Prevent NaN values for LLR

app/src/matchmaking/sprt/sprt.cpp

@@ -74,6 +74,11 @@ static double regularize(int value) {
     return value;
 }
 
+static double regularize(double value) {
+    if (value <= 1e-32) return 1e-32;
+    return value;
+}
+
 double SPRT::getLLR(const Stats& stats, bool penta) const noexcept {
     if (penta)
         return getLLR(stats.penta_WW, stats.penta_WD, stats.penta_WL, stats.penta_DD, stats.penta_LD, stats.penta_LL);
@@ -176,8 +181,8 @@ static double itp(F f, double a, double b, double f_a, double f_b, double k_1, d
 
         double x_f = (f_b * a - f_a * b) / (f_b - f_a);
 
-        double sigma = (x_half - x_f) / std::abs(x_half - x_f);
-        double x_t   = delta <= std::abs(x_half - x_f) ? x_f + sigma * delta : x_half;
+        int sigma  = (x_half - x_f) >= 0 ? 1 : -1;
+        double x_t = delta <= std::abs(x_half - x_f) ? x_f + sigma * delta : x_half;
 
         double x_itp = std::abs(x_t - x_half) <= r ? x_t : x_half - sigma * r;
 
@@ -204,7 +209,7 @@ double SPRT::getLLR_logistic(double total, std::array<double, N> scores, std::ar
     // given an empirical distribution. See proposition 1.1 of [1] for details.
     //
     // [1]: Michel Van den Bergh, Comments on Normalized Elo,
-    // https://www.cantate.be/Fishtest/normalized_elo_practical.pdf
+    // https://www.cantate.be/Fishtest/comparing_approximations.pdf
     const auto mle = [&](double s) -> std::array<double, N> {
         const double theta_epsilon = 1e-3;
 
@@ -236,7 +241,9 @@ double SPRT::getLLR_logistic(double total, std::array<double, N> scores, std::ar
     std::array<double, N> p0 = mle(s0);
     std::array<double, N> p1 = mle(s1);
     std::array<double, N> lpr;
-    for (size_t i = 0; i < N; i++) lpr[i] = std::log(p1[i]) - std::log(p0[i]);
+    for (size_t i = 0; i < N; i++)
+        lpr[i] = std::log(regularize(p1[i])) - std::log(regularize(p0[i]));
+
     return total * mean(lpr, probs);
 }
 
@@ -249,6 +256,7 @@ double SPRT::getLLR_normalized(double total, std::array<double, N> scores, std::
     // [1]: Michel Van den Bergh, Comments on Normalized Elo,
     // https://www.cantate.be/Fishtest/normalized_elo_practical.pdf
     const auto mle = [&](double mu_ref, double t_star) -> std::array<double, N> {
+        const double var_epsilon   = 1e-15;
         const double theta_epsilon = 1e-7;
         const double mle_epsilon   = 1e-4;
 
@@ -260,10 +268,14 @@ double SPRT::getLLR_normalized(double total, std::array<double, N> scores, std::
         for (int iterations = 0; iterations < 10; iterations++) {
             // Calculate phi.
             auto [mu, var] = mean_and_variance(scores, p);
+
+            // Variance too small?
+            if (var < var_epsilon) break;
+
+            double sigma = std::sqrt(var);
             std::array<double, N> phi;
             for (size_t i = 0; i < N; i++) {
                 double a_i   = scores[i];
-                double sigma = std::sqrt(var);
                 phi[i] = a_i - mu_ref - 0.5 * t_star * sigma * (1.0 + ((a_i - mu) / sigma) * ((a_i - mu) / sigma));
             }
 
@@ -305,7 +317,9 @@ double SPRT::getLLR_normalized(double total, std::array<double, N> scores, std::
     std::array<double, N> p0 = mle(0.5, t0);
     std::array<double, N> p1 = mle(0.5, t1);
     std::array<double, N> lpr;
-    for (size_t i = 0; i < N; i++) lpr[i] = std::log(p1[i]) - std::log(p0[i]);
+    for (size_t i = 0; i < N; i++)
+        lpr[i] = std::log(regularize(p1[i])) - std::log(regularize(p0[i]));
+
     return total * mean(lpr, probs);
 }