@@ -20,9 +20,88 @@
#include "libavutil/timer.h"
#include "libavutil/lfg.h"
+static const double Z_TABLE[31][10] = {
+ {0.5000, 0.5040, 0.5080, 0.5120, 0.5160, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359},
+ {0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753},
+ {0.5793, 0.5832, 0.5871, 0.5910, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141},
+ {0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.6480, 0.6517},
+ {0.6554, 0.6591, 0.6628, 0.6664, 0.6700, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879},
+ {0.6915, 0.6950, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.7190, 0.7224},
+ {0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549},
+ {0.7580, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852},
+ {0.7881, 0.7910, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133},
+ {0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.8340, 0.8365, 0.8389},
+ {0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621},
+ {0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.8770, 0.8790, 0.8810, 0.8830},
+ {0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.8980, 0.8997, 0.9015},
+ {0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177},
+ {0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319},
+ {0.9332, 0.9345, 0.9357, 0.9370, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441},
+ {0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545},
+ {0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633},
+ {0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706},
+ {0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.9750, 0.9756, 0.9761, 0.9767},
+ {0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817},
+ {0.9821, 0.9826, 0.9830, 0.9834, 0.9838, 0.9842, 0.9846, 0.9850, 0.9854, 0.9857},
+ {0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.9890},
+ {0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916},
+ {0.9918, 0.9920, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936},
+ {0.9938, 0.9940, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952},
+ {0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.9960, 0.9961, 0.9962, 0.9963, 0.9964},
+ {0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.9970, 0.9971, 0.9972, 0.9973, 0.9974},
+ {0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.9980, 0.9981},
+ {0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986},
+ {0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.9990, 0.9990} };
+
+// Inverse cumulative distribution function
+static double inv_cdf(double u)
+{
+ const double a[4] = { 2.50662823884,
+ -18.61500062529,
+ 41.39119773534,
+ -25.44106049637};
+
+ const double b[4] = {-8.47351093090,
+ 23.08336743743,
+ -21.06224101826,
+ 3.13082909833};
+
+ const double c[9] = {0.3374754822726147,
+ 0.9761690190917186,
+ 0.1607979714918209,
+ 0.0276438810333863,
+ 0.0038405729373609,
+ 0.0003951896511919,
+ 0.0000321767881768,
+ 0.0000002888167364,
+ 0.0000003960315187};
+
+ double r;
+ double x = u - 0.5;
+
+ // Beasley-Springer
+ if (fabs(x) < 0.42) {
+
+ double y = x * x;
+ r = x * (((a[3]*y+a[2])*y+a[1])*y+a[0]) /
+ ((((b[3]*y+b[2])*y+b[1])*y+b[0])*y+1.0);
+ }
+ else {// Moro
+ r = u;
+ if (x > 0.0)
+ r = 1.0 - u;
+ r = log(-log(r));
+ r = c[0] + r*(c[1]+r*(c[2]+r*(c[3]+r*(c[4]+r*(c[5]+r*(c[6]+
+ r*(c[7]+r*c[8])))))));
+ if (x < 0.0)
+ r = -r;
+ }
+
+ return r;
+}
int main(void)
{
- int x = 0;
+ int x = 0, ret = 0;
int i, j;
AVLFG state;
@@ -41,34 +120,77 @@ int main(void)
{
double mean = 1000;
double stddev = 53;
- double samp_mean = 0.0, samp_stddev = 0.0;
- double samp0, samp1;
+ double samp_mean = 0.0, samp_stddev = 0.0, QH;
+ double Z, p_value = -1, tot_samp = 1000;
+ double *PRN_arr = av_malloc_array(tot_samp, sizeof(double));
- av_lfg_init(&state, 42);
+ if (!PRN_arr) {
+ fprintf(stderr, "failed to allocate memory!\n");
+ ret = 1;
+ goto EXIT;
+ }
- for (i = 0; i < 1000; i += 2) {
+ av_lfg_init(&state, 42);
+ for (i = 0; i < tot_samp; i += 2) {
