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Mini Shell
Mini Shell
/*
Author: Pate Williams (c) 1997
Multiple-precision division. See "Handbook of
Applied Cryptography" by Alfred J. Menezes et
al 14.2.5 Section pages 598 - 599.
*/
#include <assert.h>
#include <mem.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#define BASE 10l
#define BITS_PER_LONG 32l
#define DIGITS_PER_LINE 78l
#define DEBUG
typedef long * mp;
void mp_set_length(long length, mp *mpa)
{
mp mpx = *mpa;
if (mpx) {
if (length > mpx[0]) {
mpx = realloc(mpx, (length + 2) * sizeof(long));
assert(mpx != 0);
}
memset(mpx, 0, (length + 2) * sizeof(long));
}
else {
mpx = calloc(length + 2, sizeof(long));
assert(mpx != 0);
}
mpx[0] = length;
*mpa = mpx;
}
void mp_copy(mp mpa, mp *mpb)
{
long length = mpa[0];
mp_set_length(length, mpb);
memcpy(*mpb, mpa, (length + 2) * sizeof(long));
}
void mp_extend(long length, mp mpa, mp *mpb)
{
long i, len = mpa[0], sign = mpa[len + 1];
mp mpx;
mp_set_length(length, mpb);
mpx = *mpb;
memcpy(mpx, mpa, (len + 2) * sizeof(long));
if (length == len) return;
for (i = len + 1; i <= length; i++)
mpx[i] = sign;
mpx[0] = length;
mpx[length + 1] = sign;
}
void mp_free(mp *mpa)
{
free(*mpa);
*mpa = 0;
}
void mp_add(mp mpx, mp mpy, mp *mpw)
/* calcuates w = x + y */
{
long c = 0, i, s, x_len = mpx[0], y_len = mpy[0];
long mx = max(x_len, y_len);
long w_len = mx;
mp mpa = 0, mpb = 0, mpv;
if (x_len == y_len) w_len++;
mp_extend(w_len, mpx, &mpa);
mp_extend(w_len, mpy, &mpb);
mp_set_length(w_len, mpw);
mpv = *mpw;
for (i = 1; i <= w_len + 1; i++) {
s = mpa[i] + mpb[i] + c;
mpv[i] = s % BASE;
c = s < BASE ? 0 : 1;
}
mp_free(&mpa);
mp_free(&mpb);
}
void mp_negate(mp *mpa)
{
mp mpx = *mpa;
long base_1 = BASE - 1, c = 1, i, length = mpx[0] + 1, s;
for (i = 1; i <= length; i++)
mpx[i] = base_1 - mpx[i];
for (i = 1; i <= length; i++) {
s = mpx[i] + c;
mpx[i] = s % BASE;
c = s < BASE ? 0 : 1;
}
}
int mp_compares(mp mpa, long s)
{
int value;
long a_len = mpa[0], s_sign = s < 0;
long a_sign = mpa[a_len + 1] != 0;
mp mpb = 0;
if (a_sign != s_sign)
value = a_sign ? - 1 : + 1;
else if (a_len > 1)
value = s_sign ? - 1 : + 1;
else {
if (s_sign) s = - s;
mp_copy(mpa, &mpb);
if (a_sign) mp_negate(&mpb);
if (mpb[1] == 0) value = 0;
else value = mpb[1] - s;
if (a_sign) value = - value;
}
return value;
}
void mp_dump(mp mpa)
{
char sign = '+';
long i;
mp mpb = 0;
mp_copy(mpa, &mpb);
if (mpb[mpa[0] + 1] != 0) {
mp_negate(&mpb);
sign = '-';
}
printf("%c", sign);
