static void precision_init(int prec) {
int i;
mpf_t f0;
mpf_set_default_prec(prec);
mpf_init2(epsilon, 2);
mpf_init2(negepsilon, 2);
mpf_init(recipeulere);
mpf_init(pi);
mpf_init(eulere);
mpf_set_ui(epsilon, 1);
mpf_div_2exp(epsilon, epsilon, prec);
mpf_neg(negepsilon, epsilon);
mpf_init(f0);
mpf_set_ui(eulere, 1);
mpf_set_ui(f0, 1);
for (i=1;; i++) {
mpf_div_ui(f0, f0, i);
if (mpf_cmp(f0, epsilon) < 0) {
break;
}
mpf_add(eulere, eulere, f0);
}
mpf_clear(f0);
mpf_ui_div(recipeulere, 1, eulere);
compute_pi(prec);
}
void extrapolate(index_t num_samples, mpf_t *samples, mpf_t ans) {
// The Richardson extrapolation recursive formula is
//
// A_n+1(x) = (2^n A_n(2x) - A_n(x)) / (2^n - 1)
mpf_t mult; // mult = 2^n
mpf_init_set_d(mult, 1);
mpf_t denom; // denom = 1 / (mult - 1)
mp_bitcnt_t precision = mpf_get_prec(ans);
mpf_init2(denom, precision);
mpf_t *end = samples + num_samples;
for (mpf_t *lim = samples; lim < end; lim++) { // lim - samples = n
mpf_mul_ui(mult, mult, 2);
mpf_set(denom, mult);
mpf_sub_ui(denom, denom, 1);
mpf_ui_div(denom, 1, denom);
// evaluate all extrapolations
for (mpf_t *ptr = end; --ptr > lim; ) {
// A_n+1(x) = (mult A_n(2x) - A_n(x)) * denom
mpf_mul(*ptr, *ptr, mult);
mpf_sub(*ptr, *ptr, *(ptr - 1));
mpf_mul(*ptr, *ptr, denom);
}
}
mpf_set(ans, *(end - 1)); // move to ans
// Clean
mpf_clear(mult);
mpf_clear(denom);
}
Float Float::pow(const long exponent) const
{
Float result(*this);
if (exponent < 0)
mpf_ui_div(result.value, 1, result.value);
mpf_pow_ui(result.value, result.value, std::abs(exponent));
return result;
}
// r = y/x WARNING: r cannot be the same as y.
void
my_div(mpf_t r, mpf_t y, mpf_t x)
{
unsigned long prec, bits, prec0;
prec0 = mpf_get_prec(r);
if (prec0<=DOUBLE_PREC) {
mpf_set_d(r, mpf_get_d(y)/mpf_get_d(x));
return;
}
bits = 0;
for (prec=prec0; prec>DOUBLE_PREC;) {
int bit = prec&1;
prec = (prec+bit)/2;
bits = bits*2+bit;
}
mpf_set_prec_raw(t1, DOUBLE_PREC);
mpf_ui_div(t1, 1, x);
while (prec<prec0) {
prec *=2;
if (prec<prec0) {
/* t1 = t1+t1*(1-x*t1); */
mpf_set_prec_raw(t2, prec);
mpf_mul(t2, x, t1); // full x half -> full
mpf_ui_sub(t2, 1, t2);
mpf_set_prec_raw(t2, prec/2);
mpf_mul(t2, t2, t1); // half x half -> half
mpf_set_prec_raw(t1, prec);
mpf_add(t1, t1, t2);
} else {
prec = prec0;
/* t2=y*t1, t1 = t2+t1*(y-x*t2); */
mpf_set_prec_raw(t2, prec/2);
mpf_mul(t2, t1, y); // half x half -> half
mpf_mul(r, x, t2); // full x half -> full
mpf_sub(r, y, r);
mpf_mul(t1, t1, r); // half x half -> half
mpf_add(r, t1, t2);
break;
}
prec -= (bits&1);
bits /=2;
}
}
// The Brent-Salamin algorithm
int main(int argc, char* argv[]) {
if (argc < 2) return -1;
int n = (int)strtol(argv[1], NULL, 10);
mpf_set_default_prec(1000);
mpf_t a, b, t, c, sum;
// a=1
mpf_init_set_ui(a, 1);
mpf_init_set_ui(sum, 0);
mpf_init(b);
mpf_init(t);
mpf_init(c);
mpf_init(sum);
// b=1/sqrt(2)
mpf_sqrt_ui(b, 2);
mpf_ui_div(b, 1, b);
// n次迭代的误差小于\frac{2^{n+9}}{20^{2n+1}}
for (int i = 1; i <= n; ++i) {
// t=(a+b)/2
mpf_add(t, a, b);
mpf_div_ui(t, t, 2);
// b=sqrt(a*b);
mpf_mul(b, a, b);
mpf_sqrt(b, b);
// a=t
mpf_swap(t, a);
mpf_mul(t, a, a);
mpf_mul(c, b, b);
mpf_sub(c, t, c);
mpf_mul_2exp(c, c, i + 1);
mpf_add(sum, sum, c);
}
mpf_mul(t, a, a);
mpf_mul_ui(t, t, 4);
mpf_ui_sub(sum, 1, sum);
mpf_div(t, t, sum);
mpf_out_str(stdout, 10, 0, t);
printf("\n");
mpf_clear(a);
mpf_clear(b);
mpf_clear(t);
mpf_clear(c);
mpf_clear(sum);
return 0;
}
int main(void) {
int i ;
char buf[4096] ;
mpf_t x, y , result ;
mpf_set_default_prec(LIMIT);
mpf_init ( x );
mpf_init ( y );
mpf_init (result) ;
mpf_set_str(result, "1" , 10 );
for ( i = 1 ; i < LIMIT ; i++ ) {
sprintf ( buf , "%d" , (2*i + 1) ) ;
mpf_set_str(x, buf , 10 );
mpf_ui_div (y, 1, x) ;
if ( i % 2 ) {
mpf_sub ( x , result , y ) ;
mpf_set (result , x) ;
}
else {
mpf_add ( x , result , y ) ;
mpf_set (result , x) ;
}
}
mpf_mul_ui (x, result, 4 ) ;
printf("\n pi = " ) ;
mpf_out_str (stdout , 10, 0, x) ;
printf ("\n") ;
mpf_clear (x);
mpf_clear (y);
mpf_clear (result);
return EXIT_SUCCESS;
}
int main(void)
{
clock_t begin, end;
mpf_set_default_prec(BITS_PER_DIGIT*DIGITS);
//mpf_set_default_prec(4096);
begin = clock();
mpf_init(x);
mpf_init(y);
mpf_init(p);
mpf_init(aux1);
mpf_init(aux2);
mpf_init(sqrtx);
mpf_init(invsqrtx);
/* x = sqrt(2)*/
mpf_set_ui(x, 2);
mpf_sqrt(x, x);
/* y = sqrt(sqrt(2)) = sqrt(x)*/
mpf_sqrt(y, x);
/* p = 2 + sqrt(2) = 2 + x*/
mpf_add_ui(p, x, 2);
for (i=0; i<24; i++)
{
mpf_sqrt(sqrtx, x);
mpf_ui_div(invsqrtx, 1, sqrtx);
pthread_create(&t1, NULL, thread1, NULL);
pthread_create(&t2, NULL, thread2, NULL);
pthread_join(t1, NULL);
pthread_join(t2, NULL);
mpf_div(p, aux1, aux2);
//Para ver os valores de pi a cada iteracao
//mpf_out_str(stdout, 10, DIGITS, p);
}
mpf_out_str(stdout, 10, DIGITS, p);
mpf_clear(x);
mpf_clear(y);
mpf_clear(p);
mpf_clear(aux1);
mpf_clear(aux2);
mpf_clear(sqrtx);
mpf_clear(invsqrtx);
end = clock();
printf("Took %lfs\n", (double)(end-begin)/CLOCKS_PER_SEC);
pthread_exit(0);
}
void determine_pivot_tolerances(mpf_t pivot_tol, mpf_t pivot_drop_tol, int prec)
/***************************************************************\
* USAGE: compute tolerances based on prec *
\***************************************************************/
{
int num_digits = (int) floor(prec * log10(2.0) - 2.5);
// setup pivot_tol
mpf_set_prec(pivot_tol, prec);
mpf_set_ui(pivot_tol, 10);
mpf_pow_ui(pivot_tol, pivot_tol, num_digits);
mpf_ui_div(pivot_tol, 1, pivot_tol);
// setup pivot_drop_tol
mpf_set_prec(pivot_drop_tol, prec);
mpf_set_ui(pivot_drop_tol, 10);
mpf_pow_ui(pivot_drop_tol, pivot_drop_tol, num_digits - 3);
return;
}
/**
* void initAttributes()
*
* Descricao:
* Inicializa as variaveis globas e atribui os valores iniciais necessarios para a execucao do algoritmo
* Gauss-Legendre.
