int main(void)
{
mpf_set_default_prec(300000);
mpf_class x0, y0, resA, resB, Z;
x0 = 1;
y0 = 0.5;
Z = 0.25;
mpf_sqrt(y0.get_mpf_t(), y0.get_mpf_t());
int n = 1;
for (int i = 0; i < 8; i++) {
agm(resA, resB, x0, y0);
Z -= n * (resA - x0) * (resA - x0);
n *= 2;
agm(x0, y0, resA, resB);
Z -= n * (x0 - resA) * (x0 - resA);
n *= 2;
}
x0 = x0 * x0 / Z;
gmp_printf ("%.100000Ff\n", x0.get_mpf_t());
return 0;
}
void agm(mpf_class& rop1, mpf_class& rop2, const mpf_class& op1,
const mpf_class& op2)
{
rop1 = (op1 + op2) / 2;
rop2 = op1 * op2;
mpf_sqrt(rop2.get_mpf_t(), rop2.get_mpf_t());
}
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 mpfc_abs(mpf_t r,mpfc_ptr x)
{
mpf_mul(mpfc_mpf_temp[0],x->Re,x->Re);
mpf_mul(mpfc_mpf_temp[1],x->Im,x->Im);
mpf_add(r,mpfc_mpf_temp[0],mpfc_mpf_temp[1]);
mpf_sqrt(r,r);
}
void *calc_y(thr_gmpf_t *vars)
{
/*vars.y1 = (1-sqrt(sqrt((1-pow(vars.y0,4))))) / (1+sqrt(sqrt(1-pow(vars.y0,4))));*/
/*b = sqrt(sqrt(1-y0^4))*/
mpf_pow_ui(vars->y1,vars->y0,4); /*y1 = pow(y0,4)*/
mpf_ui_sub(vars->y1,1,vars->y1); /*y1 = 1 - y1*/
mpf_sqrt(vars->y1,vars->y1);
mpf_sqrt(vars->y1,vars->y1);
/*y1 = 1-b/1+b*/
mpf_ui_sub(vars->aux_y1,1,vars->y1);
mpf_add_ui(vars->aux_y2,vars->y1,1);
mpf_div(vars->y1,vars->aux_y1,vars->aux_y2);
pthread_exit(NULL);
return NULL;
}
int sg_big_float_sqrt(sg_big_float_t *a, sg_big_float_t *res)
{
if (!a || !res)
return -1;
mpf_sqrt(res->mpf, a->mpf);
return 0;
}
mpf_class x_mpf(const mpz_class& square_, const mpz_class& minus, const mpz_class& div) {
mpf_class square = square_;
mpf_class ret = square;
mpf_sqrt(ret.get_mpf_t(), square.get_mpf_t());
ret = (ret - minus) / div;
return ret;
}
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);
}
//
// The core Gauss - Legendre routine.
// On input, 'bits' is the desired precision in bits.
// On output, 'pi' contains the calculated value.
//
static void calculatePi( unsigned bits, mpf_class & pi )
{
mpf_class lastPi( 0.0 );
mpf_class scratch;
// variables per the formal Gauss - Legendre formulae
mpf_class a;
mpf_class b;
mpf_class t;
mpf_class x;
mpf_class y;
unsigned p = 1;
// initial conditions
a = 1;
// b := 1 / sqrt( 2 )
mpf_sqrt_ui( b.get_mpf_t( ), 2 );
b = 1.0 / b;
t = 0.25;
for( ;; ) {
x = ( a + b )/2;
// y := sqrt( ab )
y = a * b;
mpf_sqrt( y.get_mpf_t( ), y.get_mpf_t( ) );
// t := t - p * ( a - x )**2
scratch = a - x;
scratch *= scratch;
scratch *= p;
t -= scratch;
a = x;
b = y;
p <<= 1;
// pi := ( ( a + b )**2 ) / 4t
pi = a + b;
pi *= pi;
pi /= ( 4 * t );
// if pi == lastPi, within the requested precision, we're done
if ( mpf_eq( pi.get_mpf_t( ), lastPi.get_mpf_t( ), bits ) ) {
break;
}
lastPi = pi;
}
}
int main (int argc, char *argv[]) {
mpf_t sq_me, sq_out, test;
mpf_set_default_prec (10000);
mpf_init(sq_me);
mpf_init(sq_out);
mpf_init(test);
mpf_set_str (sq_me, argv[1], 10);
mpf_sqrt(sq_out, sq_me);
mpf_mul(test,sq_out,sq_out);
gmp_printf ("Input: %Ff\n\n", sq_me);
gmp_printf ("Square root: %.200Ff\n\n", sq_out);
gmp_printf ("Re-squared: %Ff\n\n", test);
return 0;
}
// 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;
