< rvl
;
1233 mpd x
= (mpd
)*dvv
* (mpd
)q
+ mc
;
1235 x
= (mpd
)*svv
- MPW(x
) - sc
;
1244 mpd x
= (mpd
)*svv
- mc
- sc
;
1254 /* --- Fix if the quotient was too large --- *
1256 * This doesn't seem to happen very often.
1259 if (rvl
[-1] > MPW_MAX
/ 2) {
1260 mpx_uadd(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
1265 /* --- Done for another iteration --- */
1267 if (qvl
- qv
> scale
)
1274 /* --- Now fiddle with unnormalizing and things --- */
1276 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
1279 /* --- @mpx_udivn@ --- *
1281 * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap
1283 * @const mpw *rv, *rvl@ = dividend
1284 * @mpw d@ = single-precision divisor
1286 * Returns: Remainder after divison.
1288 * Use: Performs a single-precision division operation.
1291 mpw
mpx_udivn(mpw
*qv
, mpw
*qvl
, const mpw
*rv
, const mpw
*rvl
, mpw d
)
1294 size_t ql
= qvl
- qv
;
1300 r
= (r
<< MPW_BITS
) | rv
[i
];
1308 /*----- Test rig ----------------------------------------------------------*/
1312 #include <mLib/alloc.h>
1313 #include <mLib/dstr.h>
1314 #include <mLib/quis.h>
1315 #include <mLib/testrig.h>
1319 #define ALLOC(v, vl, sz) do { \
1320 size_t _sz = (sz); \
1321 mpw *_vv = xmalloc(MPWS(_sz)); \
1322 mpw *_vvl = _vv + _sz; \
1327 #define LOAD(v, vl, d) do { \
1328 const dstr *_d = (d); \
1330 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
1331 mpx_loadb(_v, _vl, _d->buf, _d->len); \
1336 #define MAX(x, y) ((x) > (y) ? (x) : (y))
1338 static void dumpbits(const char *msg
, const void *pp
, size_t sz
)
1340 const octet
*p
= pp
;
1343 fprintf(stderr
, " %02x", *p
++);
1344 fputc('\n', stderr
);
1347 static void dumpmp(const char *msg
, const mpw
*v
, const mpw
*vl
)
1352 fprintf(stderr
, " %08lx", (unsigned long)*--vl
);
1353 fputc('\n', stderr
);
1356 static int chkscan(const mpw
*v
, const mpw
*vl
,
1357 const void *pp
, size_t sz
, int step
)
1360 const octet
*p
= pp
;
1364 mpscan_initx(&mps
, v
, vl
);
1369 for (i
= 0; i
< 8 && MPSCAN_STEP(&mps
); i
++) {
1370 if (MPSCAN_BIT(&mps
) != (x
& 1)) {
1372 "\n*** error, step %i, bit %u, expected %u, found %u\n",
1373 step
, bit
, x
& 1, MPSCAN_BIT(&mps
));
1385 static int loadstore(dstr
*v
)
1388 size_t sz
= MPW_RQ(v
->len
) * 2, diff
;
1392 dstr_ensure(&d
, v
->len
);
1393 m
= xmalloc(MPWS(sz
));
1395 for (diff
= 0; diff
< sz
; diff
+= 5) {
1400 mpx_loadl(m
, ml
, v
->buf
, v
->len
);
1401 if (!chkscan(m
, ml
, v
->buf
, v
->len
, +1))
1403 MPX_OCTETS(oct
, m
, ml
);
1404 mpx_storel(m
, ml
, d
.buf
, d
.sz
);
1405 if (memcmp(d
.buf
, v
->buf
, oct
) != 0) {
1406 dumpbits("\n*** storel failed", d
.buf
, d
.sz
);
1410 mpx_loadb(m
, ml
, v
->buf
, v
->len
);
1411 if (!chkscan(m
, ml
, v
->buf
+ v
->len
- 1, v
->len
, -1))
1413 MPX_OCTETS(oct
, m
, ml
);
1414 mpx_storeb(m
, ml
, d
.buf
, d
.sz
);
1415 if (memcmp(d
.buf
+ d
.sz
- oct
, v
->buf
+ v
->len
