/**
* @brief Pre-calculate some of the expensive steps in reduction.
*
* This function should only be called once (normally when a session starts).
* When the session is over, bi_free_mod() should be called. bi_mod_power()
* relies on this function being called.
* @param ctx [in] The bigint session context.
* @param bim [in] The bigint modulus that will be used.
* @param mod_offset [in] There are three moduluii that can be stored - the
* standard modulus, and its two primes p and q. This offset refers to which
* modulus we are referring to.
* @see bi_free_mod(), bi_mod_power().
*/
void ICACHE_FLASH_ATTR bi_set_mod(BI_CTX *ctx, bigint *bim, int mod_offset)
{
int k = bim->size;
comp d = (comp)((long_comp)COMP_RADIX/(bim->comps[k-1]+1));
#ifdef CONFIG_BIGINT_MONTGOMERY
bigint *R, *R2;
#endif
ctx->bi_mod[mod_offset] = bim;
bi_permanent(ctx->bi_mod[mod_offset]);
ctx->bi_normalised_mod[mod_offset] = bi_int_multiply(ctx, bim, d);
bi_permanent(ctx->bi_normalised_mod[mod_offset]);
#if defined(CONFIG_BIGINT_MONTGOMERY)
/* set montgomery variables */
R = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k-1); /* R */
R2 = comp_left_shift(bi_clone(ctx, ctx->bi_radix), k*2-1); /* R^2 */
ctx->bi_RR_mod_m[mod_offset] = bi_mod(ctx, R2); /* R^2 mod m */
ctx->bi_R_mod_m[mod_offset] = bi_mod(ctx, R); /* R mod m */
bi_permanent(ctx->bi_RR_mod_m[mod_offset]);
bi_permanent(ctx->bi_R_mod_m[mod_offset]);
ctx->N0_dash[mod_offset] = modular_inverse(ctx->bi_mod[mod_offset]);
#elif defined (CONFIG_BIGINT_BARRETT)
ctx->bi_mu[mod_offset] =
bi_divide(ctx, comp_left_shift(
bi_clone(ctx, ctx->bi_radix), k*2-1), ctx->bi_mod[mod_offset], 0);
bi_permanent(ctx->bi_mu[mod_offset]);
#endif
}
/**
* @brief Perform a single montgomery reduction.
* @param ctx [in] The bigint session context.
* @param bixy [in] A bigint.
* @return The result of the montgomery reduction.
*/
bigint * ICACHE_FLASH_ATTR bi_mont(BI_CTX *ctx, bigint *bixy)
{
int i = 0, n;
uint8_t mod_offset = ctx->mod_offset;
bigint *bim = ctx->bi_mod[mod_offset];
comp mod_inv = ctx->N0_dash[mod_offset];
check(bixy);
if (ctx->use_classical) /* just use classical instead */
{
return bi_mod(ctx, bixy);
}
n = bim->size;
do
{
bixy = bi_add(ctx, bixy, comp_left_shift(
bi_int_multiply(ctx, bim, bixy->comps[i]*mod_inv), i));
} while (++i < n);
comp_right_shift(bixy, n);
if (bi_compare(bixy, bim) >= 0)
{
bixy = bi_subtract(ctx, bixy, bim, NULL);
}
return bixy;
}
int main() {
bi_initialize();
bigint sum = int_to_bi(1);
bigint last = int_to_bi(1);
int i, j;
for (i = 1; i <= (SIZE-1)/2; ++i) {
for (j = 0; j < 4; ++j) {
last = bi_add(last, bi_int_multiply(int_to_bi(i), 2));
sum = bi_add(sum, bi_copy(last));
}
}
bi_print(stdout, sum);
printf("\n");
bi_free(last);
bi_terminate();
return 0;
}
int main() {
bi_initialize();
bigint last = int_to_bi(1);
int i, j;
int number_of_primes = 0;
for (i = 1;; ++i) {
for (j = 0; j < 4; ++j) {
last = bi_add(last, bi_int_multiply(int_to_bi(i), 2));
if (j != 3 && bi_is_probable_prime(bi_copy(last), 4)) {
++number_of_primes;
}
}
if ((double)number_of_primes / (4*i+1) < 0.1) {
printf("%d\n", i*2+1);
break;
}
#ifdef DEBUG
printf("%d/%d on iteration %d ~%f\n", number_of_primes, (4*i+1), i, (float)number_of_primes/(4*i+1));
#endif
}
bi_free(last);
bi_terminate();
return 0;
}
/**
* @brief Does both division and modulo calculations.
*
* Used extensively when doing classical reduction.
* @param ctx [in] The bigint session context.
* @param u [in] A bigint which is the numerator.
* @param v [in] Either the denominator or the modulus depending on the mode.
* @param is_mod [n] Determines if this is a normal division (0) or a reduction
* (1).
* @return The result of the division/reduction.
