int main (void) {
mpf_set_default_prec (300000);
mpf_t x0, y0, resA, resB, Z, var;
mpf_init_set_ui (x0, 1);
mpf_init_set_d (y0, 0.5);
mpf_sqrt (y0, y0);
mpf_init (resA);
mpf_init (resB);
mpf_init_set_d (Z, 0.25);
mpf_init (var);
int n = 1;
for(int i=0; i<8; i++){
agm(x0, y0, resA, resB);
mpf_sub(var, resA, x0);
mpf_mul(var, var, var);
mpf_mul_ui(var, var, n);
mpf_sub(Z, Z, var);
n += n;
agm(resA, resB, x0, y0);
mpf_sub(var, x0, resA);
mpf_mul(var, var, var);
mpf_mul_ui(var, var, n);
mpf_sub(Z, Z, var);
n += n;
}
mpf_mul(x0, x0, x0);
mpf_div(x0, x0, Z);
gmp_printf ("%.100000Ff\n", x0);
return 0;
}
void
check_rand (void)
{
unsigned long min_prec = __GMPF_BITS_TO_PREC (1);
gmp_randstate_t rands;
mpf_t got, u;
unsigned long prec, v;
int i;
/* The nails code in mpf_mul_ui currently isn't exact, so suppress these
tests for now. */
if (BITS_PER_UI > GMP_NUMB_BITS)
return;
mpf_init (got);
mpf_init (u);
gmp_randinit_default(rands);
for (i = 0; i < 200; i++)
{
/* got precision */
prec = min_prec + gmp_urandomm_ui (rands, 15L);
refmpf_set_prec_limbs (got, prec);
/* u precision */
prec = min_prec + gmp_urandomm_ui (rands, 15L);
refmpf_set_prec_limbs (u, prec);
/* u, possibly negative */
mpf_rrandomb (u, rands, PREC(u), (mp_exp_t) 20);
if (gmp_urandomb_ui (rands, 1L))
mpf_neg (u, u);
/* v, 0 to BITS_PER_ULONG bits (inclusive) */
prec = gmp_urandomm_ui (rands, BITS_PER_ULONG+1);
v = gmp_urandomb_ui (rands, prec);
if ((i % 2) == 0)
{
/* separate */
mpf_mul_ui (got, u, v);
check_one ("separate", got, u, v);
}
else
{
/* overlap */
prec = refmpf_set_overlap (got, u);
mpf_mul_ui (got, got, v);
check_one ("overlap src==dst", got, u, v);
mpf_set_prec_raw (got, prec);
}
}
mpf_clear (got);
mpf_clear (u);
gmp_randclear(rands);
}
/* r = sqrt(x) */
void
my_sqrt_ui(mpf_t r, unsigned long x)
{
unsigned long prec, bits, prec0;
prec0 = mpf_get_prec(r);
if (prec0<=DOUBLE_PREC) {
mpf_set_d(r, sqrt(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_set_d(t1, 1/sqrt(x));
while (prec<prec0)
{
prec *=2;
if (prec<prec0)
{
/* t1 = t1+t1*(1-x*t1*t1)/2; */
mpf_set_prec_raw(t2, prec);
mpf_mul(t2, t1, t1); /* half x half -> full */
mpf_mul_ui(t2, t2, x);
mpf_ui_sub(t2, 1, t2);
mpf_set_prec_raw(t2, prec/2);
mpf_div_2exp(t2, t2, 1);
mpf_mul(t2, t2, t1); /* half x half -> half */
mpf_set_prec_raw(t1, prec);
mpf_add(t1, t1, t2);
}
else
{
break;
}
prec -= (bits&1);
bits /=2;
}
/* t2=x*t1, t1 = t2+t1*(x-t2*t2)/2; */
mpf_set_prec_raw(t2, prec0/2);
mpf_mul_ui(t2, t1, x);
mpf_mul(r, t2, t2); /* half x half -> full */
mpf_ui_sub(r, x, r);
mpf_mul(t1, t1, r); /* half x half -> half */
mpf_div_2exp(t1, t1, 1);
mpf_add(r, t1, t2);
}
/* merit (rop, t, v, m) -- calculate merit for spectral test result in
dimension T, see Knuth p. 105. BUGS: Only valid for 2 <= T <=
6. */
void
merit (mpf_t rop, unsigned int t, mpf_t v, mpz_t m)
{
int f;
mpf_t f_m, f_const, f_pi;
mpf_init (f_m);
mpf_set_z (f_m, m);
mpf_init_set_d (f_const, M_PI);
mpf_init_set_d (f_pi, M_PI);
switch (t)
{
case 2: /* PI */
break;
case 3: /* PI * 4/3 */
mpf_mul_ui (f_const, f_const, 4);
mpf_div_ui (f_const, f_const, 3);
break;
case 4: /* PI^2 * 1/2 */
mpf_mul (f_const, f_const, f_pi);
mpf_div_ui (f_const, f_const, 2);
break;
case 5: /* PI^2 * 8/15 */
mpf_mul (f_const, f_const, f_pi);
mpf_mul_ui (f_const, f_const, 8);
mpf_div_ui (f_const, f_const, 15);
break;
case 6: /* PI^3 * 1/6 */
mpf_mul (f_const, f_const, f_pi);
