init

lab3/modules/iue-num/CMakeLists.txt

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+cmake_minimum_required(VERSION 3.28)
+
+# define CXX interface library
+
+    # define target & alias (for other projects consuming the "source-tree")
+    add_library(iue-num_num INTERFACE)
+
+    # define sources of target
+    target_sources(iue-num_num
+                    INTERFACE FILE_SET public_headers TYPE HEADERS BASE_DIRS ${PROJECT_SOURCE_DIR} FILES numerics.hpp)
+
+    # define installation step
+    install(TARGETS iue-num_num EXPORT iue-num-export 
+                                            FILE_SET public_headers DESTINATION "./")
+
+    # define test
+
+if(BUILD_TESTING AND PROJECT_IS_TOP_LEVEL)
+    add_executable(iue-num_num.test numerics.test.cpp)
+    target_link_libraries(iue-num_num.test iue-num_num)
+    add_test(NAME iue-num_num.test COMMAND iue-num_num.test)
+endif()
+
+# export targets for consuming cmake projects
+
+    # generate and install a .cmake file to allow dependend projects consuming the "install-tree" to import all targets
+    install(EXPORT iue-num-export DESTINATION "iue-num" )
+
+    # allow dependend projects consuming the "build-tree" to use all targets
+    export(EXPORT iue-num-export)

lab3/modules/iue-num/numerics.hpp

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+/// @file
+/// @brief Supporting functionality for numeric calculations with floating point values
+
+#pragma once
+
+#include <cmath> // std::abs, std::max, std::min
+
+namespace iue::num {
+
+/// @brief Checks if two floating point values are close to each other
+/// @param a First value
+/// @param b Second value
+/// @param tabs Tolerance for the absolute difference:
+///        abs(a - b) < tabs
+/// @param trel Tolerance for the relative error (using the larger absolute value as reference):
+///        abs(a  b) < trel * max(abs(a),abs(b))
+/// @return true if the stronger of the two tolerances is met, false otherwise
+inline bool isclose(double a, double b, double tabs = 0.0, double trel = 1e-9) {
+  if (a == b) // for infinite values (which should be considered close to themselves)
+    return true;
+  auto abs_diff = std::abs(a - b);                    // absolte difference
+  auto trel_ref = std::max(std::abs(a), std::abs(b)); // reference for the relative threshold
+  return abs_diff < std::max(tabs, trel * trel_ref);
+}
+
+} // namespace iue::num

lab3/modules/iue-num/numerics.test.cpp

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+/// @file
+/// @brief Test for iue::num::islcose
+
+#include "iue-num/numerics.hpp" // iue::num::islcose
+
+#include <cassert> // assert
+#include <cstdlib> // EXIT_SUCCESS
+#include <limits>  // std::numeric_limits
+
+int main() {
+
+  const double eps = std::numeric_limits<double>::epsilon();
+  const double inf = std::numeric_limits<double>::infinity();
+  const double nan = std::numeric_limits<double>::quiet_NaN();
+
+  { // infinity
+
+    assert(iue::num::isclose(inf, inf, 0.0, 0.0));
+    assert(iue::num::isclose(-inf, -inf, 0.0, 0.0));
+    assert(!iue::num::isclose(-inf, inf, 0.0, 0.0));
+    assert(!iue::num::isclose(inf, -inf, 0.0, 0.0));
+  }
+
+  { // nan
+    assert(!iue::num::isclose(nan, nan, inf, inf));
+  }
+
+  { // around 1.0
+    double a = 1.0;
+    double b = 1.0 + eps;
+
+    // rel error
+    assert(iue::num::isclose(a, b, 0.0, 2 * eps));
+    assert(!iue::num::isclose(a, b, 0.0, 0.0));
+
+    // abs error
+    assert(iue::num::isclose(a, b, 2 * eps, 0.0));
+    assert(!iue::num::isclose(a, b, 0.0, 0.0));
+  }
+
+  { // around 1e10
+    double a = 1.0 * 1e10;
+    double b = (1.0 + eps) * 1e10;
+
+    // rel error
+    assert(iue::num::isclose(a, b, 0.0, 2 * eps));
+    assert(!iue::num::isclose(a, b, 0.0, 0.0));
+
+    // abs error
+    assert(iue::num::isclose(a, b, 1e10 * 2 * eps, 0.0));
+    assert(!iue::num::isclose(a, b, 1e9 * 2 * eps, 0.0));
+  }
+
+  { // around 1e-10
+
+    double a = 1.0 * 1e-10;
+    double b = (1.0 + eps) * 1e-10;
+
+    // rel error
+    assert(iue::num::isclose(a, b, 0.0, 2 * eps));
+    assert(!iue::num::isclose(a, b, 0.0, 0.0));
+
+    // abs error
+    assert(iue::num::isclose(a, b, 1e-10 * 2 * eps, 0.0));
+    assert(!iue::num::isclose(a, b, 1e-11 * 2 * eps, 0.0));
+  }
+
+  return EXIT_SUCCESS;
+}