Extend Math functionality

ddsrouter_utils/include/ddsrouter_utils/math/math.hpp

@@ -29,25 +29,85 @@ namespace eprosima {
 namespace ddsrouter {
 namespace utils {
 
+/**
+ * @brief Optimize % 2 operation
+ *
+ * @param number
+ *
+ * @return whether \c number is odd
+ */
+DDSROUTER_UTILS_DllAPI bool is_even(
+        uint32_t number) noexcept;
+
 /**
  * @brief Module (%) operation with performance optimization
  *
  * This function optimizes the % operation, that executes a division, by optimizing these cases:
- * - If the dividend is smaller or equal than the divisor, the result is the dividend
+ * - If the dividend is smaller than the divisor, the result is the dividend
+ * - If the dividend is equal than the divisor, the result is 0
  * - If the divisor is 2, the result is the dividend % 2 calculated by a logic AND operation
  * - If the divisor is a power of 2, the result is calculated by a logic AND operation
+ * - Otherwise uses % operation
  *
  * @param dividend Dividend
  * @param divisor Divisor (must be greater than 0 so the operation make sense)
  *
- * @attention if divisor is 0, the result is \c dividend
+ * @pre \c divisor must not be 0
+ *
+ * @return The result of the operation %
  *
- * @return The result of the operation
+ * @attention Do only use this function with non literal values. Literal values are optimized by compiler.
  */
 DDSROUTER_UTILS_DllAPI uint32_t fast_module(
         uint32_t dividend,
         uint32_t divisor) noexcept;
 
+/**
+ * @brief Integer Division (/) operation with performance optimization
+ *
+ * This function optimizes the / operation by optimizing these cases:
+ * - If \c dividend is smaller or equal than the \c, the result is \c dividend
+ * - If the \c is 2, the result is \c dividend % 2 calculated by a logic AND operation
+ * - If the \c is a power of 2, the result is calculated by a logic AND operation
+ * - Otherwise uses / operation
+ *
+ * @param dividend Dividend
+ * @param divisor Divisor
+ *
+ * @pre \c divisor must not be 0
+ *
+ * @return The result of the operation /
+ *
+ * @attention Do only use this function with non literal values. Literal values are optimized by compiler.
+ */
+DDSROUTER_UTILS_DllAPI uint32_t fast_division(
+        uint32_t dividend,
+        uint32_t divisor) noexcept;
+
+/**
+ * @brief Calculate the sum of an arithmetic progression from an initial to a final number.
+ *
+ * This function uses the fast operation to calculate an arithmetic sum:
+ * S = ((a1 + an) / 2) * (n)
+ *
+ * @pre \c interval must be greater than 0
+ * @pre \c steps must be greater than 0
+ *
+ * @param lowest lowest element of the arithmetic progression
+ * @param interval interval between two elements of the arithmetic progression
+ * @param steps number of steps of the arithmetic progression
+ *
+ * @return The result of the sum
+ *
+ * EXAMPLE OF USE
+ *   1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = arithmetic_progression_sum(1, 1, 10)
+ *   0 + 2 + 4 + 6 + 8 = arithmetic_progression_sum(0, 2, 5)
+ */
+DDSROUTER_UTILS_DllAPI uint32_t arithmetic_progression_sum(
+        uint32_t lowest,
+        uint32_t interval,
+        uint32_t steps) noexcept;
+
 } /* namespace utils */
 } /* namespace ddsrouter */
 } /* namespace eprosima */

ddsrouter_utils/src/cpp/math/math.cpp

@@ -21,12 +21,28 @@ namespace eprosima {
 namespace ddsrouter {
 namespace utils {
 