*
* Parametros de entrada:
* -
*
* Parametros de retorno:
* -
*/
void initAttributes(){
/* Atribui como precisao default 10 milhoes de casas decimais. A funcao mpf_set_default_prec() tem como parametro de entrada
* a precisao desejada em bits, ou seja, e necessario utilizar a conversao (log de 2 na base 10)*10 milhoes para obter o valor correto. */
mpf_set_default_prec((log(10)/log(2))*10000000);
int i;
mpf_t sqrt2; // Variavel auxiliar para o calculo de b0
mpf_t b0; // Variavel auxiliar para o calculo de b0
n_count = 0;
/* Arrays de variaveis utilizadas pelo algoritmo. Como o algoritmo converge para o valor correto do "pi" com 45 milhoes de casas decimais
* em apenas 25 iteracoes, serao utilizado arrays com 25 posicoes */
a_n = (mpf_t*) malloc(25*sizeof(mpf_t));
b_n = (mpf_t*) malloc(25*sizeof(mpf_t));
t_n = (mpf_t*) malloc(25*sizeof(mpf_t));
p_n = (mpf_t*) malloc(25*sizeof(mpf_t));
pi = (mpf_t*) malloc(25*sizeof(mpf_t));
for(i=0; i<25; i++){
mpf_init(a_n[i]);
mpf_init(b_n[i]);
mpf_init(p_n[i]);
mpf_init(t_n[i]);
mpf_init(pi[i]);
}
/* Atribuicao dos valores iniciais */
mpf_init(sqrt2);
mpf_init(b0);
mpf_sqrt_ui(sqrt2, 2);
mpf_ui_div(b0, 1, sqrt2);
mpf_set_d(a_n[n_count], 1.0);
mpf_set(b_n[n_count], b0);
mpf_set_d(t_n[n_count], 0.25);
mpf_set_d(p_n[n_count], 1.0);
}
/**
* Algoritmo de Borwein
*
* vars.a1 se aproxima do valor de 1/PI.
* Cada iteração quadruplica o número de dígitos corretos.
*
*/
void gmp_borwein_par()
{
/*threads*/
pthread_t init[9], calc[4];
/*variáveis para calculos*/
thr_gmpf_t vars;
mpf_set_default_prec(33219280);//(33219280); /*define a precisao do float em bits*/
vars.k = 0; /*Seta o valor inicial do iterador*/
calc[1] = 0;
calc[3] = 0;
/*Inicializa as variáveis em 0*/
pthread_create(&init[0],NULL,(void *)&mpf_init,(void *)&vars.a0);
pthread_create(&init[1],NULL,(void *)&mpf_init,(void *)&vars.a1);
pthread_create(&init[2],NULL,(void *)&mpf_init,(void *)&vars.y0);
pthread_create(&init[3],NULL,(void *)&mpf_init,(void *)&vars.y1);
pthread_create(&init[4],NULL,(void *)&mpf_init,(void *)&vars.aux_y1);
pthread_create(&init[5],NULL,(void *)&mpf_init,(void *)&vars.aux_y2);
pthread_create(&init[6],NULL,(void *)&mpf_init,(void *)&vars.aux_a1);
pthread_create(&init[7],NULL,(void *)&mpf_init,(void *)&vars.aux_a2);
pthread_create(&init[8],NULL,(void *)&mpf_init,(void *)&vars.y_valoratual);
/*A função espera as variáveis serem atualizadas*/
pthread_join(init[0],NULL);
pthread_join(init[1],NULL);
pthread_join(init[2],NULL);
pthread_join(init[3],NULL);
pthread_join(init[4],NULL);
pthread_join(init[5],NULL);
pthread_join(init[6],NULL);
pthread_join(init[7],NULL);
pthread_join(init[8],NULL);
/*TODO: verificar se é possível fazer os cálculos abaixo assim que a variável for inicializada acima*/
/*seta os valores inicias das váriaveis de precisão variável*/
/*d = sqrt(2)*/
mpf_set_ui(vars.aux_y1,2);
mpf_sqrt(vars.aux_y1,vars.aux_y1);
/*a0 = 6-4*d*/
mpf_mul_ui(vars.a0,vars.aux_y1,4);
mpf_ui_sub(vars.a0,6,vars.a0);
mpf_set(vars.a1,vars.a0); //a1=a0
/*y0 = d-1*/
mpf_sub_ui(vars.y0,vars.aux_y1,1); /*vars.y0 = sqrt(2)-1*/
while(vars.k<12)
{
/*Certifica que o valor de y está atualizado antes de calcular o próximo valor de y*/
if(calc[3] != 0)
pthread_join(calc[3],NULL);
pthread_create(&calc[0], NULL, (void *) &calc_y, (void *)&vars); //calcula valor de y-> nao depende de a nem de k, só do y anterior
/*Certifica que a já foi calculado antes de fazer a0=a1*/
if(calc[1] != 0)
pthread_join(calc[1],NULL);
pthread_create(&calc[2], NULL, (void *) &mpf_seta_thread, (void *)&vars); //troca o valor de a
pthread_join(calc[0],NULL);
mpf_set(vars.y_valoratual,vars.y1); //seta o valor de y que será usado para calcular a
/*Troca o valor de y0=y1*/
pthread_create(&calc[3], NULL, (void *) &mpf_sety_thread, (void *)&vars);
pthread_join(calc[2],NULL);
/*Calcula o novo valor de a*/
pthread_create(&calc[1], NULL, (void *) &calc_a, (void *)&vars);
}
mpf_ui_div(vars.a1,1,vars.a1); /*PI=1/vars.a1*/
gmp_printf("%.*Ff\n",10000000,vars.a1);
/*Limpa as variáveis da memória*/
mpf_clear(vars.a0),mpf_clear(vars.a1),mpf_clear(vars.y0),mpf_clear(vars.y1);
mpf_clear(vars.aux_y1),mpf_clear(vars.aux_y2),mpf_clear(vars.aux_a1),mpf_clear(vars.aux_a2);
mpf_clear(vars.y_valoratual);
}
/*
* Function: compute_bbp_second_sum_gmp
* --------------------
* Computes the second summand in the BBP formula.