mpf_mul (f_const, f_const, f_pi);
mpf_div_ui (f_const, f_const, 6);
break;
default:
fprintf (stderr,
"spect (merit): can't calculate merit for dimensions > 6\n");
mpf_set_ui (f_const, 0);
break;
}
/* rop = v^t */
mpf_set (rop, v);
for (f = 1; f < t; f++)
mpf_mul (rop, rop, v);
mpf_mul (rop, rop, f_const);
mpf_div (rop, rop, f_m);
mpf_clear (f_m);
mpf_clear (f_const);
mpf_clear (f_pi);
}
depth_t frac_generalized_celtic_gmp(
depth_t depth,
mpf_t bail,
mpf_t wim, mpf_t wre,
mpf_t c_im, mpf_t c_re,
mpf_t wim2, mpf_t wre2, mpf_t t1)
{
depth_t wz;
for (wz = 1; wz <= depth; wz++)
{
/* wim = 2.0 * wre * wim + c_im; */
mpf_mul( t1, wre, wim);
mpf_mul_ui(t1, t1, 2);
mpf_add( wim, t1, c_im);
/* wre = wre2 - wim2 + c_re; */
mpf_sub( t1, wre2, wim2);
mpf_abs( t1, t1);
mpf_add( wre, t1, c_re);
/* wim2 = wim * wim; */
mpf_mul( wim2, wim, wim);
/* wre2 = wre * wre; */
mpf_mul( wre2, wre, wre);
/* if ((wim2 + wre2) > frs_bail) */
mpf_add( t1, wim2, wre2);
if (mpf_cmp(t1, bail) > 0)
return wz;
}
return 0;
}
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 mpf_fac_ui(mpf_t rop, unsigned int n) {
unsigned int i;
gmp_printf("n: %d\n",n);
mpf_set_ui(rop,1);
for(i = n; i > 1; i--) mpf_mul_ui(rop,rop,i);
}
void FractalTexture::computeColor(unsigned char *pixel) {
#ifdef ROE_FRACTAL_GMP_USE_C
mpf_set(xPos, m_xPos);
mpf_set(yPos, m_yPos);
#else
xPos = m_xPos;
yPos = m_yPos;
#endif
for(long iteration = 0; iteration < m_iMaxIterations; ++iteration) {
#ifdef ROE_FRACTAL_GMP_USE_C
mpf_mul(xPos2, xPos, xPos);
mpf_mul(yPos2, yPos, yPos);
mpf_add(tmp, xPos2, yPos2); //save sum temporarily
if(mpf_cmp_ui(tmp,4) >= 0) {
#else
xPos2 = xPos*xPos;
yPos2 = yPos*yPos;
if(xPos2 + yPos2 > 4.0) {
#endif
//(coloured) outer
const double ratio = iteration*m_dInvMaxIterations;
//const Color c = Color::WHITE;
const Color c = colorInterpolation.interpolate(ratio);
pixel[0] = c.byter();
pixel[1] = c.byteg();
pixel[2] = c.byteb();
return;
}
#ifdef ROE_FRACTAL_GMP_USE_C
mpf_mul(yPos, yPos, xPos);
mpf_mul_ui(yPos, yPos, 2);
mpf_add(yPos, yPos, m_yPos);
mpf_sub(xPos, xPos2, yPos2);
mpf_add(xPos, xPos, m_xPos);
#else
yPos *= xPos;
yPos *= 2;
yPos += m_yPos;
xPos = xPos2;
xPos -= yPos2;
xPos += m_xPos;
#endif
}
//inner
pixel[0] = m_innerR;
pixel[1] = m_innerG;
pixel[2] = m_innerB;
}
void FractalTexture::updateMipmaps() {
S_Texture *subtex1 = &texture, *subtex2 = nullptr;
while (subtex1->next_mipmap) {
subtex2 = subtex1->next_mipmap;
Texture::scaleImage2(subtex1->data, subtex1->width, subtex1->height, subtex2->data, subtex2->width, subtex2->height, subtex1->bpp); //scaling image to new size
subtex1 = subtex2; //one level deeper
}
}
void correction_factor_Q(mpf_t Q, int N,mpf_t rho,int k){
unsigned long int f;
mpf_t tmp,tmp1,tmp2;
/*
if (PNK_N_1_rho_1_PN == 0)
cout << "Algun factor es 0 N = " << N
<< " rho = " << rho
<< " k = " << k
<< " P__0 = " << P__0
<< " P__N = " << P__N << endl;
*/
mpf_init(tmp);
mpf_init_set_d(tmp1,pow(N,k-1)); // N^(k-1)
f = 1;
mpf_set_ui(Q,0);
for (unsigned long int j = k;j < N;j++) {
/*Q += (N - j) * pow(N,j) * pow(rho,j - k) * P__0 * N_k_1 / (factorial(j - k) * PNK_N_1_rho_1_PN); */
/* Q += [(N - j) * N^j * rho^(j - k) / (j - k)!] * P__0 * N_k_1 / PNK_N_1_rho_1_PN; */
mpf_mul_ui(tmp1,tmp1,N); // * N
if (j - k > 1) mpf_div_ui(tmp1,tmp1,j - k); // / (j - k)
mpf_mul_ui(tmp,tmp1,N - j); // * (N - j)
mpf_add(Q,Q,tmp); // Q += (N - j) * N^j * rho^(j - k) / (j - k)!
