sieve of eratosthenes

include/bmath/sieve.hh

@@ -1,6 +1,60 @@
 #ifndef BMATH_SIEVE_HH
 #define BMATH_SIEVE_HH
 
-namespace bmath {};
+#include <bitset>
+#include <cstdint>
+#include <format>
+#include <stdexcept>
+
+namespace bmath {
+
+template <typename Derived, size_t Limit>
+  requires(Limit > 0)
+class Sieve {
+ public:
+  constexpr explicit Sieve() { static_cast<Derived *>(this)->build(); }
+
+ protected:
+  std::bitset<Limit + 1> sieve;
+};
+
+template <size_t Limit>
+  requires(Limit > 0)
+class Eratosthenes : public Sieve<Eratosthenes<Limit>, Limit> {
+ public:
+  constexpr void build() noexcept {
+    this->sieve.set();
+    this->sieve[0] = false;
+    this->sieve[1] = false;
+
+    for (size_t x = 2; x * x <= Limit; ++x) {
+      if (!this->sieve[x]) {
+        continue;
+      }
+
+      for (size_t current = x + x; current <= Limit; current += x) {
+        this->sieve[current] = false;
+      }
+    }
+  }
+
+  [[nodiscard]] constexpr bool operator[](size_t const number) const {
+    if consteval {
+      if (number > Limit) {
+        throw std::out_of_range(std::format(
+            "cannot determine primality of {} > LIMIT={}", number, Limit));
+      }
+    } else {
+      if (number > Limit) {
+        throw std::out_of_range(std::format(
+            "cannot determine primality of {} > LIMIT={}", number, Limit));
+      }
+    }
+
+    return this->sieve[number];
+  };
+};
+
+}  // namespace bmath
 
 #endif