*
* d: digit to be calculated
* base: the base
* c: a fixed positive integer
* p: a simple polynomial like x or x^2
*
* returns: the value of the second sum
*/
void compute_bbp_second_sum_gmp(mpf_t sum, int d, int base, int c, void (*p)(mpz_t, mpz_t))
{
mpf_set_d(sum, 0.0);
mpz_t k;
mpz_init_set_si(k, floor((double) d / (double) c) + 1);
mpf_t prev_sum;
mpf_init(prev_sum);
mpf_set(prev_sum, sum);
mpf_t base_gmp;
mpf_init(base_gmp);
mpf_set_si(base_gmp, base);
double d_diff = 0.0;
do
{
mpf_set(prev_sum, sum);
mpz_t poly_result;
mpz_init(poly_result);
(*p)(poly_result, k);
mpf_t num;
mpf_init(num);
mpz_t exponent;
mpz_init_set(exponent, k);
mpz_mul_si(exponent, exponent, c);
mpz_mul_si(exponent, exponent, -1);
mpz_add_ui(exponent, exponent, d);
signed long int exp = mpz_get_si(exponent);
unsigned long int neg_exp = -1 * exp;
mpf_pow_ui(num, base_gmp, neg_exp);
mpf_ui_div(num, 1, num);
mpz_clear(exponent);
mpf_t denom;
mpf_init_set_d(denom, mpz_get_d(poly_result));
mpz_clear(poly_result);
mpf_t quotient;
mpf_init(quotient);
mpf_div(quotient, num, denom);
mpf_clear(num);
mpf_clear(denom);
mpf_add(sum, sum, quotient);
mpf_clear(quotient);
mpz_add_ui(k, k, 1);
mpf_t diff;
mpf_init(diff);
mpf_sub(diff, prev_sum, sum);
d_diff = mpf_get_d(diff);
d_diff = fabs(d_diff);
mpf_clear(diff);
}
while (d_diff > 0.00000001);
mpz_clear(k);
mpf_clear(base_gmp);
mpf_clear(prev_sum);
}
int
main (int argc, char **argv)
{
mp_size_t size;
mp_exp_t exp;
int reps = 10000;
int i;
mpf_t u, v, w, x;
mp_size_t bprec = SIZE * GMP_LIMB_BITS;
mpf_t rerr, limit_rerr;
unsigned long ulimb, vlimb;
int single_flag;
tests_start ();
if (argc > 1)
{
reps = strtol (argv[1], 0, 0);
if (argc > 2)
bprec = strtol (argv[2], 0, 0);
}
mpf_set_default_prec (bprec);
mpf_init (rerr);
mpf_init (limit_rerr);
mpf_init (u);
mpf_init (v);
mpf_init (w);
mpf_init (x);
for (i = 0; i < reps; i++)
{
mp_size_t res_prec;
res_prec = urandom () % bprec + 1;
mpf_set_prec (w, res_prec);
mpf_set_prec (x, res_prec);
mpf_set_ui (limit_rerr, 1);
mpf_div_2exp (limit_rerr, limit_rerr, res_prec - 1);
single_flag = 0;
if ((urandom () & 1) != 0)
{
size = urandom () % (2 * SIZE) - SIZE;
exp = urandom () % SIZE;
mpf_random2 (u, size, exp);
}
else
{
ulimb = urandom ();
mpf_set_ui (u, ulimb);
single_flag = 1;
}
if ((urandom () & 1) != 0)
{
size = urandom () % (2 * SIZE) - SIZE;
exp = urandom () % SIZE;
mpf_random2 (v, size, exp);
}
else
{
vlimb = urandom ();
mpf_set_ui (v, vlimb);
single_flag = 2;
}
if (mpf_sgn (v) == 0)
continue;
mpf_div (w, u, v);
mpf_mul (x, w, v);
mpf_reldiff (rerr, u, x);
if (mpf_cmp (rerr, limit_rerr) > 0)
{
printf ("ERROR in mpf_mul or mpf_div after %d tests\n", i);
printf (" u = "); mpf_dump (u);
printf (" v = "); mpf_dump (v);
printf (" x = "); mpf_dump (x);
printf (" w = "); mpf_dump (w);
abort ();
}
if (single_flag == 2)
{
mpf_div_ui (x, u, vlimb);
mpf_reldiff (rerr, w, x);
if (mpf_cmp (rerr, limit_rerr) > 0)
{
printf ("ERROR in mpf_div or mpf_div_ui after %d tests\n", i);
printf (" u = "); mpf_dump (u);
printf (" v = "); mpf_dump (v);
printf (" x = "); mpf_dump (x);
printf (" w = "); mpf_dump (w);
abort ();
}
}
if (single_flag == 1)
{
mpf_ui_div (x, ulimb, v);
mpf_reldiff (rerr, w, x);
if (mpf_cmp (rerr, limit_rerr) > 0)
{
printf ("ERROR in mpf_div or mpf_ui_div after %d tests\n", i);
printf (" u = "); mpf_dump (u);
printf (" v = "); mpf_dump (v);
printf (" x = "); mpf_dump (x);
printf (" w = "); mpf_dump (w);
abort ();
}
}
}
mpf_clear (rerr);
mpf_clear (limit_rerr);
mpf_clear (u);
mpf_clear (v);
mpf_clear (w);
mpf_clear (x);
tests_end ();
exit (0);
}
int scanhash_m7m_hash(int thr_id, uint32_t *pdata, const uint32_t *ptarget,
uint64_t max_nonce, unsigned long *hashes_done)
{
uint32_t data[32] __attribute__((aligned(128)));
uint32_t *data_p64 = data + (M7_MIDSTATE_LEN / sizeof(data[0]));
uint32_t hash[8] __attribute__((aligned(32)));
uint8_t bhash[7][64] __attribute__((aligned(32)));
uint32_t n = pdata[19] - 1;
const uint32_t first_nonce = pdata[19];
char data_str[161], hash_str[65], target_str[65];
uint8_t *bdata = 0;
mpz_t bns[8];
int rc = 0;
int bytes, nnNonce2;
mpz_t product;
mpz_init(product);
for(int i=0; i < 8; i++){
mpz_init(bns[i]);
}
memcpy(data, pdata, 80);
sph_sha256_context ctx_final_sha256;
sph_sha256_context ctx_sha256;
sph_sha512_context ctx_sha512;
sph_keccak512_context ctx_keccak;
sph_whirlpool_context ctx_whirlpool;
sph_haval256_5_context ctx_haval;
sph_tiger_context ctx_tiger;
sph_ripemd160_context ctx_ripemd;
sph_sha256_init(&ctx_sha256);
sph_sha256 (&ctx_sha256, data, M7_MIDSTATE_LEN);
sph_sha512_init(&ctx_sha512);
sph_sha512 (&ctx_sha512, data, M7_MIDSTATE_LEN);
sph_keccak512_init(&ctx_keccak);
sph_keccak512 (&ctx_keccak, data, M7_MIDSTATE_LEN);
sph_whirlpool_init(&ctx_whirlpool);
sph_whirlpool (&ctx_whirlpool, data, M7_MIDSTATE_LEN);
sph_haval256_5_init(&ctx_haval);
sph_haval256_5 (&ctx_haval, data, M7_MIDSTATE_LEN);
sph_tiger_init(&ctx_tiger);
sph_tiger (&ctx_tiger, data, M7_MIDSTATE_LEN);
sph_ripemd160_init(&ctx_ripemd);
sph_ripemd160 (&ctx_ripemd, data, M7_MIDSTATE_LEN);
sph_sha256_context ctx2_sha256;
sph_sha512_context ctx2_sha512;
sph_keccak512_context ctx2_keccak;
