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Added first few tests and mt19937

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Asher 2025-06-23 06:33:40 +01:00
commit 85196b5d84
23 changed files with 8249 additions and 0 deletions
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#define DOCTEST_CONFIG_IMPLEMENT_WITH_MAIN
#include "./doctest.h"
#include "../math/incomplete_gamma.cpp"
TEST_CASE("igam function"){
// generate igam tests with this python script
// import scipy
// for i in range(1,10):
// for ii in range(20):
// print(f"igamtest({i/2}, {ii/2}, {scipy.special.gammainc(i/2,ii/2)});")
auto igamtest = [](double a, double x, double req) {
REQUIRE(igam(a,x)== doctest::Approx(req).epsilon(0.00000000000001));
};
{
igamtest(0.5, 0.0, 0.0);
igamtest(0.5, 0.5, 0.6826894921370859);
igamtest(0.5, 1.0, 0.8427007929497151);
igamtest(0.5, 1.5, 0.9167354833364495);
igamtest(0.5, 2.0, 0.9544997361036416);
igamtest(0.5, 2.5, 0.9746526813225318);
igamtest(0.5, 3.0, 0.9856941215645704);
igamtest(0.5, 3.5, 0.9918490284064974);
igamtest(0.5, 4.0, 0.9953222650189527);
igamtest(0.5, 4.5, 0.9973002039367398);
igamtest(0.5, 5.0, 0.9984345977419975);
igamtest(0.5, 5.5, 0.9990888811228463);
igamtest(0.5, 6.0, 0.9994679944948608);
igamtest(0.5, 6.5, 0.9996885090232326);
igamtest(0.5, 7.0, 0.9998171893670181);
igamtest(0.5, 7.5, 0.9998924888232705);
igamtest(0.5, 8.0, 0.9999366575163338);
igamtest(0.5, 8.5, 0.9999626201815983);
igamtest(0.5, 9.0, 0.9999779095030014);
igamtest(0.5, 9.5, 0.9999869281546332);
igamtest(1.0, 0.0, 0.0);
igamtest(1.0, 0.5, 0.3934693402873665);
igamtest(1.0, 1.0, 0.6321205588285577);
igamtest(1.0, 1.5, 0.7768698398515702);
igamtest(1.0, 2.0, 0.8646647167633873);
igamtest(1.0, 2.5, 0.9179150013761012);
igamtest(1.0, 3.0, 0.950212931632136);
igamtest(1.0, 3.5, 0.9698026165776815);
igamtest(1.0, 4.0, 0.9816843611112658);
igamtest(1.0, 4.5, 0.9888910034617577);
igamtest(1.0, 5.0, 0.9932620530009145);
igamtest(1.0, 5.5, 0.995913228561536);
igamtest(1.0, 6.0, 0.9975212478233336);
igamtest(1.0, 6.5, 0.9984965608070224);
igamtest(1.0, 7.0, 0.9990881180344455);
igamtest(1.0, 7.5, 0.9994469156298522);
igamtest(1.0, 8.0, 0.9996645373720975);
igamtest(1.0, 8.5, 0.9997965316309894);
igamtest(1.0, 9.0, 0.9998765901959134);
igamtest(1.0, 9.5, 0.9999251481701124);
igamtest(1.5, 0.0, 0.0);
igamtest(1.5, 0.5, 0.19874804309879915);
igamtest(1.5, 1.0, 0.42759329552912023);
igamtest(1.5, 1.5, 0.6083748237289109);
igamtest(1.5, 2.0, 0.7385358700508897);
igamtest(1.5, 2.5, 0.8282028557032668);
igamtest(1.5, 3.0, 0.8883897749052875);
igamtest(1.5, 3.5, 0.9281022275035349);
