Add methods for computing Chebyshev polynomials (#528)

* Add methods for computing Chebyshev polynomials

* Add documentation

* Apply clang-format

* size_t instead of int

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>

modules/dsp/chowdsp_math/Math/chowdsp_ChebyshevPolynomials.h

@@ -0,0 +1,60 @@
+#pragma once
+
+namespace chowdsp
+{
+#ifndef DOXYGEN
+namespace cheby_detail
+{
+    template <typename T, size_t max_order = 32>
+    constexpr auto cheby0()
+    {
+        Polynomial<T, max_order, poly_order_ascending> poly {};
+        poly.coeffs[0] = static_cast<T> (1);
+        return poly;
+    }
+
+    template <typename T, size_t max_order = 32>
+    constexpr auto cheby1()
+    {
+        Polynomial<T, max_order, poly_order_ascending> poly {};
+        poly.coeffs[1] = static_cast<T> (1);
+        return poly;
+    }
+} // namespace cheby_detail
+#endif
+
+/** Recursively computes a Chebyshev polynomial given two previous Chebyshev polynomials */
+template <typename T, size_t max_order = 32>
+constexpr auto chebyshev_polynomial_recurse (const Polynomial<T, max_order, poly_order_ascending>& cheby_n1,
+                                             const Polynomial<T, max_order, poly_order_ascending>& cheby_n2)
+{
+    Polynomial<T, max_order, poly_order_ascending> cheby_n {};
+    cheby_n.coeffs[0] = -cheby_n2.coeffs[0];
+    for (size_t i = 1; i < max_order; ++i)
+        cheby_n.coeffs[i] = (T) 2 * cheby_n1.coeffs[i - 1] - cheby_n2.coeffs[i];
+    return cheby_n;
+}
+
+/** Computes a Chebyshev polynomial of a given order. */
+template <typename T, size_t order, size_t max_order = 32>
+constexpr auto chebyshev_polynomial()
+{
+    if constexpr (order == 0)
+        return cheby_detail::cheby0<T, 32>();
+
+    if constexpr (order == 1)
+        return cheby_detail::cheby1<T, 32>();
+
+    auto cheby_n2 = cheby_detail::cheby0<T, 32>();
+    auto cheby_n1 = cheby_detail::cheby1<T, 32>();
+    auto cheby_n = Polynomial<T, max_order, poly_order_ascending> {};
+    for (size_t i = 2; i <= order; ++i)
+    {
+        cheby_n = chebyshev_polynomial_recurse<T, max_order> (cheby_n1, cheby_n2);
+        cheby_n2 = cheby_n1;
+        cheby_n1 = cheby_n;
+    }
+
+    return cheby_n;
+}
+} // namespace chowdsp

modules/dsp/chowdsp_math/chowdsp_math.h

@@ -36,6 +36,7 @@ JUCE_END_IGNORE_WARNINGS_GCC_LIKE
 #include "Math/chowdsp_OtherMathOps.h"
 #include "Math/chowdsp_MatrixOps.h"
 #include "Math/chowdsp_Polynomials.h"
+#include "Math/chowdsp_ChebyshevPolynomials.h"
 #include "Math/chowdsp_Power.h"
 #include "Math/chowdsp_RandomFloat.h"
 #include "Math/chowdsp_JacobiElliptic.h"

tests/dsp_tests/chowdsp_math_test/CMakeLists.txt

@@ -6,6 +6,7 @@ target_sources(chowdsp_math_test
         FloatVectorOperationsTest.cpp
         MatrixOpsTest.cpp
         PolynomialsTest.cpp
+        ChebyshevPolynomialTest.cpp
         PowerTest.cpp
         OtherMathOpsTest.cpp
         JacobiEllipticTest.cpp

tests/dsp_tests/chowdsp_math_test/ChebyshevPolynomialTest.cpp

@@ -0,0 +1,23 @@
+#include <CatchUtils.h>
+#include <chowdsp_math/chowdsp_math.h>
+
+static void check_poly (const chowdsp::Polynomial<float, 32, chowdsp::poly_order_ascending>& cheby_poly,
+                        std::vector<float>&& actual)
+{
+    size_t i = 0;
+    for (; i < actual.size(); ++i)
+        REQUIRE (cheby_poly.coeffs[i] == Catch::Approx { actual[i] }.margin (1.0e-6));
+    for (; i < cheby_poly.coeffs.size(); ++i)
+        REQUIRE (cheby_poly.coeffs[i] == Catch::Approx { 0.0f }.margin (1.0e-6));
+}
+
+TEST_CASE ("Chebyshev Polynomials Test", "[dsp][math]")
+{
+    check_poly (chowdsp::chebyshev_polynomial<float, 2>(), { -1.0f, 0.0f, 2.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 3>(), { 0.0f, -3.0f, 0.0f, 4.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 4>(), { 1.0f, 0.0f, -8.0f, 0.0f, 8.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 5>(), { 0.0f, 5.0f, 0.0f, -20.0f, 0.0f, 16.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 6>(), { -1.0f, 0.0f, 18.0f, 0.0f, -48.0f, 0.0f, 32.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 7>(), { 0.0f, -7.0f, 0.0f, 56.0f, 0.0f, -112.0f, 0.0f, 64.0f });
+    check_poly (chowdsp::chebyshev_polynomial<float, 8>(), { 1.0f, 0.0f, -32.0f, 0.0f, 160.0f, 0.0f, -256.0f, 0.0f, 128.0f });
+}