3 * Low-level multiprecision arithmetic
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Header files ------------------------------------------------------*/
35 #include <mLib/bits.h>
41 /*----- Loading and storing -----------------------------------------------*/
43 /* --- @mpx_storel@ --- *
45 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
46 * @void *pp@ = pointer to octet array
47 * @size_t sz@ = size of octet array
51 * Use: Stores an MP in an octet array, least significant octet
52 * first. High-end octets are silently discarded if there
53 * isn't enough space for them.
56 void mpx_storel(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
59 octet
*p
= pp
, *q
= p
+ sz
;
69 *p
++ = U8(w
| n
<< bits
);
81 /* --- @mpx_loadl@ --- *
83 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
84 * @const void *pp@ = pointer to octet array
85 * @size_t sz@ = size of octet array
89 * Use: Loads an MP in an octet array, least significant octet
90 * first. High-end octets are ignored if there isn't enough
94 void mpx_loadl(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
98 const octet
*p
= pp
, *q
= p
+ sz
;
107 if (bits
>= MPW_BITS
) {
109 w
= n
>> (MPW_BITS
- bits
+ 8);
119 /* --- @mpx_storeb@ --- *
121 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
122 * @void *pp@ = pointer to octet array
123 * @size_t sz@ = size of octet array
127 * Use: Stores an MP in an octet array, most significant octet
128 * first. High-end octets are silently discarded if there
129 * isn't enough space for them.
132 void mpx_storeb(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
135 octet
*p
= pp
, *q
= p
+ sz
;
145 *--q
= U8(w
| n
<< bits
);
147 bits
+= MPW_BITS
- 8;
157 /* --- @mpx_loadb@ --- *
159 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
160 * @const void *pp@ = pointer to octet array
161 * @size_t sz@ = size of octet array
165 * Use: Loads an MP in an octet array, most significant octet
166 * first. High-end octets are ignored if there isn't enough
170 void mpx_loadb(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
174 const octet
*p
= pp
, *q
= p
+ sz
;
183 if (bits
>= MPW_BITS
) {
185 w
= n
>> (MPW_BITS
- bits
+ 8);
195 /* --- @mpx_storel2cn@ --- *
197 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
198 * @void *pp@ = pointer to octet array
199 * @size_t sz@ = size of octet array
203 * Use: Stores a negative MP in an octet array, least significant
204 * octet first, as two's complement. High-end octets are
205 * silently discarded if there isn't enough space for them.
206 * This obviously makes the output bad.
209 void mpx_storel2cn(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
214 octet
*p
= pp
, *q
= p
+ sz
;
226 bits
+= MPW_BITS
- 8;
244 /* --- @mpx_loadl2cn@ --- *
246 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
247 * @const void *pp@ = pointer to octet array
248 * @size_t sz@ = size of octet array
252 * Use: Loads a negative MP in an octet array, least significant
253 * octet first, as two's complement. High-end octets are
254 * ignored if there isn't enough space for them. This probably
255 * means you made the wrong choice coming here.
258 void mpx_loadl2cn(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
263 const octet
*p
= pp
, *q
= p
+ sz
;
273 if (bits
>= MPW_BITS
) {
275 w
= n
>> (MPW_BITS
- bits
+ 8);
285 /* --- @mpx_storeb2cn@ --- *
287 * Arguments: @const mpw *v, *vl@ = base and limit of source vector
288 * @void *pp@ = pointer to octet array
289 * @size_t sz@ = size of octet array
293 * Use: Stores a negative MP in an octet array, most significant
294 * octet first, as two's complement. High-end octets are
295 * silently discarded if there isn't enough space for them,
296 * which probably isn't what you meant.
299 void mpx_storeb2cn(const mpw
*v
, const mpw
*vl
, void *pp
, size_t sz
)
304 octet
*p
= pp
, *q
= p
+ sz
;
316 bits
+= MPW_BITS
- 8;
328 c
= c
&& !(b
& 0xff);
334 /* --- @mpx_loadb2cn@ --- *
336 * Arguments: @mpw *v, *vl@ = base and limit of destination vector
337 * @const void *pp@ = pointer to octet array
338 * @size_t sz@ = size of octet array
342 * Use: Loads a negative MP in an octet array, most significant octet
343 * first as two's complement. High-end octets are ignored if
344 * there isn't enough space for them. This probably means you
345 * chose this function wrongly.