igamtest(1.5, 4.0, 0.9539882943107686);
igamtest(1.5, 4.5, 0.9707091134651118);
igamtest(1.5, 5.0, 0.9814338645369568);
igamtest(1.5, 5.5, 0.9882741244215786);
igamtest(1.5, 6.0, 0.9926168394946402);
igamtest(1.5, 6.5, 0.9953633945619583);
igamtest(1.5, 7.0, 0.9970948472257326);
igamtest(1.5, 7.5, 0.9981833510334277);
igamtest(1.5, 8.0, 0.9988660157102147);
igamtest(1.5, 8.5, 0.999293257607663);
igamtest(1.5, 9.0, 0.9995601503471612);
igamtest(1.5, 9.5, 0.9997266011125092);
igamtest(2.0, 0.0, 0.0);
igamtest(2.0, 0.5, 0.09020401043104986);
igamtest(2.0, 1.0, 0.2642411176571153);
igamtest(2.0, 1.5, 0.4421745996289252);
igamtest(2.0, 2.0, 0.5939941502901616);
igamtest(2.0, 2.5, 0.7127025048163542);
igamtest(2.0, 3.0, 0.8008517265285442);
igamtest(2.0, 3.5, 0.8641117745995668);
igamtest(2.0, 4.0, 0.9084218055563291);
igamtest(2.0, 4.5, 0.9389005190396673);
igamtest(2.0, 5.0, 0.9595723180054873);
igamtest(2.0, 5.5, 0.9734359856499836);
igamtest(2.0, 6.0, 0.9826487347633355);
igamtest(2.0, 6.5, 0.9887242060526682);
igamtest(2.0, 7.0, 0.9927049442755639);
igamtest(2.0, 7.5, 0.9952987828537434);
igamtest(2.0, 8.0, 0.9969808363488774);
igamtest(2.0, 8.5, 0.9980670504943989);
igamtest(2.0, 9.0, 0.9987659019591332);
igamtest(2.0, 9.5, 0.9992140557861792);
igamtest(2.5, 0.0, 0.0);
igamtest(2.5, 0.5, 0.03743422675270362);
igamtest(2.5, 1.0, 0.15085496391539038);
igamtest(2.5, 1.5, 0.3000141641213724);
igamtest(2.5, 2.0, 0.4505840486472197);
igamtest(2.5, 2.5, 0.5841198130044919);
igamtest(2.5, 3.0, 0.6937810815867218);
igamtest(2.5, 3.5, 0.7793596920632895);
igamtest(2.5, 4.0, 0.8437643724222776);
igamtest(2.5, 4.5, 0.8909358420502275);
igamtest(2.5, 5.0, 0.9247647538534879);
igamtest(2.5, 5.5, 0.9486200165169305);
igamtest(2.5, 6.0, 0.9652122194937581);
igamtest(2.5, 6.5, 0.9766212318964361);
igamtest(2.5, 7.0, 0.9843905838997331);
igamtest(2.5, 7.5, 0.9896376620842136);
igamtest(2.5, 8.0, 0.9931559260775795);
igamtest(2.5, 8.5, 0.9955002030220295);
igamtest(2.5, 9.0, 0.9970535954121197);
igamtest(2.5, 9.5, 0.998077863179057);
igamtest(3.0, 0.0, 0.0);
igamtest(3.0, 0.5, 0.01438767796697068);
igamtest(3.0, 1.0, 0.08030139707139418);
igamtest(3.0, 1.5, 0.19115316946194183);
igamtest(3.0, 2.0, 0.3233235838169364);
igamtest(3.0, 2.5, 0.4561868841166703);
igamtest(3.0, 3.0, 0.5768099188731565);
igamtest(3.0, 3.5, 0.6791528011378659);
igamtest(3.0, 4.0, 0.7618966944464557);
igamtest(3.0, 4.5, 0.8264219290899639);
igamtest(3.0, 5.0, 0.8753479805169189);
igamtest(3.0, 5.5, 0.9116235676432145);
igamtest(3.0, 6.0, 0.938031195583341);
igamtest(3.0, 6.5, 0.9569640531010171);
