complex number

Collaboration diagram for complex number:

Data Structures
struct	a_complex
	instance structure for complex number More...

Macros
#define	A_COMPLEX_C(real, imag)
#define	a_complex_c(x)
#define	a_complex_(_, x)

Typedefs
typedef struct a_complex	a_complex
	instance structure for complex number

Functions
static void	a_complex_rect (a_complex *ctx, a_real real, a_real imag)
	constructs a complex number from real and imaginary parts
void	a_complex_polar (a_complex *ctx, a_real rho, a_real theta)
	constructs a complex number from polar form
unsigned int	a_complex_parse (a_complex *ctx, char const *str)
	parse a string into a complex number
a_bool	a_complex_eq (a_complex x, a_complex y)
	complex number x is equal to complex number y
a_bool	a_complex_ne (a_complex x, a_complex y)
	complex number x is not equal to complex number y
a_real	a_complex_logabs (a_complex z)
	computes the natural logarithm of magnitude of a complex number
a_real	a_complex_abs2 (a_complex z)
	computes the squared magnitude of a complex number
a_real	a_complex_abs (a_complex z)
	computes the magnitude of a complex number
a_real	a_complex_arg (a_complex z)
	computes the phase angle of a complex number
void	a_complex_proj (a_complex *ctx, a_complex z)
	computes the projection on Riemann sphere
void	a_complex_proj_ (a_complex *ctx)
void	a_complex_conj (a_complex *ctx, a_complex z)
	computes the complex conjugate
void	a_complex_conj_ (a_complex *ctx)
void	a_complex_neg (a_complex *ctx, a_complex z)
	computes the complex negative
void	a_complex_neg_ (a_complex *ctx)
void	a_complex_add (a_complex *ctx, a_complex x, a_complex y)
	addition of complex numbers
void	a_complex_add_ (a_complex *ctx, a_complex z)
void	a_complex_add_real (a_complex *ctx, a_complex x, a_real y)
void	a_complex_add_real_ (a_complex *ctx, a_real x)
void	a_complex_add_imag (a_complex *ctx, a_complex x, a_real y)
void	a_complex_add_imag_ (a_complex *ctx, a_real x)
void	a_complex_sub (a_complex *ctx, a_complex x, a_complex y)
	subtraction of complex numbers
void	a_complex_sub_ (a_complex *ctx, a_complex z)
void	a_complex_sub_real (a_complex *ctx, a_complex x, a_real y)
void	a_complex_sub_real_ (a_complex *ctx, a_real x)
void	a_complex_sub_imag (a_complex *ctx, a_complex x, a_real y)
void	a_complex_sub_imag_ (a_complex *ctx, a_real x)
void	a_complex_mul (a_complex *ctx, a_complex x, a_complex y)
	multiplication of complex numbers
void	a_complex_mul_ (a_complex *ctx, a_complex z)
void	a_complex_mul_real (a_complex *ctx, a_complex x, a_real y)
void	a_complex_mul_real_ (a_complex *ctx, a_real x)
void	a_complex_mul_imag (a_complex *ctx, a_complex x, a_real y)
void	a_complex_mul_imag_ (a_complex *ctx, a_real x)
void	a_complex_div (a_complex *ctx, a_complex x, a_complex y)
	division of complex numbers
void	a_complex_div_ (a_complex *ctx, a_complex z)
void	a_complex_div_real (a_complex *ctx, a_complex x, a_real y)
void	a_complex_div_real_ (a_complex *ctx, a_real x)
void	a_complex_div_imag (a_complex *ctx, a_complex x, a_real y)
void	a_complex_div_imag_ (a_complex *ctx, a_real x)
void	a_complex_inv (a_complex *ctx, a_complex z)
	inverse of a complex number
void	a_complex_inv_ (a_complex *ctx)
void	a_complex_sqrt (a_complex *ctx, a_complex z)
	computes the complex square root
void	a_complex_sqrt_ (a_complex *ctx)
void	a_complex_sqrt_real (a_complex *ctx, a_real x)
void	a_complex_pow (a_complex *ctx, a_complex z, a_complex a)
	complex number z raised to complex power a
void	a_complex_pow_ (a_complex *ctx, a_complex a)
void	a_complex_pow_real (a_complex *ctx, a_complex z, a_real a)
	complex number z raised to real power a
void	a_complex_pow_real_ (a_complex *ctx, a_real a)
void	a_complex_exp (a_complex *ctx, a_complex z)
	computes the complex base-e exponential
void	a_complex_exp_ (a_complex *ctx)