348 void mpx_loadb2cn(mpw
*v
, mpw
*vl
, const void *pp
, size_t sz
)
353 const octet
*p
= pp
, *q
= p
+ sz
;
363 if (bits
>= MPW_BITS
) {
365 w
= n
>> (MPW_BITS
- bits
+ 8);
375 /*----- Logical shifting --------------------------------------------------*/
377 /* --- @mpx_lsl@ --- *
379 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
380 * @const mpw *av, *avl@ = source vector base and limit
381 * @size_t n@ = number of bit positions to shift by
385 * Use: Performs a logical shift left operation on an integer.
388 void mpx_lsl(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
393 /* --- Trivial special case --- */
396 MPX_COPY(dv
, dvl
, av
, avl
);
398 /* --- Single bit shifting --- */
407 *dv
++ = MPW((t
<< 1) | w
);
408 w
= t
>> (MPW_BITS
- 1);
417 /* --- Break out word and bit shifts for more sophisticated work --- */
422 /* --- Handle a shift by a multiple of the word size --- */
428 MPX_COPY(dv
+ nw
, dvl
, av
, avl
);
429 memset(dv
, 0, MPWS(nw
));
433 /* --- And finally the difficult case --- *
435 * This is a little convoluted, because I have to start from the end and
436 * work backwards to avoid overwriting the source, if they're both the same
442 size_t nr
= MPW_BITS
- nb
;
443 size_t dvn
= dvl
- dv
;
444 size_t avn
= avl
- av
;
451 if (dvn
> avn
+ nw
) {
452 size_t off
= avn
+ nw
+ 1;
453 MPX_ZERO(dv
+ off
, dvl
);
463 *--dvl
= MPW((t
>> nr
) | w
);
474 /* --- @mpx_lslc@ --- *
476 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
477 * @const mpw *av, *avl@ = source vector base and limit
478 * @size_t n@ = number of bit positions to shift by
482 * Use: Performs a logical shift left operation on an integer, only
483 * it fills in the bits with ones instead of zeroes.
486 void mpx_lslc(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
491 /* --- Trivial special case --- */
494 MPX_COPY(dv
, dvl
, av
, avl
);
496 /* --- Single bit shifting --- */
505 *dv
++ = MPW((t
<< 1) | w
);
506 w
= t
>> (MPW_BITS
- 1);
515 /* --- Break out word and bit shifts for more sophisticated work --- */
520 /* --- Handle a shift by a multiple of the word size --- */
526 MPX_COPY(dv
+ nw
, dvl
, av
, avl
);
527 MPX_ONE(dv
, dv
+ nw
);
531 /* --- And finally the difficult case --- *
533 * This is a little convoluted, because I have to start from the end and
534 * work backwards to avoid overwriting the source, if they're both the same
540 size_t nr
= MPW_BITS
- nb
;
541 size_t dvn
= dvl
- dv
;
542 size_t avn
= avl
- av
;
549 if (dvn
> avn
+ nw
) {
550 size_t off
= avn
+ nw
+ 1;
551 MPX_ZERO(dv
+ off
, dvl
);
561 *--dvl
= MPW((t
>> nr
) | w
);
565 *--dvl
= MPW((MPW_MAX
>> nr
) | w
);
572 /* --- @mpx_lsr@ --- *
574 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
575 * @const mpw *av, *avl@ = source vector base and limit
576 * @size_t n@ = number of bit positions to shift by
580 * Use: Performs a logical shift right operation on an integer.
583 void mpx_lsr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, size_t n
)
588 /* --- Trivial special case --- */
591 MPX_COPY(dv
, dvl
, av
, avl
);
593 /* --- Single bit shifting --- */
596 mpw w
= av
< avl ?
*av
++ >> 1 : 0;
602 *dv
++ = MPW((t
<< (MPW_BITS
- 1)) | w
);
612 /* --- Break out word and bit shifts for more sophisticated work --- */
617 /* --- Handle a shift by a multiple of the word size --- */
623 MPX_COPY(dv
, dvl
, av
+ nw
, avl
);
626 /* --- And finally the difficult case --- */
630 size_t nr
= MPW_BITS
- nb
;
633 w
= av
< avl ?
