/* -*-c-*-
*
- * $Id: mpx.c,v 1.3 1999/11/13 01:57:31 mdw Exp $
+ * $Id: mpx.c,v 1.7 1999/12/22 15:49:07 mdw Exp $
*
* Low-level multiprecision arithmetic
*
/*----- Revision history --------------------------------------------------*
*
* $Log: mpx.c,v $
+ * Revision 1.7 1999/12/22 15:49:07 mdw
+ * New function for division by a small integer.
+ *
+ * Revision 1.6 1999/11/20 22:43:44 mdw
+ * Integrate testing for MPX routines.
+ *
+ * Revision 1.5 1999/11/20 22:23:27 mdw
+ * Add function versions of some low-level macros with wider use.
+ *
+ * Revision 1.4 1999/11/17 18:04:09 mdw
+ * Add two's-complement functionality. Improve mpx_udiv a little by
+ * performing the multiplication of the divisor by q with the subtraction
+ * from r.
+ *
* Revision 1.3 1999/11/13 01:57:31 mdw
* Remove stray debugging code.
*
/*----- Unsigned arithmetic -----------------------------------------------*/
+/* --- @mpx_2c@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector
+ * @const mpw *v, *vl@ = source vector
+ *
+ * Returns: ---
+ *
+ * Use: Calculates the two's complement of @v@.
+ */
+
+void mpx_2c(mpw *dv, mpw *dvl, const mpw *v, const mpw *vl)
+{
+ mpw c = 0;
+ while (dv < dvl && v < vl)
+ *dv++ = c = MPW(~*v++);
+ if (dv < dvl) {
+ if (c > MPW_MAX / 2)
+ c = MPW(~0);
+ while (dv < dvl)
+ *dv++ = c;
+ }
+ MPX_UADDN(dv, dvl, 1);
+}
+
/* --- @mpx_ucmp@ --- *
*
* Arguments: @const mpw *av, *avl@ = first argument vector base and limit
}
}
+/* --- @mpx_uaddn@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
+ * @mpw n@ = other addend
+ *
+ * Returns: ---
+ *
+ * Use: Adds a small integer to a multiprecision number.
+ */
+
+void mpx_uaddn(mpw *dv, mpw *dvl, mpw n) { MPX_UADDN(dv, dvl, n); }
+
/* --- @mpx_usub@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
*dv++ = c;
}
+/* --- @mpx_usubn@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = source and destination base and limit
+ * @n@ = subtrahend
+ *
+ * Returns: ---
+ *
+ * Use: Subtracts a small integer from a multiprecision number.
+ */
+
+void mpx_usubn(mpw *dv, mpw *dvl, mpw n) { MPX_USUBN(dv, dvl, n); }
+
/* --- @mpx_umul@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
}
}
+/* --- @mpx_umuln@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
+ * @const mpw *av, *avl@ = multiplicand vector base and limit
+ * @mpw m@ = multiplier
+ *
+ * Returns: ---
+ *
+ * Use: Multiplies a multiprecision integer by a single-word value.
+ * The destination and source may be equal. The destination
+ * is completely cleared after use.
+ */
+
+void mpx_umuln(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m)
+{
+ MPX_UMULN(dv, dvl, av, avl, m);
+}
+
+/* --- @mpx_umlan@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination/accumulator base and limit
+ * @const mpw *av, *avl@ = multiplicand vector base and limit
+ * @mpw m@ = multiplier
+ *
+ * Returns: ---
+ *
+ * Use: Multiplies a multiprecision integer by a single-word value
+ * and adds the result to an accumulator.
+ */
+
+void mpx_umlan(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, mpw m)
+{
+ MPX_UMLAN(dv, dvl, av, avl, m);
+}
+
/* --- @mpx_usqr@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
* 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. The scratch space
- * must be at least two words larger than twice the size of the
- * divisor.
+ * must be at least one word larger than the divisor.