void	a_complex_log (a_complex *ctx, a_complex z)
	computes the complex natural logarithm
void	a_complex_log_ (a_complex *ctx)
void	a_complex_log2 (a_complex *ctx, a_complex z)
	computes the complex base-2 logarithm
void	a_complex_log2_ (a_complex *ctx)
void	a_complex_log10 (a_complex *ctx, a_complex z)
	computes the complex base-10 logarithm
void	a_complex_log10_ (a_complex *ctx)
void	a_complex_logb (a_complex *ctx, a_complex z, a_complex b)
	computes the complex base-b logarithm
void	a_complex_logb_ (a_complex *ctx, a_complex b)
void	a_complex_sin (a_complex *ctx, a_complex z)
	computes the complex sine
void	a_complex_sin_ (a_complex *ctx)
void	a_complex_cos (a_complex *ctx, a_complex z)
	computes the complex cosine
void	a_complex_cos_ (a_complex *ctx)
void	a_complex_tan (a_complex *ctx, a_complex z)
	computes the complex tangent
void	a_complex_tan_ (a_complex *ctx)
void	a_complex_sec (a_complex *ctx, a_complex z)
	computes the complex secant
void	a_complex_sec_ (a_complex *ctx)
void	a_complex_csc (a_complex *ctx, a_complex z)
	computes the complex cosecant
void	a_complex_csc_ (a_complex *ctx)
void	a_complex_cot (a_complex *ctx, a_complex z)
	computes the complex cotangent
void	a_complex_cot_ (a_complex *ctx)
void	a_complex_asin (a_complex *ctx, a_complex z)
	computes the complex arc sine
void	a_complex_asin_ (a_complex *ctx)
void	a_complex_asin_real (a_complex *ctx, a_real x)
void	a_complex_acos (a_complex *ctx, a_complex z)
	computes the complex arc cosine
void	a_complex_acos_ (a_complex *ctx)
void	a_complex_acos_real (a_complex *ctx, a_real x)
void	a_complex_atan (a_complex *ctx, a_complex z)
	computes the complex arc tangent
void	a_complex_atan_ (a_complex *ctx)
void	a_complex_asec (a_complex *ctx, a_complex z)
	computes the complex arc secant
void	a_complex_asec_ (a_complex *ctx)
void	a_complex_asec_real (a_complex *ctx, a_real x)
void	a_complex_acsc (a_complex *ctx, a_complex z)
	computes the complex arc cosecant
void	a_complex_acsc_ (a_complex *ctx)
void	a_complex_acsc_real (a_complex *ctx, a_real x)
void	a_complex_acot (a_complex *ctx, a_complex z)
	computes the complex arc cotangent
void	a_complex_acot_ (a_complex *ctx)
void	a_complex_sinh (a_complex *ctx, a_complex z)
	computes the complex hyperbolic sine
void	a_complex_sinh_ (a_complex *ctx)
void	a_complex_cosh (a_complex *ctx, a_complex z)
	computes the complex hyperbolic cosine
void	a_complex_cosh_ (a_complex *ctx)
void	a_complex_tanh (a_complex *ctx, a_complex z)
	computes the complex hyperbolic tangent
void	a_complex_tanh_ (a_complex *ctx)
void	a_complex_sech (a_complex *ctx, a_complex z)
	computes the complex hyperbolic secant
void	a_complex_sech_ (a_complex *ctx)
void	a_complex_csch (a_complex *ctx, a_complex z)
	computes the complex hyperbolic cosecant
void	a_complex_csch_ (a_complex *ctx)
void	a_complex_coth (a_complex *ctx, a_complex z)
	computes the complex hyperbolic cotangent
void	a_complex_coth_ (a_complex *ctx)
void	a_complex_asinh (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic sine
void	a_complex_asinh_ (a_complex *ctx)
void	a_complex_acosh (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic cosine
void	a_complex_acosh_ (a_complex *ctx)
void	a_complex_acosh_real (a_complex *ctx, a_real x)
void	a_complex_atanh (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic tangent
void	a_complex_atanh_ (a_complex *ctx)
void	a_complex_atanh_real (a_complex *ctx, a_real x)
void	a_complex_asech (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic secant
void	a_complex_asech_ (a_complex *ctx)
void	a_complex_acsch (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic cosecant
void	a_complex_acsch_ (a_complex *ctx)
void	a_complex_acoth (a_complex *ctx, a_complex z)
	computes the complex arc hyperbolic cotangent
void	a_complex_acoth_ (a_complex *ctx)