igamtest(3.0, 7.0, 0.9703638361194782);
igamtest(3.0, 7.5, 0.9797432849433356);
igamtest(3.0, 8.0, 0.986246032255997);
igamtest(3.0, 8.5, 0.9907167556638894);
igamtest(3.0, 9.0, 0.9937678048936227);
igamtest(3.0, 9.5, 0.9958363669624967);
igamtest(3.5, 0.0, 0.0);
igamtest(3.5, 0.5, 0.0051714634834845175);
igamtest(3.5, 1.0, 0.04015963126989843);
igamtest(3.5, 1.5, 0.11499776835684938);
igamtest(3.5, 2.0, 0.22022259152428406);
igamtest(3.5, 2.5, 0.34003677030571744);
igamtest(3.5, 3.0, 0.4602506496044427);
igamtest(3.5, 3.5, 0.5711201424469452);
igamtest(3.5, 4.0, 0.6674060974006921);
igamtest(3.5, 4.5, 0.7473439535034361);
igamtest(3.5, 5.0, 0.81142653248655);
igamtest(3.5, 5.5, 0.8613809791267045);
igamtest(3.5, 6.0, 0.8994411314916412);
igamtest(3.5, 6.5, 0.9278916089660787);
igamtest(3.5, 7.0, 0.9488186465869346);
igamtest(3.5, 7.5, 0.9640005952365712);
igamtest(3.5, 8.0, 0.9748836392531472);
igamtest(3.5, 8.5, 0.9826038174308754);
igamtest(3.5, 9.0, 0.9880299976459704);
igamtest(3.5, 9.5, 0.9918126590319385);
igamtest(4.0, 0.0, 0.0);
igamtest(4.0, 0.5, 0.001751622556290824);
igamtest(4.0, 1.0, 0.01898815687615381);
igamtest(4.0, 1.5, 0.06564245437845008);
igamtest(4.0, 2.0, 0.14287653950145296);
igamtest(4.0, 2.5, 0.2424238668669339);
igamtest(4.0, 3.0, 0.35276811121776874);
igamtest(4.0, 3.5, 0.463367332099215);
igamtest(4.0, 4.0, 0.566529879633291);
igamtest(4.0, 4.5, 0.657704044165409);
igamtest(4.0, 5.0, 0.7349740847026385);
igamtest(4.0, 5.5, 0.7983008012974713);
igamtest(4.0, 6.0, 0.8487961172233521);
igamtest(4.0, 6.5, 0.8881503883724394);
igamtest(4.0, 7.0, 0.9182345837552784);
igamtest(4.0, 7.5, 0.9408545401673161);
igamtest(4.0, 8.0, 0.957619888008316);
igamtest(4.0, 8.5, 0.9698909203107791);
igamtest(4.0, 9.0, 0.9787735136970911);
igamtest(4.0, 9.5, 0.9851403523541687);
igamtest(4.5, 0.0, 0.0);
igamtest(4.5, 0.5, 0.0005624973021675015);
igamtest(4.5, 1.0, 0.008532393371186466);
igamtest(4.5, 1.5, 0.035705027314910875);
igamtest(4.5, 2.0, 0.08858747316832083);
igamtest(4.5, 2.5, 0.16569173980659246);
igamtest(4.5, 3.0, 0.2600817079053462);
igamtest(4.5, 3.5, 0.36288059283060153);
igamtest(4.5, 4.0, 0.4658537830903085);
igamtest(4.5, 4.5, 0.5627258110861331);
igamtest(4.5, 5.0, 0.6495147876766386);
igamtest(4.5, 5.5, 0.724291063227778);
igamtest(4.5, 6.0, 0.7866906949165835);
igamtest(4.5, 6.5, 0.8373937378097005);
igamtest(4.5, 7.0, 0.8776747719613376);
igamtest(4.5, 7.5, 0.9090640234201949);
igamtest(4.5, 8.0, 0.9331184122258733);
igamtest(4.5, 8.5, 0.9512840238523587);
igamtest(4.5, 9.0, 0.9648264605330151);
igamtest(4.5, 9.5, 0.974807104918331);
}
}

