double
gsl_cdf_lognormal_Q (const double x, const double zeta, const double sigma)
{
double u = (log (x) - zeta) / sigma;
double Q = gsl_cdf_ugaussian_Q (u);
return Q;
}
double
gsl_cdf_gamma_Q (const double x, const double a, const double b)
{
double P;
double y = x / b;
if (x <= 0.0)
{
return 1.0;
}
#if 0 /* Not currently working to sufficient accuracy in tails */
if (a > LARGE_A)
{
/*
* Peizer and Pratt's approximation mentioned above.
*/
double z = norm_arg (y, a);
P = gsl_cdf_ugaussian_Q (z);
}
else
#endif
{
P = gsl_sf_gamma_inc_Q (a, y);
}
return P;
}
double
gsl_cdf_tdist_Q (const double x, const double nu)
{
double Q;
double x2 = x * x;
if (nu > 30 && x2 < 10 * nu)
{
double u = cornish_fisher (x, nu);
Q = gsl_cdf_ugaussian_Q (u);
return Q;
}
if (x2 < nu)
{
double u = x2 / nu;
double eps = u / (1 + u);
if (x >= 0)
{
Q = beta_inc_AXPY (-0.5, 0.5, 0.5, nu / 2.0, eps);
}
else
{
Q = beta_inc_AXPY (0.5, 0.5, 0.5, nu / 2.0, eps);
}
}
else
{
double v = nu / (x * x);
double eps = v / (1 + v);
if (x >= 0)
{
Q = beta_inc_AXPY (0.5, 0.0, nu / 2.0, 0.5, eps);
}
else
{
Q = beta_inc_AXPY (-0.5, 1.0, nu / 2.0, 0.5, eps);
}
}
return Q;
}
/* Purpose: calculate z test for proportions, two-tailed for two-sided hypothesis H1 != H0
Parameters: p_sample = proportion of events in sample [0..1]
p_population = proportion of events in population [0..1]
n = sample size
Returns: Probability of making an error when rejecting the NULL hypothesis
*/
double gstats_test_ZP2 (double p_sample, double p_population, int n) {
double z;
double result = 0.0;
if ((p_sample < 0.0) || (p_sample > 1.0)) {
gstats_error ("z-stat: sample proportion must be given as 0.0 - 1.0.");
}
if ((p_population < 0.0) || (p_population > 1.0)) {
gstats_error ("z-stat: population proportion must be given as 0.0 - 1.0.");
}
if (n < 2) {
gstats_error ("z-stat: size of population must be a positive integer > 0.");
}
z = (p_sample - p_population) /
(sqrt ( (p_population * (1-p_population)) / n) );
/* determine direction of numeric integration */
if ( p_sample > p_population ) {
/* we use a normal distribution, if n is at least 30, */
/* t-distribution with n - 1 degress of freedom, otherwise */
if (n >= 30) {
result = gsl_cdf_ugaussian_Q (z);
} else {
result = gsl_cdf_tdist_Q (z, (double) n-1);
}
}
if ( p_sample < p_population ) {
/* we use a normal distribution, if n is at least 30, */
/* t-distribution with n - 1 degress of freedom, otherwise */
if (n >= 30) {
result = gsl_cdf_ugaussian_P (z);
} else {
result = gsl_cdf_tdist_P (z, (double) n-1);
}
}
if ( p_sample == p_population ) {
result = 0.5;
}
return (result * 2);
}
int maurer_test(seq_t *seq, double *pvalue, void *param)
{
unsigned int i, ps, L, Q, K, *p;
double sum, sigma;
double Lparams[11][2] = {
{5.2177052, 2.954},
{6.19662507, 3.125},
{7.1836656, 3.258},
{8.1764248, 3.311},
{9.1723243, 3.356},
{10.170032, 3.384},
{11.168765, 3.401},
{12.168070, 3.410},
{13.167693, 3.416},
{14.167488, 3.419},
{15.167379, 3.421}
};
if ( seq->n < 1010*6*((unsigned int)pow(2,6)) ) {
fprintf(stderr, "Error[Maurer Test]: Sequence length too short\n");
return -1;
}
for ( L = 6; L <= 16; L++ ) {
if ( seq->n <= 1010*(L + 1)*((unsigned int)pow(2,L + 1)) )
break;
}
fprintf(stdout, "L=%d\n", L);
ps =(int)pow(2,L);
p = (unsigned int *)malloc(ps*sizeof(unsigned int));
if ( !p ) {
fprintf(stderr, "Error[Maurer Test]: Memory allocation failed\n");
return -2;
}
memset(p, 0, ps*sizeof(unsigned int));
Q = 10*((unsigned int)pow(2,L));
for ( i = 0; i < Q; i++ )
*(p + dec(seq, i*L, L)) = i + 1;
K = (int)(seq->n/L) - Q;
for ( sum = 0; i < Q + K; i ++ ) {