Detailed Description

Macro Definition Documentation

a_complex_

#define a_complex_	(		_,
			x )

Value:

a_cast_s(a_complex _, x)

A_COMPLEX_C

#define A_COMPLEX_C	(		real,
			imag )

Value:

{a_real_c(real), a_real_c(imag)}

constructs a complex number from real and imaginary parts

a_complex_c

#define a_complex_c

(

x

)

Value:

a_cast_s(a_complex, x)

static cast to complex number

Function Documentation

a_complex_abs()

a_real a_complex_abs

(

a_complex

z

)

computes the magnitude of a complex number

Parameters

z	a complex number

Returns

= $\sqrt{a^2+b^2}$

a_complex_abs2()

a_real a_complex_abs2

(

a_complex

z

)

computes the squared magnitude of a complex number

Parameters

z	a complex number

Returns

= $a^2+b^2$

a_complex_acos()

void a_complex_acos	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc cosine

Parameters

ctx	= $\arccos (z)$
z	a complex number

a_complex_acosh()

void a_complex_acosh	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic cosine

$$\mathrm{arccosh}(z)=\log (z-\sqrt{z^2-1})$$

Parameters

ctx	= $\mathrm{arccosh}(z)$
z	a complex number

a_complex_acot()

void a_complex_acot	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc cotangent

$$\mathrm{arccot}(z)=\arctan (\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arccot}(z)$
z	a complex number

a_complex_acoth()

void a_complex_acoth	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic cotangent

$$\mathrm{arccoth}(z)=\mathrm{arctanh}(\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arccoth}(z)$
z	a complex number

a_complex_acsc()

void a_complex_acsc	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc cosecant

$$\mathrm{arccsc}(z)=\arcsin (\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arccsc}(z)$
z	a complex number

a_complex_acsch()

void a_complex_acsch	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic cosecant

$$\mathrm{arccsch}(z)=\mathrm{arcsinh}(\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arccsch}(z)$
z	a complex number

a_complex_add()

void a_complex_add	(	a_complex *	ctx,
		a_complex	x,
		a_complex	y )

addition of complex numbers

$$(a+bi)+(c+di)=(a+c)+(b+d)i$$

Parameters

ctx	= $x+y$
x	complex number on the left
y	complex number on the right

a_complex_arg()

a_real a_complex_arg

(

a_complex

z

)

computes the phase angle of a complex number

Parameters

z	a complex number

Returns

= $\arctan \frac{b}{a}$

a_complex_asec()

void a_complex_asec	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc secant

$$\mathrm{arcsec}(z)=\arccos (\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arcsec}(z)$
z	a complex number

a_complex_asech()

void a_complex_asech	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic secant

$$\mathrm{arcsech}(z)=\mathrm{arccosh}(\frac{1}{z})$$

Parameters

ctx	= $\mathrm{arcsech}(z)$
z	a complex number

a_complex_asin()

void a_complex_asin	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc sine

Parameters

ctx	= $\arcsin (z)$
z	a complex number

a_complex_asinh()

void a_complex_asinh	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic sine

Parameters

ctx	= $\mathrm{arcsinh}(z)$
z	a complex number

a_complex_atan()

void a_complex_atan	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc tangent

