special_functions.hpp File Reference

#include <algorithm>
#include <cmath>
#include <limits>

Go to the source code of this file.

Namespaces
namespace	pulp
namespace	pulp::signal
namespace	pulp::signal::special

Functions
float	pulp::signal::sinc (float x)
	Sinc function: sin(pi*x) / (pi*x), with sinc(0) = 1.
float	pulp::signal::bessel_i0 (float x)
	Modified Bessel function of the first kind, order 0 Used in Kaiser window design.
float	pulp::signal::gamma_fn (float x)
	Gamma function approximation (Stirling's for large x, series for small).
float	pulp::signal::erf_fn (float x)
	Error function.
float	pulp::signal::erfc_fn (float x)
	Complementary error function.
float	pulp::signal::lanczos (float x, int a)
	Lanczos kernel (used in high-quality resampling).
float	pulp::signal::db_to_linear (float db)
	dB to linear gain conversion
float	pulp::signal::linear_to_db (float linear)
	Linear gain to dB conversion.
float	pulp::signal::freq_to_midi (float freq)
	Frequency to MIDI note number (A4 = 69).
float	pulp::signal::midi_to_freq (float note)
	MIDI note number to frequency.
double	pulp::signal::special::elliptic_K (double m)
	Complete elliptic integral of the first kind, K(m), m = k^2 in [0, 1).
double	pulp::signal::special::elliptic_E (double m)
	Complete elliptic integral of the second kind, E(m), m = k^2 in [0, 1].
double	pulp::signal::special::jacobi_nome (double m)
	Jacobi nome q(m) = exp(-pi * K(1 - m) / K(m)).
void	pulp::signal::special::jacobi_sncndn (double u, double m, double *sn_out, double *cn_out, double *dn_out)
	Jacobi elliptic functions sn(u, m), cn(u, m), dn(u, m) — all three at once because the AGM-based scheme produces them together.
double	pulp::signal::special::jacobi_sn (double u, double m)
	Convenience: sn(u, m).
double	pulp::signal::special::jacobi_cn (double u, double m)
	Convenience: cn(u, m).
double	pulp::signal::special::jacobi_dn (double u, double m)
	Convenience: dn(u, m).
double	pulp::signal::special::carlson_RF (double x, double y, double z)
	Carlson's symmetric elliptic integral of the first kind, RF(x, y, z).
double	pulp::signal::special::jacobi_asn (double x, double m)
	Inverse Jacobi sn: returns u such that sn(u, m) = x, for x in [-1, 1].

Variables
constexpr double	pulp::signal::special::kPi = 3.141592653589793238462643383279502884
	Pi as a double-precision constant. Used by every routine below.