sph_whirlpool_context ctx2_whirlpool;
sph_haval256_5_context ctx2_haval;
sph_tiger_context ctx2_tiger;
sph_ripemd160_context ctx2_ripemd;
do {
data[19] = ++n;
nnNonce2 = (int)(data[19]/2);
memset(bhash, 0, 7 * 64);
ctx2_sha256 = ctx_sha256;
sph_sha256 (&ctx2_sha256, data_p64, 80 - M7_MIDSTATE_LEN);
sph_sha256_close(&ctx2_sha256, (void*)(bhash[0]));
ctx2_sha512 = ctx_sha512;
sph_sha512 (&ctx2_sha512, data_p64, 80 - M7_MIDSTATE_LEN);
sph_sha512_close(&ctx2_sha512, (void*)(bhash[1]));
ctx2_keccak = ctx_keccak;
sph_keccak512 (&ctx2_keccak, data_p64, 80 - M7_MIDSTATE_LEN);
sph_keccak512_close(&ctx2_keccak, (void*)(bhash[2]));
ctx2_whirlpool = ctx_whirlpool;
sph_whirlpool (&ctx2_whirlpool, data_p64, 80 - M7_MIDSTATE_LEN);
sph_whirlpool_close(&ctx2_whirlpool, (void*)(bhash[3]));
ctx2_haval = ctx_haval;
sph_haval256_5 (&ctx2_haval, data_p64, 80 - M7_MIDSTATE_LEN);
sph_haval256_5_close(&ctx2_haval, (void*)(bhash[4]));
ctx2_tiger = ctx_tiger;
sph_tiger (&ctx2_tiger, data_p64, 80 - M7_MIDSTATE_LEN);
sph_tiger_close(&ctx2_tiger, (void*)(bhash[5]));
ctx2_ripemd = ctx_ripemd;
sph_ripemd160 (&ctx2_ripemd, data_p64, 80 - M7_MIDSTATE_LEN);
sph_ripemd160_close(&ctx2_ripemd, (void*)(bhash[6]));
for(int i=0; i < 7; i++){
set_one_if_zero(bhash[i]);
mpz_set_uint512(bns[i],bhash[i]);
}
mpz_set_ui(bns[7],0);
for(int i=0; i < 7; i++){
mpz_add(bns[7], bns[7], bns[i]);
}
mpz_set_ui(product,1);
for(int i=0; i < 8; i++){
mpz_mul(product,product,bns[i]);
}
mpz_pow_ui(product, product, 2);
bytes = mpz_sizeinbase(product, 256);
bdata = (uint8_t *)realloc(bdata, bytes);
mpz_export((void *)bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
int digits=(int)((sqrt((double)(nnNonce2))*(1.+EPS))/9000+75);
int iterations=20;
mpf_set_default_prec((long int)(digits*BITS_PER_DIGIT+16));
mpz_t magipi;
mpz_t magisw;
mpf_t magifpi;
mpf_t mpa1, mpb1, mpt1, mpp1;
mpf_t mpa2, mpb2, mpt2, mpp2;
mpf_t mpsft;
mpz_init(magipi);
mpz_init(magisw);
mpf_init(magifpi);
mpf_init(mpsft);
mpf_init(mpa1);
mpf_init(mpb1);
mpf_init(mpt1);
mpf_init(mpp1);
mpf_init(mpa2);
mpf_init(mpb2);
mpf_init(mpt2);
mpf_init(mpp2);
uint32_t usw_;
usw_ = sw_(nnNonce2, SW_DIVS);
if (usw_ < 1) usw_ = 1;
mpz_set_ui(magisw, usw_);
uint32_t mpzscale=mpz_size(magisw);
for(int i=0; i < NM7M; i++){
if (mpzscale > 1000) {
mpzscale = 1000;
}
else if (mpzscale < 1) {
mpzscale = 1;
}
mpf_set_ui(mpa1, 1);
mpf_set_ui(mpb1, 2);
mpf_set_d(mpt1, 0.25*mpzscale);
mpf_set_ui(mpp1, 1);
mpf_sqrt(mpb1, mpb1);
mpf_ui_div(mpb1, 1, mpb1);
mpf_set_ui(mpsft, 10);
for(int j=0; j <= iterations; j++){
mpf_add(mpa2, mpa1, mpb1);
mpf_div_ui(mpa2, mpa2, 2);
mpf_mul(mpb2, mpa1, mpb1);
mpf_abs(mpb2, mpb2);
mpf_sqrt(mpb2, mpb2);
mpf_sub(mpt2, mpa1, mpa2);
mpf_abs(mpt2, mpt2);
mpf_sqrt(mpt2, mpt2);
mpf_mul(mpt2, mpt2, mpp1);
mpf_sub(mpt2, mpt1, mpt2);
mpf_mul_ui(mpp2, mpp1, 2);
mpf_swap(mpa1, mpa2);
mpf_swap(mpb1, mpb2);
mpf_swap(mpt1, mpt2);
mpf_swap(mpp1, mpp2);
}
mpf_add(magifpi, mpa1, mpb1);
mpf_pow_ui(magifpi, magifpi, 2);
mpf_div_ui(magifpi, magifpi, 4);
mpf_abs(mpt1, mpt1);
mpf_div(magifpi, magifpi, mpt1);
mpf_pow_ui(mpsft, mpsft, digits/2);
mpf_mul(magifpi, magifpi, mpsft);
mpz_set_f(magipi, magifpi);
mpz_add(product,product,magipi);
mpz_add(product,product,magisw);
mpz_set_uint256(bns[0], (void*)(hash));
mpz_add(bns[7], bns[7], bns[0]);
mpz_mul(product,product,bns[7]);
mpz_cdiv_q (product, product, bns[0]);
if (mpz_sgn(product) <= 0) mpz_set_ui(product,1);
bytes = mpz_sizeinbase(product, 256);
mpzscale=bytes;
bdata = (uint8_t *)realloc(bdata, bytes);
mpz_export(bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
}
mpz_clear(magipi);
mpz_clear(magisw);
mpf_clear(magifpi);
mpf_clear(mpsft);
mpf_clear(mpa1);
mpf_clear(mpb1);
mpf_clear(mpt1);
mpf_clear(mpp1);
mpf_clear(mpa2);
mpf_clear(mpb2);
mpf_clear(mpt2);
mpf_clear(mpp2);
rc = fulltest_m7hash(hash, ptarget);
if (rc) {
if (opt_debug) {
bin2hex(hash_str, (unsigned char *)hash, 32);
bin2hex(target_str, (unsigned char *)ptarget, 32);
bin2hex(data_str, (unsigned char *)data, 80);
applog(LOG_DEBUG, "DEBUG: [%d thread] Found share!\ndata %s\nhash %s\ntarget %s", thr_id,
data_str,
hash_str,
target_str);
}
pdata[19] = data[19];
goto out;
}
} while (n < max_nonce && !work_restart[thr_id].restart);
pdata[19] = n;
out:
for(int i=0; i < 8; i++){
mpz_clear(bns[i]);
}
mpz_clear(product);
free(bdata);
*hashes_done = n - first_nonce + 1;
return rc;
}
bool bbp_pi(bool const & abortTask,
std::string const & digitIndex,
uint32_t const digitStep,
std::string & piSequence)
{
unsigned long const mantissa_bits = 132;
unsigned long const count_offset = 7;
// settings above gives 32 hexadecimal digits
unsigned long count = static_cast<unsigned long>(
floor(log10(pow(2.0, static_cast<double>(mantissa_bits)))));
count -= count_offset;
// starting digit
mpz_t digit;
mpz_init(digit);
if (mpz_set_str(digit, digitIndex.c_str(), 10) < 0)
return false;
mpz_sub_ui(digit, digit, 1); // subtract the 3 digit
mpz_add_ui(digit, digit, digitStep);
mpz_t tmpI[TEMPORARY_INTEGERS];
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_init(tmpI[i]);
mpf_t tmpF[TEMPORARY_FLOATS];
