/* -*-c-*-
*
- * $Id: mpx.c,v 1.1 1999/09/03 08:41:12 mdw Exp $
+ * $Id: mpx.c,v 1.20 2004/04/08 01:36:15 mdw Exp $
*
* Low-level multiprecision arithmetic
*
* MA 02111-1307, USA.
*/
-/*----- Revision history --------------------------------------------------*
- *
- * $Log: mpx.c,v $
- * 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>
#include "mptypes.h"
#include "mpx.h"
+#include "bitops.h"
/*----- Loading and storing -----------------------------------------------*/
/* --- @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)
MPX_ZERO(v, vl);
}
+/* --- @mpx_storel2cn@ --- *
+ *
+ * Arguments: @const mpw *v, *vl@ = base and limit of source vector
+ * @void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Stores a negative MP in an octet array, least significant
+ * octet first, as two's complement. High-end octets are
+ * silently discarded if there isn't enough space for them.
+ * This obviously makes the output bad.
+ */
+
+void mpx_storel2cn(const mpw *v, const mpw *vl, void *pp, size_t sz)
+{
+ unsigned c = 1;
+ unsigned b = 0;
+ mpw n, w = 0;
+ octet *p = pp, *q = p + sz;
+ unsigned bits = 0;
+
+ while (p < q) {
+ if (bits < 8) {
+ if (v >= vl) {
+ b = w;
+ break;
+ }
+ n = *v++;
+ b = w | n << bits;
+ w = n >> (8 - bits);
+ bits += MPW_BITS - 8;
+ } else {
+ b = w;
+ w >>= 8;
+ bits -= 8;
+ }
+ b = U8(~b + c);
+ c = c && !b;
+ *p++ = b;
+ }
+ while (p < q) {
+ b = U8(~b + c);
+ c = c && !b;
+ *p++ = b;
+ b = 0;
+ }
+}
+
+/* --- @mpx_loadl2cn@ --- *
+ *
+ * Arguments: @mpw *v, *vl@ = base and limit of destination vector
+ * @const void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Loads a negative MP in an octet array, least significant
+ * octet first, as two's complement. High-end octets are
+ * ignored if there isn't enough space for them. This probably
+ * means you made the wrong choice coming here.
+ */
+
+void mpx_loadl2cn(mpw *v, mpw *vl, const void *pp, size_t sz)
+{
+ unsigned n;
+ unsigned c = 1;
+ mpw w = 0;
+ const octet *p = pp, *q = p + sz;
+ unsigned bits = 0;
+
+ if (v >= vl)
+ return;
+ while (p < q) {
+ n = U8(~(*p++) + c);
+ c = c && !n;
+ w |= n << bits;
+ bits += 8;
+ if (bits >= MPW_BITS) {
+ *v++ = MPW(w);
+ w = n >> (MPW_BITS - bits + 8);
+ bits -= MPW_BITS;
+ if (v >= vl)
+ return;
+ }
+ }
+ *v++ = w;
+ MPX_ZERO(v, vl);
+}
+
+/* --- @mpx_storeb2cn@ --- *
+ *
+ * Arguments: @const mpw *v, *vl@ = base and limit of source vector
+ * @void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Stores a negative MP in an octet array, most significant
+ * octet first, as two's complement. High-end octets are
+ * silently discarded if there isn't enough space for them,
+ * which probably isn't what you meant.
+ */
+
+void mpx_storeb2cn(const mpw *v, const mpw *vl, void *pp, size_t sz)
+{
+ mpw n, w = 0;
+ unsigned b = 0;
+ unsigned c = 1;
+ octet *p = pp, *q = p + sz;
+ unsigned bits = 0;
+
+ while (q > p) {
+ if (bits < 8) {
+ if (v >= vl) {
+ b = w;
+ break;
+ }
+ n = *v++;
+ b = w | n << bits;
+ w = n >> (8 - bits);
+ bits += MPW_BITS - 8;
+ } else {
+ b = w;
+ w >>= 8;
+ bits -= 8;
+ }
+ b = U8(~b + c);
+ c = c && !b;
+ *--q = b;
+ }
+ while (q > p) {
+ b = ~b + c;
+ c = c && !(b & 0xff);
+ *--q = b;
+ b = 0;
+ }
+}
+
+/* --- @mpx_loadb2cn@ --- *
+ *
+ * Arguments: @mpw *v, *vl@ = base and limit of destination vector
+ * @const void *pp@ = pointer to octet array
+ * @size_t sz@ = size of octet array
+ *
+ * Returns: ---
+ *
+ * Use: Loads a negative MP in an octet array, most significant octet
+ * first as two's complement. High-end octets are ignored if
+ * there isn't enough space for them. This probably means you
+ * chose this function wrongly.
