/* -*-c-*-
*
- * $Id: mpx.c,v 1.1 1999/09/03 08:41:12 mdw Exp $
+ * $Id: mpx.c,v 1.2 1999/11/13 01:50:59 mdw Exp $
*
* Low-level multiprecision arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpx.c,v $
+ * Revision 1.2 1999/11/13 01:50:59 mdw
+ * Multiprecision routines finished and tested.
+ *
* Revision 1.1 1999/09/03 08:41:12 mdw
* Initial import.
*
/*----- Header files ------------------------------------------------------*/
+#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* --- @mpx_storel@ --- *
*
* Arguments: @const mpw *v, *vl@ = base and limit of source vector
- * @octet *p@ = pointer to octet array
+ * @void *pp@ = pointer to octet array
* @size_t sz@ = size of octet array
*
* Returns: ---
* isn't enough space for them.
*/
-void mpx_storel(const mpw *v, const mpw *vl, octet *p, size_t sz)
+void mpx_storel(const mpw *v, const mpw *vl, void *pp, size_t sz)
{
mpw n, w = 0;
- octet *q = p + sz;
+ octet *p = pp, *q = p + sz;
unsigned bits = 0;
while (p < q) {
/* --- @mpx_loadl@ --- *
*
* Arguments: @mpw *v, *vl@ = base and limit of destination vector
- * @const octet *p@ = pointer to octet array
+ * @const void *pp@ = pointer to octet array
* @size_t sz@ = size of octet array
*
* Returns: ---
* space for them.
*/
-void mpx_loadl(mpw *v, const mpw *vl, const octet *p, size_t sz)
+void mpx_loadl(mpw *v, mpw *vl, const void *pp, size_t sz)
{
unsigned n;
- const octet *q = p + sz;
+ mpw w = 0;
+ const octet *p = pp, *q = p + sz;
unsigned bits = 0;
if (v >= vl)
/* --- @mpx_storeb@ --- *
*
* Arguments: @const mpw *v, *vl@ = base and limit of source vector
- * @octet *p@ = pointer to octet array
+ * @void *pp@ = pointer to octet array
* @size_t sz@ = size of octet array
*
* Returns: ---
* isn't enough space for them.
*/
-void mpx_storeb(const mpw *v, const mpw *vl, octet *p, size_t sz);
+void mpx_storeb(const mpw *v, const mpw *vl, void *pp, size_t sz)
{
mpw n, w = 0;
- octet *q = p + sz;
+ octet *p = pp, *q = p + sz;
unsigned bits = 0;
while (q > p) {
/* --- @mpx_loadb@ --- *
*
* Arguments: @mpw *v, *vl@ = base and limit of destination vector
- * @const octet *p@ = pointer to octet array
+ * @const void *pp@ = pointer to octet array
* @size_t sz@ = size of octet array
*
* Returns: ---
* space for them.
*/
-void mpx_loadb(mpw *v, const mpw *vl, const octet *p, size_t sz)
+void mpx_loadb(mpw *v, mpw *vl, const void *pp, size_t sz)
{
unsigned n;
- const octet *q = p + sz;
+ mpw w = 0;
+ const octet *p = pp, *q = p + sz;
unsigned bits = 0;
if (v >= vl)
goto done;
*dv++ = MPW(w);
MPX_ZERO(dv, dvl);
+ goto done;
}
/* --- Break out word and bit shifts for more sophisticated work --- */
memset(dv, 0, MPWS(nw));
}
- /* --- And finally the difficult case --- */
+ /* --- And finally the difficult case --- *
+ *
+ * This is a little convoluted, because I have to start from the end and
+ * work backwards to avoid overwriting the source, if they're both the same
+ * block of memory.