mpf_mul(tmp1,tmp1,rho); // * rho
}
mpf_init(tmp2);
mpf_ui_sub(tmp2,1,P__N); // 1 - P__N
mpf_pow_ui(tmp1,tmp2,k); // (1 - P__N)^k
mpf_mul(tmp2,tmp2,rho); // rho * (1 - P__N)
mpf_ui_sub(tmp2,1,tmp2); // 1 - rho * (1 - P__N)
mpf_mul(Q,Q,P__0); // * P__0
mpf_mul_ui(Q,Q,factorial(N-k-1)); // * (N - k - 1)!
/* pow(1 - P__N,k) * factorial(N) * (1 - rho * (1 - P__N)) */
mpf_mul(tmp2,tmp1,tmp2); // (1 - P__N)^k * (1 - rho * (1 - P__N))
mpf_mul_ui(tmp2,tmp2,factorial(N)); // (1 - P__N)^k * (1 - rho * (1 - P__N)) * N!
mpf_div(Q,Q,tmp2); // / [(1 - P__N)^k * (1 - rho * (1 - P__N)) * N!]
mpf_clear(tmp);
mpf_clear(tmp1);
mpf_clear(tmp2);
}
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);
}
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 UniDFormF(poly_f & r, poly_f & f)
{
if(f.size()<=1)
{
r.resize(0);
return ;
}
r.resize(f.size()-1);
for(size_t i=0;i<r.size();i++)
{
mpf_mul_ui(r[i],f[i+1],i+1);
}
r.normalize();
}
void
check_various (void)
{
mpf_t u, got, want;
char *s;
mpf_init2 (u, 2*8*sizeof(long));
mpf_init2 (got, 2*8*sizeof(long));
mpf_init2 (want, 2*8*sizeof(long));
s = "0 * GMP_UI_MAX";
mpf_set_ui (u, 0L);
mpf_mul_ui (got, u, GMP_UI_MAX);
MPF_CHECK_FORMAT (got);
mpf_set_ui (want, 0L);
if (mpf_cmp (got, want) != 0)
{
error:
printf ("Wrong result from %s\n", s);
mpf_trace ("u ", u);
mpf_trace ("got ", got);
mpf_trace ("want", want);
abort ();
}
s = "1 * GMP_UI_MAX";
mpf_set_ui (u, 1L);
mpf_mul_ui (got, u, GMP_UI_MAX);
MPF_CHECK_FORMAT (got);
mpf_set_ui (want, GMP_UI_MAX);
if (mpf_cmp (got, want) != 0)
goto error;
mpf_clear (u);
mpf_clear (got);
mpf_clear (want);
}
static void
Pks (mpf_t p, mpf_t x)
{
double dt; /* temp double */
mpf_set (p, x);
mpf_mul (p, p, p); /* p = x^2 */
mpf_mul_ui (p, p, 2); /* p = 2*x^2 */
mpf_neg (p, p); /* p = -2*x^2 */
/* No pow() in gmp. Use doubles. */
/* FIXME: Use exp()? */
dt = pow (M_E, mpf_get_d (p));
mpf_set_d (p, dt);
mpf_ui_sub (p, 1, p);
}
// 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;
}
void
mpc_mod (mpc_t *rop, mpc_t op1, mpc_t op2)
{
/* I am 90% sure that this doesn't work. However, it works for
* integers, so I'll put off fixing it for a little while.
*/
mpf_t hold_op1;
mpf_t hold_op2;
mpf_t hold_res;
unsigned int prec;
mpf_init (hold_op1);
mpf_init (hold_op2);
mpf_init (hold_res);
mpf_set_z (hold_op1, op1.object);
mpf_set_z (hold_op2, op2.object);
// Get the largest precision.
prec = (op1.precision > op2.precision) ? op1.precision : op2.precision;
// Set the scalar values
while (op1.precision-- > 0)
mpf_div_ui (hold_op1, hold_op1, 10);
while (op2.precision-- > 0)
mpf_div_ui (hold_op2, hold_op2, 10);
// Get the value
mpf_div (hold_res, hold_op1, hold_op2);
mpf_floor (hold_res, hold_res);
mpf_mul (hold_res, hold_res, hold_op2);
mpf_sub (hold_res, hold_op1, hold_res);
for (rop->precision = prec; prec > 0; prec--)
mpf_mul_ui (hold_res, hold_res, 10);
mpz_set_f (rop->object, hold_res);
}
void
ks_table (mpf_t p, mpf_t val, const unsigned int n)
{
/* We use Eq. (27), Knuth p.58, skipping O(1/n) for simplicity.
This shortcut will result in too high probabilities, especially
when n is small.