*/
void mpx_udiv(mpw *qv, mpw *qvl, mpw *rv, mpw *rvl,
/* --- Normalize the dividend/remainder to match --- */
if (norm) {
- mpw *svvl = sv + (dvl - dv) + 1;
mpx_lsl(rv, rvl, rv, rvl, norm);
- mpx_lsl(sv, svvl, dv, dvl, norm);
+ mpx_lsl(sv, svl, dv, dvl, norm);
dv = sv;
- sv = svvl;
- dvl = svvl;
+ dvl = svl;
MPX_SHRINK(dv, dvl);
}
{
mpw *svv;
const mpw *dvv;
- mpw c = 0;
+ mpw mc = 0, sc = 0;
- /* --- Calculate the size of the chunk --- */
+ /* --- Calculate the size of the chunk --- *
+ *
+ * This does the whole job of calculating @r >> scale - qd@.
+ */
- for (svv = sv, dvv = dv; dvv < dvl; svv++, dvv++) {
- mpd x = (mpd)*dvv * (mpd)q + c;
+ for (svv = rv + scale, dvv = dv;
+ dvv < dvl && svv < rvl;
+ svv++, dvv++) {
+ mpd x = (mpd)*dvv * (mpd)q + mc;
+ mc = x >> MPW_BITS;
+ x = (mpd)*svv - MPW(x) - sc;
*svv = MPW(x);
- c = x >> MPW_BITS;
+ if (x >> MPW_BITS)
+ sc = 1;
+ else
+ sc = 0;
+ }
+
+ if (svv < rvl) {
+ mpd x = (mpd)*svv - mc - sc;
+ *svv++ = MPW(x);
+ if (x >> MPW_BITS)
+ sc = MPW_MAX;
+ else
+ sc = 0;
+ while (svv < rvl)
+ *svv++ = sc;
}
- if (c)
- *svv++ = c;
- /* --- Now make sure that we can cope with the difference --- *
+ /* --- Fix if the quotient was too large --- *
*
- * Take advantage of the fact that subtraction works two's-
- * complement.
+ * This doesn't seem to happen very often.
*/
- 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--;
mpx_lsr(rv, rvl, rv, rvl, norm);
}
+/* --- @mpx_udivn@ --- *
+ *
+ * Arguments: @mpw *qv, *qvl@ = storage for the quotient (may overlap
+ * dividend)
+ * @const mpw *rv, *rvl@ = dividend
+ * @mpw d@ = single-precision divisor
+ *
+ * Returns: Remainder after divison.
+ *
+ * Use: Performs a single-precision division operation.
+ */
+
+mpw mpx_udivn(mpw *qv, mpw *qvl, const mpw *rv, const mpw *rvl, mpw d)
+{
+ size_t i;
+ size_t ql = qvl - qv;
+ mpd r = 0;
+
+ i = rvl - rv;
+ while (i > 0) {
+ i--;
+ r = (r << MPW_BITS) | rv[i];
+ if (i < ql)
+ qv[i] = r / d;
+ r %= d;
+ }
+ return (MPW(r));
+}
+
+/*----- Test rig ----------------------------------------------------------*/
+
+#ifdef TEST_RIG
+
+#include <mLib/alloc.h>
+#include <mLib/dstr.h>
+#include <mLib/quis.h>
+#include <mLib/testrig.h>
+
+#include "mpscan.h"
+
+#define ALLOC(v, vl, sz) do { \
+ size_t _sz = (sz); \
+ mpw *_vv = xmalloc(MPWS(_sz)); \
+ mpw *_vvl = _vv + _sz; \
+ (v) = _vv; \
+ (vl) = _vvl; \
+} while (0)
+
+#define LOAD(v, vl, d) do { \
+ const dstr *_d = (d); \
+ mpw *_v, *_vl; \
+ ALLOC(_v, _vl, MPW_RQ(_d->len)); \
+ mpx_loadb(_v, _vl, _d->buf, _d->len); \
+ (v) = _v; \
+ (vl) = _vl; \
+} while (0)
+
+#define MAX(x, y) ((x) > (y) ? (x) : (y))
+
+static void dumpbits(const char *msg, const void *pp, size_t sz)
+{
+ const octet *p = pp;
+ fputs(msg, stderr);
+ for (; sz; sz--)
+ fprintf(stderr, " %02x", *p++);
+ fputc('\n', stderr);
+}
+
