void DoUniaryOperation(number_t result, number_t number1, char *op)
{
switch( op[0] )
{
case '!':
mpf_set_si(result, mpf_cmp_ui(number1, 0));
break;
case '~':
DO_INTEGER_OPERATION1_ON_FLOAT(mpz_com, result, number1);
break;
case '+':
if (op[1] == '+') {
mpf_add_ui(result, number1, 1);
} else {
mpf_set(result, number1);
}
break;
case '-':
if (op[1] == '-') {
mpf_sub_ui(result, number1, 1);
} else {
mpf_sub(result, result, number1);
}
break;
}
}
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);
}
void my_out_str_raw(FILE *fp, unsigned long digits, mpf_t f, unsigned long offset)
{
unsigned long d;
if (digits <= LINE_SIZE*NUM_BLOCKS) {
unsigned long cursor = offset % LINE_SIZE;
for (d = 0; d < digits; ) {
mpf_set_prec_raw(f, (int)((digits-d)*BITS_PER_DIGIT+1));
mpf_mul_ui(f, f, UNIT_MOD);
unsigned long i = mpf_get_ui(f);
mpf_sub_ui(f, f, i);
utoa(i, UNIT_SIZE);
*out_ptr++ = ' ';
d += UNIT_SIZE;
cursor += UNIT_SIZE;
if (cursor == LINE_SIZE) {
cursor = 0;
*out_ptr++ = ':';
*out_ptr++ = ' ';
utoa(offset + d, 0);
*out_ptr++ = '\n';
if ((offset + d) % (LINE_SIZE*10) == 0)
flush_out(fp);
}
}
} else {
mpf_t block, mod;
unsigned long num_units = (digits + UNIT_SIZE-1)/UNIT_SIZE;
unsigned long block_size = (num_units + NUM_BLOCKS-1)/NUM_BLOCKS*UNIT_SIZE;
mpf_set_default_prec((int)(block_size*BITS_PER_DIGIT+1));
mpf_init(block);
mpf_init_set_ui(mod, 10);
mpf_pow_ui(mod, mod, block_size);
for (d = 0; d < digits; d += block_size) {
unsigned long size = block_size < digits - d ? block_size : digits - d;
mpf_set_prec_raw(block, (int)(size*BITS_PER_DIGIT+1));
mpf_set(block, f);
my_out_str_raw(fp, size, block, offset+d);
if (block_size < digits - d) {
mpf_set_prec_raw(f, (int)((digits-d)*BITS_PER_DIGIT+1));
mpf_mul(f, f, mod);
mpf_floor(trunk, f);
mpf_sub(f, f, trunk);
}
}
mpf_clear(block);
mpf_clear(mod);
}
}
void my_out_str(FILE *fp, unsigned long base, unsigned long digits, mpf_t f)
{
unsigned long num_units = (digits + UNIT_SIZE-1)/UNIT_SIZE;
unsigned long block_size = (num_units + NUM_BLOCKS-1)/NUM_BLOCKS*UNIT_SIZE;
mpf_init2(trunk, (int)(block_size*BITS_PER_DIGIT+1));
unsigned long i = mpf_get_ui(f);
fprintf(fp, "%lu.\n", i);
mpf_sub_ui(f, f, i);
my_out_str_raw(fp, digits, f, 0);
if (out_ptr != out_buf)
flush_out(fp);
mpf_clear(trunk);
}
void
x2 (mpf_t V, /* result */
unsigned long int X[], /* data */
unsigned int k, /* #of categories */
void (P) (mpf_t, unsigned long int, void *), /* probability func */
void *x, /* extra user data passed to P() */
unsigned long int n) /* #of samples */
{
unsigned int f;
mpf_t f_t, f_t2; /* temp floats */
mpf_init (f_t); mpf_init (f_t2);
mpf_set_ui (V, 0);
for (f = 0; f < k; f++)
{
if (g_debug > DEBUG_2)
fprintf (stderr, "%u: P()=", f);
mpf_set_ui (f_t, X[f]);
mpf_mul (f_t, f_t, f_t); /* f_t = X[f]^2 */
P (f_t2, f, x); /* f_t2 = Pr(f) */
if (g_debug > DEBUG_2)
mpf_out_str (stderr, 10, 2, f_t2);
mpf_div (f_t, f_t, f_t2);
mpf_add (V, V, f_t);
if (g_debug > DEBUG_2)
{
fprintf (stderr, "\tV=");
mpf_out_str (stderr, 10, 2, V);
fprintf (stderr, "\t");
}
}
if (g_debug > DEBUG_2)
fprintf (stderr, "\n");
mpf_div_ui (V, V, n);
mpf_sub_ui (V, V, n);
mpf_clear (f_t); mpf_clear (f_t2);
}
void
ks (mpf_t Kp,
mpf_t Km,
mpf_t X[],
void (P) (mpf_t, mpf_t),
unsigned long int n)
{
mpf_t Kt; /* temp */
mpf_t f_x;
mpf_t f_j; /* j */
mpf_t f_jnq; /* j/n or (j-1)/n */
unsigned long int j;
/* Sort the vector in ascending order. */
qsort (X, n, sizeof (__mpf_struct), mpf_cmp);
/* K-S test. */
/* Kp = sqr(n) * max(j/n - F(Xj)) for all 1<=j<=n
Km = sqr(n) * max(F(Xj) - (j-1)/n)) for all 1<=j<=n
*/
