void mpfc_out_str(FILE * stream,int base, size_t n_digits,mpfc_ptr x)
{
std::cout<<"(";
mpf_out_str(stream,base,n_digits,x->Re);
std::cout<<",";
mpf_out_str(stream,base,n_digits,x->Im);
std::cout<<")";
}
void
check_data (void)
{
static const struct {
int base;
const char *f;
long want;
} data[] = {
{ 10, "0", 0L },
{ 10, "1", 1L },
{ 10, "-1", -1L },
{ 10, "2", 2L },
{ 10, "-2", -2L },
{ 10, "12345", 12345L },
{ 10, "-12345", -12345L },
/* fraction bits ignored */
{ 10, "0.5", 0L },
{ 10, "-0.5", 0L },
{ 10, "1.1", 1L },
{ 10, "-1.1", -1L },
{ 10, "1.9", 1L },
{ 10, "-1.9", -1L },
{ 16, "1.000000000000000000000000000000000000000000000000001", 1L },
{ 16, "-1.000000000000000000000000000000000000000000000000001", -1L },
/* low bits extracted (this is undocumented) */
{ 16, "1000000000000000000000000000000000000000000000000001", 1L },
{ 16, "-1000000000000000000000000000000000000000000000000001", -1L },
};
int i;
mpf_t f;
long got;
mpf_init2 (f, 2000L);
for (i = 0; i < numberof (data); i++)
{
mpf_set_str_or_abort (f, data[i].f, data[i].base);
got = mpf_get_si (f);
if (got != data[i].want)
{
printf ("mpf_get_si wrong at data[%d]\n", i);
printf (" f \"%s\"\n", data[i].f);
printf (" dec "); mpf_out_str (stdout, 10, 0, f); printf ("\n");
printf (" hex "); mpf_out_str (stdout, 16, 0, f); printf ("\n");
printf (" size %ld\n", (long) SIZ(f));
printf (" exp %ld\n", (long) EXP(f));
printf (" got %ld (0x%lX)\n", got, got);
printf (" want %ld (0x%lX)\n", data[i].want, data[i].want);
abort();
}
}
mpf_clear (f);
}
/**
* @brief Print a float to stdout (or whatever the output stream is
* atm) respecting the given options, and only with the significant
* digits.
*
* @param s A pointer to the current mps_context.
* @param f The float approximation that should be printed.
* @param rad The current inclusion radius for that approximation.
* @param out_digit The number of output digits required.
* @param sign The sign of the approximation.
*/
MPS_PRIVATE void
mps_outfloat (mps_context * s, mpf_t f, rdpe_t rad, long out_digit,
mps_boolean sign)
{
mpf_t t;
rdpe_t r, ro;
double d;
long l, digit, true_digit;
if (s->output_config->format == MPS_OUTPUT_FORMAT_FULL)
{
mpf_init2 (t, mpf_get_prec (f));
mpf_set (t, f);
mpf_out_str (s->outstr, 10, 0, t);
mpf_clear (t);
return;
}
mpf_init2 (t, s->output_config->prec);
mpf_get_rdpe (ro, f);
if (s->output_config->format == MPS_OUTPUT_FORMAT_GNUPLOT ||
s->output_config->format == MPS_OUTPUT_FORMAT_GNUPLOT_FULL)
rdpe_out_str_u (s->outstr, ro);
else
{
rdpe_abs_eq (ro);
if (rdpe_ne (ro, rdpe_zero))
rdpe_div (r, rad, ro);
else
rdpe_set_d (r, 1.0e-10);
digit = (long)(-rdpe_log10 (r) - 0.5);
if (digit <= 0)
{
rdpe_get_dl (&d, &l, ro);
fprintf (s->outstr, "0.e%ld", l);
}
else
{
true_digit = (long)(LOG10_2 * mpf_get_prec (f));
true_digit = MIN (digit, true_digit);
true_digit = MIN (true_digit, out_digit);
if (sign)
mpf_set (t, f);
else
mpf_abs (t, f);
mpf_out_str (s->outstr, 10, true_digit, t);
}
}
mpf_clear (t);
}
float evaluateFitness(float position[])
{
char stringFitness[28];
mpf_t mpfFitness, one;
float ris;
float fitness = formulae(position);
if (fitness >= 0)
{
sprintf(stringFitness, "%.20f", fitness);
mpf_init(mpfFitness);
mpf_init(one);
mpf_set_str (one, "1.0", 10);
mpf_set_str(mpfFitness, stringFitness, 10);
mpf_add(mpfFitness, mpfFitness, one);
//printf("fitness: %.20e\t", fitness);