double bmg_out[2];
av_bmg_get(&state, bmg_out);
- samp0 = bmg_out[0] * stddev + mean;
- samp1 = bmg_out[1] * stddev + mean;
- samp_mean += samp0 + samp1;
- samp_stddev += samp0 * samp0 + samp1 * samp1;
- av_log(NULL, AV_LOG_INFO,
- "%f\n%f\n",
- samp0,
- samp1);
+ PRN_arr[i ] = bmg_out[0] * stddev + mean;
+ PRN_arr[i+1] = bmg_out[1] * stddev + mean;
+ samp_mean += PRN_arr[i] + PRN_arr[i+1];
+ samp_stddev += PRN_arr[i] * PRN_arr[i] + PRN_arr[i+1] * PRN_arr[i+1];
+ printf("PRN%d : %f\n"
+ "PRN%d : %f\n",
+ i, PRN_arr[i], i+1, PRN_arr[i+1]);
}
- /* TODO: add proper normality test */
- samp_mean /= 1000;
- samp_stddev /= 999;
- samp_stddev -= (1000.0/999.0)*samp_mean*samp_mean;
+ samp_mean /= tot_samp;
+ samp_stddev /= (tot_samp - 1);
+ samp_stddev -= (tot_samp * 1.0 / (tot_samp - 1))*samp_mean*samp_mean;
samp_stddev = sqrt(samp_stddev);
- av_log(NULL, AV_LOG_INFO, "sample mean : %f\n"
- "true mean : %f\n"
- "sample stddev: %f\n"
- "true stddev : %f\n",
- samp_mean, mean, samp_stddev, stddev);
- }
+ Z = (mean - samp_mean) / (stddev / sqrt(tot_samp));
+ {
+ int x, y, a, b, flag = 0;
+
+ if (Z < 0.0) {
+ flag = !flag;
+ Z = Z * -1.0;
+ }
+
+ a = (int)(Z * 100);
+ b = ((int)Z * 100);
+ x = Z * 10;
+ y = (b > 0) ? a % b : a;
+ y = y % 10;
+ if (x > 30 || y > 9) {
+ av_log(NULL, AV_LOG_INFO, "error: out of bounds! tried to access"
+ "Z_TABLE[%d][%d]\n", x, y);
+ goto SKIP;
+ }
+ p_value = flag ? 1 - Z_TABLE[x][y] : Z_TABLE[x][y];
+ }
- return 0;
+SKIP: for (i = 0; i < tot_samp; ++i) {
+
+ if ( i < (tot_samp - 1)) {
+ double H_diff;
+ H_diff = inv_cdf((i + 2.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
+ H_diff -= inv_cdf((i + 1.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
+
+ QH += ((PRN_arr[i + 1] - PRN_arr[i]) / H_diff);
+ }
+ }
+ QH = 1.0 - QH / ((tot_samp - 1.0) * samp_stddev);
+
+ printf("sample mean : %f\n"
+ "true mean : %f\n"
+ "sample stddev: %f\n"
+ "true stddev : %f\n"
+ "z-score : %f\n"
+ "p-value : %f\n"
+ "QH[normality]: %f\n",
+ samp_mean, mean, samp_stddev, stddev, Z, p_value, QH);
+
+EXIT:
+ av_freep(&PRN_arr);
+ }
+ return ret;
}
@@ -101,6 +101,10 @@ FATE_LIBAVUTIL += fate-imgutils
fate-imgutils: libavutil/tests/imgutils$(EXESUF)
fate-imgutils: CMD = run libavutil/tests/imgutils
+FATE_LIBAVUTIL += fate-lfg
+fate-lfg: libavutil/tests/lfg$(EXESUF)
+fate-lfg: CMD = run libavutil/tests/lfg
+
FATE_LIBAVUTIL += fate-md5
fate-md5: libavutil/tests/md5$(EXESUF)
fate-md5: CMD = run libavutil/tests/md5
new file mode 100644
@@ -0,0 +1,1007 @@
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+PRN978 : 1014.840472
+PRN979 : 991.906864
+PRN980 : 947.716713
+PRN981 : 1075.346169
+PRN982 : 913.043943
+PRN983 : 1006.107228
+PRN984 : 940.937691
+PRN985 : 925.827770
+PRN986 : 870.001279
+PRN987 : 1093.348026
+PRN988 : 990.938631
+PRN989 : 1067.552107
+PRN990 : 936.441162
+PRN991 : 956.066787
+PRN992 : 1001.705214
+PRN993 : 1007.198453
+PRN994 : 956.883661
+PRN995 : 1033.645356
+PRN996 : 1036.395999
+PRN997 : 954.941658
+PRN998 : 1015.720547
+PRN999 : 1023.147999
+sample mean : 1000.303825
+true mean : 1000.000000
+sample stddev: 53.233584
+true stddev : 53.000000
+z-score : 0.181279
+p-value : 0.428600
+QH[normality]: 1.015347
The Chen-Shapiro(CS) test was used to test normality for Lagged Fibonacci PRNG. Normality Hypothesis Test: The null hypothesis formally tests if the population the sample represents is normally-distributed. For CS, when the normality hypothesis is True, the distribution of QH will have a mean close to 1. Information on CS can be found here: http://www.stata-journal.com/sjpdf.html?articlenum=st0264 http://www.originlab.com/doc/Origin-Help/NormalityTest-Algorithm Signed-off-by: Thomas Turner <thomastdt@googlemail.com> --- libavutil/tests/lfg.c | 170 ++++++-- tests/fate/libavutil.mak | 4 + tests/ref/fate/lfg | 1007 ++++++++++++++++++++++++++++++++++++++++++++++ 3 files changed, 1157 insertions(+), 24 deletions(-) create mode 100644 tests/ref/fate/lfg