void log10(const mpz_t n, mpz_t l, int prec) {
mpf_t tmp, tmp2;
mpf_inits(tmp, tmp2, NULL);
mpf_set_z(tmp, n);
log10(tmp, tmp2, prec);
mpz_set_f(l, tmp2);
mpf_clears(tmp, tmp2, NULL);
}
void log2(const mpz_t n, mpz_t l) {
mpf_t tmp, tmp2;
mpf_inits(tmp, tmp2, NULL);
mpf_set_z(tmp, n);
log2(tmp, tmp2);
mpz_set_f(l, tmp2);
mpf_clears(tmp, tmp2, NULL);
}
void log(const mpz_t n, mpz_t l, mpz_t b) {
mpf_t tmp, tmp2, tmp3;
mpf_inits(tmp, tmp2, tmp3, NULL);
mpf_set_z(tmp, n);
mpf_set_z(tmp3, b);
log(tmp, tmp2, tmp3);
mpz_set_f(l, tmp2);
mpf_clears(tmp, tmp2, tmp3, NULL);
}
void log(const mpf_t n, mpf_t l, mpf_t b) {
// l = log10(n)/log10(b)
mpf_t tmp, tmp2;
mpf_inits(tmp, tmp2, NULL);
log10(n, tmp);
log10(b, tmp2);
mpf_div(l, tmp, tmp2);
mpf_clears(tmp, tmp2, NULL);
}
void log10(const mpf_t n, mpf_t l, int prec) {
// Approximate log10 to prec digits.
// Ref.: http://www.brics.dk/RS/04/17/BRICS-RS-04-17.pdf
mpf_t tmp, tmp2;
mpf_inits(tmp, tmp2, NULL);
mpf_set(tmp, n);
stringstream res;
for (int i = 0; i < prec + 1; i++) {
int d = digits(tmp);
// m_(i+1) = (m_i / (10 ^ a_i)) ^ 10
mpf_set_ui(tmp2, 10);
mpf_pow_ui(tmp2, tmp2, d);
mpf_div(tmp2, tmp, tmp2);
mpf_pow_ui(tmp, tmp2, 10);
res << d;
if (i == 0) res << ".";
}
mpf_set_str(l, res.str().c_str(), 10);
mpf_clears(tmp, tmp2, NULL);
}
//Le but de la fonction est de calculer le développement en fractions continue jusqu'à un certain rang de racine carrée de kN et de stocker les couples (A_n-1,Q_n) comme décrit dans la section (à venir)
cfrac expand(const mpz_t N, const long long unsigned int rang, const mpz_t k)
{
cfrac res; //Contient l'ensemble des A_n-1 et l'ensemble Q_n
mpz_inits(res.N, res.k, res.g, NULL);
//Initialisation des variables
mpz_t* A = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Le tableau contenant les A_n-1
mpz_t* Q = (mpz_t*)malloc((rang+2)*sizeof(mpz_t)); //Le tableau contenant les Q_n
mpz_t* P = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Éléments reliés au Q_n
mpz_t* r = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Interviennent dans le calcul des A_n-1 & Q_n
mpz_t* q = (mpz_t*)malloc(rang*sizeof(mpz_t)); //Idem
mpz_t g, tempz; //Idem, tempz = variable à tout faire
mpf_t sqrtkN, tempf, tempf2; //sqrtkN = sqrt(k*N), tempf = variable à tout faire
//Valeurs d'initialisation de la boucle
mpz_inits(g, A[0], Q[0], r[0], tempz, NULL);
mpf_inits(tempf, sqrtkN, tempf2, NULL);
//Initialisation des différentes valeurs "indépendantes"
mpz_set(tempz, N);
mpz_mul(tempz, tempz, k);
mpf_set_z(sqrtkN, tempz);
mpf_sqrt(sqrtkN, sqrtkN);
mpf_floor(tempf, sqrtkN);
mpz_set_f(g, tempf); //g = [sqrt(kN)]
mpz_set(Q[0], k);
mpz_mul(Q[0], Q[0], N); //Q_-1 = kN = Q[0]
mpz_set(r[0], g); //r_-1 = r[0]
mpz_set_ui(A[0], 1); //A_-1 = A[0]
//Calcul de P_0 & Q_0
mpz_init_set_ui(Q[1], 1); //Q_0 = Q[1]
mpz_init_set_ui(P[0], 0); //P_0 = P[0]
for(long long int i = 0; i < rang; i++)
{
switch(i)
{
case 0:
//Calcul de q_0
mpz_init_set(q[0], g); //q_0 = [(sqrt(kN) + P_0)/Q_0] avec P_0 = 0 et Q_0 = 1
//Calcul de A_0
mpz_init_set(A[1],A[0]);
mpz_mul(A[1], A[1], q[0]); //A_0 = q_0*A_-1
mpz_mod(A[1], A[1], N); //On réduit mod N
//Calcul de r_0
mpz_init_set_ui(r[1], 0); //r_0 = P_0 + g - q_0.Q_0 = 0 + g - g.1 = 0
//Calcul de P_1
mpz_init_set(P[1], g); //P_1 = g - r_0 = g - 0 = g
//Calcul de Q_1 = Q[2]
mpz_init_set(Q[2], r[1]);
mpz_sub(Q[2], Q[2], r[0]);