//mpf_out_str (stdout, 10, 256, mpfFitness);
mpf_div(mpfFitness, one, mpfFitness);
printf("\nris %.20e\t", (float) mpf_get_d(mpfFitness));
ris = (float) mpf_get_d(mpfFitness);
mpf_out_str (stdout, 10, 256, mpfFitness);
printf("\n");
return ris;
//return 1 / (1 + fitness);
}
return 1 + fabs(fitness);
}
void
print(char *s, mpf_t x){
printf("%s: ", s);
mpf_out_str (stdout, 10, 1000, x);
printf("\n");
fflush(stdout);
}
int main( int argc, char** argv )
{
unsigned bits;
double start, end;
if ( argc < 2 ) {
usage( argv );
}
bits = atoi( argv[1] );
if ( bits == 0 ) {
usage( argv );
}
printf( "Calculating pi..." );
fflush( stdout );
start = currentTime( );
mpf_set_default_prec( bits );
mpf_class pi;
calculatePi( bits, pi );
end = currentTime( );
printf( "\npi = " );
mpf_out_str( stdout, 10, 0, pi.get_mpf_t( ) );
printf( "\n" );
printf( "total elapsed time : %.2f seconds\n", end - start );
return 0;
}
int main(int argc, char **argv)
{
unsigned bits;
double start, end;
mpf_t e;
if(argc < 2) {
usage(argv);
}
bits = atoi(argv[1]);
if(bits == 0) {
usage(argv);
}
printf("Calculating e...");
fflush(stdout);
start = currentTime();
mpf_set_default_prec(bits);
mpf_init(e);
calculateE(bits, e);
end = currentTime();
printf("\ne = ");
mpf_out_str(stdout, 10, 0, e);
printf("\n");
printf("total elapsed time : %.2f seconds\n", end - start);
return 0;
}
/**
* void filePrint()
*
* Descricao:
* Imprime a cada iteracao o valor do "pi" num arquivo de nome "gauss_legendre_sequencial_X.txt", onde
* X é o numero da iteracao, comecando em 1.
*
* Parametros de entrada:
* -
*
* Parametros de retorno:
* -
*/
void filePrint(){
char filename[30];
sprintf(filename, "gauss_legendre_sequencial_%ld.txt", n_count+1);
FILE *output = fopen(filename, "w");
mpf_out_str(output, 10, 0, pi[n_count]);
fclose(output);
}
void print_vector_coordinate(FILE *OUT, int digits, complex_vector z)
/***************************************************************\
* USAGE: prints z *
\***************************************************************/
{
int i, size = z->size, base = 10;
if (size > 0)
{ // print each coordinate
for (i = 0; i < size; i++)
{
mpf_out_str(OUT, base, digits, z->coord[i]->re);
fprintf(OUT, " ");
mpf_out_str(OUT, base, digits, z->coord[i]->im);
fprintf(OUT, "\n");
}
}
return;
}
void print_number(FILE *OUT, int digits, complex_number z)
/***************************************************************\
* USAGE: prints z to OUT *
\***************************************************************/
{
int base = 10;
// verify that z is a valid number
if (mpfr_number_p(z->re) && mpfr_number_p(z->im))
{ // print to OUT
mpf_out_str(OUT, base, digits, z->re);
if (mpfr_sgn(z->im) >= 0)
fprintf(OUT, "+");
mpf_out_str(OUT, base, digits, z->im);
fprintf(OUT, "*I");
}
else
fprintf(OUT, "NaN+NaN*I");
return;
}
void gmp_print_mpq(FILE* fp, const mpq_t qval)
{
mpf_t fval;
mpf_init(fval);
mpf_set_q(fval, qval);
mpf_out_str(fp, 10, 32, fval);
fprintf(fp, " = ");
mpq_out_str(fp, 10, qval);
fputc('\n', fp);
mpf_clear(fval);
}
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 gmp_monte_carlo_par (int numthr, int numpts)
{
/*Para realizar o metodo Monte Carlo foi utilizado uma circunferencia
de raio igual a 1 (para facilitar a comparacao que verifica se o ponto
esta dentro da circunferencia) inscrita em uma quadrado de lado igual a 2.