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_init2(tmpF[i], mantissa_bits);
// determine epsilon based on the number of digits required
mpf_t epsilon;
mpf_init2(epsilon, mantissa_bits);
mpf_set_ui(epsilon, 10);
mpf_pow_ui(epsilon, epsilon, count + count_offset);
mpf_ui_div(epsilon, 1, epsilon);
// integer constant
mpz_t sixteen;
mpz_init(sixteen);
mpz_set_ui(sixteen, 16);
// determine the series
mpf_t s1, s2, s3, s4;
mpf_init2(s1, mantissa_bits);
mpf_init2(s2, mantissa_bits);
mpf_init2(s3, mantissa_bits);
mpf_init2(s4, mantissa_bits);
series(abortTask, s1, 1, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s2, 4, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s3, 5, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
series(abortTask, s4, 6, tmpI, tmpF, sixteen, digit, epsilon);
if (abortTask)
return false;
// pid = 4. * s1 - 2. * s2 - s3 - s4;
mpf_mul_ui(s1, s1, 4);
mpf_mul_ui(s2, s2, 2);
mpf_t result;
mpf_init2(result, mantissa_bits);
mpf_sub(result, s1, s2);
mpf_sub(result, result, s3);
mpf_sub(result, result, s4);
// pid = pid - (int) pid + 1.;
mpf_t & tmp1 = tmpF[0];
mpf_floor(tmp1, result);
mpf_sub(result, result, tmp1);
mpf_add_ui(result, result, 1);
mpf_abs(result, result);
// output the result
char resultStr[256];
mp_exp_t exponent;
mpf_get_str(resultStr, &exponent, 16, 254, result);
resultStr[count + 1] = '\0'; // cut off any erroneous bits
piSequence.assign(&resultStr[1]);
// cleanup
for (size_t i = 0; i < (sizeof(tmpI) / sizeof(mpz_t)); ++i)
mpz_clear(tmpI[i]);
for (size_t i = 0; i < (sizeof(tmpF) / sizeof(mpf_t)); ++i)
mpf_clear(tmpF[i]);
mpz_clear(digit);
mpf_clear(epsilon);
mpz_clear(sixteen);
mpf_clear(s1);
mpf_clear(s2);
mpf_clear(s3);
mpf_clear(s4);
mpf_clear(result);
return true;
}
void series(bool const & abortTask, mpf_t & rop, unsigned long m,
mpz_t * const & tmpI, mpf_t * const & tmpF,
mpz_t const & sixteen, mpz_t const & digit, mpf_t const & epsilon)
{
// temporary local variables
mpf_t & tmp1 = tmpF[0];
mpf_t & t = tmpF[1];
mpz_t & tmp2 = tmpI[0];
mpz_t & k = tmpI[1];
mpz_t & p = tmpI[2];
mpz_t & ak = tmpI[3];
mpf_set_ui(rop, 0);
mpz_set_ui(k, 0);
while (mpz_cmp(k, digit) < 0) // k < digit
{
// p = id - k;
mpz_sub(p, digit, k);
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = expm (p, ak);
mpz_powm(tmp2, sixteen, p, ak);
mpf_set_z(t, tmp2);
// s = s + t / ak;
mpf_set_z(tmp1, ak);
mpf_div(tmp1, t, tmp1);
mpf_add(rop, rop, tmp1);
// s = s - (int) s;
mpf_floor(tmp1, rop);
mpf_sub(rop, rop, tmp1);
// k++
mpz_add_ui(k, k, 1);
if (abortTask)
return;
}
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = pow (16., (double) (id - k)) / ak;
mpf_set_z(tmp1, ak);
mpf_ui_div(t, 1, tmp1);
while (mpf_cmp(t, epsilon) >= 0) // t >= epsilon
{
// s = s + t;
mpf_add(rop, rop, t);
// s = s - (int) s;
mpf_floor(tmp1, rop);
mpf_sub(rop, rop, tmp1);
// k++
mpz_add_ui(k, k, 1);
// p = id - k;
mpz_sub(p, digit, k);
// ak = 8 * k + m;
mpz_set(ak, k);
mpz_mul_ui(ak, ak, 8);
mpz_add_ui(ak, ak, m);
// t = pow (16., (double) (id - k)) / ak;
mpz_pow_ui(tmp2, sixteen, mpz_get_ui(p));
mpz_mul(tmp2, tmp2, ak);
mpf_set_z(t, tmp2);
mpf_ui_div(t, 1, t);
if (abortTask)
return;
}
}
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;
}
int main ()
{
int i = 0; /*Contador de iterações*/
int k = 8; /*Fator de multiplicação*/
mpf_t pi_pas, pi_novo;
mpf_t a_pas, a_novo;
mpf_t y_pas, y_novo;
mpf_t temp1, temp2;
mpf_t e;
FILE *fileTime; /*Ponteiro do arquivo de saída*/
clock_t start, end;
double cpu_time_used;
mpf_set_default_prec(BITS_PER_DIGIT * 11000000); /*Precisão default*/
/*Inicialização das variáveis*/
mpf_init(pi_pas);
mpf_init(pi_novo);
mpf_init(a_pas);
mpf_init(y_pas);
mpf_init(temp1);
mpf_init(temp2);
mpf_init_set_d(a_novo, 32.0);
mpf_sqrt(a_novo, a_novo);
mpf_ui_sub(a_novo, 6, a_novo);
mpf_init_set_d(y_novo, 2.0);
mpf_sqrt(y_novo, y_novo);
mpf_sub_ui(y_novo, y_novo, 1);
mpf_init_set_str(e, "1e-10000000", 10);
mpf_ui_div(pi_novo, 1, a_novo);
start = clock();
/*Calcula as iterações*/
do
{
mpf_swap(pi_pas, pi_novo);
mpf_swap(a_pas, a_novo);
mpf_swap(y_pas, y_novo);
mpf_pow_ui(y_pas, y_pas, 4);
mpf_ui_sub(y_pas, 1, y_pas);
mpf_sqrt(y_pas, y_pas);
mpf_sqrt(y_pas, y_pas);
mpf_add_ui(temp1, y_pas, 1);
mpf_ui_sub(y_novo, 1, y_pas);
mpf_div(y_novo, y_novo, temp1);
mpf_add_ui(temp1, y_novo, 1);
mpf_pow_ui(temp2, y_novo, 2);
mpf_add(temp2, temp2, temp1);
mpf_mul(temp2, temp2, y_novo);
mpf_mul_ui(temp2, temp2, k);
k *= 4;
mpf_pow_ui(temp1, temp1, 4);
mpf_mul(temp1, temp1, a_pas);
mpf_sub(a_novo, temp1, temp2);
mpf_ui_div(pi_novo, 1, a_novo);
mpf_sub(pi_pas, pi_novo, pi_pas);
mpf_abs(pi_pas, pi_pas);
gmp_printf("\nIteracao %d | pi = %.25Ff", i, pi_novo);
i++;
} while ( mpf_cmp(e, pi_pas) < 0 );
end = clock();
cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
fileTime = fopen("execution_time.txt", "w");
fprintf(fileTime, "Execution time: %f\n", cpu_time_used);
fclose(fileTime);
/*Libera espaço de memória*/
mpf_clear(pi_pas);
mpf_clear(pi_novo);
mpf_clear(a_pas);
mpf_clear(a_novo);
mpf_clear(y_pas);
mpf_clear(y_novo);
mpf_clear(temp1);
mpf_clear(temp2);
mpf_clear(e);
return 0;
}
/**
* Algoritmo de Borwein
*
* a1 se aproxima do valor de 1/PI.
