feat: add plots for n m k trends

plots/data/bloom_filter_stats.csv

@@ -0,0 +1,42 @@
+n,m,k,theoretical_fpp,filter_fpp,actual_fpp
+10000,100000,2,0.03285854,0.03289392,0.03292500
+10000,100000,3,0.01741059,0.01743016,0.01755500
+10000,100000,4,0.01181327,0.01185258,0.01231500
+10000,100000,5,0.00943093,0.00940946,0.00898000
+10000,100000,6,0.00843621,0.00844959,0.00851000
+10000,100000,7,0.00819372,0.00818934,0.00823000
+10000,100000,8,0.00845547,0.00843888,0.00853000
+10000,100000,9,0.00912699,0.00915585,0.00945500
+10000,100000,10,0.01018589,0.01023808,0.01031500
+10000,100000,11,0.01164950,0.01163213,0.01149000
+10000,100000,12,0.01356057,0.01344405,0.01366000
+10000,100000,13,0.01598020,0.01592878,0.01558500
+10000,100000,14,0.01898380,0.01903601,0.01829000
+10000,100000,15,0.02265812,0.02262230,0.02297000
+1000,100000,5,0.00000028,0.00000028,0.00000000
+2000,100000,5,0.00000780,0.00000782,0.00001500
+3000,100000,5,0.00005244,0.00005258,0.00004000
+4000,100000,5,0.00019571,0.00019651,0.00019500
+5000,100000,5,0.00052956,0.00053070,0.00050500
+7500,100000,5,0.00299029,0.00298418,0.00307500
+10000,100000,5,0.00943093,0.00944119,0.00924000
+15000,100000,5,0.04089419,0.04091604,0.04042500
+20000,100000,5,0.10092519,0.10124248,0.10181000
+30000,100000,5,0.28297059,0.28242511,0.28079500
+40000,100000,5,0.48332436,0.48360202,0.48378500
+60000,100000,5,0.77464850,0.77395500,0.77450000
+80000,100000,5,0.91171555,0.91254904,0.91244000
+10000,50000,5,0.10092519,0.10099464,0.10038000
+10000,60000,5,0.05778111,0.05778597,0.05903000
+10000,70000,5,0.03465784,0.03474584,0.03495000
+10000,80000,5,0.02167922,0.02172916,0.02183500
+10000,90000,5,0.01407034,0.01406240,0.01391000
+10000,100000,5,0.00943093,0.00943771,0.00954000
+10000,125000,5,0.00389460,0.00388819,0.00400500
+10000,150000,5,0.00183031,0.00183603,0.00199000
+10000,175000,5,0.00094805,0.00094767,0.00087000
+10000,200000,5,0.00052956,0.00053068,0.00055500
+10000,250000,5,0.00019571,0.00019591,0.00028500
+10000,300000,5,0.00008527,0.00008530,0.00009500
+10000,400000,5,0.00002240,0.00002242,0.00001500
+10000,600000,5,0.00000327,0.00000327,0.00000500

plots/data/bloom_filter_stats_csv.cpp

@@ -0,0 +1,85 @@
+#include "bloom_filter/bloom_filter.hpp"
+#include <cmath>
+#include <cstdint>
+#include <cstdio>
+#include <fstream>
+#include <iostream>
+#include <random>
+#include <sstream>
+#include <string>
+#include <unordered_set>
+
+int main(int argc, char *argv[]) {
+    if (argc != 2) {
+        std::cerr << "usage: " << argv[0] << " plots/cases.csv\n";
+        return 1;
+    }
+
+    std::ifstream csv{argv[1]};
+    std::string line;
+    std::getline(csv, line); // skipping header n,m,k
+
+    std::mt19937_64 rng{}; // no seed so this is deterministic
+    constexpr uint32_t TOTAL_TRIALS = 20;
+    constexpr uint32_t ELEMS_CHECK = 10000;
+
+    std::printf("n,m,k,theoretical_fpp,filter_fpp,actual_fpp\n");
+
+    while (std::getline(csv, line)) {
+        if (line.empty()) {
+            continue;
+        }
+
+        std::stringstream ss(line);
+        std::string n_str, m_str, k_str;
+        std::getline(ss, n_str, ',');
+        std::getline(ss, m_str, ',');
+        std::getline(ss, k_str, ',');
+
+        uint64_t n = std::stoull(n_str);
+        uint64_t m = std::stoull(m_str);
+        uint32_t k = std::stoul(k_str);
+
+        double sum_theoretical_fpp = 0;
+        double sum_filter_fpp = 0;
+        double sum_actual_fpp = 0;
+
+        for (uint32_t trial = 0; trial < TOTAL_TRIALS; trial++) {
+            uint64_t seed1 = rng(), seed2 = rng();
+            BloomFilter filter{static_cast<size_t>(m), k, seed1, seed2};
+
+            std::unordered_set<uint64_t> actual_inserts;
+            for (uint64_t i = 0; i < n; i++) {
+                uint64_t num = rng();
+                actual_inserts.insert(num);
+                filter.put(&num, sizeof(num));
+            }
+
+            uint32_t fp_count = 0;
+            for (uint32_t i = 0; i < ELEMS_CHECK; i++) {
+                uint64_t test = rng();
+                bool actually_present = actual_inserts.count(test);
+                bool filter_contains = filter.may_contain(&test, sizeof(test));
+                fp_count += !actually_present && filter_contains;
+            }
+
+            double theoretical_fpp =
+                std::pow(1 - std::exp(-static_cast<double>(k) * n / m), k);
+            double filter_fpp = filter.false_positive_probability();
+            double actual_fpp = static_cast<double>(fp_count) / ELEMS_CHECK;
+
+            sum_theoretical_fpp += theoretical_fpp;
+            sum_filter_fpp += filter_fpp;
+            sum_actual_fpp += actual_fpp;
+        }
+
+        std::printf("%llu,%llu,%u,%.8f,%.8f,%.8f\n",
+                    static_cast<unsigned long long>(n),
+                    static_cast<unsigned long long>(m), k,
+                    sum_theoretical_fpp / TOTAL_TRIALS,
+                    sum_filter_fpp / TOTAL_TRIALS,
+                    sum_actual_fpp / TOTAL_TRIALS);
+    }
+
+    return 0;
+}