Foi considerado apenas o primeiro quadrante, pois assim as coordenadas dos
pontos variam de 0 a 1. */
int i =0;
mpf_t pi;
mpf_t intern_points, total_points, ratio;
pthread_t tabela_thr[1000];
/*Variavel que armazena quantos pontos vao ficar dentro da circunferencia*/
/*A precisao padrao sera no minimo 10.000.000*log10.*/
mpf_set_default_prec (34000000);
/*O objeto mpf_t deve ser inicializado antes de receber algum valor.*/
mpf_init(pi),mpf_init(intern_points),mpf_init(total_points),mpf_init(ratio);
/* Inicializa a semente para calcular o valor aleatorio*/
srand (time(NULL));
/* Para uma quantidade de quase 1 bi de pontos*/
i=0;
if(numthr>1000) numthr=1000;
while(i<numthr)
{
//printf("\nIniciando Thread: %d", i);
mpf_init(param[i].intern_points);
mpf_init(param[i].total_points);
param[i].numpoints=numpts;
pthread_create(&tabela_thr[i], NULL, (void*)&montecarlo_thr, (void*) & param[i]);
i++;
}
i=0;
while(i<numthr){
pthread_join(tabela_thr[i], NULL);
mpf_add(intern_points,intern_points,param[i].intern_points);
mpf_add(total_points,total_points,param[i].total_points);
i++;
}
/*calculando o valor de pi
pi = 4* (double) intern_points /total_points */
mpf_div (ratio,intern_points,total_points); /*ratio = intern_points / total_points*/
mpf_mul_ui (pi,ratio,4); /* pi = 4*ratio*/
mpf_out_str (stdout,10,10000000,pi);
}
/* Print "name=value\n" to stdout for an mpf_t value. */
void
mpf_trace (const char *name, mpf_srcptr f)
{
mp_trace_start (name);
if (f == NULL)
{
printf ("NULL\n");
return;
}
mpf_out_str (stdout, ABS (mp_trace_base), 0, f);
printf ("\n");
}
ats_void_type
atslib_mpf_out_str_exn (
ats_ptr_type file
, ats_int_type base
, ats_size_type ndigit
, const ats_mpf_ptr_type x
) {
size_t n = mpf_out_str((FILE*)file, base, ndigit, (mpf_ptr)x) ;
if (n == 0) {
ats_exit_errmsg (1, "exit(ATS): [mpf_out_str] failed.\n") ;
} // end of [if]
return ;
} // end of [atslib_mpf_out_str_exn]
void poly_f::print()
{
if(this->size()==0)
{
std::cout<<"0\n";
return ;
}
std::cout<<"(";
for(size_t i=0;i<this->size();i++)
{
mpf_out_str(0,10,FC_DEFAULT_PREC,this->rep[i]);
std::cout<<" ";
}
std::cout<<")\n";
return ;
}
// 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);
}
int main(int argc,char *argv[])
{
mpf_t mpfVal,mpf1;
unsigned long i;
mpf_set_default_prec(9000);
mpf_init_set_ui(mpf1,1);
printf ("%ld\n",mpf_get_default_prec());
for (i=997; i>=997; i--) {
mpf_init(mpfVal);
mpf_div_ui(mpfVal,mpf1,i);
printf("%ld: ",i);
(void) mpf_out_str(stdout,10,2000,mpfVal);
mpf_clear(mpfVal);
}
}
void UniRootF_Newton()
{
poly_f f,fd;
mpf_t x,y,den,num;
mpf_t prec;
mpf_init2(den,DigitisToBits(FC_DEFAULT_PREC));
mpf_init2(num,DigitisToBits(FC_DEFAULT_PREC));
mpf_init2(y,DigitisToBits(FC_DEFAULT_PREC));
mpf_init2(x,DigitisToBits(FC_DEFAULT_PREC));
mpf_init2(prec,1);
f.resize(3);
mpf_set_str(prec,"1e-50",10);
mpf_set_si(f[0],-2);
mpf_set_si(f[1],0);
mpf_set_si(f[2],1);
mpf_set_str(x,"1",10);
UniDFormF(fd,f);
while(1)
{
UniEvalF(num,f,x);
UniEvalF(den,fd,x);
mpf_div(y,num,den);
mpf_abs(num,y);
if(mpf_cmp(num,prec)<0)break;
mpf_sub(x,x,y);
}
mpf_sub(y,x,y);
mpf_out_str(0,10,FC_DEFAULT_PREC,y);std::cout<<"\n";
mpf_clear(prec);
mpf_clear(den);
mpf_clear(num);
mpf_clear(y);
mpf_clear(x);
f.resize(0);
fd.resize(0);
}
int main(void){
/*inicializa as variaveis*/
int cont, numThread[NUMTHREADS];
mpf_set_default_prec((long)(DIGITS*BITS_PER_DIGIT+16));
mpf_t PI, dentroCircunferencia, TOTAL;
pthread_t tID[NUMTHREADS]; // ID das threads
mpf_init(PI);
mpf_init_set_d(dentroCircunferencia, 0.0);
mpf_init_set_d(TOTAL, 0.0);