}
//------------------------------------------------------------------------------
// Name:
//------------------------------------------------------------------------------
knumber_base *knumber_float::sqrt() {
if(sign() < 0) {
delete this;
return new knumber_error(knumber_error::ERROR_UNDEFINED);
}
#ifdef KNUMBER_USE_MPFR
mpfr_t mpfr;
mpfr_init_set_f(mpfr, mpf_, rounding_mode);
mpfr_sqrt(mpfr, mpfr, rounding_mode);
mpfr_get_f(mpf_, mpfr, rounding_mode);
mpfr_clear(mpfr);
#else
mpf_sqrt(mpf_, mpf_);
#endif
return this;
}
int main (void) {
mpf_set_default_prec (65568);
mpf_t x0, y0, resA, resB;
mpf_init_set_ui (y0, 1);
mpf_init_set_d (x0, 0.5);
mpf_sqrt (x0, x0);
mpf_init (resA);
mpf_init (resB);
for(int i=0; i<7; i++){
agm(x0, y0, resA, resB);
agm(resA, resB, x0, y0);
}
gmp_printf ("%.20000Ff\n", x0);
gmp_printf ("%.20000Ff\n\n", y0);
return 0;
}
R gaunt(Int lp, Int l1, Int l2, Int mp, Int m1, Int m2)
{
R gg;
mpf_t g,h;
if((lp+l1+l2)%Int(2)==Int(1)) return R(0);
if(NewGaunt::iabs(mp)>lp || NewGaunt::iabs(m1)>l1 || NewGaunt::iabs(m2)>l2) return R(0);
mpf_init(g);
mpf_init(h);
NewGaunt::w3j(g,lp,l1,l2,0,0,0);
NewGaunt::w3j(h,lp,l1,l2,-mp,m1,m2);
mpf_mul(g,g,h);
mpf_set_si(h,(2*lp+1)*(2*l1+1)*(2*l2+1));
mpf_sqrt(h,h);
mpf_mul(g,g,h);
gg=mpf_get_d(g)/sqrt(4.0*M_PI);
if(NewGaunt::iabs(mp)%Int(2)==Int(1)) gg=-gg;
mpf_clear(g);
mpf_clear(h);
return gg;
}
//double log2(mpf_class l) {
// mpf_class r = l;
// mpf_class t,t1=l;
// int y=1;
// mpf_class resp;
// do{
// mpf_sqrt(t.get_mpf_t(),t1.get_mpf_t());
// y*=2;
// t1=t;
// } while (t>2);
// resp=y*log2(t.get_d());
// /*mpf_t a;
// mpf_init(a);
// mpf_class b(l);
// //cout<<b<<"--"<<l<<endl;
// mpf_div_2exp(a, b.get_mpf_t(), y);
// double temp = mpf_get_d(a);
// temp = pow(temp, 2);
// temp = log(temp) / log(2);
// temp = y + temp / 2;
// mpf_clear(a);
// // cout<<temp<<endl;*/
// return resp.get_d();
//
//}
mpf_class log2f(mpf_class l){
mpf_class r = l;
mpf_class t,t1=l;
int y=1;
mpf_class resp;
do{
mpf_sqrt(t.get_mpf_t(),t1.get_mpf_t());
y*=2;
t1=t;
} while (t>2);
resp=y*log2(t.get_d());
/*mpf_t a;
mpf_init(a);
mpf_class b(l);
//cout<<b<<"--"<<l<<endl;
mpf_div_2exp(a, b.get_mpf_t(), y);
double temp = mpf_get_d(a);
temp = pow(temp, 2);
temp = log(temp) / log(2);
temp = y + temp / 2;
mpf_clear(a);
// cout<<temp<<endl;*/
return resp;
}
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;
}
void
check_rand2 (void)
{
unsigned long max_prec = 20;
unsigned long min_prec = __GMPF_BITS_TO_PREC (1);
gmp_randstate_ptr rands = RANDS;
unsigned long x_prec, r_prec;
mpf_t x, r, s;
int i;
mpf_init (x);
mpf_init (r);
mpf_init (s);
refmpf_set_prec_limbs (s, 2*max_prec+10);
for (i = 0; i < 500; i++)
{
/* input precision */
x_prec = gmp_urandomm_ui (rands, max_prec-min_prec) + min_prec;
refmpf_set_prec_limbs (x, x_prec);
/* result precision */
r_prec = gmp_urandomm_ui (rands, max_prec-min_prec) + min_prec;
refmpf_set_prec_limbs (r, r_prec);
mpf_random2 (x, x_prec, 1000);
mpf_sqrt (r, x);
MPF_CHECK_FORMAT (r);
/* Expect to prec limbs of result.
