Add benchmark tests

tc/test/test_solve_speed.cpp

@@ -0,0 +1,58 @@
+#include <iostream>
+#include <string>
+#include <vector>
+
+#include <tc/groups.hpp>
+#include <tc/core.hpp>
+
+int main(int argc, char *argv[]) {
+    std::string key = argv[1];
+
+    std::cerr << "Min. cos/s: " << MINIMUM_COS_PER_SEC << std::endl;
+    std::vector<std::tuple<std::string, tc::Group, std::vector<size_t>, size_t>> groups;
+
+    // See the group orders here https://en.wikipedia.org/wiki/Coxeter_group#Properties
+    if (key == "B") {
+        groups = {
+            {"B(7)", tc::group::B(7), {}, 645120},
+            {"B(8)", tc::group::B(8), {}, 10321920},
+        };
+    }
+    if (key == "E") {
+        groups = {
+            {"E(6)", tc::group::E(6), {}, 51840},
+            {"E(7)", tc::group::E(7), {}, 2903040},
+        };
+    }
+    if (key == "T") {
+        groups = {
+            {"T(500)",  tc::group::T(500),  {}, 1000000},
+            {"T(1000)", tc::group::T(1000), {}, 4000000},
+        };
+    }
+
+    int status = EXIT_SUCCESS;
+
+    for (const auto &[name, group, sub_gens, expected]: groups) {
+        auto t0 = clock();
+        auto cos = tc::solve(group, sub_gens);
+        auto t1 = clock();
+        auto actual = cos.size();
+
+        auto sec = (double) (t1 - t0) / CLOCKS_PER_SEC;
+        auto cos_per_sec = (double) actual / sec;
+
+        if (expected != actual) {
+            std::cerr << name << " wrong. " << actual << " (" << expected << ")" << std::endl;
+            status = EXIT_FAILURE;
+        }
+
+        std::cout << name << " cos/s: " << (size_t) cos_per_sec << std::endl;
+        if (cos_per_sec < MINIMUM_COS_PER_SEC) {
+            std::cerr << name << " too slow." << std::endl;
+            status = EXIT_FAILURE;
+        }
+    }
+
+    return status;
+}