srand48(time(NULL));
// Para todas as threads, cria a i-esima thread
for (cont = 0; cont< NUMTHREADS ; cont++){
numThread[cont] = cont;
pthread_create (&tID[cont], NULL, calcula, &numThread[cont]);
}
// Para cada thread, espera que as threads terminem
for (cont = 0; cont< NUMTHREADS ; cont++)
pthread_join (tID[cont], NULL);
//Para cada thread, soma a sua parcela na conta total
for (cont = 0; cont< NUMTHREADS ; cont++){
mpf_add_ui(TOTAL, TOTAL, TOTALParcial[cont]);
mpf_add_ui(dentroCircunferencia, dentroCircunferencia, dentroCircunferenciaParcial[cont]);
}
mpf_div (PI, dentroCircunferencia, TOTAL);
mpf_mul_ui (PI, PI, 4);
mpf_out_str(stdout, 10, DIGITS, PI);
printf("\n");
mpf_clear (PI);
mpf_clear (TOTAL);
mpf_clear (dentroCircunferencia);
return 0;
}
int
main (int argc, char *argv[])
{
const char usage[] = "usage: findlc [-dv] m2exp [low_merit [high_merit]]\n";
int f;
int v_lose, m_lose, v_best, m_best;
int c;
int debug = 1;
int cnt_high_merit;
mpz_t m;
unsigned long int m2exp;
#define DIMS 6 /* dimensions run in spectral test */
mpf_t v[DIMS-1]; /* spectral test result (there's no v
for 1st dimension */
mpf_t f_merit, low_merit, high_merit;
mpz_t acc, minus8;
mpz_t min, max;
mpz_t s;
mpz_init (m);
mpz_init (a);
for (f = 0; f < DIMS-1; f++)
mpf_init (v[f]);
mpf_init (f_merit);
mpf_init_set_d (low_merit, .1);
mpf_init_set_d (high_merit, .1);
while ((c = getopt (argc, argv, "a:di:hv")) != -1)
switch (c)
{
case 'd': /* debug */
g_debug++;
break;
case 'v': /* print version */
puts (rcsid[1]);
exit (0);
case 'h':
case '?':
default:
fputs (usage, stderr);
exit (1);
}
argc -= optind;
argv += optind;
if (argc < 1)
{
fputs (usage, stderr);
exit (1);
}
/* Install signal handler. */
if (SIG_ERR == signal (SIGSEGV, sh_status))
{
perror ("signal (SIGSEGV)");
exit (1);
}
if (SIG_ERR == signal (SIGHUP, sh_status))
{
perror ("signal (SIGHUP)");
exit (1);
}
printf ("findlc: version: %s\n", rcsid[1]);
m2exp = atol (argv[0]);
mpz_init_set_ui (m, 1);
mpz_mul_2exp (m, m, m2exp);
printf ("m = 0x");
mpz_out_str (stdout, 16, m);
puts ("");
if (argc > 1) /* have low_merit */
mpf_set_str (low_merit, argv[1], 0);
if (argc > 2) /* have high_merit */
mpf_set_str (high_merit, argv[2], 0);
if (debug)
{
fprintf (stderr, "low_merit = ");
mpf_out_str (stderr, 10, 2, low_merit);
fprintf (stderr, "; high_merit = ");
mpf_out_str (stderr, 10, 2, high_merit);
fputs ("\n", stderr);
}
mpz_init (minus8);
mpz_set_si (minus8, -8L);
mpz_init_set_ui (acc, 0);
mpz_init (s);
mpz_init_set_d (min, 0.01 * pow (2.0, (double) m2exp));
mpz_init_set_d (max, 0.99 * pow (2.0, (double) m2exp));
mpz_true_random (s, m2exp); /* Start. */
mpz_setbit (s, 0); /* Make it odd. */
v_best = m_best = 2*(DIMS-1);
for (;;)
{
mpz_add (acc, acc, s);
mpz_mod_2exp (acc, acc, m2exp);
#if later
mpz_and_si (a, acc, -8L);
#else
mpz_and (a, acc, minus8);
#endif
mpz_add_ui (a, a, 5);
if (mpz_cmp (a, min) <= 0 || mpz_cmp (a, max) >= 0)
continue;
spectral_test (v, DIMS, a, m);
for (f = 0, v_lose = m_lose = 0, cnt_high_merit = DIMS-1;
f < DIMS-1; f++)
{
merit (f_merit, f + 2, v[f], m);
if (mpf_cmp_ui (v[f], 1 << (30 / (f + 2) + (f == 2))) < 0)
v_lose++;
if (mpf_cmp (f_merit, low_merit) < 0)
m_lose++;
if (mpf_cmp (f_merit, high_merit) >= 0)
cnt_high_merit--;
}
if (0 == v_lose && 0 == m_lose)
{
mpz_out_str (stdout, 10, a); puts (""); fflush (stdout);
if (0 == cnt_high_merit)
break; /* leave loop */
}
if (v_lose < v_best)
{
v_best = v_lose;
printf ("best (v_lose=%d; m_lose=%d): ", v_lose, m_lose);
mpz_out_str (stdout, 10, a); puts (""); fflush (stdout);
}
if (m_lose < m_best)