Parameters

ctx	= $\arctan (z)$
z	a complex number

a_complex_atanh()

void a_complex_atanh	(	a_complex *	ctx,
		a_complex	z )

computes the complex arc hyperbolic tangent

Parameters

ctx	= $\mathrm{arctanh}(z)$
z	a complex number

a_complex_conj()

void a_complex_conj	(	a_complex *	ctx,
		a_complex	z )

computes the complex conjugate

Parameters

ctx	= $(a,-bi)$
z	a complex number

a_complex_cos()

void a_complex_cos	(	a_complex *	ctx,
		a_complex	z )

computes the complex cosine

$$\cos (z)=\frac{\exp (zi)+\exp (-zi)}{2}$$

Parameters

ctx	= $\cos (z)$
z	a complex number

a_complex_cosh()

void a_complex_cosh	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic cosine

$$\cosh (z)=\frac{\exp (z)+\exp (-z)}{2}$$

Parameters

ctx	= $\cosh (z)$
z	a complex number

a_complex_cot()

void a_complex_cot	(	a_complex *	ctx,
		a_complex	z )

computes the complex cotangent

$$\cot (z)=\frac{1}{\tan (z)}$$

Parameters

ctx	= $\cot (z)$
z	a complex number

a_complex_coth()

void a_complex_coth	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic cotangent

$$\coth (z)=\frac{1}{\tanh (z)}$$

Parameters

ctx	= $\coth (z)$
z	a complex number

a_complex_csc()

void a_complex_csc	(	a_complex *	ctx,
		a_complex	z )

computes the complex cosecant

$$\csc (z)=\frac{1}{\sin (z)}$$

Parameters

ctx	= $\csc (z)$
z	a complex number

a_complex_csch()

void a_complex_csch	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic cosecant

$$\mathrm{csch}(z)=\frac{1}{\sinh (z)}$$

Parameters

ctx	= $\mathrm{csch}(z)$
z	a complex number

a_complex_div()

void a_complex_div	(	a_complex *	ctx,
		a_complex	x,
		a_complex	y )

division of complex numbers

$$\frac{(a+bi)}{(c+di)}=\frac{(a+bi)(c-di)}{(c+di)(c-di)}=\frac{ac+bci-adi-bd{i}^2}{c^2-(di{)}^2}=\frac{(ac+bd)+(bc-ad)i}{c^2+d^2}=\left(\frac{ac+bd}{c^2+d^2}\right)+\left(\frac{bc-ad}{c^2+d^2}\right)i$$

Parameters

ctx	= $x÷y$
x	complex number on the left
y	complex number on the right

a_complex_eq()

a_bool a_complex_eq	(	a_complex	x,
		a_complex	y )

complex number x is equal to complex number y

Parameters

x	complex number on the left
y	complex number on the right

Returns

result of comparison

a_complex_exp()

void a_complex_exp	(	a_complex *	ctx,
		a_complex	z )

computes the complex base-e exponential

Parameters

ctx	= $e^z$
z	a complex number

a_complex_inv()

void a_complex_inv	(	a_complex *	ctx,
		a_complex	z )

inverse of a complex number

$$\frac{a-bi}{a^2+b^2}=\left(\frac{a}{a^2+b^2}\right)-\left(\frac{b}{a^2+b^2}\right)i$$

Parameters

ctx	inverse or reciprocal $\frac{1}{z}$
z	a complex number

a_complex_log()

void a_complex_log	(	a_complex *	ctx,
		a_complex	z )

computes the complex natural logarithm

Parameters

ctx	= $\ln z$
z	a complex number

a_complex_log10()

void a_complex_log10	(	a_complex *	ctx,
		a_complex	z )

computes the complex base-10 logarithm

Parameters

ctx	= $\lg z$
z	a complex number

a_complex_log2()

void a_complex_log2	(	a_complex *	ctx,
		a_complex	z )

computes the complex base-2 logarithm

Parameters

ctx	= ${\log }_{2}z$
z	a complex number

a_complex_logabs()

a_real a_complex_logabs

(

a_complex

z

)

computes the natural logarithm of magnitude of a complex number

Parameters

z	a complex number

Returns

= $\log \left|x\right|$

a_complex_logb()

void a_complex_logb	(	a_complex *	ctx,
		a_complex	z,
		a_complex	b )

computes the complex base-b logarithm

Parameters

ctx	= ${\log }_{b}z$
z	a complex number
b	a complex number

a_complex_mul()

void a_complex_mul	(	a_complex *	ctx,
		a_complex	x,
		a_complex	y )

multiplication of complex numbers

$$(a+bi)(c+di)=ac+bci+adi+bd{i}^2=(ac-bd)+(bc+ad)i$$

Parameters

ctx	= $x\times y$
x	complex number on the left
y	complex number on the right

a_complex_ne()