Pr(Kp(n) <= s) = 1 - pow(e, -2*s^2) * (1 - 2/3*s/sqrt(n) + O(1/n)) */
/* We have 's' in variable VAL and store the result in P. */
mpf_t t1, t2;
mpf_init (t1); mpf_init (t2);
/* t1 = 1 - 2/3 * s/sqrt(n) */
mpf_sqrt_ui (t1, n);
mpf_div (t1, val, t1);
mpf_mul_ui (t1, t1, 2);
mpf_div_ui (t1, t1, 3);
mpf_ui_sub (t1, 1, t1);
/* t2 = pow(e, -2*s^2) */
#ifndef OLDGMP
mpf_pow_ui (t2, val, 2); /* t2 = s^2 */
mpf_set_d (t2, exp (-(2.0 * mpf_get_d (t2))));
#else
/* hmmm, gmp doesn't have pow() for floats. use doubles. */
mpf_set_d (t2, pow (M_E, -(2 * pow (mpf_get_d (val), 2))));
#endif
/* p = 1 - t1 * t2 */
mpf_mul (t1, t1, t2);
mpf_ui_sub (p, 1, t1);
mpf_clear (t1); mpf_clear (t2);
}
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;
}
void topsin_series (mpf_t a_k, unsigned int k, unsigned int prec)
{
unsigned int n;
mpf_t fourpi, numer, fact, low_bound, term, xterm;
mpz_t bino;
mpf_set_ui(a_k, 0);
/* If k == 0 then we are done */
if (0 == k) return;
mpf_init(fourpi);
mpf_init(numer);
mpf_init(fact);
mpf_init(low_bound);
mpf_init(term);
mpf_init(xterm);
mpz_init(bino);
fp_two_pi(numer, prec);
mpf_neg(numer, numer);
// fourpi is actually -4pi^2
mpf_mul(fourpi, numer, numer);
mpf_neg(fourpi, fourpi);
mpf_set_ui(fact, 1);
/* Get the number of binary bits from prec = log_2 10 * prec */
long nbits = (long) floor (3.321 * prec);
mpf_div_2exp(low_bound, fact, nbits+32);
for (n=0; n<2023123123; n++)
{
i_binomial(bino, 2*n+k, 2*n);
mpf_set_z(term, bino);
mpf_mul(xterm, term, numer);
mpf_div(term, xterm, fact);
mpf_add(a_k, a_k, term);
// #define DEBUG 1
#ifdef DEBUG
{
double h_f, q_f, b_f;
h_f = mpf_get_d(h);
q_f = mpf_get_d(qmark);
b_f = mpf_get_d(bits);
printf("duuude place=%d, bitsdone=%ld h=%g q=%g bits=%f s=%d\n",
place, bitsdone, h_f, q_f, b_f, mpf_sgn(h));
}
#endif
// If the term is small enough, we are done.
mpf_abs(xterm, term);
if (mpf_cmp(xterm, low_bound) < 0) break;
// Now iterate
mpf_mul(numer, numer, fourpi);
mpf_mul_ui(fact, fact, (2*n+3)*2*(n+1));
}
if (k%2 == 0) mpf_neg(a_k, a_k);
mpf_clear(fourpi);
mpf_clear(numer);
mpf_clear(fact);
mpf_clear(low_bound);
mpf_clear(term);
mpf_clear(xterm);
mpz_clear(bino);
}
void mpfc_mul_ui(mpfc_ptr r,mpfc_ptr x,uint a)
{
mpf_mul_ui(r->Re,x->Re,a);
mpf_mul_ui(r->Im,x->Im,a);
}
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;
}
long int julia(const mpf_t x, const mpf_t xr, long int xres, const mpf_t y, const mpf_t yr, long int yres, mpf_t *c, int flag, long int max_iteration,
float *iterations, int my_rank, int p, MPI_Comm comm)
{
double t0 = MPI_Wtime();
int i,j;
//------------julia gmp
const double maxRadius = 4.0;
// double xi, yi, savex, savex2, savey, radius;
mpf_t xi, yi, x_min, x_max, y_min, y_max, savex, savex2, savey, radius, xgap, ygap, savex_a, savex_b, savey_a, savey_b, tmp, tmp1;
mpf_init(xi);
mpf_init(yi);
mpf_init(x_min);
mpf_init(x_max);
mpf_init(y_min);
mpf_init(y_max);
mpf_init(savex);
mpf_init(savex2);
mpf_init(savey);
mpf_init(radius);
mpf_init(xgap);
mpf_init(ygap);
mpf_init(savex_a);
mpf_init(savex_b);
mpf_init(savey_a);
mpf_init(savey_b);
mpf_init(tmp);
mpf_init(tmp1);
//double x_min = x - xr;
mpf_sub(x_min, x, xr);
//double x_max = x + xr;
mpf_add(x_max, x, xr);
//double y_min = y - yr;
mpf_sub(y_min, y, yr);
//double y_max = y + yr;
mpf_add(y_max, y, yr);
// spaceing between x and y points
//double xgap = (x_max - x_min) / xres;
mpf_sub(xgap, x_max, x_min);
mpf_div_ui(xgap, xgap, xres);
//double ygap = (y_max - y_min) / yres;
mpf_sub(ygap, y_max, y_min);
mpf_div_ui(ygap, ygap, yres);
//----------------------------
long long int iteration;
long long int total_number_iterations = 0;
int k = 0;
for (j = 0; j < yres; j++){
for (i = 0; i < xres; i++){
//xi = x_min + i * xgap;
mpf_mul_ui(tmp, xgap, i);
mpf_add(xi, x_min, tmp);
//yi = y_min + j * ygap;
mpf_mul_ui(tmp, ygap, j);
mpf_add(yi, y_min, tmp);