+static void dumpmp(const char *msg, const mpw *v, const mpw *vl)
+{
+ fputs(msg, stderr);
+ MPX_SHRINK(v, vl);
+ while (v < vl)
+ fprintf(stderr, " %08lx", (unsigned long)*--vl);
+ fputc('\n', stderr);
+}
+
+static int chkscan(const mpw *v, const mpw *vl,
+ const void *pp, size_t sz, int step)
+{
+ mpscan mps;
+ const octet *p = pp;
+ unsigned bit = 0;
+ int ok = 1;
+
+ mpscan_initx(&mps, v, vl);
+ while (sz) {
+ unsigned x = *p;
+ int i;
+ p += step;
+ for (i = 0; i < 8 && MPSCAN_STEP(&mps); i++) {
+ if (MPSCAN_BIT(&mps) != (x & 1)) {
+ fprintf(stderr,
+ "\n*** error, step %i, bit %u, expected %u, found %u\n",
+ step, bit, x & 1, MPSCAN_BIT(&mps));
+ ok = 0;
+ }
+ x >>= 1;
+ bit++;
+ }
+ sz--;
+ }
+
+ return (ok);
+}
+
+static int loadstore(dstr *v)
+{
+ dstr d = DSTR_INIT;
+ size_t sz = MPW_RQ(v->len) * 2, diff;
+ mpw *m, *ml;
+ int ok = 1;
+
+ dstr_ensure(&d, v->len);
+ m = xmalloc(MPWS(sz));
+
+ for (diff = 0; diff < sz; diff += 5) {
+ size_t oct;
+
+ ml = m + sz - diff;
+
+ mpx_loadl(m, ml, v->buf, v->len);
+ if (!chkscan(m, ml, v->buf, v->len, +1))
+ ok = 0;
+ MPX_OCTETS(oct, m, ml);
+ mpx_storel(m, ml, d.buf, d.sz);
+ if (memcmp(d.buf, v->buf, oct) != 0) {
+ dumpbits("\n*** storel failed", d.buf, d.sz);
+ ok = 0;
+ }
+
+ mpx_loadb(m, ml, v->buf, v->len);
+ if (!chkscan(m, ml, v->buf + v->len - 1, v->len, -1))
+ ok = 0;
+ MPX_OCTETS(oct, m, ml);
+ mpx_storeb(m, ml, d.buf, d.sz);
+ if (memcmp(d.buf + d.sz - oct, v->buf + v->len - oct, oct) != 0) {
+ dumpbits("\n*** storeb failed", d.buf, d.sz);
+ ok = 0;
+ }
+ }
+
+ if (!ok)
+ dumpbits("input data", v->buf, v->len);
+
+ free(m);
+ dstr_destroy(&d);
+ return (ok);
+}
+
+static int lsl(dstr *v)
+{
+ mpw *a, *al;
+ int n = *(int *)v[1].buf;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(c, cl, &v[2]);
+ ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS);
+
+ mpx_lsl(d, dl, a, al, n);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** lsl(%i) failed\n", n);
+ dumpmp(" a", a, al);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(c); free(d);
+ return (ok);
+}
+
+static int lsr(dstr *v)
+{
+ mpw *a, *al;
+ int n = *(int *)v[1].buf;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(c, cl, &v[2]);
+ ALLOC(d, dl, al - a + (n + MPW_BITS - 1) / MPW_BITS + 1);
+
+ mpx_lsr(d, dl, a, al, n);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** lsr(%i) failed\n", n);
+ dumpmp(" a", a, al);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(c); free(d);
+ return (ok);
+}
+
+static int uadd(dstr *v)
+{
+ mpw *a, *al;
+ mpw *b, *bl;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(b, bl, &v[1]);
+ LOAD(c, cl, &v[2]);
+ ALLOC(d, dl, MAX(al - a, bl - b) + 1);
+
+ mpx_uadd(d, dl, a, al, b, bl);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** uadd failed\n");
+ dumpmp(" a", a, al);
