algo/core/math: Add file for probability computation

Compute the minimal number of k-mers of an uncertainty range whose mean is
given by the empirical number of k-mers found.

The probability is provided as an integer as we don't have Z-scores for every
possible value and float comparison can be a bit tricky.

algo/core/math.cpp

+#include "math.hpp"
+#include <map>
+#include <cmath>
+#include <cassert>
+#include <string>
+#include "tools.h"
+
+using namespace std;
+
+const static map<int, float> Z_SCORES = {{90, 1.2816}, {95, 1.6449}, {99, 2.3263}, {999, 3.0902}};
+
+int compute_nb_kmers_limit(int kmer_size, int nb_occ, int sequence_length, int p_value) {
+  if (Z_SCORES.count(p_value) == 0) {
+    throw invalid_argument("You can't use a p_value of "+to_string(p_value));
+  }
+  float empirical_proba = nb_occ * 1. / (sequence_length - kmer_size + 1);
+  if (empirical_proba > 1)
+    return nb_occ;
+
+  float min_proba = empirical_proba - Z_SCORES.at(p_value) * sqrt(empirical_proba * (1 - empirical_proba) / (sequence_length - kmer_size + 1));
+  if (min_proba <= 0)
+    return 0;
+
+  // “Converts” the probability to a number of k-mers
+  return min_proba * (sequence_length - kmer_size + 1);
+}

algo/core/math.hpp

+#ifndef MATH_HPP
+#define MATH_HPP
+
+/**
+ * Compute the minimal number of k-mers that is not significantly different from nb_occ
+ * Given that the k-mers used are those used for `affect` on the sequence `sequence`.
+ * @param kmer_size: size of the kmer
+ * @param nb_occ: Number of occurrences found on this sequence
+ * @param sequence_length: The sequence length
+ * @param p_value: The p_value to be used. The lower the p_value, the lower the value will be returned
+ *                 Beware! The p_value must be given as an integer to prevent issues with float equalities.
+ *                 Therefore a pvalue of .95 should be given as 95 and a p-value of .999 should be given as 999.
+ *                 Not all p-values are possible. Please refer to the keys of Z_SCORES.
+ * @return The lower bound of the confidence interval assumuing that the center of the confidence 
+ *         interval is given by `nb_occ`. In all cases the returned value will be >= 0.
+ */
+int compute_nb_kmers_limit(int kmer_size, int nb_occ, int sequence_length, int p_value=95);
+
+#endif