*av
++ : 0;
639 *dv
++ = MPW((w
>> nb
) | (t
<< nr
));
643 *dv
++ = MPW(w
>> nb
);
651 /*----- Bitwise operations ------------------------------------------------*/
653 /* --- @mpx_bitop@ --- *
655 * Arguments: @mpw *dv, *dvl@ = destination vector
656 * @const mpw *av, *avl@ = first source vector
657 * @const mpw *bv, *bvl@ = second source vector
661 * Use; Provides the dyadic boolean functions.
664 /* GCC complains about the generated code, so try to silence it. */
665 #if __GNUC__ >= 5 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)
666 # pragma GCC diagnostic push
667 # pragma GCC diagnostic ignored "-Wunused-but-set-variable"
670 #define MPX_BITBINOP(string) \
672 void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \
673 const mpw *bv, const mpw *bvl) \
675 MPX_SHRINK(av, avl); \
676 MPX_SHRINK(bv, bvl); \
680 a = (av < avl) ? *av++ : 0; \
681 b = (bv < bvl) ? *bv++ : 0; \
682 *dv++ = B##string(a, b); \
686 MPX_DOBIN(MPX_BITBINOP
)
688 #if __GNUC__ >= 5 || (__GNUC__ == 4 && __GNUC_MINOR__ >= 6)
689 # pragma GCC diagnostic pop
692 void mpx_not(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
)
698 a
= (av
< avl
) ?
*av
++ : 0;
703 /*----- Unsigned arithmetic -----------------------------------------------*/
705 /* --- @mpx_2c@ --- *
707 * Arguments: @mpw *dv, *dvl@ = destination vector
708 * @const mpw *v, *vl@ = source vector
712 * Use: Calculates the two's complement of @v@.
715 void mpx_2c(mpw
*dv
, mpw
*dvl
, const mpw
*v
, const mpw
*vl
)
718 while (dv
< dvl
&& v
< vl
)
719 *dv
++ = c
= MPW(~*v
++);
726 MPX_UADDN(dv
, dvl
, 1);
729 /* --- @mpx_ueq@ --- *
731 * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
732 * @const mpw *bv, *bvl@ = second argument vector base and limit
734 * Returns: Nonzero if the two vectors are equal.
736 * Use: Performs an unsigned integer test for equality.
739 int mpx_ueq(const mpw
*av
, const mpw
*avl
, const mpw
*bv
, const mpw
*bvl
)
743 if (avl
- av
!= bvl
- bv
)
752 /* --- @mpx_ucmp@ --- *
754 * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
755 * @const mpw *bv, *bvl@ = second argument vector base and limit
757 * Returns: Less than, equal to, or greater than zero depending on
758 * whether @a@ is less than, equal to or greater than @b@,
761 * Use: Performs an unsigned integer comparison.
764 int mpx_ucmp(const mpw
*av
, const mpw
*avl
, const mpw
*bv
, const mpw
*bvl
)
769 if (avl
- av
> bvl
- bv
)
771 else if (avl
- av
< bvl
- bv
)
773 else while (avl
> av
) {
774 mpw a
= *--avl
, b
= *--bvl
;
783 /* --- @mpx_uadd@ --- *
785 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
786 * @const mpw *av, *avl@ = first addend vector base and limit
787 * @const mpw *bv, *bvl@ = second addend vector base and limit
791 * Use: Performs unsigned integer addition. If the result overflows
792 * the destination vector, high-order bits are discarded. This
793 * means that two's complement addition happens more or less for
794 * free, although that's more a side-effect than anything else.
795 * The result vector may be equal to either or both source
796 * vectors, but may not otherwise overlap them.
799 void mpx_uadd(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
800 const mpw
*bv
, const mpw
*bvl
)
804 while (av
< avl
|| bv
< bvl
) {
809 a
= (av
< avl
) ?
*av
++ : 0;
810 b
= (bv
< bvl
) ?
*bv
++ : 0;
811 x
= (mpd
)a
+ (mpd
)b
+ c
;
821 /* --- @mpx_uaddn@ --- *
823 * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
824 * @mpw n@ = other addend
828 * Use: Adds a small integer to a multiprecision number.