- oct
, oct
) != 0) {
1416 dumpbits("\n*** storeb failed", d
.buf
, d
.sz
);
1422 dumpbits("input data", v
->buf
, v
->len
);
1429 static int twocl(dstr
*v
)
1436 sz
= v
[0].len
; if (v
[1].len
> sz
) sz
= v
[1].len
;
1437 dstr_ensure(&d
, sz
);
1440 m
= xmalloc(MPWS(sz
));
1443 mpx_loadl(m
, ml
, v
[0].buf
, v
[0].len
);
1444 mpx_storel2cn(m
, ml
, d
.buf
, v
[1].len
);
1445 if (memcmp(d
.buf
, v
[1].buf
, v
[1].len
)) {
1446 dumpbits("\n*** storel2cn failed", d
.buf
, v
[1].len
);
1450 mpx_loadl2cn(m
, ml
, v
[1].buf
, v
[1].len
);
1451 mpx_storel(m
, ml
, d
.buf
, v
[0].len
);
1452 if (memcmp(d
.buf
, v
[0].buf
, v
[0].len
)) {
1453 dumpbits("\n*** loadl2cn failed", d
.buf
, v
[0].len
);
1458 dumpbits("pos", v
[0].buf
, v
[0].len
);
1459 dumpbits("neg", v
[1].buf
, v
[1].len
);
1468 static int twocb(dstr
*v
)
1475 sz
= v
[0].len
; if (v
[1].len
> sz
) sz
= v
[1].len
;
1476 dstr_ensure(&d
, sz
);
1479 m
= xmalloc(MPWS(sz
));
1482 mpx_loadb(m
, ml
, v
[0].buf
, v
[0].len
);
1483 mpx_storeb2cn(m
, ml
, d
.buf
, v
[1].len
);
1484 if (memcmp(d
.buf
, v
[1].buf
, v
[1].len
)) {
1485 dumpbits("\n*** storeb2cn failed", d
.buf
, v
[1].len
);
1489 mpx_loadb2cn(m
, ml
, v
[1].buf
, v
[1].len
);
1490 mpx_storeb(m
, ml
, d
.buf
, v
[0].len
);
1491 if (memcmp(d
.buf
, v
[0].buf
, v
[0].len
)) {
1492 dumpbits("\n*** loadb2cn failed", d
.buf
, v
[0].len
);
1497 dumpbits("pos", v
[0].buf
, v
[0].len
);
1498 dumpbits("neg", v
[1].buf
, v
[1].len
);
1507 static int lsl(dstr
*v
)
1510 int n
= *(int *)v
[1].buf
;
1517 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
);
1519 mpx_lsl(d
, dl
, a
, al
, n
);
1520 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1521 fprintf(stderr
, "\n*** lsl(%i) failed\n", n
);
1522 dumpmp(" a", a
, al
);
1523 dumpmp("expected", c
, cl
);
1524 dumpmp(" result", d
, dl
);
1528 xfree(a
); xfree(c
); xfree(d
);
1532 static int lslc(dstr
*v
)
1535 int n
= *(int *)v
[1].buf
;
1542 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
);
1544 mpx_lslc(d
, dl
, a
, al
, n
);
1545 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1546 fprintf(stderr
, "\n*** lslc(%i) failed\n", n
);
1547 dumpmp(" a", a
, al
);
1548 dumpmp("expected", c
, cl
);
1549 dumpmp(" result", d
, dl
);
1553 xfree(a
); xfree(c
); xfree(d
);
1557 static int lsr(dstr
*v
)
1560 int n
= *(int *)v
[1].buf
;
1567 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
+ 1);
1569 mpx_lsr(d
, dl
, a
, al
, n
);
1570 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1571 fprintf(stderr
, "\n*** lsr(%i) failed\n", n
);
1572 dumpmp(" a", a
, al
);
1573 dumpmp("expected", c
, cl
);
1574 dumpmp(" result", d
, dl
);
1578 xfree(a
); xfree(c
); xfree(d
);
1582 static int uadd(dstr
*v
)
1593 ALLOC(d
, dl
, MAX(al
- a
, bl
- b
) + 1);
1595 mpx_uadd(d
, dl
, a
, al
, b
, bl
);
1596 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1597 fprintf(stderr