a_bool a_complex_ne	(	a_complex	x,
		a_complex	y )

complex number x is not equal to complex number y

Parameters

x	complex number on the left
y	complex number on the right

Returns

result of comparison

a_complex_neg()

void a_complex_neg	(	a_complex *	ctx,
		a_complex	z )

computes the complex negative

Parameters

ctx	= $(-a,-bi)$
z	a complex number

a_complex_parse()

unsigned int a_complex_parse	(	a_complex *	ctx,
		char const *	str )

parse a string into a complex number

Parameters

ctx	points to an instance structure for complex number
str	complex number string to be parsed

Returns

number of parsed characters

a_complex_polar()

void a_complex_polar	(	a_complex *	ctx,
		a_real	rho,
		a_real	theta )

constructs a complex number from polar form

Parameters

ctx	= $(\rho \cos \theta ,\rho \sin \theta i)$
rho	a distance from a reference point
theta	an angle from a reference direction

a_complex_pow()

void a_complex_pow	(	a_complex *	ctx,
		a_complex	z,
		a_complex	a )

complex number z raised to complex power a

Parameters

ctx	= $z^a$
z	a complex number
a	a complex number

a_complex_pow_real()

void a_complex_pow_real	(	a_complex *	ctx,
		a_complex	z,
		a_real	a )

complex number z raised to real power a

Parameters

ctx	= $z^a$
z	a complex number
a	a real number

a_complex_proj()

void a_complex_proj	(	a_complex *	ctx,
		a_complex	z )

computes the projection on Riemann sphere

Parameters

ctx	= $z$ or $(inf,\mathrm{c}\mathrm{o}\mathrm{p}\mathrm{y}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}(0,\mathrm{b})\mathrm{i})$
z	a complex number

a_complex_rect()

static void a_complex_rect ( a_complex * ctx, a_real real, a_real imag )

inlinestatic

constructs a complex number from real and imaginary parts

Parameters

ctx	= $(\mathrm{R}\mathrm{e},\mathrm{I}\mathrm{m})$
real	real part of complex number
imag	imaginary part of complex number

a_complex_sec()

void a_complex_sec	(	a_complex *	ctx,
		a_complex	z )

computes the complex secant

$$\sec (z)=\frac{1}{\cos (z)}$$

Parameters

ctx	= $\sec (z)$
z	a complex number

a_complex_sech()

void a_complex_sech	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic secant

$$\mathrm{sech}(z)=\frac{1}{\cosh (z)}$$

Parameters

ctx	= $\mathrm{sech}(z)$
z	a complex number

a_complex_sin()

void a_complex_sin	(	a_complex *	ctx,
		a_complex	z )

computes the complex sine

$$\sin (z)=\frac{\exp (zi)-\exp (-zi)}{2i}$$

Parameters

ctx	= $\sin (z)$
z	a complex number

a_complex_sinh()

void a_complex_sinh	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic sine

$$\sinh (z)=\frac{\exp (z)-\exp (-z)}{2}$$

Parameters

ctx	= $\sinh (z)$
z	a complex number

a_complex_sqrt()

void a_complex_sqrt	(	a_complex *	ctx,
		a_complex	z )

computes the complex square root

Parameters

ctx	= $\sqrt{z}$
z	a complex number

a_complex_sub()

void a_complex_sub	(	a_complex *	ctx,
		a_complex	x,
		a_complex	y )

subtraction of complex numbers

$$(a+bi)-(c+di)=(a-c)+(b-d)i$$

Parameters

ctx	= $x-y$
x	complex number on the left
y	complex number on the right

a_complex_tan()

void a_complex_tan	(	a_complex *	ctx,
		a_complex	z )

computes the complex tangent

$$\tan (z)=\frac{\sin (z)}{\cos (z)}$$

Parameters

ctx	= $\tan (z)$
z	a complex number

a_complex_tanh()

void a_complex_tanh	(	a_complex *	ctx,
		a_complex	z )

computes the complex hyperbolic tangent

$$\tanh (z)=\frac{\sinh (z)}{\cosh (z)}$$

Parameters

ctx	= $\tanh (z)$
z	a complex number