+ */
else {
mpw w;
size_t nr = MPW_BITS - nb;
+ size_t dvn = dvl - dv;
+ size_t avn = avl - av;
- if (dv + nw >= dvl) {
+ if (dvn <= nw) {
MPX_ZERO(dv, dvl);
goto done;
}
- memset(dv, 0, MPWS(nw));
- dv += nw;
- w = *av++;
- while (av < avl) {
- mpw t;
- if (dv >= dvl)
- goto done;
- t = *av++;
- *dv++ = MPW((w >> nr) | (t << nb));
- w = t;
+ if (dvn > avn + nw) {
+ size_t off = avn + nw + 1;
+ MPX_ZERO(dv + off, dvl);
+ dvl = dv + off;
+ w = 0;
+ } else {
+ avl = av + dvn - nw;
+ w = *--avl << nb;
}
- if (dv < dvl) {
- *dv++ = MPW(w >> nr);
- MPX_ZERO(dv, dvl);
+ while (avl > av) {
+ mpw t = *--avl;
+ *--dvl = (t >> nr) | w;
+ w = t << nb;
}
+
+ *--dvl = w;
+ MPX_ZERO(dv, dvl);
}
done:;
goto done;
*dv++ = MPW(w);
MPX_ZERO(dv, dvl);
+ goto done;
}
/* --- Break out word and bit shifts for more sophisticated work --- */
return;
a = (av < avl) ? *av++ : 0;
b = (bv < bvl) ? *bv++ : 0;
- x = (mpd)a - (mpd)b + c;
+ x = (mpd)a - (mpd)b - c;
*dv++ = MPW(x);
- if (c >> MPW_BITS)
- c = MPW(~0u);
+ if (x >> MPW_BITS)
+ c = 1;
+ else
+ c = 0;
}
- c = c ? ~0u : 0;
+ if (c)
+ c = MPW_MAX;
while (dv < dvl)
- *dv++ = c
+ *dv++ = c;
}
/* --- @mpx_umul@ --- *
/* --- Deal with a multiply by zero --- */
if (bv == bvl) {
- MPX_COPY(dv, dvl, bv, bvl);
+ MPX_ZERO(dv, dvl);
return;
}
/* --- Do the remaining multiply/accumulates --- */
- while (bv < bvl) {
+ while (dv < dvl && bv < bvl) {
mpw m = *bv++;
- mpw c = ;
+ mpw c = 0;
const mpw *avv = av;
mpw *dvv = ++dv;
mpd x;
if (dvv >= dvl)
goto next;
- x = *dvv + m * *av++ + c;
- *dv++ = MPW(x);
+ x = (mpd)*dvv + (mpd)m * (mpd)*avv++ + c;
+ *dvv++ = MPW(x);
c = x >> MPW_BITS;
}
- if (dvv < dvl)
- *dvv++ = MPW(c);
+ MPX_UADDN(dvv, dvl, c);
next:;
}
}
+/* --- @mpx_usqr@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
+ * @const mpw *av, *av@ = source vector base and limit
+ *
+ * Returns: ---
+ *
+ * Use: Performs unsigned integer squaring. The result vector must
+ * not overlap the source vector in any way.
+ */
+
+void mpx_usqr(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl)
+{
+ MPX_ZERO(dv, dvl);
+
+ /* --- Main loop --- */
+
+ while (av < avl) {
+ const mpw *avv = av;
+ mpw *dvv = dv;
+ mpw a = *av;
+ mpd c;
+
+ /* --- Stop if I've run out of destination --- */
+
+ if (dvv >= dvl)
+ break;
+
+ /* --- Work out the square at this point in the proceedings --- */
+
+ {
+ mpw d = *dvv;
+ mpd x = (mpd)a * (mpd)a + *dvv;
+ *dvv++ = MPW(x);
+ c = MPW(x >> MPW_BITS);
+ }
+
+ /* --- Now fix up the rest of the vector upwards --- */
+
+ avv++;
+ while (dvv < dvl && avv < avl) {
+ mpw aa = *avv;
+ mpd x = (mpd)a * (mpd)*avv++;
+ mpd y = ((x << 1) & MPW_MAX) + c + *dvv;
+ c = (x >> (MPW_BITS - 1)) + (y >> MPW_BITS);
+ *dvv++ = MPW(y);
+ }
+ while (dvv < dvl && c) {
+ mpd x = c + *dvv;
+ *dvv++ = MPW(x);
+ c = x >> MPW_BITS;
+ }
+
+ /* --- Get ready for the next round --- */
+
+ av++;
+ dv += 2;
+ }
+}
+
/* --- @mpx_udiv@ --- *
*
* Arguments: @mpw *qv, *qvl@ = quotient vector base and limit
* @mpw *rv, *rvl@ = dividend/remainder vector base and limit
* @const mpw *dv, *dvl@ = divisor vector base and limit
+ * @mpw *sv, *svl@ = scratch workspace
*
* Returns: ---
*
* may not overlap in any way. Yes, I know it's a bit odd
* requiring the dividend to be in the result position but it
* does make some sense really. The remainder must have
- * headroom for at least two extra words.
+ * headroom for at least two extra words. The scratch space
+ * must be at least two words larger than twice the size of the
+ * divisor.