for (i = mpb[0]; i >= 1; i--)
printf("%ld", mpb[i]);
printf("\n");
}
void mp_sub(mp mpx, mp mpy, mp *mpw)
/* calculates w = x - y */
{
mp mpz = 0;
mp_copy(mpy, &mpz);
mp_negate(&mpz);
mp_add(mpx, mpz, mpw);
mp_free(&mpz);
}
int mp_compare(mp mpx, mp mpy)
{
int zero;
long i, length, sign;
mp mpz = 0;
mp_sub(mpx, mpy, &mpz);
length = mpz[0];
sign = mpz[length + 1];
if (sign != 0) return - 1;
for (zero = 1, i = length; i >= 1 && zero; i--)
zero = mpz[i] == 0;
if (zero) return 0;
return + 1;
}
void mp_adds(mp mpx, long y, mp *mpw)
/* calcuates w = x + y */
{
int zero;
long c = y, i, s, sign, x_len = mpx[0];
long w_len = x_len + 1;
mp mpv;
mp_set_length(w_len, mpw);
mpv = *mpw;
for (i = 1; i <= w_len; i++) {
s = mpx[i] + c;
mpv[i] = s % BASE;
c = s < BASE ? 0 : 1;
}
sign = mpv[w_len + 1];
for (i = w_len, zero = mpv[w_len] == 0; i >= 3 && zero; i--)
zero = mpv[i - 1] == 0, mpv[0]--;
mpv[mpv[0] + 1] = sign;
}
void mp_base_left_shift(mp mpa, long count, mp *mpb)
{
long i, length = mpa[0];
mp mpc;
mp_set_length(length + count, mpb);
mpc = *mpb;
for (i = 1; i <= count; i++)
mpc[i] = 0;
for (i = 1; i <= length; i++)
mpc[i + count] = mpa[i];
}
void mp_div(mp mpx, mp mpy, mp *mpq, mp *mpr)
/* calcuates q = x / y, r = x % y */
{
int zero = 1;
long c, l, qj, sign, u, uv, v, xi, xi1, xi2, yt, yt1;
long i, j, k, x_len = mpx[0], y_len = mpy[0];
long a_len, q_len = x_len - y_len + 1, r_len = y_len;
long x_sign = mpx[x_len + 1], y_sign = mpy[y_len + 1];
mp mpa = 0, mpb = 0, mpc = 0, mpd = 0, mpe = 0;
mp mpu, mpv, mpw = 0;
/* test for zero divisor */
for (i = y_len; i >= 1 && zero; i--)
zero = mpy[i] == 0;
assert(zero == 0);
mp_copy(mpx, &mpa);
mp_copy(mpy, &mpb);
if (x_sign != 0) mp_negate(&mpa);
if (y_sign != 0) mp_negate(&mpb);
/* check for dividend < divisor */
if (mp_compare(mpa, mpb) < 0) {
mp_set_length(1, mpq);
(*mpq)[1] = 0;
if (mpx[x_len + 1] == 0)
mp_copy(mpx, mpr);
else
mp_add(mpx, mpy, mpr);
}
else {
mp_set_length(q_len, mpq);
mp_set_length(r_len, mpr);
mpu = *mpq;
mp_base_left_shift(mpb, x_len - y_len, &mpc);
while (mp_compare(mpa, mpc) >= 0) {
mpu[q_len]++;
mp_sub(mpa, mpc, &mpd);
mp_copy(mpd, &mpa);
}
#ifdef DEBUG
for (j = mpu[0]; j >= 1; j--)
printf("%ld", mpu[j]);
printf(" ");
for (j = mpa[0]; j >= 1; j--)
printf("%ld", mpa[j]);
printf("\n");
#endif
for (i = mpa[0], zero = mpa[i] == 0; i >= 1 && zero; i--)
zero = mpa[i - 1] == 0, mpa[0]--;
mpa[mpa[0] + 1] = 0;
yt = mpb[y_len];
yt1 = mpb[y_len - 1];
for (i = x_len; i >= y_len + 1; i--) {
