Complex API

The complex number API serves as a replacement for C and C++'s <complex.h>, offering fast, accelerated approximations for each routine. The API is mostly modeled after C99's <complex.h>, although it also supports being used from C++ via shz::complex. The API also features shz_fft(), an SH4 optimized fast-fourier transform.

• C header: #include <sh4zam/shz_complex.h>
• C++ header: #include <sh4zam/shz_complex.hpp>
• C++ types: shz::complex
• Symbols: 52

Suffixes

Suffixes used in this module. The full list is in Naming and Suffixes.

• _fsrra: Uses FSRRA (fast approximate 1/sqrt(x)). The argument or denominator must be positive. Faster, less precise.

Preprocessor

Macros and preprocessor constants.

Symbol	Description
SHZ_CMPLXF	Initializes a complex number.
SHZ_CMPLXF32	Initializes a complex number.
SHZ_I	Unit imaginary constant, 'I'.

Basic

Basic operations on complex numbers.

Symbol	Description
shz_cinitf	Returns a complex number which has been initialized to contain the given component values.
shz_cpolarf	Returns a complex number with a magnitude of r, and a phase angle of theta (in radians).
shz_cequalf	Checks for equality between two complex numbers with either an absolute or relative tolerance.
shz_crealf	Returns the real component of a complex number.
shz_cimagf	Returns the imaginary component of a complex number.

Arithmetic

Arithmetic operations on complex numbers.

Symbol	Description
shz_caddf	Adds two complex numbers together and returns the result.
shz_csubf	Subtracts rhs from lhs and returns the complex result.
shz_cmulf	Multiplies two complex numbers together, returning the complex result.
shz_cdivf	Divides lhs by rhs, returning the complex result.
shz_cscalef	Scales both componets of the complex number, c, by the value, v, returning the result.
shz_crecipf	Returns the multiplicative inverse or reciprocal of the complex number, c.

Manipulation

Extract or modify complex components.

Symbol	Description
shz_cabsf	Returns the absolute value (or magnitude) of the complex number, c.
shz_inv_cabsf	Returns the inverse of the absolute value (or inverse of the magnitude) of the complex number, c.
shz_cnormf	Returns the squared magnitude of the complex number, c.
shz_cargf	Returns the phase angle of the complex number, c.
shz_conjf	Returns the complex conjugate of c.
shz_cprojf	Calculates the projection of the complex number, c, onto the Riemann sphere.

Transcendental

Complex transcendental functions.

Symbol	Description
shz_csqrtf	Computes and returns the complex square root of c.
shz_cpowf	Raises the complex base to the complex exp power, returning a complex result.
shz_cexpf	Returns the complex base e exponential of c.
shz_clogf	Computes and returns the complex natural logarithm of c.
shz_clog10f	Computes and returns the complex base 10 logarithm of c.

Spherical Trigonometry

Complex spherical trigonometric functions.

Symbol	Description
shz_csinf	Calculates and returns the complex sine of c.
shz_ccosf	Calculates and returns the complex cosine of c.
shz_ctanf	Calculates and returns the complex tangent of c.
shz_ccscf	Calculates and returns the complex cosecant of c.
shz_csecf	Calculates and returns the complex secant of c.
shz_ccotf	Calculates and returns the complex cotangent of c.
shz_casinf	Calculates and returns the complex arcsine of c.
shz_cacosf	Calculates and returns the complex arccosine of c.
shz_catanf	Calculates and returns the complex arctangent of c.
shz_cacscf	Calculates and returns the complex arccosecant of c.
shz_casecf	Calculates and returns the complex arcsecant of c.
shz_cacotf	Calculates and returns the complex arccotangent of c.

Hyperbolic Trigonometry

Complex hyperbolic trigonometric functions.

Symbol	Description
shz_csinhf	Calculates and returns the complex hyperbolic sine of c.
shz_ccoshf	Calculates and returns the complex hyperbolic cosine of c.
shz_ctanhf	Calculates and returns the complex hyperbolic tangent of c.
shz_ccschf	Calculates and returns the complex hyperbolic cosecant of c.
shz_csechf	Calculates and returns the complex hyperbolic secant of c.
shz_ccothf	Calculates and returns the complex hyperbolic cotangent of c.
shz_casinhf	Calculates and returns the complex hyperbolic arcsine of c.
shz_cacoshf	Calculates and returns the complex hyperbolic arccosine of c.
shz_catanhf	Calculates and returns the complex hyperbolic arctangent of c.
shz_cacschf	Calculates and returns the complex hyperbolic arccosecant of c.
shz_casechf	Calculates and returns the complex hyperbolic arcsecant of c.
shz_cacothf	Calculates and returns the complex hyperbolic arccotangent of c.

Signal Processing

Functions for processing complex signals.

Symbol	Description
shz_fft	Fast Fourier Transform.

Types

Symbol	Description
shz_complex_t	Represents a floating-point complex number real/imaginary pair.
shz_complex	shz_complex_t alias for those who don't like POSIX-style.