+ */
+
+void mpx_loadb2cn(mpw *v, mpw *vl, const void *pp, size_t sz)
+{
+ unsigned n;
+ unsigned c = 1;
+ mpw w = 0;
+ const octet *p = pp, *q = p + sz;
+ unsigned bits = 0;
+
+ if (v >= vl)
+ return;
+ while (q > p) {
+ n = U8(~(*--q) + c);
+ c = c && !n;
+ w |= n << bits;
+ bits += 8;
+ if (bits >= MPW_BITS) {
+ *v++ = MPW(w);
+ w = n >> (MPW_BITS - bits + 8);
+ bits -= MPW_BITS;
+ if (v >= vl)
+ return;
+ }
+ }
+ *v++ = w;
+ MPX_ZERO(v, vl);
+}
+
/*----- Logical shifting --------------------------------------------------*/
/* --- @mpx_lsl@ --- *
goto done;
*dv++ = MPW(w);
MPX_ZERO(dv, dvl);
+ goto done;
}
/* --- Break out word and bit shifts for more sophisticated work --- */
/* --- Handle a shift by a multiple of the word size --- */
if (nb == 0) {
- MPX_COPY(dv + nw, dvl, av, avl);
- memset(dv, 0, MPWS(nw));
+ if (nw >= dvl - dv)
+ MPX_ZERO(dv, dvl);
+ else {
+ MPX_COPY(dv + nw, dvl, av, avl);
+ 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++;
+ 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;
+ }
+
+ while (avl > av) {
+ mpw t = *--avl;
+ *--dvl = (t >> nr) | w;
+ w = t << nb;
+ }
+
+ *--dvl = w;
+ MPX_ZERO(dv, dvl);
+ }
+
+done:;
+}
+
+/* --- @mpx_lslc@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector base and limit
+ * @const mpw *av, *avl@ = source vector base and limit
+ * @size_t n@ = number of bit positions to shift by
+ *
+ * Returns: ---
+ *
+ * Use: Performs a logical shift left operation on an integer, only
+ * it fills in the bits with ones instead of zeroes.
+ */
+
+void mpx_lslc(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, size_t n)
+{
+ size_t nw;
+ unsigned nb;
+
+ /* --- Trivial special case --- */
+
+ if (n == 0)
+ MPX_COPY(dv, dvl, av, avl);
+
+ /* --- Single bit shifting --- */
+
+ else if (n == 1) {
+ mpw w = 1;
while (av < avl) {
mpw t;
if (dv >= dvl)
goto done;
t = *av++;
- *dv++ = MPW((w >> nr) | (t << nb));
- w = t;
+ *dv++ = MPW((t << 1) | w);
+ w = t >> (MPW_BITS - 1);
}
+ if (dv >= dvl)
+ goto done;
+ *dv++ = MPW(w);
+ MPX_ZERO(dv, dvl);
+ goto done;
+ }
- if (dv < dvl) {
- *dv++ = MPW(w >> nr);
- MPX_ZERO(dv, dvl);
+ /* --- Break out word and bit shifts for more sophisticated work --- */
+
+ nw = n / MPW_BITS;
+ nb = n % MPW_BITS;
+
+ /* --- Handle a shift by a multiple of the word size --- */
+
+ if (nb == 0) {
+ if (nw >= dvl - dv)
+ MPX_ONE(dv, dvl);
+ else {
+ MPX_COPY(dv + nw, dvl, av, avl);
+ MPX_ONE(dv, dv + nw);
}
}
+ /* --- 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 (dvn <= nw) {
+ MPX_ONE(dv, dvl);
+ goto done;
+ }
+
+ 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;
+ }
+
+ while (avl > av) {
+ mpw t = *--avl;
+ *--dvl = (t >> nr) | w;
+ w = t << nb;
+ }
+
+ *--dvl = (MPW_MAX >> nr) | w;
+ MPX_ONE(dv, dvl);
+ }
+
done:;
}
/* --- Single bit shifting --- */
else if (n == 1) {
- mpw w = *av++ >> 1;
+ mpw w = av < avl ? *av++ >> 1 : 0;
while (av < avl) {
mpw t;
if (dv >= dvl)
goto done;
*dv++ = MPW(w);
MPX_ZERO(dv, dvl);
+ goto done;
}
/* --- Break out word and bit shifts for more sophisticated work --- */
/* --- Handle a shift by a multiple of the word size --- */
- if (nb == 0)
- MPX_COPY(dv, dvl, av + nw, avl);
+ if (nb == 0) {
+ if (nw >= avl - av)
+ MPX_ZERO(dv, dvl);
+ else
+ MPX_COPY(dv, dvl, av + nw, avl);
+ }
/* --- And finally the difficult case --- */
size_t nr = MPW_BITS - nb;
av += nw;
- w = *av++;
+ w = av < avl ? *av++ : 0;
while (av < avl) {
mpw t;
if (dv >= dvl)
done:;
}
+/*----- Bitwise operations ------------------------------------------------*/
+
+/* --- @mpx_bitop@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination vector
+ * @const mpw *av, *avl@ = first source vector
+ * @const mpw *bv, *bvl@ = second source vector
+ *
+ * Returns: ---
+ *
+ * Use; Provides the dyadic boolean functions.