* Cada iteração quadruplica o número de dígitos corretos.
*
*/
void gmp_borwein()
{
/*variáveis para calculo com respectivos valores iniciais*/
mpf_t a0, a1, y0, y1, aux1, aux2;
/*contador de iterações*/
long unsigned int k=0;
//mpf_set_default_prec(33220); /*define a precisao do float em bits*/
mpf_set_default_prec(33219280);//(33219280); /*define a precisao do float em bits*/
mpf_init(a0),mpf_init(a1),mpf_init(y0),mpf_init(y1),mpf_init(aux1),mpf_init(aux2); /*Inicializa as variáveis em 0*/
/*seta os valores inicias das váriaveis de precisão variável*/
/*a0 = 6-4*sqrt(2)*/
mpf_set_ui(aux1,2);
mpf_sqrt(aux1,aux1); /*sqrt(2)*/
mpf_mul_ui(a0,aux1,4);
mpf_ui_sub(a0,6,a0);
//mpf_set_d(a0, 6-4*sqrt(2));
mpf_sub_ui(y0,aux1,1); /*y0 = sqrt(2)-1*/
while(k<12)
{
/*y1 = (1-sqrt(sqrt((1-pow(y0,4))))) / (1+sqrt(sqrt(1-pow(y0,4))));*/
mpf_pow_ui(y1,y0,4); /*y1 = pow(y0,4)*/
mpf_ui_sub(y1,1,y1); /*y1 = 1 - y1*/
mpf_sqrt(y1,y1);
mpf_sqrt(y1,y1);
mpf_ui_sub(aux1,1,y1);
mpf_add_ui(aux2,y1,1);
mpf_div(y1,aux1,aux2);
/*a1 = a0*pow(1 + y1,4) - pow(2,2*k+3)*y1*(1+y1+pow(y1,2));*/
mpf_add_ui(a1,y1,1); /*a1 = y1+1*/
mpf_pow_ui(a1,a1,4); /*a1 = a1^4*/
mpf_mul(a1,a0,a1); /*a1 = a0*a1*/
mpf_pow_ui(aux2,y1,2); /*aux2 = pow(y1,2)*/
mpf_add(aux2,aux2,y1); /*aux2 += y1*/
mpf_add_ui(aux2,aux2,1); /*aux2++*/
mpf_mul(aux2,aux2,y1); /*aux2 *= y1*/
mpf_set_ui(aux1,2); /* aux1=2 */
mpf_pow_ui(aux1,aux1,2*k+3); /* aux1 = pow(aux1,2*k+3)*/
mpf_mul(aux1,aux1,aux2); /*aux1 = aux1*aux2*/
mpf_sub(a1,a1,aux1);
/*troca os valores das variáveis de maneira eficiente*/
mpf_swap(a0,a1);
mpf_swap(y0,y1);
k++;
/*gmp_printf("k=%ld, y1=%.*Ff, 1/PI=%.*Ff\n", k, 20, y1, 20, a1);
gmp_printf("a0=%.*Ff, y0=%.*Ff\n", 20, a0, 20, y0);*/
}
mpf_ui_div(a1,1,a1); /*PI=1/a1*/
gmp_printf("%.*Ff\n",10000000,a1);
mpf_clear(a0),mpf_clear(a1),mpf_clear(y0),mpf_clear(y1),mpf_clear(aux1),mpf_clear(aux2); /*Limpa as variáveis da memória*/
}
//#define SW_MAX 1000
void m7magi_hash(const char* input, char* output)
{
unsigned int nnNonce;
uint32_t pdata[32];
memcpy(pdata, input, 80);
// memcpy(&nnNonce, input+76, 4);
int i, j, bytes, nnNonce2;
nnNonce2 = (int)(pdata[19]/2);
size_t sz = 80;
uint8_t bhash[7][64];
uint32_t hash[8];
memset(bhash, 0, 7 * 64);
sph_sha256_context ctx_final_sha256;
sph_sha256_context ctx_sha256;
sph_sha512_context ctx_sha512;
sph_keccak512_context ctx_keccak;
sph_whirlpool_context ctx_whirlpool;
sph_haval256_5_context ctx_haval;
sph_tiger_context ctx_tiger;
sph_ripemd160_context ctx_ripemd;
sph_sha256_init(&ctx_sha256);
// ZSHA256;
sph_sha256 (&ctx_sha256, input, sz);
sph_sha256_close(&ctx_sha256, (void*)(bhash[0]));
sph_sha512_init(&ctx_sha512);
// ZSHA512;
sph_sha512 (&ctx_sha512, input, sz);
sph_sha512_close(&ctx_sha512, (void*)(bhash[1]));
sph_keccak512_init(&ctx_keccak);
// ZKECCAK;
sph_keccak512 (&ctx_keccak, input, sz);
sph_keccak512_close(&ctx_keccak, (void*)(bhash[2]));
sph_whirlpool_init(&ctx_whirlpool);
// ZWHIRLPOOL;
sph_whirlpool (&ctx_whirlpool, input, sz);
sph_whirlpool_close(&ctx_whirlpool, (void*)(bhash[3]));
sph_haval256_5_init(&ctx_haval);
// ZHAVAL;
sph_haval256_5 (&ctx_haval, input, sz);
sph_haval256_5_close(&ctx_haval, (void*)(bhash[4]));
sph_tiger_init(&ctx_tiger);
// ZTIGER;
sph_tiger (&ctx_tiger, input, sz);
sph_tiger_close(&ctx_tiger, (void*)(bhash[5]));
sph_ripemd160_init(&ctx_ripemd);
// ZRIPEMD;
sph_ripemd160 (&ctx_ripemd, input, sz);
sph_ripemd160_close(&ctx_ripemd, (void*)(bhash[6]));
// printf("%s\n", hash[6].GetHex().c_str());
mpz_t bns[8];
for(i=0; i < 8; i++){
mpz_init(bns[i]);
}
//Take care of zeros and load gmp
for(i=0; i < 7; i++){
set_one_if_zero(bhash[i]);
mpz_set_uint512(bns[i],bhash[i]);
}
mpz_set_ui(bns[7],0);
for(i=0; i < 7; i++)
mpz_add(bns[7], bns[7], bns[i]);
mpz_t product;
mpz_init(product);
mpz_set_ui(product,1);
// mpz_pow_ui(bns[7], bns[7], 2);
for(i=0; i < 8; i++){
mpz_mul(product,product,bns[i]);
}
mpz_pow_ui(product, product, 2);
bytes = mpz_sizeinbase(product, 256);
// printf("M7M data space: %iB\n", bytes);
char *data = (char*)malloc(bytes);
mpz_export(data, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
// ZSHA256;
sph_sha256 (&ctx_final_sha256, data, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
free(data);
int digits=(int)((sqrt((double)(nnNonce2))*(1.+EPS))/9000+75);
// int iterations=(int)((sqrt((double)(nnNonce2))+EPS)/500+350); // <= 500
// int digits=100;
int iterations=20; // <= 500
mpf_set_default_prec((long int)(digits*BITS_PER_DIGIT+16));
mpz_t magipi;
mpz_t magisw;
mpf_t magifpi;
mpf_t mpa1, mpb1, mpt1, mpp1;
mpf_t mpa2, mpb2, mpt2, mpp2;
mpf_t mpsft;
mpz_init(magipi);
mpz_init(magisw);
mpf_init(magifpi);
mpf_init(mpsft);
mpf_init(mpa1);
mpf_init(mpb1);
mpf_init(mpt1);
mpf_init(mpp1);
mpf_init(mpa2);
mpf_init(mpb2);
mpf_init(mpt2);
mpf_init(mpp2);
uint32_t usw_;
usw_ = sw_(nnNonce2, SW_DIVS);
if (usw_ < 1) usw_ = 1;