831 void mpx_uaddn(mpw
*dv
, mpw
*dvl
, mpw n
) { MPX_UADDN(dv
, dvl
, n
); }
833 /* --- @mpx_uaddnlsl@ --- *
835 * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
836 * @mpw a@ = second argument
837 * @unsigned o@ = offset in bits
841 * Use: Computes %$d + 2^o a$%. If the result overflows then
842 * high-order bits are discarded, as usual. We must have
843 * @0 < o < MPW_BITS@.
846 void mpx_uaddnlsl(mpw
*dv
, mpw
*dvl
, mpw a
, unsigned o
)
850 while (x
&& dv
< dvl
) {
857 /* --- @mpx_usub@ --- *
859 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
860 * @const mpw *av, *avl@ = first argument vector base and limit
861 * @const mpw *bv, *bvl@ = second argument vector base and limit
865 * Use: Performs unsigned integer subtraction. If the result
866 * overflows the destination vector, high-order bits are
867 * discarded. This means that two's complement subtraction
868 * happens more or less for free, althuogh that's more a side-
869 * effect than anything else. The result vector may be equal to
870 * either or both source vectors, but may not otherwise overlap
874 void mpx_usub(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
875 const mpw
*bv
, const mpw
*bvl
)
879 while (av
< avl
|| bv
< bvl
) {
884 a
= (av
< avl
) ?
*av
++ : 0;
885 b
= (bv
< bvl
) ?
*bv
++ : 0;
886 x
= (mpd
)a
- (mpd
)b
- c
;
899 /* --- @mpx_usubn@ --- *
901 * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
906 * Use: Subtracts a small integer from a multiprecision number.
909 void mpx_usubn(mpw
*dv
, mpw
*dvl
, mpw n
) { MPX_USUBN(dv
, dvl
, n
); }
911 /* --- @mpx_uaddnlsl@ --- *
913 * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
914 * @mpw a@ = second argument
915 * @unsigned o@ = offset in bits
919 * Use: Computes %$d + 2^o a$%. If the result overflows then
920 * high-order bits are discarded, as usual. We must have
921 * @0 < o < MPW_BITS@.
924 void mpx_usubnlsl(mpw
*dv
, mpw
*dvl
, mpw a
, unsigned o
)
926 mpw b
= a
>> (MPW_BITS
- o
);
930 mpd x
= (mpd
)*dv
- MPW(a
);
934 MPX_USUBN(dv
, dvl
, b
);
938 /* --- @mpx_umul@ --- *
940 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
941 * @const mpw *av, *avl@ = multiplicand vector base and limit
942 * @const mpw *bv, *bvl@ = multiplier vector base and limit
946 * Use: Performs unsigned integer multiplication. If the result
947 * overflows the desination vector, high-order bits are
948 * discarded. The result vector may not overlap the argument
949 * vectors in any way.
952 void mpx_umul(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
,
953 const mpw
*bv
, const mpw
*bvl
)
955 /* --- This is probably worthwhile on a multiply --- */
960 /* --- Deal with a multiply by zero --- */
967 /* --- Do the initial multiply and initialize the accumulator --- */
969 MPX_UMULN(dv
, dvl
, av
, avl
, *bv
++);
971 /* --- Do the remaining multiply/accumulates --- */
973 while (dv
< dvl
&& bv
< bvl
) {
983 x
= (mpd
)*dvv
+ (mpd
)m
* (mpd
)*avv
++ + c
;
987 MPX_UADDN(dvv
, dvl
, c
);
992 /* --- @mpx_umuln@ --- *
994 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
995 * @const mpw *av, *avl@ = multiplicand vector base and limit
996 * @mpw m@ = multiplier
1000 * Use: Multiplies a multiprecision integer by a single-word value.
1001 * The destination and source may be equal. The destination
1002 * is completely cleared after use.
1005 void mpx_umuln(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, mpw m
)
1006 { MPX_UMULN(dv
, dvl
, av
, avl
, m
); }
1008 /* --- @mpx_umlan@ --- *
1010 * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit
1011 * @const mpw *av, *avl@ = multiplicand vector base and limit
1012 * @mpw m@ = multiplier
1016 * Use: Multiplies a multiprecision integer by a single-word value
1017 * and adds the result to an accumulator.