In the current implementation there's no stripping of low zero
limbs in mpf_sqrt, so size should be exactly prec. */
if (SIZ(r) != r_prec)
{
printf ("mpf_sqrt wrong number of result limbs\n");
mpf_trace (" x", x);
mpf_trace (" r", r);
printf (" r_prec=%lu\n", r_prec);
printf (" SIZ(r) %ld\n", (long) SIZ(r));
printf (" PREC(r) %ld\n", (long) PREC(r));
abort ();
}
/* Must have r^2 <= x, since r has been truncated. */
mpf_mul (s, r, r);
if (! (mpf_cmp (s, x) <= 0))
{
printf ("mpf_sqrt result too big\n");
mpf_trace (" x", x);
printf (" r_prec=%lu\n", r_prec);
mpf_trace (" r", r);
mpf_trace (" s", s);
abort ();
}
/* Must have (r+ulp)^2 > x, or else r is too small. */
refmpf_add_ulp (r);
mpf_mul (s, r, r);
if (! (mpf_cmp (s, x) > 0))
{
printf ("mpf_sqrt result too small\n");
mpf_trace (" x", x);
printf (" r_prec=%lu\n", r_prec);
mpf_trace (" r+ulp", r);
mpf_trace (" s", s);
abort ();
}
}
mpf_clear (x);
mpf_clear (r);
mpf_clear (s);
}
extern void _jl_mpf_sqrt(mpf_t* rop, mpf_t* op) {
mpf_sqrt(*rop, *op);
}
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 main(void)
{
mp_float a, b, c, d, e;
int err;
mpf_init_multi(100, &a, &b, &c, &d, &e, NULL);
mpf_const_d(&a, 1);
draw(&a);
mpf_const_d(&b, 2);
draw(&b);
mpf_const_d(&c, 3);
draw(&c);
mpf_const_d(&d, 4);
draw(&d);
mpf_add(&b, &c, &e);
printf("2 + 3 == ");
draw(&e);
mpf_sub(&b, &c, &e);
printf("2 - 3 ==");
draw(&e);
mpf_mul(&b, &c, &e);
printf("2 * 3 == ");
draw(&e);
mpf_div(&b, &c, &e);
printf("2 / 3 == ");
draw(&e);
mpf_add_d(&b, 3, &e);
printf("2 + 3 == ");
draw(&e);
mpf_sub_d(&b, 3, &e);
printf("2 - 3 ==");
draw(&e);
mpf_mul_d(&b, 3, &e);
printf("2 * 3 == ");
draw(&e);
mpf_div_d(&b, 3, &e);
printf("2 / 3 == ");
draw(&e);
mpf_const_d(&e, 0);
mpf_add_d(&e, 1, &e);
printf("0 + 1 == ");
draw(&e);
mpf_const_d(&e, 0);
mpf_sub_d(&e, 1, &e);
printf("0 - 1 == ");
draw(&e);
printf("\n");
mpf_invsqrt(&d, &e);
printf("1/sqrt(4) == 1/2 == ");
draw(&e);
mpf_invsqrt(&c, &e);
printf("1/sqrt(3) == ");
draw(&e);
mpf_inv(&a, &e);
printf("1/1 == ");
draw(&e);
mpf_inv(&b, &e);
printf("1/2 == ");
draw(&e);
mpf_inv(&c, &e);
printf("1/3 == ");
draw(&e);
mpf_inv(&d, &e);
printf("1/4 == ");
draw(&e);
printf("\n");
mpf_const_pi(&e);
printf("Pi == ");
draw(&e);
printf("\n");
mpf_const_e(&e);
printf("e == ");
draw(&e);
mpf_exp(&c, &e);
printf("e^3 == ");
draw(&e);
mpf_sqrt(&e, &e);
printf("sqrt(e^3) == ");
draw(&e);
mpf_sqr(&e, &e);
printf("sqrt(e^3)^2 == ");
draw(&e);
printf("\n");
mpf_cos(&a, &e);
printf("cos(1) == ");
draw(&e);
mpf_cos(&b, &e);
printf("cos(2) == ");
draw(&e);
mpf_cos(&c, &e);
printf("cos(3) == ");
draw(&e);
mpf_cos(&d, &e);
printf("cos(4) == ");
draw(&e);
mpf_sin(&a, &e);
printf("sin(1) == ");
draw(&e);
mpf_sin(&b, &e);
printf("sin(2) == ");
draw(&e);
mpf_sin(&c, &e);
printf("sin(3) == ");
draw(&e);
mpf_sin(&d, &e);
printf("sin(4) == ");
draw(&e);
mpf_tan(&a, &e);
printf("tan(1) == ");
draw(&e);
mpf_tan(&b, &e);
printf("tan(2) == ");
draw(&e);
mpf_tan(&c, &e);
printf("tan(3) == ");
draw(&e);
mpf_tan(&d, &e);
printf("tan(4) == ");
draw(&e);
mpf_inv(&a, &e);
mpf_atan(&e, &e);
printf("atan(1/1) == ");
draw(&e);
mpf_inv(&b, &e);
mpf_atan(&e, &e);
printf("atan(1/2) == ");
draw(&e);
mpf_inv(&c, &e);
mpf_atan(&e, &e);
printf("atan(1/3) == ");
draw(&e);
mpf_inv(&d, &e);
mpf_atan(&e, &e);
printf("atan(1/4) == ");
draw(&e);
printf("\n");
#define lntest(x) if ((err = mpf_const_ln_d(&e, x)) != MP_OKAY) { printf("Failed ln(%3d), %d\n", x, err); } else { printf("ln(%3d) == ", x); draw(&e); };
lntest(0);
lntest(1);
lntest(2);
lntest(4);
lntest(8);
lntest(17);
lntest(1000);
lntest(100000);
lntest(250000);
return 0;
}
//Le but de la fonction est de calculer le développement en fractions continue jusqu'à un certain rang de racine carrée de kN et de stocker les couples (A_n-1,Q_n) comme décrit dans la section (à venir)