sum += log( (double)(i + 1) - (double)(*(p + dec(seq, i*L, L))))/log(2);
*(p + dec(seq, i*L, L)) = i + 1;
}
sum /= (double)K;
sigma = (0.7 - 0.8/((double)L) + (4.0 + 32.0/((double)L))*pow(K, -3.0/((double)L))/15.0)*sqrt(Lparams[L - 6][1]/((double)K));
*pvalue = 2*gsl_cdf_ugaussian_Q(fabs((sum - Lparams[L - 6][0])/sigma));
free(p);
return 0;
}
void MBitBer::Finish() {
ofstream ofs;
string fn( fname() );
if (fn != "cout")
ofs.open( fname(),ios::app);
if (! ofs ) {
cerr << BlockName << ": error opening "
<< fn << endl;
exit(_ERROR_OPEN_FILE_);
}
unsigned int minimum, maximum, sum;
minimum = (unsigned int)GSL_POSINF;
maximum = sum = 0;
for (int u=0;u<M();u++) { // user loop
if (gsl_vector_uint_get(bitcount,u)!=0) {
if (fn != "cout") {
ofs.width(NUMWIDTH);
ofs << u;
ofs.width(NUMWIDTH);
ofs << value();
ofs.width(NUMWIDTH);
ofs << 1.0*gsl_vector_uint_get(errcount,u)/gsl_vector_uint_get(bitcount,u);
ofs.width(NUMWIDTH);
ofs << gsl_vector_uint_get(bitcount,u);
ofs.width(NUMWIDTH);
ofs << gsl_vector_uint_get(errcount,u) << endl;
}
else {
cout.width(NUMWIDTH);
cout << u;
cout.width(NUMWIDTH);
cout << value();
cout.width(NUMWIDTH);
cout << 1.0*gsl_vector_uint_get(errcount,u)/gsl_vector_uint_get(bitcount,u);
cout.width(NUMWIDTH);
cout << gsl_vector_uint_get(bitcount,u);
cout.width(NUMWIDTH);
cout << gsl_vector_uint_get(errcount,u) << endl;
}
}
// find maximum
if (gsl_vector_uint_get(errcount,u)>maximum)
maximum = gsl_vector_uint_get(errcount,u);
// find minimum
if (gsl_vector_uint_get(errcount,u)<minimum)
minimum = gsl_vector_uint_get(errcount,u);
sum += gsl_vector_uint_get(errcount,u);
} // user loop
// min, max and mean
if (gsl_vector_uint_get(bitcount,0)!=0) {
if (fn != "cout") {
ofs.width(NUMWIDTH);
ofs << "min";
ofs.width(NUMWIDTH);
ofs << value();
ofs.width(NUMWIDTH);
ofs << 1.0*minimum/gsl_vector_uint_get(bitcount,0);
ofs.width(NUMWIDTH);
ofs << gsl_vector_uint_get(bitcount,0);
ofs.width(NUMWIDTH);
ofs << minimum << endl;
ofs.width(NUMWIDTH);
ofs << "max";
ofs.width(NUMWIDTH);
ofs << value();
ofs.width(NUMWIDTH);
ofs << 1.0*maximum/gsl_vector_uint_get(bitcount,0);
ofs.width(NUMWIDTH);
ofs << gsl_vector_uint_get(bitcount,0);
ofs.width(NUMWIDTH);
ofs << maximum << endl;
ofs.width(NUMWIDTH);
ofs << "mean";
ofs.width(NUMWIDTH);
ofs << value();
ofs.width(NUMWIDTH);
ofs << 1.0*sum/gsl_vector_uint_get(bitcount,0)/M();
ofs.width(NUMWIDTH);
ofs << gsl_vector_uint_get(bitcount,0);
ofs.width(NUMWIDTH);
ofs << sum/M() << endl;
}
else {
cout.width(NUMWIDTH);
cout << "min";
cout.width(NUMWIDTH);
cout << value();
cout.width(NUMWIDTH);
cout << 1.0*minimum/gsl_vector_uint_get(bitcount,0);
cout.width(NUMWIDTH);
cout << gsl_vector_uint_get(bitcount,0);
cout.width(NUMWIDTH);
cout << minimum << endl;
cout.width(NUMWIDTH);
cout << "max";
cout.width(NUMWIDTH);
cout << value();
cout.width(NUMWIDTH);
cout << 1.0*maximum/gsl_vector_uint_get(bitcount,0);
cout.width(NUMWIDTH);
cout << gsl_vector_uint_get(bitcount,0);
cout.width(NUMWIDTH);
cout << maximum << endl;
cout.width(NUMWIDTH);
cout << "mean";
cout.width(NUMWIDTH);
cout << value();
cout.width(NUMWIDTH);
cout << 1.0*sum/gsl_vector_uint_get(bitcount,0)/M();
cout.width(NUMWIDTH);
cout << gsl_vector_uint_get(bitcount,0);
cout.width(NUMWIDTH);
cout << sum/M() << endl;
}
}
ofs.close();
double ebnol=pow(10.0,(value()/10.0));
cout << "\n BPSK reference BER (AWGN) = " << gsl_cdf_ugaussian_Q(sqrt(2*ebnol)) << endl;
gsl_vector_uint_free(lasterrs);
gsl_vector_uint_free(errcount);
gsl_vector_uint_free(bitcount);
gsl_vector_uint_free(dumperrs);
}
double
gsl_cdf_gaussian_Q (const double x, const double sigma)
{
return gsl_cdf_ugaussian_Q (x / sigma);
}