//flag betwee[n julia or mandelbrot
//savex = flag * c[0] + (1 - flag) * xi;
mpf_mul_ui(savex_a, c[0], flag);
mpf_mul_ui(savex_b, xi, (1-flag));
mpf_add(savex, savex_a, savex_b);
//savey = flag * c[1] + (1 - flag) * yi;
mpf_mul_ui(savey_a, c[1], flag);
mpf_mul_ui(savey_b, yi, (1-flag));
mpf_add(savey, savey_a, savey_b);
//radius = 0;
mpf_set_ui(radius, 0);
iteration = 0;
//while ((radius <= maxRadius) && (iteration < max_iteration)){
while ((mpf_cmp_d(radius, maxRadius)<=0) && (iteration < max_iteration)){
//savex2 = xi;
mpf_add_ui(savex2, xi, 0);
//xi = xi * xi - yi * yi + savex;
mpf_mul(xi, xi, xi);
mpf_mul(tmp, yi, yi);
mpf_sub(xi, xi, tmp);
mpf_add(xi, xi, savex);
//yi = 2.0f * savex2 * yi + savey;
mpf_mul_ui(tmp, savex2, 2);
mpf_mul(yi, yi, tmp);
mpf_add(yi, yi, savey);
//radius = xi * xi + yi * yi;
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(radius, tmp, tmp1);
iteration++;
}
total_number_iterations += iteration;
float *p = iterations + k*xres + i;
//if (radius > maxRadius){
if (mpf_cmp_d(radius, maxRadius)>0){
//float zn = sqrt(xi*xi + yi*yi);
mpf_t zn;
mpf_init(zn);
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(zn, tmp, tmp1);
mpf_sqrt(zn, zn);
double n = mpf_get_d(zn);
//float nu = log(log(zn) / log(2))/log(2);
double nu = log(log(n) / log(2))/log(2);
//the point has escaped at iteration at any of the iterations 0,1,2,3...
*p = iteration + 1 - nu;
}
else
// zij stays within the region up to max_iteration
{
assert(iteration==max_iteration);
*p = -1;
}
}
k++;
}
//reduce max iteration count
long long int total_reduced_iterations = -1;
//printf("rank: %i, total_reduced_iterations: %i\n", my_rank, total_number_iterations);
MPI_Reduce(&total_number_iterations, &total_reduced_iterations, 1, MPI_LONG_LONG_INT, MPI_SUM, 0, comm);
double t4 = MPI_Wtime();
double max_reduced_time = -1;
double total_time = t4 - t0;
MPI_Reduce(&total_time, &max_reduced_time, 1, MPI_DOUBLE, MPI_MAX, 0, comm);
printf("np: %i, time: %f , iterations: %lld\n",p, max_reduced_time, total_reduced_iterations);
//clear
//printf("proc: %i, total time: %lf sec, init: %lf sec, calc: %lf sec, collect: %lf\n", my_rank, t4-t0, t1-t0, t2-t1, t3-t2);
return total_reduced_iterations;
}
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;
}
/**
* void calculate_p()
*
* Descricao:
* Calcula o valor da variavel p na n-esima iteracao.
*
* Parametros de entrada:
* -
*
* Parametros de retorno:
* -
*/
void calculate_p(){
mpf_mul_ui(p_n[n_count+1], p_n[n_count], 2);
}
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;
}
int main(int argc, char *argv[])
{
int my_rank, p;
long long total;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &my_rank);
MPI_Comm_size(MPI_COMM_WORLD, &p);
// MPI_Aint offsets[11];
int error_code;
char *params;
char *image;
char *image_type;
// char *timestats;
// double starttime,endtime;
int *flag;
int *width;
int *height;
int *maxiter;
int framepos=0;
mpf_t *cc;
mpf_t *xrange;
mpf_t *yrange;
mpf_t *cr;
mpf_t *ci;
mpf_t *x;
mpf_t *y;
mpf_t *init_xr;
mpf_t *init_yr;
mpf_t *final_xr;
mpf_t *final_yr;
mpf_t *zoom_rate;
mpf_t *xd;
mpf_t *yd;
//Change for Int
flag = (int*)malloc(sizeof(int));
width = (int*)malloc(sizeof(int));
height = (int*)malloc(sizeof(int));
maxiter = (int*)malloc(sizeof(int));
//zoom_rate = (double *)malloc(sizeof(double));
cr = (mpf_t*)malloc(sizeof(mpf_t));
ci = (mpf_t*)malloc(sizeof(mpf_t));
x = (mpf_t*)malloc(sizeof(mpf_t));
y = (mpf_t*)malloc(sizeof(mpf_t));
init_xr = (mpf_t*)malloc(sizeof(mpf_t)); //
init_yr = (mpf_t*)malloc(sizeof(mpf_t)); //
final_xr = (mpf_t*)malloc(sizeof(mpf_t)); //
final_yr = (mpf_t*)malloc(sizeof(mpf_t)); //
xd = (mpf_t*)malloc(sizeof(mpf_t));
yd = (mpf_t*)malloc(sizeof(mpf_t));
zoom_rate = (mpf_t*)malloc(sizeof(mpf_t));
image_type = (char*)malloc(sizeof(char)*STRLENTH);
image = (char*)malloc(sizeof(char)*STRLENTH);