*/
bigint * ICACHE_FLASH_ATTR bi_divide(BI_CTX *ctx, bigint *u, bigint *v, int is_mod)
{
int n = v->size, m = u->size-n;
int j = 0, orig_u_size = u->size;
uint8_t mod_offset = ctx->mod_offset;
comp d;
bigint *quotient, *tmp_u;
comp q_dash;
check(u);
check(v);
/* if doing reduction and we are < mod, then return mod */
if (is_mod && bi_compare(v, u) > 0)
{
bi_free(ctx, v);
return u;
}
quotient = alloc(ctx, m+1);
tmp_u = alloc(ctx, n+1);
v = trim(v); /* make sure we have no leading 0's */
d = (comp)((long_comp)COMP_RADIX/(V1+1));
/* clear things to start with */
memset(quotient->comps, 0, ((quotient->size)*COMP_BYTE_SIZE));
/* normalise */
if (d > 1)
{
u = bi_int_multiply(ctx, u, d);
if (is_mod)
{
v = ctx->bi_normalised_mod[mod_offset];
}
else
{
v = bi_int_multiply(ctx, v, d);
}
}
if (orig_u_size == u->size) /* new digit position u0 */
{
more_comps(u, orig_u_size + 1);
}
do
{
/* get a temporary short version of u */
memcpy(tmp_u->comps, &u->comps[u->size-n-1-j], (n+1)*COMP_BYTE_SIZE);
/* calculate q' */
if (U(0) == V1)
{
q_dash = COMP_RADIX-1;
}
else
{
q_dash = (comp)(((long_comp)U(0)*COMP_RADIX + U(1))/V1);
if (v->size > 1 && V2)
{
/* we are implementing the following:
if (V2*q_dash > (((U(0)*COMP_RADIX + U(1) -
q_dash*V1)*COMP_RADIX) + U(2))) ... */
comp inner = (comp)((long_comp)COMP_RADIX*U(0) + U(1) -
(long_comp)q_dash*V1);
if ((long_comp)V2*q_dash > (long_comp)inner*COMP_RADIX + U(2))
{
q_dash--;
}
}
}
/* multiply and subtract */
if (q_dash)
{
int is_negative;
tmp_u = bi_subtract(ctx, tmp_u,
bi_int_multiply(ctx, bi_copy(v), q_dash), &is_negative);
more_comps(tmp_u, n+1);
Q(j) = q_dash;
/* add back */
if (is_negative)
{
Q(j)--;
tmp_u = bi_add(ctx, tmp_u, bi_copy(v));
/* lop off the carry */
tmp_u->size--;
v->size--;
}
}
else
{
Q(j) = 0;
}
/* copy back to u */
memcpy(&u->comps[u->size-n-1-j], tmp_u->comps, (n+1)*COMP_BYTE_SIZE);
} while (++j <= m);
bi_free(ctx, tmp_u);
bi_free(ctx, v);
if (is_mod) /* get the remainder */
{
bi_free(ctx, quotient);
return bi_int_divide(ctx, trim(u), d);
}
else /* get the quotient */
{
bi_free(ctx, u);
return trim(quotient);
}
}
int main() {
bi_initialize();
bigint sum = int_to_bi(0);
int a,b,c,d,e,f,g,h,i,j;
int n;
for (a=9;a>0;--a) {
for (b=9;b>=0;--b) {
if (b==a) continue;
for (c=9;c>=0;--c) {
if (c==a||c==b) continue;
for (d=9;d>=0;--d) {
if (d==a||d==b||d==c) continue;
for (e=9;e>=0;--e) {
if (e==a||e==b||e==c||e==d) continue;
for (f=9;f>=0;--f) {
if (f==a||f==b||f==c||f==d||f==e) continue;
for (g=9;g>=0;--g) {
if (g==a||g==b||g==c||g==d||g==e||g==f) continue;
for (h=9;h>=0;--h) {
if (h==a||h==b||h==c||h==d||h==e||h==f||h==g) continue;
for (i=9;i>=0;--i) {
if (i==a||i==b||i==c||i==d||i==e||i==f||i==g||i==h) continue;
for (j=9;j>=0;--j) {
if (j==a||j==b||j==c||j==d||j==e||j==f||j==g||j==h||j==i) continue;
if ((b * 100 + c * 10 + d) % 2 == 0)
if ((c * 100 + d * 10 + e) % 3 == 0)
if ((d * 100 + e * 10 + f) % 5 == 0)
if ((e * 100 + f * 10 + g) % 7 == 0)
if ((f * 100 + g * 10 + h) % 11 == 0)
if ((g * 100 + h * 10 + i) % 13 == 0)
if ((h * 100 + i * 10 + j) % 17 == 0) {
n =
b * 100000000 +
c * 10000000 +
d * 1000000 +
e * 100000 +
f * 10000 +
g * 1000 +
h * 100 +
i * 10 +
j * 1;
sum = bi_add(sum, int_to_bi(n));
sum = bi_add(sum, bi_int_multiply(int_to_bi(1000000000), a));
#ifdef DEBUG
printf("%d%d%d%d%d%d%d%d%d%d\n", a,b,c,d,e,f,g,h,i,j);
bi_print(stdout,bi_copy(sum));
printf("\n");
#endif
}
}
}
}
}
}
}
}
}
}
}
bi_print(stdout,sum);
printf("\n");
bi_terminate();
return 0;
}