// if(fDebugMagi) printf("usw_: %d\n", usw_);
mpz_set_ui(magisw, usw_);
uint32_t mpzscale=mpz_size(magisw);
for(i=0; i < NM7M; i++)
{
if (mpzscale > 1000) {
mpzscale = 1000;
}
else if (mpzscale < 1) {
mpzscale = 1;
}
// if(fDebugMagi) printf("mpzscale: %d\n", mpzscale);
mpf_set_ui(mpa1, 1);
mpf_set_ui(mpb1, 2);
mpf_set_d(mpt1, 0.25*mpzscale);
mpf_set_ui(mpp1, 1);
mpf_sqrt(mpb1, mpb1);
mpf_ui_div(mpb1, 1, mpb1);
mpf_set_ui(mpsft, 10);
for(j=0; j <= iterations; j++)
{
mpf_add(mpa2, mpa1, mpb1);
mpf_div_ui(mpa2, mpa2, 2);
mpf_mul(mpb2, mpa1, mpb1);
mpf_abs(mpb2, mpb2);
mpf_sqrt(mpb2, mpb2);
mpf_sub(mpt2, mpa1, mpa2);
mpf_abs(mpt2, mpt2);
mpf_sqrt(mpt2, mpt2);
mpf_mul(mpt2, mpt2, mpp1);
mpf_sub(mpt2, mpt1, mpt2);
mpf_mul_ui(mpp2, mpp1, 2);
mpf_swap(mpa1, mpa2);
mpf_swap(mpb1, mpb2);
mpf_swap(mpt1, mpt2);
mpf_swap(mpp1, mpp2);
}
mpf_add(magifpi, mpa1, mpb1);
mpf_pow_ui(magifpi, magifpi, 2);
mpf_div_ui(magifpi, magifpi, 4);
mpf_abs(mpt1, mpt1);
mpf_div(magifpi, magifpi, mpt1);
// mpf_out_str(stdout, 10, digits+2, magifpi);
mpf_pow_ui(mpsft, mpsft, digits/2);
mpf_mul(magifpi, magifpi, mpsft);
mpz_set_f(magipi, magifpi);
//mpz_set_ui(magipi,1);
mpz_add(product,product,magipi);
mpz_add(product,product,magisw);
mpz_set_uint256(bns[0], (void*)(hash));
mpz_add(bns[7], bns[7], bns[0]);
mpz_mul(product,product,bns[7]);
mpz_cdiv_q (product, product, bns[0]);
if (mpz_sgn(product) <= 0) mpz_set_ui(product,1);
bytes = mpz_sizeinbase(product, 256);
mpzscale=bytes;
// printf("M7M data space: %iB\n", bytes);
char *bdata = (char*)malloc(bytes);
mpz_export(bdata, NULL, -1, 1, 0, 0, product);
sph_sha256_init(&ctx_final_sha256);
// ZSHA256;
sph_sha256 (&ctx_final_sha256, bdata, bytes);
sph_sha256_close(&ctx_final_sha256, (void*)(hash));
free(bdata);
}
//Free the memory
for(i=0; i < 8; i++){
mpz_clear(bns[i]);
}
// mpz_clear(dSpectralWeight);
mpz_clear(product);
mpz_clear(magipi);
mpz_clear(magisw);
mpf_clear(magifpi);
mpf_clear(mpsft);
mpf_clear(mpa1);
mpf_clear(mpb1);
mpf_clear(mpt1);
mpf_clear(mpp1);
mpf_clear(mpa2);
mpf_clear(mpb2);
mpf_clear(mpt2);
mpf_clear(mpp2);
memcpy(output, hash, 32);
}
int main() {
pthread_t thread_a, thread_b; /* My threads*/
int i;
FILE *filePi, *fileTime;
clock_t start, end;
double cpu_time_used;
mpf_set_default_prec(BITS_PER_DIGIT * 11000000);
/* Borwein Variable Initialization */
for(i=0; i<2; i++)
for(j=0; j<2; j++)
mpf_init(params[i][j]);
mpf_init(real_pi);
mpf_init(y0Aux);
mpf_init(y0Aux2);
mpf_init(a0Aux);
mpf_init(a0Aux2);
mpf_init(pi[0]);
mpf_init(pi[1]);
mpf_init_set_str(error, "1e-10000000", 10);
/* Initial value setting */
mpf_sqrt_ui(params[A][0], 2.0); /* a0 = sqrt(2)*/
mpf_mul_ui(params[A][0], params[A][0], 4.0); /* a0 = 4 * sqrt(2) */
mpf_ui_sub(params[A][0], 6.0, params[A][0]); /* a0 = 6 - 4 * sqrt(2) */
mpf_sqrt_ui(params[Y][0], 2.0); /* y0 = sqrt(2) */
mpf_sub_ui(params[Y][0], params[Y][0], 1.0); /* y0 = sqrt(2) - 1 */
mpf_set_ui(pi[0], 0);
mpf_set_ui(pi[1], 0);
i = 1;
j = 1;
iteracoes = 0;
x = 0;
/* Load the reals digits of pi */
filePi = fopen("pi.txt", "r");
gmp_fscanf(filePi, "%Ff", real_pi);
fclose(filePi);
start = clock();
while(1){
/* y = ( 1 - (1 - y0 ^ 4) ^ 0.25 ) / ( 1 + ( 1 - y0 ^ 4) ^ 0.25 ) */
mpf_pow_ui(y0Aux, params[Y][0], 4);
mpf_ui_sub(y0Aux, 1.0, y0Aux);
mpf_sqrt(y0Aux, y0Aux);
mpf_sqrt(y0Aux, y0Aux);
mpf_add_ui(y0Aux2, y0Aux, 1.0);
mpf_ui_sub(y0Aux, 1.0, y0Aux);
mpf_div(params[Y][1], y0Aux, y0Aux2);
/* a = a0 * ( 1 + params[Y][1] ) ^ 4 - 2 ^ ( 2 * i + 3 ) * params[Y][1] * ( 1 + params[Y][1] + params[Y][1] ^ 2 ) */
/* Threads creation */
pthread_create(&thread_a, NULL, calc_a, NULL);
pthread_create(&thread_b, NULL, calc_b, NULL);
pthread_join(thread_a, NULL);
pthread_join(thread_b, NULL);
/* 2 ^ ( 2 * i + 3 ) * params[Y][1] * ( 1 + params[Y][1] + params[Y][1] ^ 2 ) */
mpf_mul(a0Aux, a0Aux, a0Aux2);
/*a0 * ( 1 + params[Y][1] ) ^ 4*/
mpf_add_ui(a0Aux2, params[Y][1], 1);
mpf_pow_ui(a0Aux2, a0Aux2, 4);
mpf_mul(a0Aux2, params[A][0], a0Aux2);
/* form the entire expression */
mpf_sub(params[A][1], a0Aux2, a0Aux);
mpf_set(params[A][0], params[A][1]);
mpf_set(params[Y][0], params[Y][1]);
mpf_ui_div(pi[j], 1, params[A][0]);
gmp_printf("\nIteracao %d | pi = %.25Ff", iteracoes, pi[j]);
/* Calculate the error */
mpf_sub(pi[(j+1)%2], real_pi, pi[j]);
mpf_abs(pi[(j+1) % 2], pi[(j+1) % 2]);
if(mpf_cmp(pi[(j+1)%2], error) < 0){
printf("\n%d iteracoes para alcancar 10 milhoes de digitos de corretos.", iteracoes);
break;
}
j = (j+1) % 2;
iteracoes++;
i++;
}
end = clock();
cpu_time_used = ((double) (end - start)) / CLOCKS_PER_SEC;
fileTime = fopen("execution_time.txt", "w");
fprintf(fileTime, "Execution time: %f\n", cpu_time_used);
fclose(fileTime);
/* Clean up*/
for(i=0; i<2; i++)
for(j=0; j<2; j++)
mpf_clear(params[i][j]);
mpf_clear(pi[0]);
mpf_clear(pi[1]);
mpf_clear(real_pi);
mpf_clear(error);
return 0;
}
//
// The core Gauss-Legendre routine.