// filename = (char*)malloc(sizeof(char)*STRLENTH);
params = (char*)malloc(sizeof(char)*STRLENTH*15);
xrange = (mpf_t*)malloc(sizeof(mpf_t)*2);
yrange = (mpf_t*)malloc(sizeof(mpf_t)*2);
cc = (mpf_t*)malloc(sizeof(mpf_t)*2);
mpf_init(xrange[0]);
mpf_init(xrange[1]);
mpf_init(yrange[0]);
mpf_init(yrange[1]);
mpf_init(*xd);
mpf_init(*yd);
mpf_init(cc[0]);
mpf_init(cc[1]);
if (my_rank == 0)
{
if(argc >=2){
getParams(params, argv);
} else {
printf("Indicate the file name containing the parameters. kthxbye!\n");
}
}
//Receive data
error_code = MPI_Bcast(params, STRLENTH*15, MPI_CHAR, 0, MPI_COMM_WORLD);
#ifdef debug
if (my_rank == 2)
{
printf("RANK = %d As chars-------------\n",my_rank);
//See data as Char
int i;
for(i=0;i<=14;i++)
{
printf("%s\n",¶ms[i*256]);
}
}
#endif
MPI_Barrier(MPI_COMM_WORLD);
xtractParams(flag, cr, ci, x, y, init_xr, init_yr,final_xr,final_yr, width, height, maxiter, zoom_rate, image,image_type, params, my_rank);
#ifdef debug
if (my_rank == 2)
{
printf("RANK = %d AS datatypes-------------\n",my_rank);
//See data as their types
printf("Flag: %d \n", *flag);
gmp_printf ("cr: %.Ff\n", *cr);
gmp_printf ("ci:%.Ff\n", *ci);
gmp_printf ("x: %.Ff\n", *x);
gmp_printf ("y: %.Ff\n", *y);
gmp_printf ("init_xr: %.Ff\n", *init_xr);
gmp_printf ("init_yr: %.Ff\n", *init_yr);
gmp_printf ("final_xr: %.Ff\n", *final_xr);
gmp_printf ("final_yr: %.Ff\n", *final_yr);
printf("Width: %d \n", *width);
printf("Height: %d \n", *height);
printf("Maxiter: %d \n", *maxiter);
printf("Zoom: %f \n", *zoom_rate);
printf("file: %s\n",image);
printf("Type: %s\n",image_type);
}
#endif
mpf_mul_ui(*xd,*final_xr,2); //what is this for?
mpf_mul_ui(*yd,*final_yr,2); //Why is this here?
if(framepos==0){
if(my_rank ==0) printf("Creating Frames! Progress: \n\n");
}
for(framepos = 0; framepos < FRAMECNT;framepos++ )
{
char num[15];
sprintf(num, "%d", framepos);
char filename[256];
strcpy(filename,image);
strcat(filename,num);
strcat(filename,image_type);
//calculate progress!
double numer = (double)framepos;
double denum = (double)FRAMECNT;
if(my_rank ==0) printf("Frame %d of %d ....%.1f%% \r", framepos+1, FRAMECNT,((numer/denum)*100));
//coordinate calculations
//start
if(framepos ==0)
{
mpf_set(cc[0], *cr);
mpf_set(cc[1], *ci);
mpf_sub(xrange[0], *x, *init_xr);
mpf_add(xrange[1], *x, *init_xr);
mpf_sub(yrange[0], *y, *init_yr);
mpf_add(yrange[1], *y, *init_yr);
total = parallelJulia(xrange, *width, yrange, *height, cc, *flag, maxiter, my_rank, p, MPI_COMM_WORLD, filename);
}
else
{
mpf_div(*init_xr,*init_xr,*zoom_rate);
mpf_div(*init_yr,*init_yr,*zoom_rate);
mpf_sub(xrange[0], *x, *init_xr);
mpf_add(xrange[1], *x, *init_xr);
mpf_sub(yrange[0], *y, *init_yr);
mpf_add(yrange[1], *y, *init_yr);
total = parallelJulia(xrange, *width, yrange, *height, cc, *flag, maxiter, my_rank, p, MPI_COMM_WORLD, filename);
}
MPI_Barrier(MPI_COMM_WORLD);
}
if(my_rank ==0){printf("Done!");}
free(flag);
free(width);
free(height);
free(maxiter);
free(cr);
free(ci);
free(x);
free(y);
free(init_yr);
free(init_xr);
free(final_yr);
free(final_xr);
free(xd);
free(yd);
// free(iterations);
free(cc);
free(xrange);
free(yrange);
free(image);
free(image_type);
free(zoom_rate);
free(params);
// free(timestats);
MPI_Finalize();
return 0;
}
void
cpx_confluent (cpx_t em, cpx_t a, cpx_t b, cpx_t z, unsigned int prec)
{
mpf_t fact;
cpx_t zee, z_n, term;
cpx_t ay, be, poch_a, poch_b;
mpf_init (fact);
cpx_init (zee);
cpx_init (z_n);
cpx_init (term);
cpx_init (ay);
cpx_init (be);
cpx_init (poch_a);
cpx_init (poch_b);
/* Make copy of arguments now! */
cpx_set (zee, z);
cpx_set (z_n, zee);
cpx_set (ay, a);
cpx_set (poch_a, a);
cpx_set (be, b);
cpx_set (poch_b, b);
cpx_set_ui (em, 1, 0);
mpf_set_ui (fact, 1);
mpf_t mag;
mpf_init (mag);
/* Use 10^{-2 * prec} for smallest term in sum */
mpf_t maxterm;
mpf_init (maxterm);
fp_epsilon (maxterm, prec);