1020 void mpx_umlan(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
, mpw m
)
1021 { MPX_UMLAN(dv
, dvl
, av
, avl
, m
); }
1023 /* --- @mpx_usqr@ --- *
1025 * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
1026 * @const mpw *av, *av@ = source vector base and limit
1030 * Use: Performs unsigned integer squaring. The result vector must
1031 * not overlap the source vector in any way.
1034 void mpx_usqr(mpw
*dv
, mpw
*dvl
, const mpw
*av
, const mpw
*avl
)
1038 /* --- Main loop --- */
1041 const mpw
*avv
= av
;
1046 /* --- Stop if I've run out of destination --- */
1051 /* --- Work out the square at this point in the proceedings --- */
1054 mpd x
= (mpd
)a
* (mpd
)a
+ *dvv
;
1056 c
= MPW(x
>> MPW_BITS
);
1059 /* --- Now fix up the rest of the vector upwards --- */
1062 while (dvv
< dvl
&& avv
< avl
) {
1063 mpd x
= (mpd
)a
* (mpd
)*avv
++;
1064 mpd y
= ((x
<< 1) & MPW_MAX
) + c
+ *dvv
;
1065 c
= (x
>> (MPW_BITS
- 1)) + (y
>> MPW_BITS
);
1068 while (dvv
< dvl
&& c
) {
1074 /* --- Get ready for the next round --- */
1081 /* --- @mpx_udiv@ --- *
1083 * Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
1084 * @mpw *rv, *rvl@ = dividend/remainder vector base and limit
1085 * @const mpw *dv, *dvl@ = divisor vector base and limit
1086 * @mpw *sv, *svl@ = scratch workspace
1090 * Use: Performs unsigned integer division. If the result overflows
1091 * the quotient vector, high-order bits are discarded. (Clearly
1092 * the remainder vector can't overflow.) The various vectors
1093 * may not overlap in any way. Yes, I know it's a bit odd
1094 * requiring the dividend to be in the result position but it
1095 * does make some sense really. The remainder must have
1096 * headroom for at least two extra words. The scratch space
1097 * must be at least one word larger than the divisor.
1100 void mpx_udiv(mpw
*qv
, mpw
*qvl
, mpw
*rv
, mpw
*rvl
,
1101 const mpw
*dv
, const mpw
*dvl
,
1108 /* --- Initialize the quotient --- */
1112 /* --- Perform some sanity checks --- */
1114 MPX_SHRINK(dv
, dvl
);
1115 assert(((void)"division by zero in mpx_udiv", dv
< dvl
));
1117 /* --- Normalize the divisor --- *
1119 * The algorithm requires that the divisor be at least two digits long.
1120 * This is easy to fix.
1127 for (b
= MPW_P2
; b
; b
>>= 1) {
1128 if (d
<= (MPW_MAX
>> b
)) {
1137 /* --- Normalize the dividend/remainder to match --- */
1140 mpx_lsl(rv
, rvl
, rv
, rvl
, norm
);
1141 mpx_lsl(sv
, svl
, dv
, dvl
, norm
);
1144 MPX_SHRINK(dv
, dvl
);
1147 MPX_SHRINK(rv
, rvl
);
1151 /* --- Work out the relative scales --- */
1154 size_t rvn
= rvl
- rv
;
1155 size_t dvn
= dvl
- dv
;
1157 /* --- If the divisor is clearly larger, notice this --- */
1160 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
1167 /* --- Calculate the most significant quotient digit --- *
1169 * Because the divisor has its top bit set, this can only happen once. The
1170 * pointer arithmetic is a little contorted, to make sure that the
1171 * behaviour is defined.
1174 if (MPX_UCMP(rv
+ scale
, rvl
, >=, dv
, dvl
)) {
1175 mpx_usub(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
1176 if (qvl
- qv
> scale
)
1180 /* --- Now for the main loop --- */
1189 /* --- Get an estimate for the next quotient digit --- */
1196 rh
= ((mpd
)r
<< MPW_BITS
) | rr
;
1202 /* --- Refine the estimate --- */
1205 mpd yh
= (mpd
)d
* q
;
1206 mpd yy
= (mpd
)dd
* q
;
1210 yh
+= yy
>> MPW_BITS
;
1213 while (yh
> rh
|| (yh
== rh
&& yl
> rrr
)) {
1222 /* --- Remove a chunk from the dividend --- */
1229 /* --- Calculate the size of the chunk --- *
1231 * This does the whole job of calculating @r >> scale - qd@.