plots/data/cases.csv

@@ -0,0 +1,42 @@
+n,m,k
+10000,100000,2
+10000,100000,3
+10000,100000,4
+10000,100000,5
+10000,100000,6
+10000,100000,7
+10000,100000,8
+10000,100000,9
+10000,100000,10
+10000,100000,11
+10000,100000,12
+10000,100000,13
+10000,100000,14
+10000,100000,15
+1000,100000,5
+2000,100000,5
+3000,100000,5
+4000,100000,5
+5000,100000,5
+7500,100000,5
+10000,100000,5
+15000,100000,5
+20000,100000,5
+30000,100000,5
+40000,100000,5
+60000,100000,5
+80000,100000,5
+10000,50000,5
+10000,60000,5
+10000,70000,5
+10000,80000,5
+10000,90000,5
+10000,100000,5
+10000,125000,5
+10000,150000,5
+10000,175000,5
+10000,200000,5
+10000,250000,5
+10000,300000,5
+10000,400000,5
+10000,600000,5

plots/gnuplot/fpp_vs_k.gp

@@ -0,0 +1,13 @@
+set datafile separator comma
+set terminal pngcairo size 1000,700 enhanced font "Arial,12"
+set output "plots/png/fpp_vs_k.png"
+
+set title "Bloom filter false-positive rate vs k (n=10000, m=100000)"
+set xlabel "hash functions (k)"
+set ylabel "false-positive rate"
+set grid
+set key outside
+
+plot "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $2 == 100000) ? $3 : 1/0):4 every ::1 with linespoints title "theoretical", \
+     "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $2 == 100000) ? $3 : 1/0):5 every ::1 with linespoints title "filter estimate", \
+     "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $2 == 100000) ? $3 : 1/0):6 every ::1 with linespoints title "observed"

plots/gnuplot/fpp_vs_m.gp

@@ -0,0 +1,16 @@
+set datafile separator comma
+set terminal pngcairo size 1000,700 enhanced font "Arial,12"
+set output "plots/png/fpp_vs_m.png"
+
+set title "Bloom filter false-positive rate vs m (n=10000, k=5)"
+set xlabel "filter size in bits (m)"
+set ylabel "false-positive rate"
+set logscale x 10
+set logscale y 10
+set yrange [1e-5:0.2]
+set grid
+set key outside
+
+plot "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $3 == 5) ? $2 : 1/0):4 every ::1 with linespoints title "theoretical", \
+     "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $3 == 5) ? $2 : 1/0):5 every ::1 with linespoints title "filter estimate", \
+     "plots/data/bloom_filter_stats.csv" using (($1 == 10000 && $3 == 5) ? $2 : 1/0):6 every ::1 with linespoints title "observed"

plots/gnuplot/fpp_vs_n.gp

@@ -0,0 +1,14 @@
+set datafile separator comma
+set terminal pngcairo size 1000,700 enhanced font "Arial,12"
+set output "plots/png/fpp_vs_n.png"
+
+set title "Bloom filter false-positive rate vs n (m=100000, k=5)"
+set xlabel "inserted keys (n)"
+set ylabel "false-positive rate"
+set logscale x 10
+set grid
+set key outside
+
+plot "plots/data/bloom_filter_stats.csv" using (($2 == 100000 && $3 == 5) ? $1 : 1/0):4 every ::1 with linespoints title "theoretical", \
+     "plots/data/bloom_filter_stats.csv" using (($2 == 100000 && $3 == 5) ? $1 : 1/0):5 every ::1 with linespoints title "filter estimate", \
+     "plots/data/bloom_filter_stats.csv" using (($2 == 100000 && $3 == 5) ? $1 : 1/0):6 every ::1 with linespoints title "observed"