24 {0.5000, 0.5040, 0.5080, 0.5120, 0.5160, 0.5199, 0.5239, 0.5279, 0.5319, 0.5359},
25 {0.5398, 0.5438, 0.5478, 0.5517, 0.5557, 0.5596, 0.5636, 0.5675, 0.5714, 0.5753},
26 {0.5793, 0.5832, 0.5871, 0.5910, 0.5948, 0.5987, 0.6026, 0.6064, 0.6103, 0.6141},
27 {0.6179, 0.6217, 0.6255, 0.6293, 0.6331, 0.6368, 0.6406, 0.6443, 0.6480, 0.6517},
28 {0.6554, 0.6591, 0.6628, 0.6664, 0.6700, 0.6736, 0.6772, 0.6808, 0.6844, 0.6879},
29 {0.6915, 0.6950, 0.6985, 0.7019, 0.7054, 0.7088, 0.7123, 0.7157, 0.7190, 0.7224},
30 {0.7257, 0.7291, 0.7324, 0.7357, 0.7389, 0.7422, 0.7454, 0.7486, 0.7517, 0.7549},
31 {0.7580, 0.7611, 0.7642, 0.7673, 0.7704, 0.7734, 0.7764, 0.7794, 0.7823, 0.7852},
32 {0.7881, 0.7910, 0.7939, 0.7967, 0.7995, 0.8023, 0.8051, 0.8078, 0.8106, 0.8133},
33 {0.8159, 0.8186, 0.8212, 0.8238, 0.8264, 0.8289, 0.8315, 0.8340, 0.8365, 0.8389},
34 {0.8413, 0.8438, 0.8461, 0.8485, 0.8508, 0.8531, 0.8554, 0.8577, 0.8599, 0.8621},
35 {0.8643, 0.8665, 0.8686, 0.8708, 0.8729, 0.8749, 0.8770, 0.8790, 0.8810, 0.8830},
36 {0.8849, 0.8869, 0.8888, 0.8907, 0.8925, 0.8944, 0.8962, 0.8980, 0.8997, 0.9015},
37 {0.9032, 0.9049, 0.9066, 0.9082, 0.9099, 0.9115, 0.9131, 0.9147, 0.9162, 0.9177},
38 {0.9192, 0.9207, 0.9222, 0.9236, 0.9251, 0.9265, 0.9279, 0.9292, 0.9306, 0.9319},
39 {0.9332, 0.9345, 0.9357, 0.9370, 0.9382, 0.9394, 0.9406, 0.9418, 0.9429, 0.9441},
40 {0.9452, 0.9463, 0.9474, 0.9484, 0.9495, 0.9505, 0.9515, 0.9525, 0.9535, 0.9545},
41 {0.9554, 0.9564, 0.9573, 0.9582, 0.9591, 0.9599, 0.9608, 0.9616, 0.9625, 0.9633},
42 {0.9641, 0.9649, 0.9656, 0.9664, 0.9671, 0.9678, 0.9686, 0.9693, 0.9699, 0.9706},
43 {0.9713, 0.9719, 0.9726, 0.9732, 0.9738, 0.9744, 0.9750, 0.9756, 0.9761, 0.9767},
44 {0.9772, 0.9778, 0.9783, 0.9788, 0.9793, 0.9798, 0.9803, 0.9808, 0.9812, 0.9817},
45 {0.9821, 0.9826, 0.9830, 0.9834, 0.9838, 0.9842, 0.9846, 0.9850, 0.9854, 0.9857},
46 {0.9861, 0.9864, 0.9868, 0.9871, 0.9875, 0.9878, 0.9881, 0.9884, 0.9887, 0.9890},
47 {0.9893, 0.9896, 0.9898, 0.9901, 0.9904, 0.9906, 0.9909, 0.9911, 0.9913, 0.9916},
48 {0.9918, 0.9920, 0.9922, 0.9925, 0.9927, 0.9929, 0.9931, 0.9932, 0.9934, 0.9936},
49 {0.9938, 0.9940, 0.9941, 0.9943, 0.9945, 0.9946, 0.9948, 0.9949, 0.9951, 0.9952},
50 {0.9953, 0.9955, 0.9956, 0.9957, 0.9959, 0.9960, 0.9961, 0.9962, 0.9963, 0.9964},
51 {0.9965, 0.9966, 0.9967, 0.9968, 0.9969, 0.9970, 0.9971, 0.9972, 0.9973, 0.9974},
52 {0.9974, 0.9975, 0.9976, 0.9977, 0.9977, 0.9978, 0.9979, 0.9979, 0.9980, 0.9981},
53 {0.9981, 0.9982, 0.9982, 0.9983, 0.9984, 0.9984, 0.9985, 0.9985, 0.9986, 0.9986},
54 {0.9987, 0.9987, 0.9987, 0.9988, 0.9988, 0.9989, 0.9989, 0.9989, 0.9990, 0.9990} };
59 const double a[4] = { 2.50662823884,
64 const double b[4] = {-8.47351093090,
69 const double c[9] = {0.3374754822726147,
86 r = x * (((a[3]*y+a[2])*y+a[1])*y+a[0]) /
87 ((((b[3]*y+b[2])*y+b[1])*y+b[0])*y+1.0);
94 r = c[0] + r*(c[1]+r*(c[2]+r*(c[3]+r*(c[4]+r*(c[5]+r*(c[6]+
95 r*(c[7]+r*c[8])))))));
108 for (j = 0; j < 10000; j++) {
109 for (i = 0; i < 624; i++) {