3
rng/rng/codetest.sh Executable file
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g++ -std=c++11 code_tests/test.cpp -o testcode.o
./testcode.o
rm testcode.o

43
rng/rng/generators/LCG/lehmer.cpp Normal file
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//
// lehmer.cpp
// rng
//
// Created by Asher Falcon on 20/06/2025.
//
#include "../../rng.h"
// parameters recommended by Nakazawa & Nakazawa
// https://en.wikipedia.org/wiki/Lehmer_random_number_generator
uint64_t lehmer_minstd(uint64_t prev){
uint64_t a = 7759097958782935LL;
uint64_t m = 18055400005099021LL;
uint64_t result = (a * prev) % m;
return result;
}
class lehmer_generator {
uint64_t seed;
public:
uint32_t generate(){
seed = lehmer_minstd(seed);
return seed;
}
lehmer_generator(uint64_t genSeed){
seed = genSeed;
}
};
// std::vector<std::bitset<32>> lehmer_generate(int seed, int amount){
// std::vector<std::bitset<32>> bits(amount);
// for(int i=0; i<amount; i++){
// seed = lehmer_minstd(seed);
// bits[i]=seed;
// }
// return bits;
// }

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rng/rng/generators/mt19937.cpp Normal file
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#include "../rng.h"
// more specifically this will be mt19937 - 32 bit
std::array<uint32_t,624> mt19937_init(uint32_t seed){
std::array<uint32_t,624> state;
state[0] = seed;
for(int i=1; i<624; i++){
state[i]= 1812433253*(state[i-1] ^ (state[i-1] >> 30)) + i;
}
return state;
}
std::array<uint32_t,624> mt19937_twist(std::array<uint32_t,624> state){
std::array<uint32_t,624> newstate;
for(int i=0; i<624; i++){
uint32_t x;
// concating the MSB and LSB from next
if(i+1<624){
x = (state[i] & 0x80000000) | (state[(i+1)] & 0x7FFFFFFF);
}else{
x = (state[i] & 0x80000000) | (newstate[(i+1)%624] & 0x7FFFFFFF);
}
// does the *A part
if(x&1){
x = (x>>1) ^ 0x9908B0DFUL;
}else{
x=x>>1;
}
uint32_t y;
if(i+397<624){
y = state[i+397] ^ x;
}else{
y = newstate[(i+397) % 624] ^ x;
}
newstate[i] = y;
}
return newstate;
}
std::array<uint32_t,624> mt19937_temper(std::array<uint32_t,624> state){
std::array<uint32_t, 624> tempered;
for(int i=0; i<624; i++){
uint32_t y = state[i];
y = y ^ (y >> 11);
y = y ^ ((y << 7) & 0x9D2C5680UL);
y = y ^ ((y << 15) & 0xEFC60000UL);
tempered[i] = y ^ (y >> 18);
}
return tempered;
}
class mt19937_generator {
public:
uint32_t seed;
uint32_t generate() {
uint32_t generated = random_values[position];
position++;
if(position>=624){
nextblock();
}
return generated;
}
double generate_01(){
return ((double)generate())/(4294967295);
}
mt19937_generator(uint32_t genSeed){
seed = genSeed;
state = mt19937_init(seed);
nextblock();
}
private:
std::array<uint32_t,624> state;
std::array<uint32_t,624> random_values;
int position;
// goes to next block of 624 values
void nextblock() {
state = mt19937_twist(state);
random_values = mt19937_temper(state);
position = 0;
}
};