j = i - y_len;
a_len = mpa[0];
if (i <= a_len) xi = mpa[i]; else xi = 0;
if (i - 1 <= a_len) xi1 = mpa[i - 1]; else xi1 = 0;
if (i - 2 <= a_len) xi2 = mpa[i - 2]; else xi2 = 0;
if (xi == yt)
qj = BASE - 1;
else
qj = (BASE * xi + xi1) / yt;
while (qj * (yt * BASE + yt1) >
xi * BASE * BASE + xi1 * BASE + xi2)
qj--;
if (qj != 0) {
mp_base_left_shift(mpb, j - 1, &mpc);
c = 0;
l = mpc[0];
mp_set_length(l + 1, &mpw);
for (k = 1; k <= l; k++) {
uv = mpw[k] + qj * mpc[k] + c;
u = uv / BASE;
v = uv % BASE;
mpw[k] = v;
c = u;
}
mpw[l + 1] = u;
mp_sub(mpa, mpw, &mpd);
if (mpd[mpd[0] + 1] != 0) {
mp_add(mpa, mpc, &mpe);
mp_copy(mpe, &mpd);
qj--;
}
mp_copy(mpd, &mpa);
}
mpu[j] = qj;
for (j = mpu[0], zero = mpu[j] == 0; j >= 1 && zero; j--)
zero = mpu[j - 1] == 0, mpu[0]--;
for (j = mpa[0], zero = mpa[j] == 0; j >= 1 && zero; j--)
zero = mpa[j - 1] == 0, mpa[0]--;
mpu[mpu[0] + 1] = 0;
mpa[mpa[0] + 1] = 0;
#ifdef DEBUG
for (j = mpu[0]; j >= 1; j--)
printf("%ld", mpu[j]);
printf(" ");
for (j = mpa[0]; j >= 1; j--)
printf("%ld", mpa[j]);
printf("\n");
#endif
}
mp_copy(mpa, mpr);
for (i = q_len, zero = mpu[q_len] == 0; i >= 3 && zero; i--)
zero = mpu[i - 1] == 0, q_len--;
mpu[0] = q_len;
mpu[q_len + 1] = 0;
if (x_sign != 0 && y_sign == 0) {
mp_adds(*mpq, 1l, &mpc);
mp_copy(mpc, mpq);
mp_negate(mpq);
mp_negate(mpr);
mp_add(*mpr, mpb, &mpc);
mp_copy(mpc, mpr);
mpv = *mpr;
for (i = r_len, zero = mpv[r_len] == 0; i >= 3 && zero; i--)
zero = mpv[i - 1] == 0, r_len--;
mpv[0] = r_len;
mpv[r_len + 1] = 0;
}
else if (x_sign == 0 && y_sign != 0) {
mp_adds(*mpq, 1l, &mpc);
mp_copy(mpc, mpq);
mp_negate(mpq);
mp_add(*mpr, mpy, &mpc);
mp_copy(mpc, mpr);
mpv = *mpr;
sign = mpv[r_len + 1];
for (i = r_len, zero = mpv[r_len] == 0; i >= 3 && zero; i--)
zero = mpv[i - 1] == 0, r_len--;
mpv[0] = r_len;
mpv[r_len + 1] = sign;
}
else if (x_sign != 0 && y_sign != 0) {
mp_negate(mpr);
mpv = *mpr;
sign = mpv[r_len + 1];
for (i = r_len, zero = mpv[r_len] == 0; i >= 3 && zero; i--)
zero = mpv[i - 1] == 0, r_len--;
mpv[0] = r_len;
mpv[r_len + 1] = sign;
}
}
mp_free(&mpa);
mp_free(&mpb);
mp_free(&mpc);
mp_free(&mpd);
mp_free(&mpe);
mp_free(&mpw);
}
void mp_mul(mp mpx, mp mpy, mp *mpw)
/* calcuates w = x * y */
{
long c, i, ij, j, x_len = mpx[0], y_len = mpy[0];
long u, uv, v, w_len = x_len + y_len + 2, w_sign;
long x_sign = mpx[x_len + 1], y_sign = mpy[y_len + 1];
mp mpa = 0, mpb = 0, mpv;
mp_copy(mpx, &mpa);
mp_copy(mpy, &mpb);
if (x_sign != 0) mp_negate(&mpa);