, "\n*** uadd failed\n");
1598 dumpmp(" a", a
, al
);
1599 dumpmp(" b", b
, bl
);
1600 dumpmp("expected", c
, cl
);
1601 dumpmp(" result", d
, dl
);
1605 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1609 static int usub(dstr
*v
)
1620 ALLOC(d
, dl
, al
- a
);
1622 mpx_usub(d
, dl
, a
, al
, b
, bl
);
1623 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1624 fprintf(stderr
, "\n*** usub failed\n");
1625 dumpmp(" a", a
, al
);
1626 dumpmp(" b", b
, bl
);
1627 dumpmp("expected", c
, cl
);
1628 dumpmp(" result", d
, dl
);
1632 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1636 static int umul(dstr
*v
)
1647 ALLOC(d
, dl
, (al
- a
) + (bl
- b
));
1649 mpx_umul(d
, dl
, a
, al
, b
, bl
);
1650 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1651 fprintf(stderr
, "\n*** umul failed\n");
1652 dumpmp(" a", a
, al
);
1653 dumpmp(" b", b
, bl
);
1654 dumpmp("expected", c
, cl
);
1655 dumpmp(" result", d
, dl
);
1659 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1663 static int usqr(dstr
*v
)
1672 ALLOC(d
, dl
, 2 * (al
- a
));
1674 mpx_usqr(d
, dl
, a
, al
);
1675 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1676 fprintf(stderr
, "\n*** usqr failed\n");
1677 dumpmp(" a", a
, al
);
1678 dumpmp("expected", c
, cl
);
1679 dumpmp(" result", d
, dl
);
1683 xfree(a
); xfree(c
); xfree(d
);
1687 static int udiv(dstr
*v
)
1697 ALLOC(a
, al
, MPW_RQ(v
[0].len
) + 2); mpx_loadb(a
, al
, v
[0].buf
, v
[0].len
);
1701 ALLOC(qq
, qql
, al
- a
);
1702 ALLOC(s
, sl
, (bl
- b
) + 1);
1704 mpx_udiv(qq
, qql
, a
, al
, b
, bl
, s
, sl
);
1705 if (!mpx_ueq(qq
, qql
, q
, ql
) ||
1706 !mpx_ueq(a
, al
, r
, rl
)) {
1707 fprintf(stderr
, "\n*** udiv failed\n");
1708 dumpmp(" divisor", b
, bl
);
1709 dumpmp("expect r", r
, rl
);
1710 dumpmp("result r", a
, al
);
1711 dumpmp("expect q", q
, ql
);
1712 dumpmp("result q", qq
, qql
);
1716 xfree(a
); xfree(b
); xfree(r
); xfree(q
); xfree(s
); xfree(qq
);
1720 static test_chunk defs
[] = {
1721 { "load-store", loadstore
, { &type_hex
, 0 } },
1722 { "2cl", twocl
, { &type_hex
, &type_hex
, } },
1723 { "2cb", twocb
, { &type_hex
, &type_hex
, } },
1724 { "lsl", lsl
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1725 { "lslc", lslc
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1726 { "lsr", lsr
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1727 { "uadd", uadd
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1728 { "usub", usub
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1729 { "umul", umul
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1730 { "usqr", usqr
, { &type_hex
, &type_hex
, 0 } },
1731 { "udiv", udiv
, { &type_hex
, &type_hex
, &type_hex
, &type_hex
, 0 } },
1735 int main(int argc
, char *argv
[])
1737 test_run(argc
, argv
, defs
, SRCDIR
"/tests/mpx");
1743 /*----- That's all, folks -------------------------------------------------*/