+ dumpmp(" b", b, bl);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(b); free(c); free(d);
+ return (ok);
+}
+
+static int usub(dstr *v)
+{
+ mpw *a, *al;
+ mpw *b, *bl;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(b, bl, &v[1]);
+ LOAD(c, cl, &v[2]);
+ ALLOC(d, dl, al - a);
+
+ mpx_usub(d, dl, a, al, b, bl);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** usub failed\n");
+ dumpmp(" a", a, al);
+ dumpmp(" b", b, bl);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(b); free(c); free(d);
+ return (ok);
+}
+
+static int umul(dstr *v)
+{
+ mpw *a, *al;
+ mpw *b, *bl;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(b, bl, &v[1]);
+ LOAD(c, cl, &v[2]);
+ ALLOC(d, dl, (al - a) + (bl - b));
+
+ mpx_umul(d, dl, a, al, b, bl);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** umul failed\n");
+ dumpmp(" a", a, al);
+ dumpmp(" b", b, bl);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(b); free(c); free(d);
+ return (ok);
+}
+
+static int usqr(dstr *v)
+{
+ mpw *a, *al;
+ mpw *c, *cl;
+ mpw *d, *dl;
+ int ok = 1;
+
+ LOAD(a, al, &v[0]);
+ LOAD(c, cl, &v[1]);
+ ALLOC(d, dl, 2 * (al - a));
+
+ mpx_usqr(d, dl, a, al);
+ if (MPX_UCMP(d, dl, !=, c, cl)) {
+ fprintf(stderr, "\n*** usqr failed\n");
+ dumpmp(" a", a, al);
+ dumpmp("expected", c, cl);
+ dumpmp(" result", d, dl);
+ ok = 0;
+ }
+
+ free(a); free(c); free(d);
+ return (ok);
+}
+
+static int udiv(dstr *v)
+{
+ mpw *a, *al;
+ mpw *b, *bl;
+ mpw *q, *ql;
+ mpw *r, *rl;
+ mpw *qq, *qql;
+ mpw *s, *sl;
+ int ok = 1;
+
+ ALLOC(a, al, MPW_RQ(v[0].len) + 2); mpx_loadb(a, al, v[0].buf, v[0].len);
+ LOAD(b, bl, &v[1]);
+ LOAD(q, ql, &v[2]);
+ LOAD(r, rl, &v[3]);
+ ALLOC(qq, qql, al - a);
+ ALLOC(s, sl, (bl - b) + 1);
+
+ mpx_udiv(qq, qql, a, al, b, bl, s, sl);
+ if (MPX_UCMP(qq, qql, !=, q, ql) ||
+ MPX_UCMP(a, al, !=, r, rl)) {
+ fprintf(stderr, "\n*** udiv failed\n");
+ dumpmp(" divisor", b, bl);
+ dumpmp("expect r", r, rl);
+ dumpmp("result r", a, al);
+ dumpmp("expect q", q, ql);
+ dumpmp("result q", qq, qql);
+ ok = 0;
+ }
+
+ free(a); free(b); free(r); free(q); free(s); free(qq);
+ return (ok);
+}
+
+static test_chunk defs[] = {
+ { "load-store", loadstore, { &type_hex, 0 } },
+ { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } },
+ { "lsr", lsr, { &type_hex, &type_int, &type_hex, 0 } },
+ { "uadd", uadd, { &type_hex, &type_hex, &type_hex, 0 } },
+ { "usub", usub, { &type_hex, &type_hex, &type_hex, 0 } },
+ { "umul", umul, { &type_hex, &type_hex, &type_hex, 0 } },
+ { "usqr", usqr, { &type_hex, &type_hex, 0 } },
+ { "udiv", udiv, { &type_hex, &type_hex, &type_hex, &type_hex, 0 } },
+ { 0, 0, { 0 } }
+};
+
+int main(int argc, char *argv[])
+{
+ test_run(argc, argv, defs, SRCDIR"/tests/mpx");
+ return (0);
+}
+
+
+#endif
+
/*----- That's all, folks -------------------------------------------------*/
projects / u / mdw / catacomb / blobdiff