mpf_init (Kt); mpf_init (f_x); mpf_init (f_j); mpf_init (f_jnq);
mpf_set_ui (Kp, 0); mpf_set_ui (Km, 0);
for (j = 1; j <= n; j++)
{
P (f_x, X[j-1]);
mpf_set_ui (f_j, j);
mpf_div_ui (f_jnq, f_j, n);
mpf_sub (Kt, f_jnq, f_x);
if (mpf_cmp (Kt, Kp) > 0)
mpf_set (Kp, Kt);
if (g_debug > DEBUG_2)
{
printf ("j=%lu ", j);
printf ("P()="); mpf_out_str (stdout, 10, 2, f_x); printf ("\t");
printf ("jnq="); mpf_out_str (stdout, 10, 2, f_jnq); printf (" ");
printf ("diff="); mpf_out_str (stdout, 10, 2, Kt); printf (" ");
printf ("Kp="); mpf_out_str (stdout, 10, 2, Kp); printf ("\t");
}
mpf_sub_ui (f_j, f_j, 1);
mpf_div_ui (f_jnq, f_j, n);
mpf_sub (Kt, f_x, f_jnq);
if (mpf_cmp (Kt, Km) > 0)
mpf_set (Km, Kt);
if (g_debug > DEBUG_2)
{
printf ("jnq="); mpf_out_str (stdout, 10, 2, f_jnq); printf (" ");
printf ("diff="); mpf_out_str (stdout, 10, 2, Kt); printf (" ");
printf ("Km="); mpf_out_str (stdout, 10, 2, Km); printf (" ");
printf ("\n");
}
}
mpf_sqrt_ui (Kt, n);
mpf_mul (Kp, Kp, Kt);
mpf_mul (Km, Km, Kt);
mpf_clear (Kt); mpf_clear (f_x); mpf_clear (f_j); mpf_clear (f_jnq);
}
int
main (void)
{
mpf_t f, f0p5;
int got;
const char *expr;
int error = 0;
tests_start ();
mpf_init2 (f, 200L);
mpf_init2 (f0p5, 200L);
/* 0.5 */
mpf_set_ui (f0p5, 1L);
mpf_div_2exp (f0p5, f0p5, 1L);
mpf_set_ui (f, 0L);
expr = "0";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_ui (f, 1L);
expr = "1";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, -1L);
expr = "-1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
expr = "USHRT_MAX";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
mpf_add (f, f, f0p5);
expr = "USHRT_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
mpf_set_ui (f, (unsigned long) USHRT_MAX);
mpf_add_ui (f, f, 1L);
expr = "USHRT_MAX + 1";
EXPECT (mpf_fits_ushort_p, 0);
mpf_set_ui (f, (unsigned long) UINT_MAX);
expr = "UINT_MAX";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
mpf_set_ui (f, (unsigned long) UINT_MAX);
mpf_add (f, f, f0p5);
expr = "UINT_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
mpf_set_ui (f, (unsigned long) UINT_MAX);
mpf_add_ui (f, f, 1L);
expr = "UINT_MAX + 1";
EXPECT (mpf_fits_uint_p, 0);
mpf_set_ui (f, ULONG_MAX);
expr = "ULONG_MAX";
EXPECT (mpf_fits_ulong_p, 1);
mpf_set_ui (f, ULONG_MAX);
mpf_add (f, f, f0p5);
expr = "ULONG_MAX + 0.5";
EXPECT (mpf_fits_ulong_p, 1);
mpf_set_ui (f, ULONG_MAX);
mpf_add_ui (f, f, 1L);
expr = "ULONG_MAX + 1";
EXPECT (mpf_fits_ulong_p, 0);
mpf_set_si (f, (long) SHRT_MAX);
expr = "SHRT_MAX";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MAX);
expr = "SHRT_MAX + 0.5";
mpf_add (f, f, f0p5);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MAX);
mpf_add_ui (f, f, 1L);
expr = "SHRT_MAX + 1";
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_si (f, (long) INT_MAX);
expr = "INT_MAX";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MAX);
mpf_add (f, f, f0p5);
expr = "INT_MAX + 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MAX);
mpf_add_ui (f, f, 1L);
expr = "INT_MAX + 1";
EXPECT (mpf_fits_sint_p, 0);
mpf_set_si (f, LONG_MAX);
expr = "LONG_MAX";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MAX);
mpf_add (f, f, f0p5);
expr = "LONG_MAX + 0.5";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MAX);
mpf_add_ui (f, f, 1L);
expr = "LONG_MAX + 1";
EXPECT (mpf_fits_slong_p, 0);
mpf_set_si (f, (long) SHRT_MIN);
expr = "SHRT_MIN";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MIN);
mpf_sub (f, f, f0p5);
expr = "SHRT_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_si (f, (long) SHRT_MIN);
mpf_sub_ui (f, f, 1L);
expr = "SHRT_MIN + 1";