mpz_mul(Q[2], Q[2], q[0]);
mpz_add(Q[2], Q[2], Q[0]);
break;
default:
//Calcul q_i
mpz_init(q[i]);
mpf_set_z(tempf, P[i]);
mpf_set_z(tempf2, Q[i+1]);
mpf_add(tempf, tempf, sqrtkN); //sqrt(kN) + P_i
mpf_div(tempf, tempf, tempf2);
mpf_floor(tempf, tempf); //floor((sqrt(kN) + P_i)/Q_i)
mpz_set_f(q[i], tempf);
//Calcul de r_n = r[n+1]
mpz_init(r[i+1]);
mpz_submul(r[i+1], q[i], Q[i+1]);
mpz_add(r[i+1], r[i+1], P[i]);
mpz_add(r[i+1], r[i+1], g);
//Calcul de A_n = A[n+1]
mpz_init_set(A[i+1],A[i]);
mpz_mul(A[i+1], A[i+1], q[i]); //A_i-1*q_i
mpz_add(A[i+1], A[i+1], A[i-1]); //A_i-1*q_i + A_i-2
mpz_mod(A[i+1], A[i+1], N); //réduction modulo N
//Calcul P_n+1
mpz_init_set(P[i+1], g);
mpz_sub(P[i+1], P[i+1], r[i+1]); //P[n+1] = g - r_n = g - r[n+1]
//Calcul Q_n+1 = Q[n+2]
mpz_init_set(Q[i+2], r[i+1]);
mpz_sub(Q[i+2], Q[i+2], r[i]); //(r_n - r_n-1)
mpz_mul(Q[i+2], Q[i+2], q[i]); //q_n(r_n - r_n-1)
mpz_add(Q[i+2], Q[i+2], Q[i]); //Q_n-1 + q_n(r_n - r_n-1)
break;
}
}
//Test de routine pour voir si le développement de la fraction continue s'est bien passé
mpz_t tempsqrt;
mpz_init(tempsqrt);
mpz_set(tempsqrt, k);
mpz_mul(tempsqrt, tempsqrt, N);
mpz_sqrt(tempsqrt, tempsqrt);
mpz_mul_ui(tempsqrt, tempsqrt, 2);
for(int i = 1; i < rang; i++) //Éviter de commencer à i = 0 puisque cela représente Q_-1 qui n'intervient uniquement dans l'algo et non dans le développement en fraction continue
{
if(mpz_cmp(Q[i], tempsqrt) >= 0) //Si Q_n >= 2sqrt(kN)
{
res.rang = 0;
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
}
//Assignation des tableaux dans le résultat
res.A = A;
res.Q = Q;
res.r = r;
res.q = q;
res.P = P;
mpz_set(res.N, N);
mpz_set(res.k, k);
res.rang = rang;
mpz_set(res.g, g);
//Libération de mémoire
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
void
check_random (long reps)
{
unsigned long test;
gmp_randstate_ptr rands = RANDS;
mpf_t a, b, x;
mpz_t ds;
int hibits, lshift1, lshift2;
int xtra;
#define HIBITS 10
#define LSHIFT1 10
#define LSHIFT2 10
mpf_set_default_prec ((1 << HIBITS) + (1 << LSHIFT1) + (1 << LSHIFT2));
mpz_init (ds);
mpf_inits (a, b, x, NULL);
for (test = 0; test < reps; test++)
{
mpz_urandomb (ds, rands, HIBITS);
hibits = mpz_get_ui (ds) + 1;
mpz_urandomb (ds, rands, hibits);
mpz_setbit (ds, hibits - 1); /* make sure msb is set */
mpf_set_z (a, ds);
mpf_set_z (b, ds);
mpz_urandomb (ds, rands, LSHIFT1);
lshift1 = mpz_get_ui (ds);
mpf_mul_2exp (a, a, lshift1 + 1);
mpf_mul_2exp (b, b, lshift1 + 1);
mpf_add_ui (a, a, 1); /* make a one-bit difference */
mpz_urandomb (ds, rands, LSHIFT2);
lshift2 = mpz_get_ui (ds);
mpf_mul_2exp (a, a, lshift2);
mpf_mul_2exp (b, b, lshift2);
mpz_urandomb (ds, rands, lshift2);
mpf_set_z (x, ds);
mpf_add (a, a, x);
mpf_add (b, b, x);
insert_random_low_zero_limbs (a, rands);
insert_random_low_zero_limbs (b, rands);
if (mpf_eq (a, b, lshift1 + hibits) == 0 ||
mpf_eq (b, a, lshift1 + hibits) == 0)
{
dump_abort (a, b, lshift1 + hibits, lshift1, lshift2, hibits, 1, test);
}
for (xtra = 1; xtra < 100; xtra++)
if (mpf_eq (a, b, lshift1 + hibits + xtra) != 0 ||
mpf_eq (b, a, lshift1 + hibits + xtra) != 0)
{
dump_abort (a, b, lshift1 + hibits + xtra, lshift1, lshift2, hibits, 0, test);
}
}
mpf_clears (a, b, x, NULL);
mpz_clear (ds);
}
void *chudnovsky_chunk(void *arguments)
{
unsigned long int k, threek, total_iterations;
mpz_t a, b, c, d, e, rt, rb;
mpf_t rtf, rbf, r;