{
m_best = m_lose;
printf ("best (v_lose=%d; m_lose=%d): ", v_lose, m_lose);
mpz_out_str (stdout, 10, a); puts (""); fflush (stdout);
}
}
mpz_clear (m);
mpz_clear (a);
for (f = 0; f < DIMS-1; f++)
mpf_clear (v[f]);
mpf_clear (f_merit);
mpf_clear (low_merit);
mpf_clear (high_merit);
printf ("done.\n");
return 0;
}
int
main (int argc, char **argv)
{
#if GMP_NAIL_BITS == 0
static const struct {
int f_base;
const char *f;
int z_base;
const char *want_num;
const char *want_den;
} data[] = {
{ -2, "0", 16, "0", "1" },
{ -2, "1", 16, "1", "1" },
{ -2, "1@1", 16, "2", "1" },
{ -2, "1@2", 16, "4", "1" },
{ -2, "1@3", 16, "8", "1" },
{ -2, "1@30", 16, "40000000", "1" },
{ -2, "1@31", 16, "80000000", "1" },
{ -2, "1@32", 16, "100000000", "1" },
{ -2, "1@33", 16, "200000000", "1" },
{ -2, "1@34", 16, "400000000", "1" },
{ -2, "1@62", 16, "4000000000000000", "1" },
{ -2, "1@63", 16, "8000000000000000", "1" },
{ -2, "1@64", 16, "10000000000000000", "1" },
{ -2, "1@65", 16, "20000000000000000", "1" },
{ -2, "1@66", 16, "40000000000000000", "1" },
{ -2, "1@126", 16, "40000000000000000000000000000000", "1" },
{ -2, "1@127", 16, "80000000000000000000000000000000", "1" },
{ -2, "1@128", 16, "100000000000000000000000000000000", "1" },
{ -2, "1@129", 16, "200000000000000000000000000000000", "1" },
{ -2, "1@130", 16, "400000000000000000000000000000000", "1" },
{ -2, "1@-1", 16, "1", "2" },
{ -2, "1@-2", 16, "1", "4" },
{ -2, "1@-3", 16, "1", "8" },
{ -2, "1@-30", 16, "1", "40000000" },
{ -2, "1@-31", 16, "1", "80000000" },
{ -2, "1@-32", 16, "1", "100000000" },
{ -2, "1@-33", 16, "1", "200000000" },
{ -2, "1@-34", 16, "1", "400000000" },
{ -2, "1@-62", 16, "1", "4000000000000000" },
{ -2, "1@-63", 16, "1", "8000000000000000" },
{ -2, "1@-64", 16, "1", "10000000000000000" },
{ -2, "1@-65", 16, "1", "20000000000000000" },
{ -2, "1@-66", 16, "1", "40000000000000000" },
{ -2, "1@-126", 16, "1", "40000000000000000000000000000000" },
{ -2, "1@-127", 16, "1", "80000000000000000000000000000000" },
{ -2, "1@-128", 16, "1", "100000000000000000000000000000000" },
{ -2, "1@-129", 16, "1", "200000000000000000000000000000000" },
{ -2, "1@-130", 16, "1", "400000000000000000000000000000000" },
{ -2, "1@-30", 16, "1", "40000000" },
{ -2, "1@-31", 16, "1", "80000000" },
{ -2, "1@-32", 16, "1", "100000000" },
{ -2, "1@-33", 16, "1", "200000000" },
{ -2, "1@-34", 16, "1", "400000000" },
{ -2, "11@-62", 16, "3", "4000000000000000" },
{ -2, "11@-63", 16, "3", "8000000000000000" },
{ -2, "11@-64", 16, "3", "10000000000000000" },
{ -2, "11@-65", 16, "3", "20000000000000000" },
{ -2, "11@-66", 16, "3", "40000000000000000" },
{ 16, "80000000.00000001", 16, "8000000000000001", "100000000" },
{ 16, "80000000.00000008", 16, "1000000000000001", "20000000" },
{ 16, "80000000.8", 16, "100000001", "2" },
};
mpf_t f;
mpq_t got;
mpz_t want_num, want_den;
int i, neg;
tests_start ();
mpf_init2 (f, 1024L);
mpq_init (got);
mpz_init (want_num);
mpz_init (want_den);
for (i = 0; i < numberof (data); i++)
{
for (neg = 0; neg <= 1; neg++)
{
mpf_set_str_or_abort (f, data[i].f, data[i].f_base);
mpz_set_str_or_abort (want_num, data[i].want_num, data[i].z_base);
mpz_set_str_or_abort (want_den, data[i].want_den, data[i].z_base);
if (neg)
{
mpf_neg (f, f);
mpz_neg (want_num, want_num);
}
mpq_set_f (got, f);
MPQ_CHECK_FORMAT (got);
if (mpz_cmp (mpq_numref(got), want_num) != 0
|| mpz_cmp (mpq_denref(got), want_den) != 0)
{
printf ("wrong at data[%d]\n", i);
printf (" f_base %d, z_base %d\n",
data[i].f_base, data[i].z_base);