*/
void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl,
- const mpw *dv, const mpw *dvl)
+ const mpw *dv, const mpw *dvl,
+ mpw *sv, mpw *svl)
{
- mpw spare[2];
unsigned norm = 0;
size_t scale;
mpw d, dd;
MPX_ZERO(qv, qvl);
+ /* --- Perform some sanity checks --- */
+
+ MPX_SHRINK(dv, dvl);
+ assert(((void)"division by zero in mpx_udiv", dv < dvl));
+
/* --- Normalize the divisor --- *
*
* The algorithm requires that the divisor be at least two digits long.
* This is easy to fix.
*/
- MPX_SHRINK(dv, dvl);
-
- assert(((void)"division by zero in mpx_udiv", dv < dvl));
-
- d = dvl[-1];
- if (dv + 1 == dvl) {
- spare[0] = 0;
- spare[1] = d;
- dv = spare;
- dvl = spare + 2;
- norm += MPW_BITS;
- }
+ {
+ unsigned b;
- while (d < MPW_MAX / 2) {
- d <<= 1;
- norm += 1;
+ d = dvl[-1];
+ for (b = MPW_BITS / 2; b; b >>= 1) {
+ if (d < (MPW_MAX >> b)) {
+ d <<= b;
+ norm += b;
+ }
+ }
+ if (dv + 1 == dvl)
+ norm += MPW_BITS;
}
- dd = dvl[-2];
/* --- Normalize the dividend/remainder to match --- */
- mpx_lsl(rv, rvl, rv, rvl, norm);
+ if (norm) {
+ mpw *svvl = sv + (dvl - dv) + 1;
+ mpx_lsl(rv, rvl, rv, rvl, norm);
+ mpx_lsl(sv, svvl, dv, dvl, norm);
+ dv = sv;
+ sv = svvl;
+ dvl = svvl;
+ MPX_SHRINK(dv, dvl);
+ }
+
MPX_SHRINK(rv, rvl);
+ d = dvl[-1];
+ dd = dvl[-2];
/* --- Work out the relative scales --- */
{
size_t rvn = rvl - rv;
- size_t dvn = dvn - dv;
+ size_t dvn = dvl - dv;
/* --- If the divisor is clearly larger, notice this --- */
/* --- Now for the main loop --- */
{
- mpw *rvv;
- mpw r;
-
- scale--;
- rvv = rvl - 2;
- r = rvv[1];
+ mpw *rvv = rvl - 2;
while (scale) {
- mpw q, rr;
+ mpw q;
+ mpd rh;
/* --- Get an estimate for the next quotient digit --- */
- rr = *rvv--;
+ mpw r = rvv[1];
+ mpw rr = rvv[0];
+ mpw rrr = *--rvv;
+
+ scale--;
+ rh = ((mpd)r << MPW_BITS) | rr;
if (r == d)
q = MPW_MAX;
- else {
- mpd rx = (r << MPW_BITS) | rr;
- q = MPW(rx / d);
- }
+ else
+ q = MPW(rh / d);
/* --- Refine the estimate --- */
{
mpd yh = (mpd)d * q;
mpd yl = (mpd)dd * q;
-
+
+ if (yl > MPW_MAX) {
+ yh += yl >> MPW_BITS;
+ yl &= MPW_MAX;
+ }
+
+ while (yh > rh || (yh == rh && yl > rrr)) {
+ q--;
+ yh -= d;
+ if (yl < dd) {
+ yh++;
+ yl += MPW_MAX;
+ }
+ yl -= dd;
+ }
+ }
+
+ /* --- Remove a chunk from the dividend --- */
+
+ {
+ mpw *svv;
+ const mpw *dvv;
+ mpw c = 0;
+
+ /* --- Calculate the size of the chunk --- */
+
+ for (svv = sv, dvv = dv; dvv < dvl; svv++, dvv++) {
+ mpd x = (mpd)*dvv * (mpd)q + c;
+ *svv = MPW(x);
+ c = x >> MPW_BITS;
+ }
+ if (c)
+ *svv++ = c;
+
+ /* --- Now make sure that we can cope with the difference --- *
+ *
+ * Take advantage of the fact that subtraction works two's-
+ * complement.
+ */
+
+ mpx_usub(rv + scale, rvl, rv + scale, rvl, sv, svv);
+ if (rvl[-1] > MPW_MAX / 2) {
+ mpx_uadd(rv + scale, rvl, rv + scale, rvl, dv, dvl);
+ q--;
+ }
+ }
+
+ /* --- Done for another iteration --- */
+
+ if (qvl - qv > scale)
+ qv[scale] = q;
+ r = rr;
+ rr = rrr;
+ }
+ }
+
+ /* --- Now fiddle with unnormalizing and things --- */
+
+ mpx_lsr(rv, rvl, rv, rvl, norm);
}
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / commitdiff