Adding sin and cosine approximations

include/math_approx/math_approx.hpp

@@ -8,3 +8,4 @@ namespace math_approx
 
 #include "src/tanh_approx.hpp"
 #include "src/sigmoid_approx.hpp"
+#include "src/sin_approx.hpp"

include/math_approx/src/basic_math.hpp

@@ -36,6 +36,12 @@ T rsqrt (T x)
     //    return x * r;
 }
 
+template <typename T>
+T select (bool q, T t, T f)
+{
+    return q ? t : f;
+}
+
 #if defined(XSIMD_HPP)
 template <typename T>
 struct scalar_of<xsimd::batch<T>>
@@ -54,5 +60,11 @@ xsimd::batch<T> rsqrt (xsimd::batch<T> x)
     r *= (S) -0.5;
     return x * r;
 }
+
+template <typename T>
+xsimd::batch<T> select (xsimd::batch_bool<T> q, xsimd::batch<T> t, xsimd::batch<T> f)
+{
+    return xsimd::select (q, t, f);
+}
 #endif
 } // namespace math_approx

include/math_approx/src/tanh_approx.hpp

@@ -67,7 +67,7 @@ namespace tanh_detail
 template <int order, typename T>
 T tanh (T x)
 {
-    static_assert (order % 2 == 1 && order <= 11 && order >= 3, "Order must e an odd number within [3, 9]");
+    static_assert (order % 2 == 1 && order <= 11 && order >= 3, "Order must e an odd number within [3, 11]");
 
     T x_poly {};
     if constexpr (order == 11)

test/CMakeLists.txt

@@ -30,3 +30,5 @@ endfunction(setup_catch_test)
 
 setup_catch_test(tanh_approx_test)
 setup_catch_test(sigmoid_approx_test)
+setup_catch_test(sin_approx_test)
+setup_catch_test(cos_approx_test)

test/src/cos_approx_test.cpp

@@ -1,3 +1,46 @@
-//
-// Created by jatin on 11/22/23.
-//
+#include "test_helpers.hpp"
+#include <catch2/catch_test_macros.hpp>
+#include <iostream>
+
+#include <math_approx/math_approx.hpp>
+
+TEST_CASE ("Cosine Approx Test")
+{
+#if ! defined(WIN32)
+    const auto all_floats = test_helpers::all_32_bit_floats (-10.0f, 10.0f, 1.0e-3f);
+#else
+    const auto all_floats = test_helpers::all_32_bit_floats (-10.0f, 10.0f, 1.0e-1f);
+#endif
+    const auto y_exact = test_helpers::compute_all (all_floats, [] (auto x)
+                                                    { return std::cos (x); });
+
+    const auto test_approx = [&all_floats, &y_exact] (auto&& f_approx, float err_bound)
+    {
+        const auto y_approx = test_helpers::compute_all (all_floats, f_approx);
+
+        const auto error = test_helpers::compute_error (y_exact, y_approx);
+        const auto max_error = test_helpers::abs_max (error);
+
+        std::cout << max_error << std::endl;
+        REQUIRE (std::abs (max_error) < err_bound);
+    };
+
+    SECTION ("9th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::cos<9> (x); },
+                     7.0e-7f);
+    }
+    SECTION ("7th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::cos<7> (x); },
+                     1.8e-5f);
+    }
+    SECTION ("5th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::cos<5> (x); },
+                     7.5e-4f);
+    }
+}

test/src/sin_approx_test.cpp

@@ -1,3 +1,46 @@
-//
-// Created by jatin on 11/22/23.
-//
+#include "test_helpers.hpp"
+#include <catch2/catch_test_macros.hpp>
+#include <iostream>
+
+#include <math_approx/math_approx.hpp>
+
+TEST_CASE ("Sine Approx Test")
+{
+#if ! defined(WIN32)
+    const auto all_floats = test_helpers::all_32_bit_floats (-10.0f, 10.0f, 1.0e-3f);
+#else
+    const auto all_floats = test_helpers::all_32_bit_floats (-10.0f, 10.0f, 1.0e-1f);
+#endif
+    const auto y_exact = test_helpers::compute_all (all_floats, [] (auto x)
+                                                    { return std::sin (x); });
+
+    const auto test_approx = [&all_floats, &y_exact] (auto&& f_approx, float err_bound)
+    {
+        const auto y_approx = test_helpers::compute_all (all_floats, f_approx);
+
+        const auto error = test_helpers::compute_error (y_exact, y_approx);
+        const auto max_error = test_helpers::abs_max (error);
+
+        // std::cout << max_error << std::endl;
+        REQUIRE (std::abs (max_error) < err_bound);
+    };
+
+    SECTION ("9th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::sin<9> (x); },
+                     8.5e-7f);
+    }
+    SECTION ("7th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::sin<7> (x); },
+                     1.8e-5f);
+    }
+    SECTION ("5th-Order")
+    {
+        test_approx ([] (auto x)
+                     { return math_approx::sin<5> (x); },
+                     7.5e-4f);
+    }
+}

tools/plotter/plotter.cpp

@@ -57,19 +57,17 @@ void plot_function (std::span<const float> all_floats,
 int main()
 {
     plt::figure();
-    const auto range = std::make_pair (-10.0f, 10.0f);
+    const auto range = std::make_pair (-3.141f, 3.141f);
     static constexpr auto tol = 1.0e-2f;
 
     const auto all_floats = test_helpers::all_32_bit_floats (range.first, range.second, tol);
     const auto y_exact = test_helpers::compute_all (all_floats, [] (float x)
-                                                    { return 1.0f / (1.0f + std::exp (-x)); });
+                                                    { return std::cos (x); });
 
-    plot_error (
-        all_floats,
-        y_exact,
-        [] (float x)
-        { return math_approx::sigmoid_exp<3> (x); },
-        "Sigmoid-Exp-5");
+    // // plot_error (all_floats, y_exact, [] (float x) { return math_approx::sin<5> (x); }, "Sin-5");
+    // // plot_error (all_floats, y_exact, [] (float x) { return math_approx::sin<7> (x); }, "Sin-7");
+    plot_ulp_error (all_floats, y_exact, [] (float x) { return math_approx::cos_mpi_pi<9> (x); }, "Cos-9");
+    // plot_function (all_floats, [] (float x) { return math_approx::cos_mpi_pi<9> (x); }, "Cos-9");
 
     plt::legend ({ { "loc", "upper right" } });
     plt::xlim (range.first, range.second);