cfrac expand(const mpz_t N, const long long unsigned int rang, const mpz_t k)
{
cfrac res; //Contient l'ensemble des A_n-1 et l'ensemble Q_n
mpz_inits(res.N, res.k, res.g, NULL);
//Initialisation des variables
mpz_t* A = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Le tableau contenant les A_n-1
mpz_t* Q = (mpz_t*)malloc((rang+2)*sizeof(mpz_t)); //Le tableau contenant les Q_n
mpz_t* P = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Éléments reliés au Q_n
mpz_t* r = (mpz_t*)malloc((rang+1)*sizeof(mpz_t)); //Interviennent dans le calcul des A_n-1 & Q_n
mpz_t* q = (mpz_t*)malloc(rang*sizeof(mpz_t)); //Idem
mpz_t g, tempz; //Idem, tempz = variable à tout faire
mpf_t sqrtkN, tempf, tempf2; //sqrtkN = sqrt(k*N), tempf = variable à tout faire
//Valeurs d'initialisation de la boucle
mpz_inits(g, A[0], Q[0], r[0], tempz, NULL);
mpf_inits(tempf, sqrtkN, tempf2, NULL);
//Initialisation des différentes valeurs "indépendantes"
mpz_set(tempz, N);
mpz_mul(tempz, tempz, k);
mpf_set_z(sqrtkN, tempz);
mpf_sqrt(sqrtkN, sqrtkN);
mpf_floor(tempf, sqrtkN);
mpz_set_f(g, tempf); //g = [sqrt(kN)]
mpz_set(Q[0], k);
mpz_mul(Q[0], Q[0], N); //Q_-1 = kN = Q[0]
mpz_set(r[0], g); //r_-1 = r[0]
mpz_set_ui(A[0], 1); //A_-1 = A[0]
//Calcul de P_0 & Q_0
mpz_init_set_ui(Q[1], 1); //Q_0 = Q[1]
mpz_init_set_ui(P[0], 0); //P_0 = P[0]
for(long long int i = 0; i < rang; i++)
{
switch(i)
{
case 0:
//Calcul de q_0
mpz_init_set(q[0], g); //q_0 = [(sqrt(kN) + P_0)/Q_0] avec P_0 = 0 et Q_0 = 1
//Calcul de A_0
mpz_init_set(A[1],A[0]);
mpz_mul(A[1], A[1], q[0]); //A_0 = q_0*A_-1
mpz_mod(A[1], A[1], N); //On réduit mod N
//Calcul de r_0
mpz_init_set_ui(r[1], 0); //r_0 = P_0 + g - q_0.Q_0 = 0 + g - g.1 = 0
//Calcul de P_1
mpz_init_set(P[1], g); //P_1 = g - r_0 = g - 0 = g
//Calcul de Q_1 = Q[2]
mpz_init_set(Q[2], r[1]);
mpz_sub(Q[2], Q[2], r[0]);
mpz_mul(Q[2], Q[2], q[0]);
mpz_add(Q[2], Q[2], Q[0]);
break;
default:
//Calcul q_i
mpz_init(q[i]);
mpf_set_z(tempf, P[i]);
mpf_set_z(tempf2, Q[i+1]);
mpf_add(tempf, tempf, sqrtkN); //sqrt(kN) + P_i
mpf_div(tempf, tempf, tempf2);
mpf_floor(tempf, tempf); //floor((sqrt(kN) + P_i)/Q_i)
mpz_set_f(q[i], tempf);
//Calcul de r_n = r[n+1]
mpz_init(r[i+1]);
mpz_submul(r[i+1], q[i], Q[i+1]);
mpz_add(r[i+1], r[i+1], P[i]);
mpz_add(r[i+1], r[i+1], g);
//Calcul de A_n = A[n+1]
mpz_init_set(A[i+1],A[i]);
mpz_mul(A[i+1], A[i+1], q[i]); //A_i-1*q_i
mpz_add(A[i+1], A[i+1], A[i-1]); //A_i-1*q_i + A_i-2
mpz_mod(A[i+1], A[i+1], N); //réduction modulo N
//Calcul P_n+1
mpz_init_set(P[i+1], g);
mpz_sub(P[i+1], P[i+1], r[i+1]); //P[n+1] = g - r_n = g - r[n+1]
//Calcul Q_n+1 = Q[n+2]
mpz_init_set(Q[i+2], r[i+1]);
mpz_sub(Q[i+2], Q[i+2], r[i]); //(r_n - r_n-1)
mpz_mul(Q[i+2], Q[i+2], q[i]); //q_n(r_n - r_n-1)
mpz_add(Q[i+2], Q[i+2], Q[i]); //Q_n-1 + q_n(r_n - r_n-1)
break;
}
}
//Test de routine pour voir si le développement de la fraction continue s'est bien passé
mpz_t tempsqrt;
mpz_init(tempsqrt);
mpz_set(tempsqrt, k);
mpz_mul(tempsqrt, tempsqrt, N);
mpz_sqrt(tempsqrt, tempsqrt);
mpz_mul_ui(tempsqrt, tempsqrt, 2);
for(int i = 1; i < rang; i++) //Éviter de commencer à i = 0 puisque cela représente Q_-1 qui n'intervient uniquement dans l'algo et non dans le développement en fraction continue
{
if(mpz_cmp(Q[i], tempsqrt) >= 0) //Si Q_n >= 2sqrt(kN)
{
res.rang = 0;
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
}
//Assignation des tableaux dans le résultat
res.A = A;
res.Q = Q;
res.r = r;
res.q = q;
res.P = P;
mpz_set(res.N, N);
mpz_set(res.k, k);
res.rang = rang;
mpz_set(res.g, g);
//Libération de mémoire
mpz_clears(g, tempz, NULL);
mpf_clears(sqrtkN, tempf, tempf2, NULL);
return res;
}
/**
* void calculate_b()
*
* Descricao:
* Calcula o valor da variavel b na n-esima iteracao.