120 double samp_mean = 0.0, samp_stddev = 0.0, QH = 0;
121 double Z, p_value = -1, tot_samp = 1000;
125 fprintf(stderr,
"failed to allocate memory!\n");
130 for (i = 0; i < tot_samp; i += 2) {
133 PRN_arr[
i ] = bmg_out[0] * stddev +
mean;
134 PRN_arr[i+1] = bmg_out[1] * stddev +
mean;
135 samp_mean += PRN_arr[
i] + PRN_arr[i+1];
136 samp_stddev += PRN_arr[
i] * PRN_arr[
i] + PRN_arr[i+1] * PRN_arr[i+1];
139 i, PRN_arr[i], i+1, PRN_arr[i+1]);
141 samp_mean /= tot_samp;
142 samp_stddev /= (tot_samp - 1);
143 samp_stddev -= (tot_samp * 1.0 / (tot_samp - 1))*samp_mean*samp_mean;
144 samp_stddev = sqrt(samp_stddev);
145 Z = (mean - samp_mean) / (stddev / sqrt(tot_samp));
157 y = (b > 0) ? a % b : a;
159 if (x > 30 || y > 9) {
161 "Z_TABLE[%d][%d]\n", x, y);
167 SKIP:
for (i = 0; i < tot_samp; ++
i) {
169 if ( i < (tot_samp - 1)) {
171 H_diff =
inv_cdf((i + 2.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
172 H_diff -=
inv_cdf((i + 1.0 - (3.0/8.0)) / (tot_samp + (1.0/4.0)));
174 QH += ((PRN_arr[i + 1] - PRN_arr[
i]) / H_diff);
177 QH = 1.0 - QH / ((tot_samp - 1.0) * samp_stddev);
179 printf(
"sample mean : %f\n" 181 "sample stddev: %f\n" 185 "QH[normality]: %f\n",
186 samp_mean, mean, samp_stddev, stddev, Z, p_value, QH);
Context structure for the Lagged Fibonacci PRNG.
The reader does not expect b to be semantically here and if the code is changed by maybe adding a a division or other the signedness will almost certainly be mistaken To avoid this confusion a new type was SUINT is the C unsigned type but it holds a signed int to use the same example SUINT a
Undefined Behavior In the C some operations are like signed integer dereferencing freed accessing outside allocated Undefined Behavior must not occur in a C it is not safe even if the output of undefined operations is unused The unsafety may seem nit picking but Optimizing compilers have in fact optimized code on the assumption that no undefined Behavior occurs Optimizing code based on wrong assumptions can and has in some cases lead to effects beyond the output of computations The signed integer overflow problem in speed critical code Code which is highly optimized and works with signed integers sometimes has the problem that often the output of the computation does not c
#define u(width, name, range_min, range_max)
void av_bmg_get(AVLFG *lfg, double out[2])
Get the next two numbers generated by a Box-Muller Gaussian generator using the random numbers issued...
high precision timer, useful to profile code
#define AV_LOG_ERROR
Something went wrong and cannot losslessly be recovered.
static __device__ float fabs(float a)
static float mean(const float *input, int size)
#define AV_LOG_INFO
Standard information.
static unsigned int av_lfg_get(AVLFG *c)
Get the next random unsigned 32-bit number using an ALFG.
av_cold void av_lfg_init(AVLFG *c, unsigned int seed)
static double inv_cdf(double u)
printf("static const uint8_t my_array[100] = {\n")
#define av_malloc_array(a, b)
static const double Z_TABLE[31][10]