1234 for (svv
= rv
+ scale
, dvv
= dv
;
1235 dvv
< dvl
&& svv
< rvl
;
1237 mpd x
= (mpd
)*dvv
* (mpd
)q
+ mc
;
1239 x
= (mpd
)*svv
- MPW(x
) - sc
;
1248 mpd x
= (mpd
)*svv
- mc
- sc
;
1258 /* --- Fix if the quotient was too large --- *
1260 * This doesn't seem to happen very often.
1263 if (rvl
[-1] > MPW_MAX
/ 2) {
1264 mpx_uadd(rv
+ scale
, rvl
, rv
+ scale
, rvl
, dv
, dvl
);
1269 /* --- Done for another iteration --- */
1271 if (qvl
- qv
> scale
)
1278 /* --- Now fiddle with unnormalizing and things --- */
1280 mpx_lsr(rv
, rvl
, rv
, rvl
, norm
);
1283 /* --- @mpx_udivn@ --- *
1285 * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap
1287 * @const mpw *rv, *rvl@ = dividend
1288 * @mpw d@ = single-precision divisor
1290 * Returns: Remainder after divison.
1292 * Use: Performs a single-precision division operation.
1295 mpw
mpx_udivn(mpw
*qv
, mpw
*qvl
, const mpw
*rv
, const mpw
*rvl
, mpw d
)
1298 size_t ql
= qvl
- qv
;
1304 r
= (r
<< MPW_BITS
) | rv
[i
];
1312 /*----- Test rig ----------------------------------------------------------*/
1316 #include <mLib/alloc.h>
1317 #include <mLib/dstr.h>
1318 #include <mLib/quis.h>
1319 #include <mLib/testrig.h>
1323 #define ALLOC(v, vl, sz) do { \
1324 size_t _sz = (sz); \
1325 mpw *_vv = xmalloc(MPWS(_sz)); \
1326 mpw *_vvl = _vv + _sz; \
1331 #define LOAD(v, vl, d) do { \
1332 const dstr *_d = (d); \
1334 ALLOC(_v, _vl, MPW_RQ(_d->len)); \
1335 mpx_loadb(_v, _vl, _d->buf, _d->len); \
1340 #define MAX(x, y) ((x) > (y) ? (x) : (y))
1342 static void dumpbits(const char *msg
, const void *pp
, size_t sz
)
1344 const octet
*p
= pp
;
1347 fprintf(stderr
, " %02x", *p
++);
1348 fputc('\n', stderr
);
1351 static void dumpmp(const char *msg
, const mpw
*v
, const mpw
*vl
)
1356 fprintf(stderr
, " %08lx", (unsigned long)*--vl
);
1357 fputc('\n', stderr
);
1360 static int chkscan(const mpw
*v
, const mpw
*vl
,
1361 const void *pp
, size_t sz
, int step
)
1364 const octet
*p
= pp
;
1368 mpscan_initx(&mps
, v
, vl
);
1373 for (i
= 0; i
< 8 && MPSCAN_STEP(&mps
); i
++) {
1374 if (MPSCAN_BIT(&mps
) != (x
& 1)) {
1376 "\n*** error, step %i, bit %u, expected %u, found %u\n",
1377 step
, bit
, x
& 1, MPSCAN_BIT(&mps
));
1389 static int loadstore(dstr
*v
)
1392 size_t sz
= MPW_RQ(v
->len
) * 2, diff
;
1396 dstr_ensure(&d
, v
->len
);
1397 m
= xmalloc(MPWS(sz
));
1399 for (diff
= 0; diff
< sz
; diff
+= 5) {
1404 mpx_loadl(m
, ml
, v
->buf
, v
->len
);
1405 if (!chkscan(m
, ml
, v
->buf
, v
->len
, +1))
1407 MPX_OCTETS(oct
, m
, ml
);
1408 mpx_storel(m
, ml
, d
.buf
, d
.sz
);
1409 if (memcmp(d
.buf
, v
->buf
, oct
) != 0) {
1410 dumpbits("\n*** storel failed", d
.buf
, d
.sz
);
1414 mpx_loadb(m
, ml
, v
->buf
, v
->len
);
1415 if (!chkscan(m
, ml
, v
->buf
+ v
->len
- 1, v
->len
, -1))
1417 MPX_OCTETS(oct
, m
, ml
);
1418 mpx_storeb(m
, ml
, d
.buf
, d
.sz
);
1419 if (memcmp(d
.buf
+ d
.sz