*
* Parametros de entrada:
* -
*
* Parametros de retorno:
* -
*/
void calculate_b(){
mpf_mul(b_n[n_count+1], a_n[n_count], b_n[n_count]);
mpf_sqrt(b_n[n_count+1], b_n[n_count+1]);
}
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 agm (const mpf_t in1, const mpf_t in2, mpf_t out1, mpf_t out2) {
mpf_add (out1, in1, in2);
mpf_div_ui (out1, out1, 2);
mpf_mul (out2, in1, in2);
mpf_sqrt (out2, out2);
}
static int fill_spougecache(size_t A, int accuracy, long eps)
{
int err, n;
mp_float factrl, e, t1, t2, t3, pi;
size_t start;
if ((err =
mpf_init_multi(eps, &factrl, &e, &t1, &t2, &t3, NULL)) != MP_OKAY) {
return err;
}
err = MP_OKAY;
if (spougecache_len < A || spougecache_eps < accuracy) {
//puts("filling spougecache");
if ((err = mpf_const_d(&factrl, 1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_const_e(&e)) != MP_OKAY) {
goto _ERR;
}
if (spougecache_len != 0) {
spougecache = realloc(spougecache, (A + 1) * sizeof(mp_float));
if (spougecache == NULL) {
return MP_MEM;
}
start = spougecache_len;
} else {
spougecache = malloc((A + 1) * sizeof(mp_float));
if (spougecache == NULL) {
return MP_MEM;
}
start = 1;
if ((err = mpf_init(&pi, eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_const_pi(&pi)) != MP_OKAY) {
goto _ERR;
}
pi.exp += 1;
if ((err = mpf_init(&(spougecache[0]), eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sqrt(&pi, &(spougecache[0]))) != MP_OKAY) {
goto _ERR;
}
mpf_clear(&pi);
}
for (n = start; n < (int) A; n++) {
// to avoid the more expensive exp(log(a-n)*(n-0.5))
// TODO: check if exp() is fast enough now
if ((err = mpf_set_int(&t1, (int) (A - n))) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_pow_d(&t1, (int) (n - 1), &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_sqrt(&t1, &t1)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&t2, &t1, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_pow_d(&e, (int) (A - n), &t3)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&t2, &t3, &t2)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_init(&(spougecache[n]), eps)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_div(&t2, &factrl, &(spougecache[n]))) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_set_int(&t1, -n)) != MP_OKAY) {
goto _ERR;
}
if ((err = mpf_mul(&factrl, &t1, &factrl)) != MP_OKAY) {
goto _ERR;
}
}
spougecache_eps = accuracy;
spougecache_len = A;
}
_ERR:
mpf_clear_multi(&factrl, &e, &t1, &t2, &t3, NULL);
return err;
}
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
check_rand1 (int argc, char **argv)
{
mp_size_t size;
mp_exp_t exp;
int reps = 20000;
int i;
mpf_t x, y, y2;
mp_size_t bprec = 100;
mpf_t rerr, max_rerr, limit_rerr;
if (argc > 1)
{
reps = strtol (argv[1], 0, 0);
if (argc > 2)
bprec = strtol (argv[2], 0, 0);
}
mpf_set_default_prec (bprec);
mpf_init_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 (x);
mpf_init (y);
mpf_init (y2);
for (i = 0; i < reps; i++)
{
size = urandom () % SIZE;
exp = urandom () % SIZE;
mpf_random2 (x, size, exp);
mpf_sqrt (y, x);
MPF_CHECK_FORMAT (y);
mpf_mul (y2, y, y);
mpf_reldiff (rerr, x, y2);
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 (" x = "); mpf_dump (x);
printf (" y = "); mpf_dump (y);
printf (" y2 = "); mpf_dump (y2);
printf (" rerr = "); mpf_dump (rerr);
printf (" limit_rerr = "); mpf_dump (limit_rerr);