// On input, 'bits' is the desired precision in bits.
// On output, 'pi' contains the calculated value.
//
static void calculatePi( unsigned bits, mpf_t pi)
{
mpf_t lastPi;
mpf_t scratch;
// variables per the formal Gauss-Legendre formulae
mpf_t a;
mpf_t b;
mpf_t t;
mpf_t x;
mpf_t y;
unsigned p = 1;
mpf_init_set_ui(lastPi, 0);
mpf_init(x);
mpf_init(y);
mpf_init(scratch);
// initial conditions
mpf_init_set_ui(a, 1); // a := 1
mpf_init(b); // b := 1 / sqrt(2)
mpf_sqrt_ui(b, 2);
mpf_ui_div(b, 1, b);
mpf_init_set_ui(t, 4); // t := 1/4
mpf_ui_div(t, 1, t);
for(;;) {
// x := (a+b)/2
mpf_add(x, a, b);
mpf_div_ui(x, x, 2);
// y := sqrt(a*b)
mpf_mul(y, a, b);
mpf_sqrt(y, y);
// t := t - p * (a-x)**2
mpf_sub(scratch, a, x);
mpf_pow_ui(scratch, scratch, 2);
mpf_mul_ui(scratch, scratch, p);
mpf_sub(t, t, scratch);
// a := x
// b := y
// p := 2p
mpf_set(a, x);
mpf_set(b, y);
p <<= 1;
// pi := ((a + b)**2) / 4t
mpf_add(pi, a, b);
mpf_pow_ui(pi, pi, 2);
mpf_mul_ui(scratch, t, 4);
mpf_div(pi, pi, scratch);
// if pi == lastPi, within the requested precision, we're done
if(mpf_eq(pi, lastPi, bits)) {
break;
}
mpf_set(lastPi, pi);
}
// free memory associated with mpf_t's we allocated
mpf_clear(a);
mpf_clear(b);
mpf_clear(t);
mpf_clear(x);
mpf_clear(y);
mpf_clear(lastPi);
mpf_clear(scratch);
}
int fractal_gmp_calculate_line(image_info* img, int line)
{
int ret = 1;
int ix = 0;
int mx = 0;
int chk_px = ((rthdata*)img->rth_ptr)->check_stop_px;
int img_width = img->real_width;
int* raw_data = &img->raw_data[line * img_width];
depth_t depth = img->depth;
mpf_t x, y;
mpf_t x2, y2;
mpf_t c_re, c_im;
/* working variables: */
mpf_t wre, wim;
mpf_t wre2, wim2;
mpf_t frs_bail;
mpf_t width, img_rw, img_xmin;
mpf_t t1;
mpf_init2(x, img->precision);
mpf_init2(y, img->precision);
mpf_init2(x2, img->precision);
mpf_init2(y2, img->precision);
mpf_init2(c_re, img->precision);
mpf_init2(c_im, img->precision);
mpf_init2(wre, img->precision);
mpf_init2(wim, img->precision);
mpf_init2(wre2, img->precision);
mpf_init2(wim2, img->precision);
mpf_init2(frs_bail,img->precision);
mpf_init2(width, img->precision);
mpf_init2(img_rw, img->precision);
mpf_init2(img_xmin,img->precision);
mpf_init2(t1, img->precision);
mpf_set_si(frs_bail, 4);
mpf_set_si(img_rw, img_width);
mpf_set( img_xmin, img->gxmin);
mpf_set( width, img->gwidth);
/* y = img->ymax - ((img->xmax - img->xmin)
/ (long double)img->real_width)
* (long double)img->lines_done; */
mpf_div( t1, width, img_rw);
mpf_mul_ui( t1, t1, line);
mpf_sub( y, img->gymax, t1);
mpf_mul( y2, y, y);
while (ix < img_width)
{
mx += chk_px;
if (mx > img_width)
mx = img_width;
for (; ix < mx; ++ix, ++raw_data)
{
/* x = ((long double)ix / (long double)img->real_width)
* (img->xmax - img->xmin) + img->xmin; */
mpf_ui_div(t1, ix, img_rw);
mpf_mul(x, t1, width);
mpf_add(x, x, img_xmin);
mpf_mul( x2, x, x);
mpf_set( wre, x);
mpf_set( wim, y);
mpf_set( wre2, x2);
mpf_set( wim2, y2);
switch (img->family)
{
case FAMILY_MANDEL:
mpf_set(c_re, x);
mpf_set(c_im, y);
break;
case FAMILY_JULIA:
mpfr_to_gmp(img->u.julia.c_re, c_re);
mpfr_to_gmp(img->u.julia.c_im, c_im);
break;
}
switch(img->fractal)
{
case BURNING_SHIP:
*raw_data = frac_burning_ship_gmp(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case GENERALIZED_CELTIC:
*raw_data = frac_generalized_celtic_gmp(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case VARIANT:
*raw_data = frac_variant_gmp(
depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
break;
case MANDELBROT:
default:
*raw_data = frac_mandel_gmp(depth, frs_bail,
wim, wre,
c_im, c_re,
wim2, wre2, t1);
}
}
if (rth_render_should_stop((rthdata*)img->rth_ptr))
{
ret = 0;
break;
}
}
mpf_clear(x);
mpf_clear(y);
mpf_clear(x2);
mpf_clear(y2);
mpf_clear(c_re);
mpf_clear(c_im);
mpf_clear(wre);
mpf_clear(wim);
mpf_clear(wre2);
mpf_clear(wim2);
mpf_clear(frs_bail);
mpf_clear(width);
mpf_clear(img_rw);
mpf_clear(t1);
return ret;
}