- oct
, v
->buf
+ v
->len
- oct
, oct
) != 0) {
1420 dumpbits("\n*** storeb failed", d
.buf
, d
.sz
);
1426 dumpbits("input data", v
->buf
, v
->len
);
1433 static int twocl(dstr
*v
)
1440 sz
= v
[0].len
; if (v
[1].len
> sz
) sz
= v
[1].len
;
1441 dstr_ensure(&d
, sz
);
1444 m
= xmalloc(MPWS(sz
));
1447 mpx_loadl(m
, ml
, v
[0].buf
, v
[0].len
);
1448 mpx_storel2cn(m
, ml
, d
.buf
, v
[1].len
);
1449 if (memcmp(d
.buf
, v
[1].buf
, v
[1].len
)) {
1450 dumpbits("\n*** storel2cn failed", d
.buf
, v
[1].len
);
1454 mpx_loadl2cn(m
, ml
, v
[1].buf
, v
[1].len
);
1455 mpx_storel(m
, ml
, d
.buf
, v
[0].len
);
1456 if (memcmp(d
.buf
, v
[0].buf
, v
[0].len
)) {
1457 dumpbits("\n*** loadl2cn failed", d
.buf
, v
[0].len
);
1462 dumpbits("pos", v
[0].buf
, v
[0].len
);
1463 dumpbits("neg", v
[1].buf
, v
[1].len
);
1472 static int twocb(dstr
*v
)
1479 sz
= v
[0].len
; if (v
[1].len
> sz
) sz
= v
[1].len
;
1480 dstr_ensure(&d
, sz
);
1483 m
= xmalloc(MPWS(sz
));
1486 mpx_loadb(m
, ml
, v
[0].buf
, v
[0].len
);
1487 mpx_storeb2cn(m
, ml
, d
.buf
, v
[1].len
);
1488 if (memcmp(d
.buf
, v
[1].buf
, v
[1].len
)) {
1489 dumpbits("\n*** storeb2cn failed", d
.buf
, v
[1].len
);
1493 mpx_loadb2cn(m
, ml
, v
[1].buf
, v
[1].len
);
1494 mpx_storeb(m
, ml
, d
.buf
, v
[0].len
);
1495 if (memcmp(d
.buf
, v
[0].buf
, v
[0].len
)) {
1496 dumpbits("\n*** loadb2cn failed", d
.buf
, v
[0].len
);
1501 dumpbits("pos", v
[0].buf
, v
[0].len
);
1502 dumpbits("neg", v
[1].buf
, v
[1].len
);
1511 static int lsl(dstr
*v
)
1514 int n
= *(int *)v
[1].buf
;
1521 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
);
1523 mpx_lsl(d
, dl
, a
, al
, n
);
1524 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1525 fprintf(stderr
, "\n*** lsl(%i) failed\n", n
);
1526 dumpmp(" a", a
, al
);
1527 dumpmp("expected", c
, cl
);
1528 dumpmp(" result", d
, dl
);
1532 xfree(a
); xfree(c
); xfree(d
);
1536 static int lslc(dstr
*v
)
1539 int n
= *(int *)v
[1].buf
;
1546 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
);
1548 mpx_lslc(d
, dl
, a
, al
, n
);
1549 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1550 fprintf(stderr
, "\n*** lslc(%i) failed\n", n
);
1551 dumpmp(" a", a
, al
);
1552 dumpmp("expected", c
, cl
);
1553 dumpmp(" result", d
, dl
);
1557 xfree(a
); xfree(c
); xfree(d
);
1561 static int lsr(dstr
*v
)
1564 int n
= *(int *)v
[1].buf
;
1571 ALLOC(d
, dl
, al
- a
+ (n
+ MPW_BITS
- 1) / MPW_BITS
+ 1);
1573 mpx_lsr(d
, dl
, a
, al
, n
);
1574 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1575 fprintf(stderr
, "\n*** lsr(%i) failed\n", n
);
1576 dumpmp(" a", a
, al
);
1577 dumpmp("expected", c
, cl
);
1578 dumpmp(" result", d
, dl
);
1582 xfree(a
); xfree(c
); xfree(d
);
1586 static int uadd(dstr
*v
)
1597 ALLOC(d
, dl
, MAX(al
- a
, bl
- b
) + 1);
1599 mpx_uadd(d
, dl
, a
, al
, b
, bl
);
1600 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1601 fprintf(stderr