printf (" f \"%s\" hex ", data[i].f);
mpf_out_str (stdout, 16, 0, f);
printf ("\n");
printf (" want num 0x");
mpz_out_str (stdout, 16, want_num);
printf ("\n");
printf (" want den 0x");
mpz_out_str (stdout, 16, want_den);
printf ("\n");
printf (" got num 0x");
mpz_out_str (stdout, 16, mpq_numref(got));
printf ("\n");
printf (" got den 0x");
mpz_out_str (stdout, 16, mpq_denref(got));
printf ("\n");
abort ();
}
}
}
mpf_clear (f);
mpq_clear (got);
mpz_clear (want_num);
mpz_clear (want_den);
tests_end ();
#endif
exit (0);
}
int
main(int argc,char *argv[])
{
mpf_t pi,qi,ci;
mpz_t pstack,qstack,gstack;
long d=100,out=0,threads=1,depth,psize,qsize;
double begin, mid0, mid3, mid4, end;
double wbegin, wmid0, wmid3, wmid4, wend;
prog_name = argv[0];
if (argc==1) {
fprintf(stderr,"\nSyntax: %s <digits> <option> <threads>\n",prog_name);
fprintf(stderr," <digits> digits of pi to output\n");
fprintf(stderr," <option> 0 - just run (default)\n");
fprintf(stderr," 1 - output digits\n");
fprintf(stderr," <threads> number of threads (default 1)\n");
exit(1);
}
if (argc>1)
d = strtoul(argv[1],0,0);
if (argc>2)
out = atoi(argv[2]);
if (argc>3)
threads = atoi(argv[3]);
terms = d/DIGITS_PER_ITER;
depth = 0;
while ((1L<<depth)<terms)
depth++;
depth++;
fprintf(stderr,"#terms=%ld, depth=%ld, threads=%ld cores=%d\n", terms, depth, threads, get_nprocs());
begin = cpu_time();
wbegin = wall_clock();
mpz_init(pstack);
mpz_init(qstack);
mpz_init(gstack);
/* begin binary splitting process */
if (terms<=0) {
mpz_set_ui(pstack,1);
mpz_set_ui(qstack,0);
mpz_set_ui(gstack,1);
} else {
#ifdef _OPENMP
#pragma omp parallel num_threads(threads)
#pragma omp single nowait
{
bs(0,terms,1,pstack,qstack,gstack);
}
#else
bs(0,terms,1,pstack,qstack,gstack);
#endif
}
mid0 = cpu_time();
wmid0 = wall_clock();
fprintf(stderr,"bs cputime = %6.2f wallclock = %6.2f factor = %6.1f\n",
mid0-begin,wmid0-wbegin,(mid0-begin)/(wmid0-wbegin));
fflush(stderr);
mpz_clear(gstack);
/* prepare to convert integers to floats */
mpf_set_default_prec((long)(d*BITS_PER_DIGIT+16));
/*
p*(C/D)*sqrt(C)
pi = -----------------
(q+A*p)
*/
psize = mpz_sizeinbase(pstack,10);
qsize = mpz_sizeinbase(qstack,10);
mpz_addmul_ui(qstack,pstack,A);
mpz_mul_ui(pstack,pstack,C/D);
mpf_init(pi);
mpf_set_z(pi,pstack);
mpz_clear(pstack);
mpf_init(qi);
mpf_set_z(qi,qstack);
mpz_clear(qstack);
/* final step */
mid3 = cpu_time();
wmid3 = wall_clock();
#ifdef _OPENMP
#pragma omp parallel num_threads(threads)
#pragma omp single nowait
{
#pragma omp task shared(qi,pi)
{
mpf_div(qi,pi,qi);
mpf_clear(pi);
}
#pragma omp task shared(ci)
{
mpf_init(ci);
mpf_sqrt_ui(ci,C);
}
#pragma omp taskwait
}
#else
mpf_div(qi, pi, qi);
mpf_clear(pi);
mpf_init(ci);
mpf_sqrt_ui(ci, C);
#endif
mid4 = cpu_time();
wmid4 = wall_clock();
fprintf(stderr,"div/sqrt cputime = %6.2f wallclock = %6.2f factor = %6.1f\n",
mid4-mid3,wmid4-wmid3,(mid4-mid3)/(wmid4-wmid3));
mpf_mul(qi,qi,ci);
mpf_clear(ci);
end = cpu_time();
wend = wall_clock();
fprintf(stderr,"mul cputime = %6.2f wallclock = %6.2f factor = %6.1f\n",
end-mid4,wend-wmid4,(end-mid4)/(wend-wmid4));
fprintf(stderr,"total cputime = %6.2f wallclock = %6.2f factor = %6.1f\n",
end-begin,wend-wbegin,(end-begin)/(wend-wbegin));
fflush(stderr);
fprintf(stderr," P size=%ld digits (%f)\n"
" Q size=%ld digits (%f)\n",
psize, (double)psize/d, qsize, (double)qsize/d);
/* output Pi and timing statistics */
if (out&1) {
fprintf(stdout,"pi(0,%ld)=\n", terms);
mpf_out_str(stdout,10,d,qi);
fprintf(stdout,"\n");
}
/* free float resources */
mpf_clear(qi);
exit (0);
}
int
