shz_complex.h File Reference

#include "shz_cdefs.h"
#include <stddef.h>
#include <stdbool.h>
#include "inline/shz_complex.inl.h"

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Data Structures
struct	shz_complex_t

Macros
Preprocessor
Macros and preprocessor constants.
#define	SHZ_CMPLXF(x, y)
#define	SHZ_CMPLXF32(x, y)
#define	SHZ_I

Typedefs
typedef shz_complex_t	shz_complex

Functions
Basic
Basic operations on complex numbers.
shz_complex_t	shz_cinitf (float real, float imag) noexcept
shz_complex_t	shz_cpolarf (float r, float theta) noexcept
bool	shz_cequalf (shz_complex_t lhs, shz_complex_t rhs) noexcept
float	shz_crealf (shz_complex_t c) noexcept
float	shz_cimagf (shz_complex_t c) noexcept
Arithmetic
Arithmetic operations on complex numbers.
shz_complex_t	shz_caddf (shz_complex_t lhs, shz_complex_t rhs) noexcept
shz_complex_t	shz_csubf (shz_complex_t lhs, shz_complex_t rhs) noexcept
shz_complex_t	shz_cmulf (shz_complex_t lhs, shz_complex_t rhs) noexcept
shz_complex_t	shz_cdivf (shz_complex_t lhs, shz_complex_t rhs) noexcept
shz_complex_t	shz_cscalef (shz_complex_t c, float v) noexcept
shz_complex_t	shz_crecipf (shz_complex_t c) noexcept
Manipulation
Extract or modify complex components.
float	shz_cabsf (shz_complex_t c) noexcept
float	shz_inv_cabsf (shz_complex_t c) noexcept
float	shz_cnormf (shz_complex_t c) noexcept
float	shz_cargf (shz_complex_t c) noexcept
shz_complex_t	shz_conjf (shz_complex_t c) noexcept
shz_complex_t	shz_cprojf (shz_complex_t c) noexcept
Transcendental
Complex transcendental functions.
shz_complex_t	shz_csqrtf (shz_complex_t c) noexcept
shz_complex_t	shz_cpowf (shz_complex_t base, shz_complex_t exp) noexcept
shz_complex_t	shz_cexpf (shz_complex_t c) noexcept
shz_complex_t	shz_clogf (shz_complex_t c) noexcept
shz_complex_t	shz_clog10f (shz_complex_t c) noexcept
Spherical Trigonometry
Complex spherical trigonometric functions.
shz_complex_t	shz_csinf (shz_complex_t c) noexcept
shz_complex_t	shz_ccosf (shz_complex_t c) noexcept
shz_complex_t	shz_ctanf (shz_complex_t c) noexcept
shz_complex_t	shz_ccscf (shz_complex_t c) noexcept
shz_complex_t	shz_csecf (shz_complex_t c) noexcept
shz_complex_t	shz_ccotf (shz_complex_t c) noexcept
shz_complex_t	shz_casinf (shz_complex_t c) noexcept
shz_complex_t	shz_cacosf (shz_complex_t c) noexcept
shz_complex_t	shz_catanf (shz_complex_t c) noexcept
shz_complex_t	shz_cacscf (shz_complex_t c) noexcept
shz_complex_t	shz_casecf (shz_complex_t c) noexcept
shz_complex_t	shz_cacotf (shz_complex_t c) noexcept
Hyperbolic Trigonometry
Complex hyperbolic trigonometric functions.
shz_complex_t	shz_csinhf (shz_complex_t c) noexcept
shz_complex_t	shz_ccoshf (shz_complex_t c) noexcept
shz_complex_t	shz_ctanhf (shz_complex_t c) noexcept
shz_complex_t	shz_ccschf (shz_complex_t c) noexcept
shz_complex_t	shz_csechf (shz_complex_t c) noexcept
shz_complex_t	shz_ccothf (shz_complex_t c) noexcept
shz_complex_t	shz_casinhf (shz_complex_t c) noexcept
shz_complex_t	shz_cacoshf (shz_complex_t c) noexcept
shz_complex_t	shz_catanhf (shz_complex_t c) noexcept
shz_complex_t	shz_cacschf (shz_complex_t c) noexcept
shz_complex_t	shz_casechf (shz_complex_t c) noexcept
shz_complex_t	shz_cacothf (shz_complex_t c) noexcept
Signal Processing
Functions for processing complex signals.
void	shz_fft (shz_complex_t *s, size_t size) noexcept

Detailed Description

Complex number API.

