Add dsp/approx.hpp.

include/dsp/approx.hpp

@@ -0,0 +1,42 @@
+#pragma once
+#include <dsp/common.hpp>
+
+
+namespace rack {
+namespace dsp {
+
+
+/*
+In this header, function names are divided into two or more parts, separated by "_".
+The functionality is the first part, and the approximation methods are the following parts.
+
+Glossary:
+https://en.wikipedia.org/wiki/Taylor_series
+https://en.wikipedia.org/wiki/Pad%C3%A9_approximant
+https://en.wikipedia.org/wiki/Horner%27s_method
+https://en.wikipedia.org/wiki/Estrin%27s_scheme
+*/
+
+
+/** Returns 2^x, assuming that x >= 0.
+Maximum 0.00024% error.
+Roughly 7x faster than `std::pow(2, x)`.
+
+If negative powers are needed, you may use a lower bound and rescale.
+
+	approxExp2(x + 20) / 1048576
+*/
+template <typename T>
+T approxExp2_taylor5(T x) {
+	int xi = x;
+	x -= xi;
+	T y = 1 << xi;
+	// Fifth order expansion of 2^x around 0.4752 in Horner form.
+	// The center is chosen so that the endpoints of [0, 1] have equal error, creating no discontinuity at integers.
+	y *= T(0.9999976457798443) + x * (T(0.6931766804601935) + x * (T(0.2400729486415728) + x * (T(0.05592817518644387) + x * (T(0.008966320633544) + x * T(0.001853512473884202)))));
+	return y;
+}
+
+
+} // namespace dsp
+} // namespace rack

include/rack.hpp

@@ -91,6 +91,7 @@
 #include <dsp/ringbuffer.hpp>
 #include <dsp/vumeter.hpp>
 #include <dsp/window.hpp>
+#include <dsp/approx.hpp>
 
 #include <simd/vector.hpp>
 #include <simd/functions.hpp>