mpf_mul (maxterm, maxterm, maxterm);
unsigned int n=1;
while(1)
{
cpx_div_mpf (term, z_n, fact);
cpx_mul (term, term, poch_a);
cpx_div (term, term, poch_b);
cpx_add (em, em, term);
/* Don't go no farther than this */
cpx_mod_sq (mag, term);
if (mpf_cmp (mag, maxterm) < 0) break;
n++;
cpx_mul (z_n, z_n, zee);
mpf_mul_ui (fact, fact, n);
mpf_add_ui (ay[0].re, ay[0].re, 1);
mpf_add_ui (be[0].re, be[0].re, 1);
cpx_mul (poch_a, poch_a, ay);
cpx_mul (poch_b, poch_b, be);
}
mpf_clear (fact);
mpf_clear (mag);
mpf_clear (maxterm);
cpx_clear (zee);
cpx_clear (z_n);
cpx_clear (term);
cpx_clear (ay);
cpx_clear (be);
cpx_clear (poch_a);
cpx_clear (poch_b);
}
long int julia(const mpf_t x, const mpf_t xr, long int xres, const mpf_t y, const mpf_t yr, long int yres, mpf_t *c, int flag, long int max_iteration,
float *iterations, int my_rank, int p, MPI_Comm comm)
{
double t0 = MPI_Wtime();
int i,j;
// Find how many rows per process.
int *rows;
rows = (int*)malloc(sizeof(int)*p);
for (i=0; i < p; i++)
rows[i] = yres/p;
for (i=0; i < yres % p; i++)
rows[i]++;
//allocate memory for each processor
if(my_rank > 0){
iterations = (float*)malloc( sizeof(float) * xres * rows[my_rank]);
assert(iterations);
}
//------------julia gmp
const double maxRadius = 4.0;
mpf_t xi, yi, x_min, x_max, y_min, y_max, savex, savex2, savey, radius, xgap, ygap, savex_a, savex_b, savey_a, savey_b, tmp, tmp1;
mpf_init(xi);
mpf_init(yi);
mpf_init(x_min);
mpf_init(x_max);
mpf_init(y_min);
mpf_init(y_max);
mpf_init(savex);
mpf_init(savex2);
mpf_init(savey);
mpf_init(radius);
mpf_init(xgap);
mpf_init(ygap);
mpf_init(savex_a);
mpf_init(savex_b);
mpf_init(savey_a);
mpf_init(savey_b);
mpf_init(tmp);
mpf_init(tmp1);
//double x_min = x - xr;
mpf_sub(x_min, x, xr);
//double x_max = x + xr;
mpf_add(x_max, x, xr);
//double y_min = y - yr;
mpf_sub(y_min, y, yr);
//double y_max = y + yr;
mpf_add(y_max, y, yr);
// spaceing between x and y points
//double xgap = (x_max - x_min) / xres;
mpf_sub(xgap, x_max, x_min);
mpf_div_ui(xgap, xgap, xres);
//double ygap = (y_max - y_min) / yres;
mpf_sub(ygap, y_max, y_min);
mpf_div_ui(ygap, ygap, yres);
//----------------------------
long long int iteration;
long long int total_number_iterations = 0;
int k = 0;
for (j = my_rank; j < yres; j+=p){
if(my_rank==0)
k = j; //needed for root
for (i = 0; i < xres; i++){
//xi = x_min + i * xgap;
mpf_mul_ui(tmp, xgap, i);
mpf_add(xi, x_min, tmp);
//yi = y_min + j * ygap;
mpf_mul_ui(tmp, ygap, j);
mpf_add(yi, y_min, tmp);
//flag betwee[n julia or mandelbrot
//savex = flag * c[0] + (1 - flag) * xi;
mpf_mul_ui(savex_a, c[0], flag);
mpf_mul_ui(savex_b, xi, (1-flag));
mpf_add(savex, savex_a, savex_b);
//savey = flag * c[1] + (1 - flag) * yi;
mpf_mul_ui(savey_a, c[1], flag);
mpf_mul_ui(savey_b, yi, (1-flag));
mpf_add(savey, savey_a, savey_b);
//radius = 0;
mpf_set_ui(radius, 0);
iteration = 0;
//while ((radius <= maxRadius) && (iteration < max_iteration)){
while ((mpf_cmp_d(radius, maxRadius)<=0) && (iteration < max_iteration)){
//savex2 = xi;
mpf_add_ui(savex2, xi, 0);
//xi = xi * xi - yi * yi + savex;
mpf_mul(xi, xi, xi);
mpf_mul(tmp, yi, yi);
mpf_sub(xi, xi, tmp);
mpf_add(xi, xi, savex);
//yi = 2.0f * savex2 * yi + savey;
mpf_mul_ui(tmp, savex2, 2);
mpf_mul(yi, yi, tmp);
mpf_add(yi, yi, savey);
//radius = xi * xi + yi * yi;
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(radius, tmp, tmp1);
iteration++;
}
total_number_iterations += iteration;
float *p = iterations + k*xres + i;
//if (radius > maxRadius){
if (mpf_cmp_d(radius, maxRadius)>0){
//float zn = sqrt(xi*xi + yi*yi);
mpf_t zn;
mpf_init(zn);
mpf_mul(tmp, xi, xi);
mpf_mul(tmp1, yi, yi);
mpf_add(zn, tmp, tmp1);
mpf_sqrt(zn, zn);
double n = mpf_get_d(zn);
//float nu = log(log(zn) / log(2))/log(2);
double nu = log(log(n) / log(2))/log(2);
//the point has escaped at iteration at any of the iterations 0,1,2,3...