, "\n*** uadd failed\n");
1602 dumpmp(" a", a
, al
);
1603 dumpmp(" b", b
, bl
);
1604 dumpmp("expected", c
, cl
);
1605 dumpmp(" result", d
, dl
);
1609 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1613 static int usub(dstr
*v
)
1624 ALLOC(d
, dl
, al
- a
);
1626 mpx_usub(d
, dl
, a
, al
, b
, bl
);
1627 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1628 fprintf(stderr
, "\n*** usub failed\n");
1629 dumpmp(" a", a
, al
);
1630 dumpmp(" b", b
, bl
);
1631 dumpmp("expected", c
, cl
);
1632 dumpmp(" result", d
, dl
);
1636 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1640 static int umul(dstr
*v
)
1651 ALLOC(d
, dl
, (al
- a
) + (bl
- b
));
1653 mpx_umul(d
, dl
, a
, al
, b
, bl
);
1654 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1655 fprintf(stderr
, "\n*** umul failed\n");
1656 dumpmp(" a", a
, al
);
1657 dumpmp(" b", b
, bl
);
1658 dumpmp("expected", c
, cl
);
1659 dumpmp(" result", d
, dl
);
1663 xfree(a
); xfree(b
); xfree(c
); xfree(d
);
1667 static int usqr(dstr
*v
)
1676 ALLOC(d
, dl
, 2 * (al
- a
));
1678 mpx_usqr(d
, dl
, a
, al
);
1679 if (!mpx_ueq(d
, dl
, c
, cl
)) {
1680 fprintf(stderr
, "\n*** usqr failed\n");
1681 dumpmp(" a", a
, al
);
1682 dumpmp("expected", c
, cl
);
1683 dumpmp(" result", d
, dl
);
1687 xfree(a
); xfree(c
); xfree(d
);
1691 static int udiv(dstr
*v
)
1701 ALLOC(a
, al
, MPW_RQ(v
[0].len
) + 2); mpx_loadb(a
, al
, v
[0].buf
, v
[0].len
);
1705 ALLOC(qq
, qql
, al
- a
);
1706 ALLOC(s
, sl
, (bl
- b
) + 1);
1708 mpx_udiv(qq
, qql
, a
, al
, b
, bl
, s
, sl
);
1709 if (!mpx_ueq(qq
, qql
, q
, ql
) ||
1710 !mpx_ueq(a
, al
, r
, rl
)) {
1711 fprintf(stderr
, "\n*** udiv failed\n");
1712 dumpmp(" divisor", b
, bl
);
1713 dumpmp("expect r", r
, rl
);
1714 dumpmp("result r", a
, al
);
1715 dumpmp("expect q", q
, ql
);
1716 dumpmp("result q", qq
, qql
);
1720 xfree(a
); xfree(b
); xfree(r
); xfree(q
); xfree(s
); xfree(qq
);
1724 static test_chunk defs
[] = {
1725 { "load-store", loadstore
, { &type_hex
, 0 } },
1726 { "2cl", twocl
, { &type_hex
, &type_hex
, } },
1727 { "2cb", twocb
, { &type_hex
, &type_hex
, } },
1728 { "lsl", lsl
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1729 { "lslc", lslc
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1730 { "lsr", lsr
, { &type_hex
, &type_int
, &type_hex
, 0 } },
1731 { "uadd", uadd
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1732 { "usub", usub
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1733 { "umul", umul
, { &type_hex
, &type_hex
, &type_hex
, 0 } },
1734 { "usqr", usqr
, { &type_hex
, &type_hex
, 0 } },
1735 { "udiv", udiv
, { &type_hex
, &type_hex
, &type_hex
, &type_hex
, 0 } },
1739 int main(int argc
, char *argv
[])
1741 test_run(argc
, argv
, defs
, SRCDIR
"/t/mpx");
1747 /*----- That's all, folks -------------------------------------------------*/