add(numerics): add prime number generator/iterator

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/tests/util/numerics/CMakeLists.txt

@@ -19,3 +19,6 @@ add_test(float ${CMAKE_CURRENT_BINARY_DIR}/float)
 add_executable(xnumeral xnumeral.cpp)
 target_link_libraries(xnumeral ${EXTRA_LIBS})
 add_test(xnumeral ${CMAKE_CURRENT_BINARY_DIR}/xnumeral)
+add_executable(primes primes.cpp)
+target_link_libraries(primes ${EXTRA_LIBS})
+add_test(primes ${CMAKE_CURRENT_BINARY_DIR}/primes)

src/tests/util/numerics/primes.cpp

@@ -0,0 +1,31 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include <iostream>
+#include "util/test.h"
+#include "util/numerics/primes.h"
+using namespace lean;
+
+#define NUM_SMALL_PRIMES 168
+static uint64 small_primes[NUM_SMALL_PRIMES] = {
+    2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997
+};
+
+static void tst1() {
+    prime_iterator it;
+    for (unsigned i = 0; i < NUM_SMALL_PRIMES; i++) {
+        uint64 p = it.next();
+        lean_assert_eq(p, small_primes[i]);
+        std::cout << p << " ";
+    }
+    std::cout << "\n";
+}
+
+int main() {
+    tst1();
+    return has_violations() ? 1 : 0;
+}
+

src/util/numerics/CMakeLists.txt

@@ -1,2 +1,2 @@
-add_library(numerics gmp_init.cpp mpz.cpp mpq.cpp mpbq.cpp mpfp.cpp float.cpp double.cpp numeric_traits.cpp)
+add_library(numerics gmp_init.cpp mpz.cpp mpq.cpp mpbq.cpp mpfp.cpp float.cpp double.cpp numeric_traits.cpp primes.cpp)
 target_link_libraries(numerics ${LEAN_LIBS} ${EXTRA_LIBS})

src/util/numerics/primes.cpp

@@ -0,0 +1,109 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include <vector>
+#include <mutex>
+#include "util/uint64.h"
+#include "util/debug.h"
+#include "util/exception.h"
+#include "util/numerics/primes.h"
+
+#ifndef LEAN_PRIME_LIST_MAX_SIZE
+#define LEAN_PRIME_LIST_MAX_SIZE 1<<20
+#endif
+
+namespace lean {
+class prime_generator {
+    std::vector<uint64> m_primes;
+    void process_next_k_numbers(uint64 k) {
+        std::vector<uint64> todo;
+        uint64 begin = m_primes.back() + 2;
+        uint64 end   = begin + k;
+        for (uint64 i = begin; i < end; i += 2) {
+            todo.push_back(i);
+        }
+        unsigned j = 1;
+        lean_assert(m_primes[j] == 3);
+        while (!todo.empty()) {
+            unsigned sz = m_primes.size();
+            for (; j < sz; j++) {
+                uint64 p = m_primes[j];
+                unsigned todo_sz = todo.size();
+                unsigned k1 = 0;
+                unsigned k2 = 0;
+                for (; k1 < todo_sz; k1++) {
+                    if (todo[k1] % p == 0)
+                        continue;
+                    todo[k2] = todo[k1];
+                    k2++;
+                }
+                todo.resize(k2);
+                if (k2 == 0)
+                    return;
+                if (p > (todo[k2-1] / p) + 1) {
+                    // all numbers in todo are primes
+                    for (unsigned k1 = 0; k1 < k2; k1++) {
+                        m_primes.push_back(todo[k1]);
+                    }
+                    return;
+                }
+            }
+            uint64 p = m_primes.back();
+            p = p*p;
+            unsigned todo_sz = todo.size();
+            unsigned k1 = 0;
+            for (k1 = 0; k1 < todo_sz; k1++) {
+                if (todo[k1] < p) {
+                    m_primes.push_back(todo[k1]);
+                }
+                break;
+            }
+            unsigned k2 = 0;
+            for (; k1 < todo_sz; k1++, k2++) {
+                todo[k2] = todo[k1];
+            }
+            todo.resize(k2);
+        }
+    }
+
+public:
+    prime_generator() {
+        m_primes.push_back(2);
+        m_primes.push_back(3);
+        process_next_k_numbers(128);
+    }
+
+    uint64 operator()(unsigned idx) {
+        if (idx < m_primes.size())
+            return m_primes[idx];
+        if (idx > LEAN_PRIME_LIST_MAX_SIZE)
+            throw exception("prime generator capacity exceeded");
+        process_next_k_numbers(1024);
+        if (idx < m_primes.size())
+            return m_primes[idx];
+        while (idx <= m_primes.size())
+            process_next_k_numbers(1024*16);
+        return m_primes[idx];
+    }
+};
+
+static prime_generator g_prime_generator;
+static std::mutex      g_prime_generator_mutex;
+
+
+prime_iterator::prime_iterator():
+    m_idx(0) {
+}
+
+uint64 prime_iterator::next() {
+    unsigned idx = m_idx;
+    m_idx++;
+    {
+        std::lock_guard<std::mutex> guard(g_prime_generator_mutex);
+        return g_prime_generator(idx);
+    }
+}
+}

src/util/numerics/primes.h

@@ -0,0 +1,19 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "util/uint64.h"
+
+namespace lean {
+/**
+   \brief Prime number iterator. It can be used to enumerate the first LEAN_PRIME_LIST_MAX_SIZE primes.
+*/
+class prime_iterator {
+    unsigned m_idx;
+public:
+    prime_iterator();
+    uint64 next();
+};
+}

src/util/uint64.h

@@ -0,0 +1,10 @@
+/*
+Copyright (c) 2013 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+namespace lean {
+typedef unsigned long long uint64;
+static_assert(sizeof(uint64) == 8, "unexpected uint64 size");
+}