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_si (f, (long) INT_MIN);
expr = "INT_MIN";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MIN);
mpf_sub (f, f, f0p5);
expr = "INT_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
mpf_set_si (f, (long) INT_MIN);
mpf_sub_ui (f, f, 1L);
expr = "INT_MIN + 1";
EXPECT (mpf_fits_sint_p, 0);
mpf_set_si (f, LONG_MIN);
expr = "LONG_MIN";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MIN);
mpf_sub (f, f, f0p5);
expr = "LONG_MIN - 0.5";
EXPECT (mpf_fits_slong_p, 1);
mpf_set_si (f, LONG_MIN);
mpf_sub_ui (f, f, 1L);
expr = "LONG_MIN + 1";
EXPECT (mpf_fits_slong_p, 0);
mpf_set_str_or_abort (f, "0.5", 10);
expr = "0.5";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "-0.5", 10);
expr = "-0.5";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "1.000000000000000000000000000000000001", 16);
expr = "1.000000000000000000000000000000000001 base 16";
EXPECT (mpf_fits_ulong_p, 1);
EXPECT (mpf_fits_uint_p, 1);
EXPECT (mpf_fits_ushort_p, 1);
EXPECT (mpf_fits_slong_p, 1);
EXPECT (mpf_fits_sint_p, 1);
EXPECT (mpf_fits_sshort_p, 1);
mpf_set_str_or_abort (f, "1@1000", 16);
expr = "1@1000 base 16";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 1);
mpf_sub_ui (f, f, 1L);
expr = "2^(BITS_PER_ULONG+1) - 1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 1);
mpf_sub_ui (f, f, 1L);
mpf_neg (f, f);
expr = "- (2^(BITS_PER_ULONG+1) - 1)";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
mpf_set_ui (f, 1L);
mpf_mul_2exp (f, f, BITS_PER_ULONG + 5);
mpf_sub_ui (f, f, 1L);
expr = "2^(BITS_PER_ULONG+5) - 1";
EXPECT (mpf_fits_ulong_p, 0);
EXPECT (mpf_fits_uint_p, 0);
EXPECT (mpf_fits_ushort_p, 0);
EXPECT (mpf_fits_slong_p, 0);
EXPECT (mpf_fits_sint_p, 0);
EXPECT (mpf_fits_sshort_p, 0);
if (error)
abort ();
mpf_clear (f);
mpf_clear (f0p5);
tests_end ();
exit (0);
}
void
check_rand (int argc, char **argv)
{
mp_size_t size;
mp_exp_t exp;
int reps = 20000;
int i;
mpf_t u, v, w, wref;
mp_size_t bprec = 100;
mpf_t rerr, max_rerr, limit_rerr;
gmp_randstate_t rands;
if (argc > 1)
{
reps = strtol (argv[1], 0, 0);
if (argc > 2)
bprec = strtol (argv[2], 0, 0);
}
mpf_set_default_prec (bprec);
gmp_randinit_default(rands);
mpf_init_set_ui (limit_rerr, 1);
mpf_div_2exp (limit_rerr, limit_rerr, bprec);
#if VERBOSE
mpf_dump (limit_rerr);
#endif
mpf_init (rerr);
mpf_init_set_ui (max_rerr, 0);
mpf_init (u);
mpf_init (v);
mpf_init (w);
mpf_init (wref);
for (i = 0; i < reps; i++)
{
size = urandom (rands) % (2 * SIZE) - SIZE;
exp = urandom (rands) % SIZE;
mpf_rrandomb (u, rands, size, exp);
size = urandom (rands) % (2 * SIZE) - SIZE;
exp = urandom (rands) % SIZE;
mpf_rrandomb (v, rands, size, exp);
if ((urandom (rands) & 1) != 0)
mpf_add_ui (u, v, 1);
else if ((urandom (rands) & 1) != 0)
mpf_sub_ui (u, v, 1);
mpf_sub (w, u, v);
refmpf_sub (wref, u, v);
mpf_reldiff (rerr, w, wref);
if (mpf_cmp (rerr, max_rerr) > 0)
{
mpf_set (max_rerr, rerr);
#if VERBOSE
mpf_dump (max_rerr);
#endif
if (mpf_cmp (rerr, limit_rerr) > 0)
{
printf ("ERROR after %d tests\n", i);
printf (" u = ");
mpf_dump (u);
printf (" v = ");
mpf_dump (v);
printf ("wref = ");
mpf_dump (wref);
printf (" w = ");
mpf_dump (w);
abort ();
}
}
}
mpf_clear (limit_rerr);
mpf_clear (rerr);
mpf_clear (max_rerr);
mpf_clear (u);
mpf_clear (v);
mpf_clear (w);
mpf_clear (wref);
gmp_randclear(rands);
}
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;
}
/**
* 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*/
}
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
*
* 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);
}