This file contains a collection of routines for working with complex (real + imaginary) numbers. The API is mostly modeled after C99's <complex.h>, although it also supports being used from C++ as well.

Author

2026 Falco Girgis

Copyright

MIT License

Todo

• to/from shz_mat2x2_t and XMTRX
• FFT utilities
• inverse FFT

Definition in file shz_complex.h.

Macro Definition Documentation

SHZ_CMPLXF

#define SHZ_CMPLXF	(		x,
			y )

Initializes a complex number.

Definition at line 38 of file shz_complex.h.

SHZ_CMPLXF32

#define SHZ_CMPLXF32	(		x,
			y )

Initializes a complex number.

Definition at line 39 of file shz_complex.h.

SHZ_I

#define SHZ_I

Unit imaginary constant, 'I'.

Definition at line 40 of file shz_complex.h.

Typedef Documentation

shz_complex

typedef shz_complex_t shz_complex

shz_complex_t alias for those who don't like POSIX-style.

Definition at line 53 of file shz_complex.h.

Function Documentation

shz_cinitf()

shz_complex_t shz_cinitf ( float real, float imag )

noexcept

Returns a complex number which has been initialized to contain the given component values.

shz_cpolarf()

shz_complex_t shz_cpolarf ( float r, float theta )

noexcept

Returns a complex number with a magnitude of r, and a phase angle of theta (in radians).

shz_cequalf()

bool shz_cequalf ( shz_complex_t lhs, shz_complex_t rhs )

noexcept

Checks for equality between two complex numbers with either an absolute or relative tolerance.

shz_crealf()

float shz_crealf ( shz_complex_t c )

noexcept

Returns the real component of a complex number.

shz_cimagf()

float shz_cimagf ( shz_complex_t c )

noexcept

Returns the imaginary component of a complex number.

shz_caddf()

shz_complex_t shz_caddf ( shz_complex_t lhs, shz_complex_t rhs )

noexcept

Adds two complex numbers together and returns the result.

shz_csubf()

shz_complex_t shz_csubf ( shz_complex_t lhs, shz_complex_t rhs )

noexcept

Subtracts rhs from lhs and returns the complex result.

shz_cmulf()

shz_complex_t shz_cmulf ( shz_complex_t lhs, shz_complex_t rhs )

noexcept

Multiplies two complex numbers together, returning the complex result.

shz_cdivf()

shz_complex_t shz_cdivf ( shz_complex_t lhs, shz_complex_t rhs )

noexcept

Divides lhs by rhs, returning the complex result.

shz_cscalef()

shz_complex_t shz_cscalef ( shz_complex_t c, float v )

noexcept

Scales both componets of the complex number, c, by the value, v, returning the result.

shz_crecipf()

shz_complex_t shz_crecipf ( shz_complex_t c )

noexcept

Returns the multiplicative inverse or reciprocal of the complex number, c.

shz_cabsf()

float shz_cabsf ( shz_complex_t c )

noexcept

Returns the absolute value (or magnitude) of the complex number, c.

shz_inv_cabsf()

float shz_inv_cabsf ( shz_complex_t c )

noexcept

Returns the inverse of the absolute value (or inverse of the magnitude) of the complex number, c.

shz_cnormf()

float shz_cnormf ( shz_complex_t c )

noexcept

Returns the squared magnitude of the complex number, c.

shz_cargf()

float shz_cargf ( shz_complex_t c )

noexcept

Returns the phase angle of the complex number, c.

shz_conjf()

shz_complex_t shz_conjf ( shz_complex_t c )

noexcept

Returns the complex conjugate of c.

shz_cprojf()

shz_complex_t shz_cprojf ( shz_complex_t c )

noexcept

Calculates the projection of the complex number, c, onto the Riemann sphere.