+ */
+
+#define MPX_BITBINOP(string) \
+ \
+void mpx_bit##string(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl, \
+ const mpw *bv, const mpw *bvl) \
+{ \
+ MPX_SHRINK(av, avl); \
+ MPX_SHRINK(bv, bvl); \
+ \
+ while (dv < dvl) { \
+ mpw a, b; \
+ a = (av < avl) ? *av++ : 0; \
+ b = (bv < bvl) ? *bv++ : 0; \
+ *dv++ = B##string(a, b); \
+ } \
+}
+
+MPX_DOBIN(MPX_BITBINOP)
+
+void mpx_not(mpw *dv, mpw *dvl, const mpw *av, const mpw *avl)
+{
+ MPX_SHRINK(av, avl);
+
+ while (dv < dvl) {
+ mpw a;
+ a = (av < avl) ? *av++ : 0;
+ *dv++ = ~a;
+ }
+}
+
/*----- 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_ueq@ --- *
+ *
+ * Arguments: @const mpw *av, *avl@ = first argument vector base and limit
+ * @const mpw *bv, *bvl@ = second argument vector base and limit
+ *
+ * Returns: Nonzero if the two vectors are equal.
+ *
+ * Use: Performs an unsigned integer test for equality.
+ */
+
+int mpx_ueq(const mpw *av, const mpw *avl, const mpw *bv, const mpw *bvl)
+{
+ MPX_SHRINK(av, avl);
+ MPX_SHRINK(bv, bvl);
+ if (avl - av != bvl - bv)
+ return (0);
+ while (av < avl) {
+ if (*av++ != *bv++)
+ return (0);
+ }
+ return (1);
+}
+
/* --- @mpx_ucmp@ --- *
*
* Arguments: @const mpw *av, *avl@ = first argument vector base and limit
}
return (0);
}
-
+
/* --- @mpx_uadd@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination 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_uaddnlsl@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
+ * @mpw a@ = second argument
+ * @unsigned o@ = offset in bits
+ *
+ * Returns: ---
+ *
+ * Use: Computes %$d + 2^o a$%. If the result overflows then
+ * high-order bits are discarded, as usual. We must have
+ * @0 < o < MPW_BITS@.
+ */
+
+void mpx_uaddnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o)
+{
+ mpd x = (mpd)a << o;
+
+ while (x && dv < dvl) {
+ x += *dv;
+ *dv++ = MPW(x);
+ x >>= MPW_BITS;
+ }
+}
+
/* --- @mpx_usub@ --- *
*
* Arguments: @mpw *dv, *dvl@ = destination vector base and limit
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_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_uaddnlsl@ --- *
+ *
+ * Arguments: @mpw *dv, *dvl@ = destination and first argument vector
+ * @mpw a@ = second argument
+ * @unsigned o@ = offset in bits
+ *
+ * Returns: ---
+ *
+ * Use: Computes %$d + 2^o a$%. If the result overflows then
+ * high-order bits are discarded, as usual. We must have
+ * @0 < o < MPW_BITS@.