printf ("in hex:\n");
mp_trace_base = 16;
mpf_trace (" x ", x);
mpf_trace (" y ", y);
mpf_trace (" y2 ", y2);
mpf_trace (" rerr ", rerr);
mpf_trace (" limit_rerr", limit_rerr);
abort ();
}
}
}
mpf_clear (limit_rerr);
mpf_clear (rerr);
mpf_clear (max_rerr);
mpf_clear (x);
mpf_clear (y);
mpf_clear (y2);
}
void
spectral_test (mpf_t rop[], unsigned int T, mpz_t a, mpz_t m)
{
/* Knuth "Seminumerical Algorithms, Third Edition", section 3.3.4
(pp. 101-103). */
/* v[t] = min { sqrt (x[1]^2 + ... + x[t]^2) |
x[1] + a*x[2] + ... + pow (a, t-1) * x[t] is congruent to 0 (mod m) } */
/* Variables. */
unsigned int ui_t;
unsigned int ui_i, ui_j, ui_k, ui_l;
mpf_t f_tmp1, f_tmp2;
mpz_t tmp1, tmp2, tmp3;
mpz_t U[GMP_SPECT_MAXT][GMP_SPECT_MAXT],
V[GMP_SPECT_MAXT][GMP_SPECT_MAXT],
X[GMP_SPECT_MAXT],
Y[GMP_SPECT_MAXT],
Z[GMP_SPECT_MAXT];
mpz_t h, hp, r, s, p, pp, q, u, v;
/* GMP inits. */
mpf_init (f_tmp1);
mpf_init (f_tmp2);
for (ui_i = 0; ui_i < GMP_SPECT_MAXT; ui_i++)
{
for (ui_j = 0; ui_j < GMP_SPECT_MAXT; ui_j++)
{
mpz_init_set_ui (U[ui_i][ui_j], 0);
mpz_init_set_ui (V[ui_i][ui_j], 0);
}
mpz_init_set_ui (X[ui_i], 0);
mpz_init_set_ui (Y[ui_i], 0);
mpz_init (Z[ui_i]);
}
mpz_init (tmp1);
mpz_init (tmp2);
mpz_init (tmp3);
mpz_init (h);
mpz_init (hp);
mpz_init (r);
mpz_init (s);
mpz_init (p);
mpz_init (pp);
mpz_init (q);
mpz_init (u);
mpz_init (v);
/* Implementation inits. */
if (T > GMP_SPECT_MAXT)
T = GMP_SPECT_MAXT; /* FIXME: Lazy. */
/* S1 [Initialize.] */
ui_t = 2 - 1; /* NOTE: `t' in description == ui_t + 1
for easy indexing */
mpz_set (h, a);
mpz_set (hp, m);
mpz_set_ui (p, 1);
mpz_set_ui (pp, 0);
mpz_set (r, a);
mpz_pow_ui (s, a, 2);
mpz_add_ui (s, s, 1); /* s = 1 + a^2 */
/* S2 [Euclidean step.] */
while (1)
{
if (g_debug > DEBUG_1)
{
mpz_mul (tmp1, h, pp);
mpz_mul (tmp2, hp, p);
mpz_sub (tmp1, tmp1, tmp2);
if (mpz_cmpabs (m, tmp1))
{
printf ("***BUG***: h*pp - hp*p = ");
mpz_out_str (stdout, 10, tmp1);
printf ("\n");
}
}
if (g_debug > DEBUG_2)
{
printf ("hp = ");
mpz_out_str (stdout, 10, hp);
printf ("\nh = ");
mpz_out_str (stdout, 10, h);
printf ("\n");
fflush (stdout);
}
if (mpz_sgn (h))
mpz_tdiv_q (q, hp, h); /* q = floor(hp/h) */
else
mpz_set_ui (q, 1);
if (g_debug > DEBUG_2)
{
printf ("q = ");
mpz_out_str (stdout, 10, q);
printf ("\n");
fflush (stdout);
}
mpz_mul (tmp1, q, h);
mpz_sub (u, hp, tmp1); /* u = hp - q*h */
mpz_mul (tmp1, q, p);
mpz_sub (v, pp, tmp1); /* v = pp - q*p */
mpz_pow_ui (tmp1, u, 2);
mpz_pow_ui (tmp2, v, 2);
mpz_add (tmp1, tmp1, tmp2);
if (mpz_cmp (tmp1, s) < 0)
{
mpz_set (s, tmp1); /* s = u^2 + v^2 */
mpz_set (hp, h); /* hp = h */
mpz_set (h, u); /* h = u */
mpz_set (pp, p); /* pp = p */
mpz_set (p, v); /* p = v */
}
else
break;
}
/* S3 [Compute v2.] */
mpz_sub (u, u, h);
mpz_sub (v, v, p);
mpz_pow_ui (tmp1, u, 2);
mpz_pow_ui (tmp2, v, 2);
mpz_add (tmp1, tmp1, tmp2);
if (mpz_cmp (tmp1, s) < 0)
{
mpz_set (s, tmp1); /* s = u^2 + v^2 */
mpz_set (hp, u);
mpz_set (pp, v);
}
mpf_set_z (f_tmp1, s);
mpf_sqrt (rop[ui_t - 1], f_tmp1);
/* S4 [Advance t.] */
mpz_neg (U[0][0], h);
mpz_set (U[0][1], p);
mpz_neg (U[1][0], hp);
mpz_set (U[1][1], pp);
mpz_set (V[0][0], pp);
mpz_set (V[0][1], hp);
mpz_neg (V[1][0], p);
mpz_neg (V[1][1], h);
if (mpz_cmp_ui (pp, 0) > 0)
{
mpz_neg (V[0][0], V[0][0]);
mpz_neg (V[0][1], V[0][1]);