main (void)
{
mpf_t x;
mpfr_t y, z;
unsigned long i;
mpfr_exp_t e;
int inex;
tests_start_mpfr ();
mpfr_init (y);
mpfr_init (z);
mpf_init (x);
i = 1;
while (i)
{
mpfr_set_ui (y, i, MPFR_RNDN);
if (mpfr_get_f (x, y, MPFR_RNDN) != 0 || mpf_cmp_ui (x, i))
{
printf ("Error: mpfr_get_f(%lu) fails\n", i);
exit (1);
}
if (i <= - (unsigned long) LONG_MIN)
{
long j = i < - (unsigned long) LONG_MIN ? - (long) i : LONG_MIN;
mpfr_set_si (y, j, MPFR_RNDN);
if (mpfr_get_f (x, y, MPFR_RNDN) != 0 || mpf_cmp_si (x, j))
{
printf ("Error: mpfr_get_f(-%lu) fails\n", i);
exit (1);
}
}
i *= 2;
}
/* same tests, but with a larger precision for y, which requires to
round it */
mpfr_set_prec (y, 100);
i = 1;
while (i)
{
mpfr_set_ui (y, i, MPFR_RNDN);
inex = mpfr_get_f (x, y, MPFR_RNDN);
if (! SAME_SIGN (inex, - mpfr_cmp_f (y, x)) || mpf_cmp_ui (x, i))
{
printf ("Error: mpfr_get_f(%lu) fails\n", i);
exit (1);
}
mpfr_set_si (y, (signed long) -i, MPFR_RNDN);
inex = mpfr_get_f (x, y, MPFR_RNDN);
if (! SAME_SIGN (inex, - mpfr_cmp_f (y, x))
|| mpf_cmp_si (x, (signed long) -i))
{
printf ("Error: mpfr_get_f(-%lu) fails\n", i);
exit (1);
}
i *= 2;
}
/* bug reported by Jim White */
for (e = 0; e <= 2 * GMP_NUMB_BITS; e++)
{
/* test with 2^(-e) */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_div_2exp (y, y, e, MPFR_RNDN);
inex = mpfr_get_f (x, y, MPFR_RNDN);
mpf_mul_2exp (x, x, e);
if (inex != 0 || mpf_cmp_ui (x, 1) != 0)
{
printf ("Error: mpfr_get_f(x,y,MPFR_RNDN) fails\n");
printf ("y=");
mpfr_dump (y);
printf ("x=");
mpf_div_2exp (x, x, e);
mpf_out_str (stdout, 2, 0, x);
exit (1);
}
/* test with 2^(e) */
mpfr_set_ui (y, 1, MPFR_RNDN);
mpfr_mul_2exp (y, y, e, MPFR_RNDN);
inex = mpfr_get_f (x, y, MPFR_RNDN);
mpf_div_2exp (x, x, e);
if (inex != 0 || mpf_cmp_ui (x, 1) != 0)
{
printf ("Error: mpfr_get_f(x,y,MPFR_RNDN) fails\n");
printf ("y=");
mpfr_dump (y);
printf ("x=");
mpf_mul_2exp (x, x, e);
mpf_out_str (stdout, 2, 0, x);
exit (1);
}
}
/* Bug reported by Yury Lukach on 2006-04-05 */
mpfr_set_prec (y, 32);
mpfr_set_prec (z, 32);
mpf_set_prec (x, 32);
mpfr_set_ui_2exp (y, 0xc1234567, -30, MPFR_RNDN);
mpfr_get_f (x, y, MPFR_RNDN);
inex = mpfr_set_f (z, x, MPFR_RNDN);
if (inex != 0 || ! mpfr_equal_p (y, z))
{
printf ("Error in mpfr_get_f:\n inex = %d, y = ", inex);
mpfr_dump (z);
printf ("Expected:\n inex = 0, y = ");
mpfr_dump (y);
exit (1);
}
mpfr_clear (y);
mpfr_clear (z);
mpf_clear (x);
special_test ();
prec_test ();
ternary_test ();
tests_end_mpfr ();
return 0;
}
void
check_data (void)
{
static const struct {
int a_base;
const char *a;
const char *b;
int want;
} data[] = {
{ 10, "0", "1", -1 },
{ 10, "0", "0", 0 },
{ 10, "0", "-1", 1 },
{ 10, "1", "1", 0 },
{ 10, "1", "0", 1 },
{ 10, "1", "-1", 1 },
{ 10, "-1", "1", -1 },
{ 10, "-1", "0", -1 },
{ 10, "-1", "-1", 0 },
{ 16, "0", "-0x80000000", 1 },
{ 16, "80000000", "-0x80000000", 1 },
{ 16, "80000001", "-0x80000000", 1 },
{ 16, "-80000000", "-0x80000000", 0 },
{ 16, "-80000001", "-0x80000000", -1 },
{ 16, "-FF0080000001", "-0x80000000", -1 },
{ 16, "0", "-0x8000000000000000", 1 },
{ 16, "8000000000000000", "-0x8000000000000000", 1 },
{ 16, "8000000000000001", "-0x8000000000000000", 1 },
{ 16, "-8000000000000000", "-0x8000000000000000", 0 },
{ 16, "-8000000000000001", "-0x8000000000000000", -1 },
{ 16, "-FF008000000000000001", "-0x8000000000000000", -1 },
};
mpf_t a;
mpz_t bz;
long b;
int got;
int i;
mpf_init (a);
mpz_init (bz);
for (i = 0; i < numberof (data); i++)
{
mpf_set_str_or_abort (a, data[i].a, data[i].a_base);
mpz_set_str_or_abort (bz, data[i].b, 0);
