added UnitCircle with sine and cosine functions

README.md

@@ -72,3 +72,9 @@ Some everyday helpers:
 When working with [Analog-to-digital](https://en.wikipedia.org/wiki/Analog-to-digital_converter) and [Digital-to-analog](https://en.wikipedia.org/wiki/Digital-to-analog_converter) converters, we often face the ugly truth, that we can't always have a precise [Sampling](https://en.wikipedia.org/wiki/Sampling_(signal_processing)) rate.
 But if we can estimate the Sampling frequency offset, we can correct it by [Resampling](https://en.wikipedia.org/wiki/Sample-rate_conversion) the sampled data.
 
+### [unit_circle.hh](unit_circle.hh)
+
+Sometimes we only need [trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions) that stay on the [unit circle](https://en.wikipedia.org/wiki/Unit_circle):
+* [sine function](https://en.wikipedia.org/wiki/Sine)
+* [cosine function](https://en.wikipedia.org/wiki/Trigonometric_functions#cosine)
+

tests/unit_circle_test.cc

@@ -0,0 +1,35 @@
+/*
+Test for the UnitCircle functions
+
+Copyright 2019 Ahmet Inan <inan@aicodix.de>
+*/
+
+#include <cassert>
+#include <iostream>
+#include <limits>
+#include <cmath>
+#include "unit_circle.hh"
+#include "const.hh"
+
+template <typename TYPE, typename PRECISE>
+void test(int MAX)
+{
+	for (int N = 1; N <= MAX; ++N) {
+		for (int n = 0; n < N; ++n) {
+			PRECISE x = DSP::Const<PRECISE>::TwoPi() * PRECISE(n) / PRECISE(N);
+			PRECISE cos_err = std::abs(DSP::UnitCircle<TYPE>::cos(n, N) - std::cos(x));
+			assert(cos_err < std::numeric_limits<TYPE>::epsilon());
+			PRECISE sin_err = std::abs(DSP::UnitCircle<TYPE>::sin(n, N) - std::sin(x));
+			assert(sin_err < std::numeric_limits<TYPE>::epsilon());
+		}
+	}
+}
+
+int main()
+{
+	test<float, double>(5000);
+	test<double, long double>(5000);
+	std::cerr << "UnitCircle functions test passed!" << std::endl;
+	return 0;
+}
+

unit_circle.hh

@@ -0,0 +1,77 @@
+/*
+Trigonometric functions on the unit circle
+
+Constants below lifted from the Cephes Mathematical Library:
+https://www.netlib.org/cephes/cmath.tgz
+
+Copyright 2019 Ahmet Inan <inan@aicodix.de>
+*/
+
+#pragma once
+
+#include "const.hh"
+
+namespace DSP {
+
+template <typename TYPE>
+class UnitCircle
+{
+	static constexpr TYPE
+		a1 = 1.0,
+		a2 = -0.5,
+		a3 = -1.66666666666666307295E-1,
+		a4 = 4.16666666666665929218E-2,
+		a5 = 8.33333333332211858878E-3,
+		a6 = -1.38888888888730564116E-3,
+		a7 = -1.98412698295895385996E-4,
+		a8 = 2.48015872888517045348E-5,
+		a9 = 2.75573136213857245213E-6,
+		a10 = -2.75573141792967388112E-7,
+		a11 = -2.50507477628578072866E-8,
+		a12 = 2.08757008419747316778E-9,
+		a13 = 1.58962301576546568060E-10,
+		a14 = -1.13585365213876817300E-11;
+
+	static constexpr TYPE cosine_kernel(TYPE xx)
+	{
+		return a1 + xx * (xx * (xx * (xx * (xx * (xx * (xx * a14 + a12) + a10) + a8) + a6) + a4) + a2);
+	}
+	static constexpr TYPE sine_kernel(TYPE x, TYPE xx)
+	{
+		return x * (xx * (xx * (xx * (xx * (xx * (xx * a13 + a11) + a9) + a7) + a5) + a3) + a1);
+	}
+	static constexpr TYPE cosine_approx(TYPE x)
+	{
+		return cosine_kernel(x * x);
+	}
+	static constexpr TYPE sine_approx(TYPE x)
+	{
+		return sine_kernel(x, x * x);
+	}
+public:
+	static constexpr TYPE rad(int n, int N)
+	{
+		return Const<TYPE>::TwoPi() * TYPE(n) / TYPE(N);
+	}
+	static constexpr TYPE cos(int n, int N)
+	{
+		return
+			8*n < 1*N ? cosine_approx(rad(n, N)) :
+			8*n < 3*N ? -sine_approx(rad(4*n-N, 4*N)) :
+			8*n < 5*N ? -cosine_approx(rad(2*n-N, 2*N)) :
+			8*n < 7*N ? sine_approx(rad(4*n-3*N, 4*N)) :
+			cosine_approx(rad(n-N, N));
+	}
+	static constexpr TYPE sin(int n, int N)
+	{
+		return
+			8*n < 1*N ? sine_approx(rad(n, N)) :
+			8*n < 3*N ? cosine_approx(rad(4*n-N, 4*N)) :
+			8*n < 5*N ? -sine_approx(rad(2*n-N, 2*N)) :
+			8*n < 7*N ? -cosine_approx(rad(4*n-3*N, 4*N)) :
+			sine_approx(rad(n-N, N));
+	}
+};
+
+}
+