+ */
+
+void mpx_usubnlsl(mpw *dv, mpw *dvl, mpw a, unsigned o)
+{
+ mpw b = a >> (MPW_BITS - o);
+ a <<= o;
+
+ if (dv < dvl) {
+ mpd x = (mpd)*dv - (mpd)a;
+ *dv++ = MPW(x);
+ if (x >> MPW_BITS)
+ b++;
+ MPX_USUBN(dv, dvl, b);
+ }
}
/* --- @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_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
+ * @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 --- */
+
+ {
+ 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) {
+ 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 one word larger than 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) {
+ mpx_lsl(rv, rvl, rv, rvl, norm);
+ mpx_lsl(sv, svl, dv, dvl, norm);
+ dv = sv;
+ dvl = svl;
+ 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;
-
+ mpd yy = (mpd)dd * q;
+ mpw yl;
+
+ if (yy > MPW_MAX)
+ yh += yy >> MPW_BITS;
+ yl = MPW(yy);
+
+ while (yh > rh || (yh == rh && yl > rrr)) {
+ q--;
+ yh -= d;
+ if (yl < dd)
+ yh--;
+ yl = MPW(yl - dd);
+ }
+ }
+
+ /* --- Remove a chunk from the dividend --- */
+
+ {
+ mpw *svv;
+ const mpw *dvv;
+ mpw mc = 0, sc = 0;
+
+ /* --- Calculate the size of the chunk --- *
+ *
+ * This does the whole job of calculating @r >> scale - qd@.
+ */
+
+ 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);
+ 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;
+ }
+
+ /* --- Fix if the quotient was too large --- *
+ *
+ * This doesn't seem to happen very often.
+ */
+
+ 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);
+}
+
+/* --- @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 twocl(dstr *v)
+{
+ dstr d = DSTR_INIT;
+ mpw *m, *ml;
+ size_t sz;
+ int ok = 1;
+
+ sz = v[0].len; if (v[1].len > sz) sz = v[1].len;
+ dstr_ensure(&d, sz);
+
+ sz = MPW_RQ(sz);
+ m = xmalloc(MPWS(sz));
+ ml = m + sz;
+
+ mpx_loadl(m, ml, v[0].buf, v[0].len);
+ mpx_storel2cn(m, ml, d.buf, v[1].len);
+ if (memcmp(d.buf, v[1].buf, v[1].len)) {
+ dumpbits("\n*** storel2cn failed", d.buf, v[1].len);
+ ok = 0;
+ }
+
+ mpx_loadl2cn(m, ml, v[1].buf, v[1].len);
+ mpx_storel(m, ml, d.buf, v[0].len);
+ if (memcmp(d.buf, v[0].buf, v[0].len)) {
+ dumpbits("\n*** loadl2cn failed", d.buf, v[0].len);
+ ok = 0;
+ }
+
+ if (!ok) {
+ dumpbits("pos", v[0].buf, v[0].len);
+ dumpbits("neg", v[1].buf, v[1].len);
+ }
+
+ free(m);
+ dstr_destroy(&d);
+
+ return (ok);
+}
+
+static int twocb(dstr *v)
+{
+ dstr d = DSTR_INIT;
+ mpw *m, *ml;
+ size_t sz;
+ int ok = 1;
+
+ sz = v[0].len; if (v[1].len > sz) sz = v[1].len;
+ dstr_ensure(&d, sz);
+
+ sz = MPW_RQ(sz);
+ m = xmalloc(MPWS(sz));
+ ml = m + sz;
+
+ mpx_loadb(m, ml, v[0].buf, v[0].len);
+ mpx_storeb2cn(m, ml, d.buf, v[1].len);
+ if (memcmp(d.buf, v[1].buf, v[1].len)) {
+ dumpbits("\n*** storeb2cn failed", d.buf, v[1].len);
+ ok = 0;
+ }
+
+ mpx_loadb2cn(m, ml, v[1].buf, v[1].len);
+ mpx_storeb(m, ml, d.buf, v[0].len);
+ if (memcmp(d.buf, v[0].buf, v[0].len)) {
+ dumpbits("\n*** loadb2cn failed", d.buf, v[0].len);
+ ok = 0;
+ }
+
+ if (!ok) {
+ dumpbits("pos", v[0].buf, v[0].len);
+ dumpbits("neg", v[1].buf, v[1].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_ueq(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 lslc(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_lslc(d, dl, a, al, n);
+ if (!mpx_ueq(d, dl, c, cl)) {
+ fprintf(stderr, "\n*** lslc(%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_ueq(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_ueq(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_ueq(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_ueq(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_ueq(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_ueq(qq, qql, q, ql) ||
+ !mpx_ueq(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 } },
+ { "2cl", twocl, { &type_hex, &type_hex, } },
+ { "2cb", twocb, { &type_hex, &type_hex, } },
+ { "lsl", lsl, { &type_hex, &type_int, &type_hex, 0 } },
+ { "lslc", lslc, { &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