+#include <assert.h>
+
 #include <ddsrouter_utils/math/math.hpp>
 
+bool is_even(
+        uint32_t number) noexcept
+{
+    return (number & 0x1) == 0;
+}
+
+bool is_power_of_2(
+        uint32_t number) noexcept
+{
+    return number && (!(number & (number-1)));
+}
+
 uint32_t fast_module(
         uint32_t dividend,
         uint32_t divisor) noexcept
 {
+    assert(divisor != 0);
+
     if (dividend < divisor)
     {
         // Optimize to 1 operation [if]
@@ -42,13 +58,68 @@ uint32_t fast_module(
         // Optimize to 4 operations [if, if, if, and]
         return dividend & 1;
     }
+    else if (is_power_of_2(divisor))
+    {
+        // Optimize to ~6 operations [if, if, if, if(and), and]
+        return dividend & (divisor - 1);
+    }
+    else
+    {
+        // Not optimum
+        return dividend % divisor;
+    }
+}
+
+uint32_t fast_division(
+        uint32_t dividend,
+        uint32_t divisor) noexcept
+{
+    assert(divisor != 0);
+
+    if (dividend < divisor)
+    {
+        // Optimize to 1 operation [if]
+        return 0;
+    }
+    else if (dividend == divisor)
+    {
+        // Optimize to 2 operation [if, if]
+        return 1;
+    }
+    else if (divisor == 1)
+    {
+        // Optimize to 3 operations [if, if, if]
+        return dividend;
+    }
+    else if (divisor == 2)
+    {
+        // Optimize to 5 operations [if, if, if, if, swift]
+        return (dividend >> 1);
+    }
+    else if (is_power_of_2(divisor))
+    {
+        while (divisor != 1)
+        {
+            dividend >>= 1;
+            divisor >>= 1;
+        }
+        return dividend;
+    }
     else
     {
-        // Optimize to 7 operations [if, if, if, -, and, -, and] in case E(n){divisor = 2^n}
-        return divisor & (divisor - 1) ? dividend % divisor : dividend& (divisor - 1);
+        // Not optimum
+        return dividend / divisor;
     }
 }
 
+uint32_t arithmetic_progression_sum(
+        uint32_t lowest,
+        uint32_t interval,
+        uint32_t steps) noexcept
+{
+    return (((2 * lowest + ((steps - 1) * interval)) * steps) / 2);
+}
+
 } /* namespace utils */
 } /* namespace ddsrouter */
 } /* namespace eprosima */

ddsrouter_utils/test/unittest/math/CMakeLists.txt

@@ -20,7 +20,10 @@ set(TEST_SOURCES
     )
 
 set(TEST_LIST
+        is_even
         fast_module
+        fast_division
+        arithmetic_progression_sum
     )
 
 set(TEST_EXTRA_LIBRARIES

ddsrouter_utils/test/unittest/math/mathTest.cpp

@@ -26,11 +26,55 @@ namespace ddsrouter {
 namespace utils {
 namespace test {
 
-void compare_fast_module(
+uint32_t NUMBERS_TO_TEST = 1000;
+uint32_t NUMBERS_TO_TEST_SHORT = 100;
+
+bool compare_is_even(
+        uint32_t number)
+{
+    return (
+        is_even(number)
+        ==
+        number % 2 == 0);
+}
+
+bool compare_fast_module(
+        uint32_t dividend,
+        uint32_t divisor)
+{
+    return (
+        fast_module(dividend, divisor)
+        ==
+        dividend % divisor);
+}
+
+bool compare_fast_division(
         uint32_t dividend,
         uint32_t divisor)
 {
-    ASSERT_EQ(fast_module(dividend, divisor), dividend % divisor) << dividend << " % " << divisor;
+    return (
+        fast_division(dividend, divisor)
+        ==
+        dividend / divisor);
+}
+
+bool compare_arithmetic_progression_sum(
+        uint32_t lowest,
+        uint32_t interval,
+        uint32_t steps)
+{
+    uint32_t current_number = lowest;
+    uint32_t real_result = 0;
+    for (int i = 0; i < steps; ++i)
+    {
+        real_result += current_number;
+        current_number += interval;
+    }
+
+    return (
+        arithmetic_progression_sum(lowest, interval, steps)
+        ==
+        real_result);
 }
 