mpz_neg (V[1][0], V[1][0]);
mpz_neg (V[1][1], V[1][1]);
}
while (ui_t + 1 != T) /* S4 loop */
{
ui_t++;
mpz_mul (r, a, r);
mpz_mod (r, r, m);
/* Add new row and column to U and V. They are initialized with
all elements set to zero, so clearing is not necessary. */
mpz_neg (U[ui_t][0], r); /* U: First col in new row. */
mpz_set_ui (U[ui_t][ui_t], 1); /* U: Last col in new row. */
mpz_set (V[ui_t][ui_t], m); /* V: Last col in new row. */
/* "Finally, for 1 <= i < t,
set q = round (vi1 * r / m),
vit = vi1*r - q*m,
and Ut=Ut+q*Ui */
for (ui_i = 0; ui_i < ui_t; ui_i++)
{
mpz_mul (tmp1, V[ui_i][0], r); /* tmp1=vi1*r */
zdiv_round (q, tmp1, m); /* q=round(vi1*r/m) */
mpz_mul (tmp2, q, m); /* tmp2=q*m */
mpz_sub (V[ui_i][ui_t], tmp1, tmp2);
for (ui_j = 0; ui_j <= ui_t; ui_j++) /* U[t] = U[t] + q*U[i] */
{
mpz_mul (tmp1, q, U[ui_i][ui_j]); /* tmp=q*uij */
mpz_add (U[ui_t][ui_j], U[ui_t][ui_j], tmp1); /* utj = utj + q*uij */
}
}
/* s = min (s, zdot (U[t], U[t]) */
vz_dot (tmp1, U[ui_t], U[ui_t], ui_t + 1);
if (mpz_cmp (tmp1, s) < 0)
mpz_set (s, tmp1);
ui_k = ui_t;
ui_j = 0; /* WARNING: ui_j no longer a temp. */
/* S5 [Transform.] */
if (g_debug > DEBUG_2)
printf ("(t, k, j, q1, q2, ...)\n");
do
{
if (g_debug > DEBUG_2)
printf ("(%u, %u, %u", ui_t + 1, ui_k + 1, ui_j + 1);
for (ui_i = 0; ui_i <= ui_t; ui_i++)
{
if (ui_i != ui_j)
{
vz_dot (tmp1, V[ui_i], V[ui_j], ui_t + 1); /* tmp1=dot(Vi,Vj). */
mpz_abs (tmp2, tmp1);
mpz_mul_ui (tmp2, tmp2, 2); /* tmp2 = 2*abs(dot(Vi,Vj) */
vz_dot (tmp3, V[ui_j], V[ui_j], ui_t + 1); /* tmp3=dot(Vj,Vj). */
if (mpz_cmp (tmp2, tmp3) > 0)
{
zdiv_round (q, tmp1, tmp3); /* q=round(Vi.Vj/Vj.Vj) */
if (g_debug > DEBUG_2)
{
printf (", ");
mpz_out_str (stdout, 10, q);
}
for (ui_l = 0; ui_l <= ui_t; ui_l++)
{
mpz_mul (tmp1, q, V[ui_j][ui_l]);
mpz_sub (V[ui_i][ui_l], V[ui_i][ui_l], tmp1); /* Vi=Vi-q*Vj */
mpz_mul (tmp1, q, U[ui_i][ui_l]);
mpz_add (U[ui_j][ui_l], U[ui_j][ui_l], tmp1); /* Uj=Uj+q*Ui */
}
vz_dot (tmp1, U[ui_j], U[ui_j], ui_t + 1); /* tmp1=dot(Uj,Uj) */
if (mpz_cmp (tmp1, s) < 0) /* s = min(s,dot(Uj,Uj)) */
mpz_set (s, tmp1);
ui_k = ui_j;
}
else if (g_debug > DEBUG_2)
printf (", #"); /* 2|Vi.Vj| <= Vj.Vj */
}
else if (g_debug > DEBUG_2)
printf (", *"); /* i == j */
}
if (g_debug > DEBUG_2)
printf (")\n");
/* S6 [Advance j.] */
if (ui_j == ui_t)
ui_j = 0;
else
ui_j++;
}
while (ui_j != ui_k); /* S5 */
/* From Knuth p. 104: "The exhaustive search in steps S8-S10
reduces the value of s only rarely." */
#ifdef DO_SEARCH
/* S7 [Prepare for search.] */
/* Find minimum in (x[1], ..., x[t]) satisfying condition
x[k]^2 <= f(y[1], ...,y[t]) * dot(V[k],V[k]) */
ui_k = ui_t;
if (g_debug > DEBUG_2)
{
printf ("searching...");
/*for (f = 0; f < ui_t*/
fflush (stdout);
}
/* Z[i] = floor (sqrt (floor (dot(V[i],V[i]) * s / m^2))); */
mpz_pow_ui (tmp1, m, 2);
mpf_set_z (f_tmp1, tmp1);
mpf_set_z (f_tmp2, s);
mpf_div (f_tmp1, f_tmp2, f_tmp1); /* f_tmp1 = s/m^2 */
for (ui_i = 0; ui_i <= ui_t; ui_i++)
{
vz_dot (tmp1, V[ui_i], V[ui_i], ui_t + 1);
mpf_set_z (f_tmp2, tmp1);
mpf_mul (f_tmp2, f_tmp2, f_tmp1);
f_floor (f_tmp2, f_tmp2);
mpf_sqrt (f_tmp2, f_tmp2);
mpz_set_f (Z[ui_i], f_tmp2);
}
/* S8 [Advance X[k].] */
do
{
if (g_debug > DEBUG_2)
{
printf ("X[%u] = ", ui_k);
mpz_out_str (stdout, 10, X[ui_k]);
printf ("\tZ[%u] = ", ui_k);
mpz_out_str (stdout, 10, Z[ui_k]);