shz_csqrtf()

shz_complex_t shz_csqrtf ( shz_complex_t c )

noexcept

Computes and returns the complex square root of c.

shz_cpowf()

shz_complex_t shz_cpowf ( shz_complex_t base, shz_complex_t exp )

noexcept

Raises the complex base to the complex exp power, returning a complex result.

shz_cexpf()

shz_complex_t shz_cexpf ( shz_complex_t c )

noexcept

Returns the complex base e exponential of c.

shz_clogf()

shz_complex_t shz_clogf ( shz_complex_t c )

noexcept

Computes and returns the complex natural logarithm of c.

shz_clog10f()

shz_complex_t shz_clog10f ( shz_complex_t c )

noexcept

Computes and returns the complex base 10 logarithm of c.

shz_csinf()

shz_complex_t shz_csinf ( shz_complex_t c )

noexcept

Calculates and returns the complex sine of c.

shz_ccosf()

shz_complex_t shz_ccosf ( shz_complex_t c )

noexcept

Calculates and returns the complex cosine of c.

shz_ctanf()

shz_complex_t shz_ctanf ( shz_complex_t c )

noexcept

Calculates and returns the complex tangent of c.

shz_ccscf()

shz_complex_t shz_ccscf ( shz_complex_t c )

noexcept

Calculates and returns the complex cosecant of c.

shz_csecf()

shz_complex_t shz_csecf ( shz_complex_t c )

noexcept

Calculates and returns the complex secant of c.

shz_ccotf()

shz_complex_t shz_ccotf ( shz_complex_t c )

noexcept

Calculates and returns the complex cotangent of c.

shz_casinf()

shz_complex_t shz_casinf ( shz_complex_t c )

noexcept

Calculates and returns the complex arcsine of c.

shz_cacosf()

shz_complex_t shz_cacosf ( shz_complex_t c )

noexcept

Calculates and returns the complex arccosine of c.

shz_catanf()

shz_complex_t shz_catanf ( shz_complex_t c )

noexcept

Calculates and returns the complex arctangent of c.

shz_cacscf()

shz_complex_t shz_cacscf ( shz_complex_t c )

noexcept

Calculates and returns the complex arccosecant of c.

shz_casecf()

shz_complex_t shz_casecf ( shz_complex_t c )

noexcept

Calculates and returns the complex arcsecant of c.

shz_cacotf()

shz_complex_t shz_cacotf ( shz_complex_t c )

noexcept

Calculates and returns the complex arccotangent of c.

shz_csinhf()

shz_complex_t shz_csinhf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic sine of c.

shz_ccoshf()

shz_complex_t shz_ccoshf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic cosine of c.

shz_ctanhf()

shz_complex_t shz_ctanhf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic tangent of c.

shz_ccschf()

shz_complex_t shz_ccschf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic cosecant of c.

shz_csechf()

shz_complex_t shz_csechf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic secant of c.

shz_ccothf()

shz_complex_t shz_ccothf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic cotangent of c.

shz_casinhf()

shz_complex_t shz_casinhf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arcsine of c.

shz_cacoshf()

shz_complex_t shz_cacoshf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arccosine of c.

shz_catanhf()

shz_complex_t shz_catanhf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arctangent of c.

shz_cacschf()

shz_complex_t shz_cacschf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arccosecant of c.

shz_casechf()

shz_complex_t shz_casechf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arcsecant of c.

shz_cacothf()

shz_complex_t shz_cacothf ( shz_complex_t c )

noexcept

Calculates and returns the complex hyperbolic arccotangent of c.

shz_fft()

void shz_fft ( shz_complex_t * s, size_t size )

noexcept

Fast Fourier Transform.

Applies a fast fourier transform to convert the complex array of samples, s, of the given size, from the time to the frequency domain. The conversion is done in-place.

Note

The underlying implementation uses the Radix2 variant of the Cooley-Tukey FFT algorithm, using an XMTRX-accelerated 2 point butterfly DIF.

Warning

size must be a power-of-two!

s must be aligned to 8-byte boundaries!

This routine clobbers XMTRX!