 } /* namespace test */
@@ -39,62 +83,66 @@ void compare_fast_module(
 } /* namespace eprosima */
 
 /**
- * Test \c is_file_accesible method
- *
- * CASES:
- * - dividend lower than divisor
- * - dividend equal to divisor
- * - divisor = 2
- * - divisor = 2^N
- * - divisor even no 2^N
- * - divisor odd
+ * Test \c is_even method
  */
-TEST(mathTest, fast_module)
+TEST(mathTest, is_even)
 {
-    // dividend lower than divisor
+    // calculate module in many cases
+    for (uint32_t number = 0; number < test::NUMBERS_TO_TEST; ++number)
     {
-        test::compare_fast_module(3, 4);
-        test::compare_fast_module(0, 4);
-        test::compare_fast_module(101223, 20921341);
-    }
-
-    // dividend equal to divisor
-    {
-        test::compare_fast_module(3, 3);
-        test::compare_fast_module(4, 4);
-        test::compare_fast_module(66666, 66666);
-    }
-
-    // divisor = 2
-    {
-        test::compare_fast_module(3, 2);
-        test::compare_fast_module(4, 2);
-        test::compare_fast_module(66666, 2);
-        test::compare_fast_module(431253426, 2);
+        ASSERT_TRUE(test::compare_is_even(number))
+            << number;
     }
+}
 
-    // divisor = 2^N
+/**
+ * Test \c fast_module method
+ */
+TEST(mathTest, fast_module)
+{
+    // calculate module in many cases
+    for (uint32_t dividend = 0; dividend < test::NUMBERS_TO_TEST; ++dividend)
     {
-        test::compare_fast_module(3, 4);
-        test::compare_fast_module(32, 8);
-        test::compare_fast_module(66666, 128);
-        test::compare_fast_module(431253426, 2048);
+        for (uint32_t divisor = 1; divisor < test::NUMBERS_TO_TEST; ++divisor)
+        {
+            ASSERT_TRUE(test::compare_fast_module(dividend, divisor))
+                << dividend << " % " << divisor;
+        }
     }
+}
 
-    // divisor even no 2^N
+/**
+ * Test \c fast_division method
+ */
+TEST(mathTest, fast_division)
+{
+    // calculate module in many cases
+    for (uint32_t dividend = 0; dividend < test::NUMBERS_TO_TEST; ++dividend)
     {
-        test::compare_fast_module(3, 8);
-        test::compare_fast_module(12, 10);
-        test::compare_fast_module(66666, 120);
-        test::compare_fast_module(431253426, 2040);
+        for (uint32_t divisor = 1; divisor < test::NUMBERS_TO_TEST; ++divisor)
+        {
+            ASSERT_TRUE(test::compare_fast_division(dividend, divisor))
+                << dividend << " % " << divisor;
+        }
     }
+}
 
-    // divisor odd
+/**
+ * Test \c arithmetic_progression_sum method
+ */
+TEST(mathTest, arithmetic_progression_sum)
+{
+    // calculate module in many cases
+    for (uint32_t lowest = 0; lowest < test::NUMBERS_TO_TEST_SHORT; ++lowest)
     {
-        test::compare_fast_module(3, 5);
-        test::compare_fast_module(12, 11);
-        test::compare_fast_module(66666, 127);
-        test::compare_fast_module(431253426, 2041);
+        for (uint32_t interval = 1; interval < test::NUMBERS_TO_TEST_SHORT; ++interval)
+        {
+            for (uint32_t steps = 1; steps < test::NUMBERS_TO_TEST_SHORT; ++steps)
+            {
+                ASSERT_TRUE(test::compare_arithmetic_progression_sum(lowest, interval, steps))
+                    << lowest << " , " << interval << " , " << steps;
+            }
+        }
     }
 }