printf ("\n");
fflush (stdout);
}
if (mpz_cmp (X[ui_k], Z[ui_k]))
{
mpz_add_ui (X[ui_k], X[ui_k], 1);
for (ui_i = 0; ui_i <= ui_t; ui_i++)
mpz_add (Y[ui_i], Y[ui_i], U[ui_k][ui_i]);
/* S9 [Advance k.] */
while (++ui_k <= ui_t)
{
mpz_neg (X[ui_k], Z[ui_k]);
mpz_mul_ui (tmp1, Z[ui_k], 2);
for (ui_i = 0; ui_i <= ui_t; ui_i++)
{
mpz_mul (tmp2, tmp1, U[ui_k][ui_i]);
mpz_sub (Y[ui_i], Y[ui_i], tmp2);
}
}
vz_dot (tmp1, Y, Y, ui_t + 1);
if (mpz_cmp (tmp1, s) < 0)
mpz_set (s, tmp1);
}
}
while (--ui_k);
#endif /* DO_SEARCH */
mpf_set_z (f_tmp1, s);
mpf_sqrt (rop[ui_t - 1], f_tmp1);
#ifdef DO_SEARCH
if (g_debug > DEBUG_2)
printf ("done.\n");
#endif /* DO_SEARCH */
} /* S4 loop */
/* Clear GMP variables. */
mpf_clear (f_tmp1);
mpf_clear (f_tmp2);
for (ui_i = 0; ui_i < GMP_SPECT_MAXT; ui_i++)
{
for (ui_j = 0; ui_j < GMP_SPECT_MAXT; ui_j++)
{
mpz_clear (U[ui_i][ui_j]);
mpz_clear (V[ui_i][ui_j]);
}
mpz_clear (X[ui_i]);
mpz_clear (Y[ui_i]);
mpz_clear (Z[ui_i]);
}
mpz_clear (tmp1);
mpz_clear (tmp2);
mpz_clear (tmp3);
mpz_clear (h);
mpz_clear (hp);
mpz_clear (r);
mpz_clear (s);
mpz_clear (p);
mpz_clear (pp);
mpz_clear (q);
mpz_clear (u);
mpz_clear (v);
return;
}
void
omega(long int n, long int m, double tau, long int q,
long int k1, long int k2, mpf_t *factoriales, mpf_t pi) {
mpf_t aux, aux2, aux3, sqrf, acum, Ltau, z, zelev;
int j;
unsigned long int qsqr;
/*
* Set n = min(n,m), and m = max(n,m)
*/
j = n;
n = min(n,m);
m = max(j,m);
/*
* The sqrt(n!m!) pre-factor
*/
mpf_init(aux);
mpf_init(sqrf);
mpf_mul(aux, factoriales[n], factoriales[m]);
mpf_sqrt(sqrf, aux);
/*
* Calculus of tau
*/
mpf_init(aux2);
mpf_init_set_d(Ltau, tau);
mpf_init(z);
mpf_init(zelev);
qsqr = (unsigned long int) q;
mpf_set_d(aux, (double) pow((double) k1, (double) 2));
mpf_mul(aux, aux, Ltau);
mpf_set_d(aux2, (double) pow((double) k2, (double) 2));
mpf_div(aux, aux, Ltau);
mpf_add(aux, aux, aux2);
mpf_div_ui(aux, aux, qsqr);
mpf_mul(z, aux, pi);
if ( ((m-n)%2) == 0)
mpf_pow_ui(zelev, z, (unsigned long int) (m-n)/2);
else {
mpf_pow_ui(zelev, z, m-n);
mpf_sqrt(zelev, zelev);
}
/* mpf_pow_ui(zelev, z, m-n);
*mpf_pow_ui(z, z, 2);
*/
/* mpf_out_str(stdout, 10, 20, z);
printf("\n");*/
/*
* The loop
*/
mpf_init(acum);
mpf_init(aux3);
mpf_set_ui(acum, (unsigned long int) 0);
for (j=0; j <= n; j++) {
mpf_mul(aux, factoriales[j], factoriales[n-j]);
mpf_mul(aux2, aux, factoriales[j+m-n]);
mpf_pow_ui(aux3, z, j);
mpf_div(aux, aux3, aux2);
if ((j%2) == 0)
mpf_set(aux2, aux);
else
mpf_neg(aux2, aux);
mpf_add(acum, acum, aux2);
}
mpf_mul(aux, acum, sqrf);
mpf_mul(aux, aux, zelev);
gmp_printf("%4d %4d %4d %4d %20.20Fe\n", n, m, k1, k2, aux);
/*mpf_out_str(stdout, 10, 20, aux);*/
}
void w3j(mpf_t w, long j1, long j2, long j3, long m1, long m2, long m3)
{
mpq_t delta_sq,r;
mpz_t i;
mpf_t h;
mpq_init(delta_sq);
mpq_init(r);
mpz_init(i);
mpf_init(h);
mpq_set_si(r,0,1);
if(m1+m2+m3!=0) return;
if((iabs(m1)>j1) || (iabs(m2)>j2) || (iabs(m3)>j3)) return;
if((j3<iabs(j1-j2)) || ((j1+j2)<j3)) return;
w3j_Delta_sq(delta_sq, j1, j2, j3);
w3j_intterm(i, j1, j2, j3, m1, m2, m3);
if(iabs(j1-j2-m3)%2 == 1) mpz_neg(i,i);
w3j_sqrt_sq(r, j1, j2, j3, m1, m2, m3);
mpq_mul(r,r,delta_sq);
mpf_set_q(w,r);
mpf_sqrt(w,w);
mpf_set_z(h,i);
mpf_mul(w,w,h);
mpf_clear(h);
mpz_clear(i);
mpq_clear(r);
mpq_clear(delta_sq);
}