if (mpz_fits_slong_p (bz))
{
b = mpz_get_si (bz);
got = mpf_cmp_si (a, b);
if (SGN (got) != data[i].want)
{
printf ("mpf_cmp_si wrong on data[%d]\n", i);
printf (" a="); mpf_out_str (stdout, 10, 0, a);
printf (" (%s)\n", data[i].a);
printf (" b=%ld (%s)\n", b, data[i].b);
printf (" got=%d\n", got);
printf (" want=%d\n", data[i].want);
abort();
}
}
}
mpf_clear (a);
mpz_clear (bz);
}
/* Test that there is no lost of accuracy when converting a mpfr_t number
into a mpf_t number (test with various precisions and exponents). */
static void
prec_test (void)
{
int px, py;
for (py = 3; py <= 136; py++)
{
mpfr_t y1, y2, y3;
mpfr_init2 (y1, py);
mpfr_init2 (y2, py);
mpfr_init2 (y3, py);
for (px = 32; px <= 160; px += 32)
{
mpf_t x1, x2, x3;
int e;
mpf_init (x1);
mpf_init (x2);
mpf_init (x3);
mpfr_set_ui_2exp (y1, 1, py - 1, MPFR_RNDN);
mpfr_get_f (x1, y1, MPFR_RNDN); /* exact (power of 2) */
mpf_set (x2, x1);
mpfr_set (y2, y1, MPFR_RNDN);
for (e = py - 2; e >= 0; e--)
{
int inex;
mpf_div_2exp (x2, x2, 1);
mpf_add (x1, x1, x2);
mpfr_div_2exp (y2, y2, 1, MPFR_RNDN);
inex = mpfr_add (y1, y1, y2, MPFR_RNDN);
MPFR_ASSERTN (inex == 0);
mpfr_set_f (y3, x1, MPFR_RNDN);
if (! mpfr_equal_p (y1, y3))
break;
inex = mpfr_get_f (x3, y3, MPFR_RNDN);
if (mpf_cmp (x1, x3) != 0)
{
printf ("Error in prec_test (px = %d, py = %d, e = %d)\n",
px, py, e);
printf ("x1 = ");
mpf_out_str (stdout, 16, 0, x1);
printf ("\nx2 = ");
mpf_out_str (stdout, 16, 0, x2);
printf ("\n");
exit (1);
}
if (inex != 0)
{
printf ("Error in prec_test (px = %d, py = %d, e = %d)\n",
px, py, e);
printf ("wrong ternary value got: %+d, expected: 0\n",
inex);
exit (1);
}
}
mpf_clear (x1);
mpf_clear (x2);
mpf_clear (x3);
}
mpfr_clear (y1);
mpfr_clear (y2);
mpfr_clear (y3);
}
}
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);
}
static void
ternary_test (void)
{
int prec;
int rnd;
int inex, expected_inex;
mpf_t x;
mpfr_t y;
mpf_init2 (x, 256);
mpfr_init2 (y, 256);
for (prec = 2; prec <= 256; prec++)
{
mpf_set_prec (x, prec);
mpfr_set_prec (y, PREC (x) * GMP_NUMB_BITS + 1);
/* y == 1 */
mpfr_set_ui_2exp (y, 1, prec, MPFR_RNDN);
RND_LOOP (rnd)
{
inex = mpfr_get_f (x, y, (mpfr_rnd_t) rnd);
if (inex != 0 || mpfr_cmp_f (y, x) !=0)
{
printf ("Error in mpfr_get_f (x, y, %s)\nx = ",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpf_out_str (stdout, 2, 0, x);
printf ("\ny = ");
mpfr_dump (y);
if (inex != 0)
printf ("got ternary value = %+d, expected: 0\n", inex);
exit (1);
}
}
/* y == 1 + epsilon */
mpfr_nextbelow (y);
RND_LOOP (rnd)
{
switch (rnd)
{
case MPFR_RNDU: case MPFR_RNDA:
case MPFR_RNDN:
expected_inex = +1;
break;
default :
expected_inex = -1;
}
inex = mpfr_get_f (x, y, (mpfr_rnd_t) rnd);
if (! SAME_SIGN (expected_inex, inex)
|| SAME_SIGN (expected_inex, mpfr_cmp_f (y, x)))
{
printf ("Error in mpfr_get_f (x, y, %s)\nx = ",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpf_out_str (stdout, 2, 0, x);
printf ("\ny = ");
mpfr_dump (y);
if (! SAME_SIGN (expected_inex, inex))
printf ("got ternary value = %+d, expected: %+d\n",
inex, expected_inex);
exit (1);
}
}
/* y == positive random float */
mpfr_random2 (y, MPFR_LIMB_SIZE (y), 1024, RANDS);
RND_LOOP (rnd)
{
inex = mpfr_get_f (x, y, (mpfr_rnd_t) rnd);
if (! SAME_SIGN (inex, -mpfr_cmp_f (y, x)))
{
printf ("Error in mpfr_get_f (x, y, %s)\nx = ",
mpfr_print_rnd_mode ((mpfr_rnd_t) rnd));
mpf_out_str (stdout, 2, 0, x);
printf ("\ny = ");
mpfr_dump (y);
printf ("got ternary value = %+d, expected: %+d\n",
inex, -mpfr_cmp_f (y, x));
exit (1);
}
}
}
mpf_clear (x);
mpfr_clear (y);
}