struct thread_args *args = (struct thread_args *)arguments;
total_iterations = args->iter;
/* Init libgmp variables */
mpz_inits(a, b, c, d, e, rt, rb, NULL);
mpf_inits(rtf, rbf, r, NULL);
/* Main loop of a thread */
while (1) {
/* Check which k needs calculation */
pthread_mutex_lock(&args->start_mutex);
k = args->k;
args->k++;
pthread_mutex_unlock(&args->start_mutex);
/* If all ks are done, say return */
if (k > total_iterations) break;
/* 3k */
threek = k * 3;
/* (6k!) */
mpz_fac_ui(a, threek << 1);
/* 545140134k */
mpz_set_ui(b, BCONST1);
mpz_mul_ui(b, b, k);
/* 13591409 + 545140134k */
mpz_add_ui(b, b, BCONST2);
/* (3k)! */
mpz_fac_ui(c, threek);
/* (k!)^3 */
mpz_fac_ui(d, k);
mpz_pow_ui(d, d, DCONST1);
/* (-640320)^3k */
mpz_set_ui(e, ECONST1);
mpz_pow_ui(e, e, threek);
if ((threek & 1) == 1) mpz_neg(e, e);
/* Get everything together */
/* (6k)! (13591409 + 545140134k) */
mpz_mul(rt, a, b);
/* (3k)! (k!)^3 */
mpz_mul(rb, c, d);
mpz_mul(rb, rb, e);
/* Switch to floats */
mpf_set_z(rtf, rt);
mpf_set_z(rbf, rb);
/* divide top/bottom */
mpf_div(r, rtf, rbf);
/* add result to the sum */
pthread_mutex_lock(&args->sum_mutex);
mpf_add(args->sum, args->sum, r);
pthread_mutex_unlock(&args->sum_mutex);
}
/* Deinit variables, result is passed via args->sum */
mpz_clears(a, b, c, d, e, rt, rb, NULL);
mpf_clears(rtf, rbf, r, NULL);
}
int chudnovsky(int digits, int threads)
{
int res = 0;
unsigned long int i, iter, precision, rest, per_cpu, k;
mpf_t ltf, sum, result;
pthread_t *pthreads;
struct thread_args targs;
mp_exp_t exponent;
char *pi;
/* If threads is not specified, check how many CPUs are avail */
if (threads == 0) {
threads = get_cpu_count();
}
pthreads = malloc(threads * sizeof(pthread_t));
if (pthreads == NULL) {
res = -ENOMEM;
goto chudnovsky_exit;
}
/* Calculate and set precision */
precision = (digits * BPD) + 1;
mpf_set_default_prec(precision);
/* Calculate number of iterations */
iter = digits/DPI + 1;
/* Init all objects */
mpf_inits(ltf, sum, result, targs.sum, NULL);
mpf_set_ui(sum, 0);
mpf_set_ui(targs.sum, 0);
/* Set pthread specific stuff */
targs.k = 0;
targs.iter = iter;
pthread_mutex_init(&targs.start_mutex, NULL);
pthread_mutex_init(&targs.sum_mutex, NULL);
/* Prepare the constant from the left side of the equation */
mpf_sqrt_ui(ltf, LTFCON1);
mpf_mul_ui(ltf, ltf, LTFCON2);
printf("Starting summing, using:\n"
"%d digits - %lu iterations - %d threads\n",
digits, iter, threads);
for (i = 0; i < threads; i++) {
pthread_create(&pthreads[i], NULL, &chudnovsky_chunk, (void *) &targs);
}
/* Wait for threads to finish and take their sums */
for (i = 0; i < threads; i++) {
pthread_join(pthreads[i], NULL);
}
printf("Starting final steps\n");
/* Invert sum */
mpf_ui_div(sum, 1, targs.sum);
mpf_mul(result, sum, ltf);
/* Get one more char then needed and then trunc to avoid rounding */
pi = mpf_get_str(NULL, &exponent, 10, digits + 2, result);
pi[digits+1] = '\0';
if (strlen(pi) < LAST_DIGITS_PRINT + 1) {
printf("Calculated PI:\n");
printf("\t%.*s.%s\n", (int)exponent, pi, pi + exponent);
} else {
printf("Last digits of Pi are:\n");
printf("\t%s\n", pi+(digits-(LAST_DIGITS_PRINT-1)));
}
free(pi);
mpf_clears(ltf, sum, result, NULL);
pthread_mutex_destroy(&targs.start_mutex);
pthread_mutex_destroy(&targs.sum_mutex);
/* TODO: add verification here! */
chudnovsky_free_pthreads:
free(pthreads);
chudnovsky_exit:
return res;
}