52
rng/rng/main.cpp Normal file
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//
// main.cpp
// rng
//
// Created by Asher Falcon on 17/06/2025.
//
#include "rng.h"
#include "generators/LCG/lehmer.cpp"
#include "generators/mt19937.cpp"
#include "randomness_tests/frequency_monobit.cpp"
#include "randomness_tests/frequency_block.cpp"
#include "randomness_tests/runs.cpp"
int main(int argc, const char * argv[]) {
int seed = 8898;
int blocksgenerated = 1000000;
mt19937_generator mt2 = mt19937_generator(seed);
lehmer_generator lg = lehmer_generator(seed);
std::vector<std::bitset<32>> mtbits;
std::vector<std::bitset<32>> lgbits;
for(int i=0; i<blocksgenerated; i++){
mtbits.push_back(mt2.generate());
lgbits.push_back(lg.generate());
}
// for(auto bs : lgbits){
// for(int i=0; i<32; i++){
// std::cout << bs[i];
// }
// }
int freqblocksize = (blocksgenerated * 32) / 120;
std::cout << "Linear Congruential Generator:\n";
std::cout << " - FreqMonobit = "<< std::fixed << std::setprecision(10) << test_frequency_monobit(lgbits) << "\n";
std::cout << " - FreqBlock (n/120) = "<< std::fixed << std::setprecision(10) << test_frequency_block(lgbits, freqblocksize) << "\n";
std::cout << " - Runs = "<< std::fixed << std::setprecision(10) << test_runs(lgbits) << "\n";
std::cout << "Mersenne Twister mt19937-32:\n";
std::cout << " - FreqMonobit = "<< std::fixed << std::setprecision(10) << test_frequency_monobit(mtbits) << "\n";
std::cout << " - FreqBlock (n/120) = "<< std::fixed << std::setprecision(10) << test_frequency_block(mtbits, freqblocksize) << "\n";
std::cout << " - Runs = "<< std::fixed << std::setprecision(10) << test_runs(mtbits) << "\n";
return 0;
}

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rng/rng/math/incomplete_gamma.cpp Normal file
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#include "../rng.h"
#pragma once
double igam(double a, double x) {
double maxlog = 7.09782712893383996732E2;
double machep = 1.11022302462515654042E-16;
double big = 4.503599627370496e15;
double biginv = 2.22044604925031308085e-16;
double ans, ax, c, r;
if( (x<=0 || a<=0)){
return 0.0;
}
// if (x>1.0 && x>a){
// return 1.0 - igamc(a,x);
// }
ax = a * std::log(x) - x - std::lgamma(a);
if (ax < -maxlog){
// std::cout << "max log error on incomplete gamma function\n";
return 0.0;
}
ax = std::exp(ax);
r = a;
c = 1.0;
ans = 1.0;
do {
r+=1;
c*= x/r;
ans +=c;
}while(c/ans > machep);
return ans * ax/a;
}
// regularized left tail of incomplete gamma
// Q(s, x) = \frac{1}{\Gamma(s)} \int_x^\infty t^{s-1} e^{-t} \, dt
double igamc(double a, double x){
return 1-igam(a,x);
// double maxlog = 7.09782712893383996732E2;
// double machep = 1.11022302462515654042E-16;
// double big = 4.503599627370496e15;
// double biginv = 2.22044604925031308085e-16;
// if(x<=0 || a<=0){
// return 1.0;
// }
// if( (x < 1.0 ) || ( x < a)){
// std::cout << "bad\n";
// return 1.0 - igam(a,x);
// }
// double ax = a * std::log(x) - std::lgamma(a);
// // maxlog?
// if(ax < -maxlog){
// std::cout << "max log error on incomplete gamma function\n";
// return 0.0;
// }
// ax = std::exp(ax);
// double y = 1.0 - a;
// double z = x + y + 1.0;
// double c = 0.0;
// double pkm2 = 1.0;
// double qkm2 = x;
// double pkm1 = x + 1.0;
// double qkm1 = z * x;
// double ans = pkm1/qkm1;
// double pk,qk,r,t,yc;
// t = 1.0;
// do {
// c+=1.0;
// y+=1.0;
// z+=2.0;
// yc = y*c;
// pk = pkm1 * z - pkm2 * yc;
// qk = qkm1 * z - qkm2 * yc;
// if (qk !=0){
// r = pk/qk;
// t = std::fabs((ans-r)/r);
// ans = r;
// }else{
// t = 1.0;
// }
// pkm2 = pkm1;
// pkm1 = pk;
// qkm2 = qkm1;
// qkm1 = qk;
// if(std::fabs(pk) > big){
// pkm2 *= biginv;
// pkm1 *= biginv;
// qkm2 *= biginv;
// qkm1 *= biginv;
// }
// std::cout << ans << "-\n";
// } while (t>machep);
// return ans * ax;
}