*p = iteration + 1 - nu;
}
else
// zij stays within the region up to max_iteration
{
assert(iteration==max_iteration);
*p = -1;
}
}
k++;
}
//collect various data
MPI_Status status;
if(my_rank == 0){
int i,j;
for(i = 1; i < p; i++){
for(j = 0; j < rows[i]; j++){
MPI_Recv((iterations + (i + j * p) * xres), xres, MPI_FLOAT, i, 0, comm, &status);
//MPI_Irecv((iterations + (i + j * p) * xres), xres, MPI_FLOAT, i, 0, comm, NULL);
}
}
}
else{
int i;
for(i = 0; i < rows[my_rank]; i++)
MPI_Send((iterations + i *xres), xres, MPI_FLOAT, 0, 0, comm);
}
//reduce max iteration count
long long int total_reduced_iterations = -1;
//printf("rank: %i, total_reduced_iterations: %i\n", my_rank, total_number_iterations);
MPI_Reduce(&total_number_iterations, &total_reduced_iterations, 1, MPI_LONG_LONG_INT, MPI_SUM, 0, comm);
double t4 = MPI_Wtime();
double max_reduced_time = -1;
double total_time = t4 - t0;
MPI_Reduce(&total_time, &max_reduced_time, 1, MPI_DOUBLE, MPI_MAX, 0, comm);
if(my_rank == 0){
printf("np: %i, time: %f , iterations: %lld\n",p, max_reduced_time, total_reduced_iterations);
//printf("%i\t%.2e\n", p, max_reduced_time);
}
//clear
//printf("proc: %i, total time: %lf sec, init: %lf sec, calc: %lf sec, collect: %lf\n", my_rank, t4-t0, t1-t0, t2-t1, t3-t2);
return total_reduced_iterations;
}
void
mpc_div (mpc_t *rop, mpc_t op1, mpc_t op2)
{
/* This function needs to be fixed. At the current moment I am tired
* of having to mess around with the precision values, so I'm just
* going to convert the values to 'mpf's and call it quits for the
* day. I'll fix it later.
* Division by zero is not checked for in this function.
*/
mpf_t hold_op1;
mpf_t hold_op2;
mpf_t hold_res;
unsigned int prec;
mpf_init (hold_op1);
mpf_init (hold_op2);
mpf_init (hold_res);
mpf_set_z (hold_op1, op1.object);
mpf_set_z (hold_op2, op2.object);
// Get the largest precision
prec = (op1.precision > op2.precision) ? op1.precision : op2.precision;
if (prec == 0)
prec = default_prec;
// Set the scalar values
while (op1.precision-- > 0)
mpf_div_ui (hold_op1, hold_op1, 10);
while (op2.precision-- > 0)
mpf_div_ui (hold_op2, hold_op2, 10);
// Get the value
mpf_div (hold_res, hold_op1, hold_op2);
for (rop->precision = prec; prec > 0; prec--)
mpf_mul_ui (hold_res, hold_res, 10);
mpz_set_f (rop->object, hold_res);
/*
temp.precision = (op1.precision < op2.precision) ? op2.precision : op1.precision;
if (!op1.precision && !op2.precision)
{
temp.precision = default_prec;
mpz_set (temp.object, op1.object);
power_of_ten (temp.object, default_prec);
mpz_tdiv_q (temp_res, temp.object, op2.object);
}
else if (op1.precision < op2.precision)
{
temp.precision = op2.precision;
mpz_set (temp.object, op1.object);
power_of_ten (temp.object, op2.precision - op1.precision);
mpz_tdiv_q (temp_res, temp.object, op2.object);
}
else if (op1.precision > op2.precision)
{
temp.precision = op1.precision;
mpz_set (temp.object, op2.object);
power_of_ten (temp.object, op1.precision - op2.precision);
mpz_tdiv_q (temp_res, op1.object, temp.object);
}
else
{
temp.precision = op1.precision;
mpz_set (temp.object, op1.object);
mpz_tdiv_q (temp_res, temp.object, op2.object);
}
rop->precision = temp.precision;
mpz_set (rop->object, temp_res);
*/
}