if (y_sign != 0) mp_negate(&mpb);
w_sign = (x_sign == y_sign) ? 0 : BASE - 1;
mp_set_length(w_len, mpw);
mpv = *mpw;
for (i = 1; i <= y_len; i++) {
c = 0;
for (j = 1; j <= x_len; j++) {
ij = i + j - 1;
uv = mpv[ij] + mpa[j] * mpb[i] + c;
u = uv / BASE;
v = uv % BASE;
mpv[ij] = v;
c = u;
}
mpv[i + x_len] = u;
}
for (i = w_len; i >= 1 && mpv[i] == 0; i--) mpv[0]--;
if (w_sign != 0) mp_negate(mpw);
mp_free(&mpa);
mp_free(&mpb);
}
int mp_odd(mp mpa)
/* returns nonzero if a is odd */
{
return (int) (mpa[1] & 1l);
}
void mp_one(mp *mpa)
/* a = 1 */
{
mp_set_length(1, mpa);
(*mpa)[1] = 1;
}
void mp_zero(mp *mpa)
/* a = 0 */
{
mp_set_length(1, mpa);
}
void mp_long_to_mp(long l, mp *mpa)
{
long digits[256], i = 0, j, sign = l < 0;
if (sign) l = - l;
do {
digits[i++] = l % BASE;
l /= BASE;
} while (l > 0);
mp_set_length(i, mpa);
for (j = 1; j <= i; j++) (*mpa)[j] = digits[j - 1];
if (sign) mp_negate(mpa);
}
void mp_print(mp mpa)
{
char digits[2048];
long count, i = 0, j, k, left, sign = 0;
mp mpb = 0, mpc = 0, mpq = 0, mpr = 0;
mp_copy(mpa, &mpb);
if (mpb[mpb[0] + 1] != 0) {
sign = 1;
mp_negate(&mpb);
}
mp_long_to_mp(10l, &mpc);
do {
mp_div(mpb, mpc, &mpq, &mpr);
digits[i++] = (char) (mpr[1] + '0');
mp_copy(mpq, &mpb);
} while (mp_compares(mpq, 0l) > 0);
digits[i] = 0;
strrev(digits);
count = i / DIGITS_PER_LINE;
left = i % DIGITS_PER_LINE;
if (sign == 1) printf("-");
for (i = 0; i < count; i++) {
j = i * DIGITS_PER_LINE;
for (k = 0; k < DIGITS_PER_LINE; k++)
printf("%c", digits[j + k]);
printf("\\\n");
}
i = count * DIGITS_PER_LINE;
for (j = 0; j < left; j++)
printf("%c", digits[i + j]);
printf("\n");
mp_free(&mpb);
mp_free(&mpc);
mp_free(&mpq);
mp_free(&mpr);
}
int main(void)
{
mp mpq = 0, mpr = 0, mpx = 0, mpy = 0;
mp_set_length(9, &mpx);
mp_set_length(5, &mpy);
mpx[1] = 7, mpx[2] = 2, mpx[3] = 3, mpx[4] = 8;
mpx[5] = 4, mpx[6] = 9, mpx[7] = 1, mpx[8] = 2, mpx[9] = 7;
mpy[1] = 1, mpy[2] = 6, mpy[3] = 4, mpy[4] = 4, mpy[5] = 8;
mp_div(mpx, mpy, &mpq, &mpr);
mp_dump(mpx);
mp_dump(mpy);
mp_dump(mpq);
mp_dump(mpr);
mp_negate(&mpx);
mp_div(mpx, mpy, &mpq, &mpr);
mp_dump(mpx);
mp_dump(mpy);
mp_dump(mpq);
mp_dump(mpr);
mp_negate(&mpx);
mp_negate(&mpy);
mp_div(mpx, mpy, &mpq, &mpr);
mp_dump(mpx);
mp_dump(mpy);
mp_dump(mpq);
mp_dump(mpr);
mp_negate(&mpx);
mp_div(mpx, mpy, &mpq, &mpr);
mp_dump(mpx);
mp_dump(mpy);
mp_dump(mpq);
mp_dump(mpr);
mp_free(&mpq);
mp_free(&mpr);
mp_free(&mpx);
mp_free(&mpy);
return 0;
}
Zerion Mini Shell 1.0