20
rng/rng/plot_data.py Normal file
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import matplotlib.pyplot as plt
x_coords = []
y_coords = []
with open("data.txt", "r") as file:
for line in file:
x_coords.append(float(line.split(",")[0]))
y_coords.append(float(line.split(",")[1]))
plt.figure(figsize=(10, 8))
plt.scatter(x_coords, y_coords, alpha=0.6, s=1)
plt.grid(True, alpha=0.3)
plt.axis('equal')
plt.xlim(-0.05, 1.05)
plt.ylim(-0.05, 1.05)
plt.tight_layout()
plt.show()

51
rng/rng/randomness_tests/frequency_block.cpp Normal file
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//
// frequency_monobit.cpp
// rng
//
// Created by Asher Falcon on 21/06/2025.
//
#include "../rng.h"
#include "../math/incomplete_gamma.cpp"
/**
* Returns the p value from the block frequency test
*/
double test_frequency_block(std::vector<std::bitset<32>> data, u_long block_size){
// std::cout << "BLOCK SIZE: "<< block_size<<"\n";
long long bitcount = data.size() * 32;
long long chunks = bitcount / block_size;
double x2stat = 0;
for(int chunkIndex = 0; chunkIndex < chunks; chunkIndex++){
// std::cout << "NEWCHUNK: ";
double onecount = 0;
for(int i=0; i<block_size; i++){
int dataIndex = (((chunkIndex * block_size)+i) / 32);
int bitIndex = (((chunkIndex * block_size)+i) % 32);
onecount += data[dataIndex][bitIndex];
// std::cout << data[dataIndex][bitIndex];
}
double oneproportion = onecount / (double)block_size;
x2stat += 4*block_size*std::pow((oneproportion - 0.5),2);
// std::cout << "\n";
}
// std::cout << "[debug] calling igamc with "<<(chunks/2) <<','<<(x2stat/2) << "\n";
double p = igam(chunks/2, x2stat/2);
return p;
}
/**
* It is recommended that each sequence to be tested consist of a minimum of 100 bits (i.e., n ≥ 100). Note
that n ≥ MN. The block size M should be selected such that M ≥ 20, M > .01n and N < 100.
*/
bool pass_frequency_monobit(std::vector<std::bitset<32>> data, int chunkSize){
double pv = test_frequency_block(data, chunkSize);
return pv >= 0.01;
}

35
rng/rng/randomness_tests/frequency_monobit.cpp Normal file
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//
// frequency_monobit.cpp
// rng
//
// Created by Asher Falcon on 21/06/2025.
//
#include "../rng.h"
double test_frequency_monobit(std::vector<std::bitset<32>> data){
long long s = 0;
for(auto bitset : data){
for(int i=0; i<32; i++){
s += (2*bitset[i])-1;
}
}
// std::cout << " [sval: "<<s<<"] ";
double sobs = ((double)std::abs(s))/std::sqrt(data.size()*32);
double pvalue = std::erfc(sobs/std::sqrt(2));
return pvalue;
}
bool pass_frequency_monobit(std::vector<std::bitset<32>> data){
double pv = test_frequency_monobit(data);
return pv >= 0.01;
}

26
rng/rng/randomness_tests/runs.cpp Normal file
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#include "../rng.h"
double test_runs(std::vector<std::bitset<32>> data){
long long totalSize = data.size() * 32;
double vnobs = 1;
double onesproportion = 0;
for(int i=0; i<totalSize-1; i++){
if(data[i/32][i%32]!=data[(i+1)/32][(i+1)%32]){
vnobs++;
}
onesproportion+=data[i/32][i%32];
}
onesproportion/=totalSize;
return std::erfc(
std::abs(vnobs-(2*totalSize*onesproportion*(1-onesproportion)))
/
(2*std::sqrt(2*totalSize)*onesproportion*(1-onesproportion))
);
}

16
rng/rng/rng.h Normal file
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//
// include.h
// rng
//
// Created by Asher Falcon on 20/06/2025.
//
#pragma once
#include <iostream>
#include <fstream>
#include <array>
#include <random>
#include <vector>
#include <cmath>
#include <iomanip>

3
rng/rng/run.sh Executable file
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g++ -std=c++11 main.cpp -o main.o
./main.o
rm main.o