complex number

Collaboration diagram for complex number:

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

Macros
#define	A_COMPLEX_PRI(RF, RC, IF, IC)
#define	A_COMPLEX_C(R, I)
#define	a_complex_c(r, i)

Typedefs
typedef struct a_complex	a_complex
	instance structure for complex number

Functions
static void	a_complex_rect (a_complex *ctx, double real, double imag)
	constructs a complex number from real and imaginary parts
void	a_complex_polar (a_complex *ctx, double rho, double 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
bool	a_complex_eq (a_complex x, a_complex y)
	complex number x is equal to complex number y
bool	a_complex_ne (a_complex x, a_complex y)
	complex number x is not equal to complex number y
double	a_complex_logabs (a_complex z)
	computes the natural logarithm of magnitude of a complex number
double	a_complex_abs2 (a_complex z)
	computes the squared magnitude of a complex number
double	a_complex_abs (a_complex z)
	computes the magnitude of a complex number
double	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, double y)
void	a_complex_add_real_ (a_complex *ctx, double x)
void	a_complex_add_imag (a_complex *ctx, a_complex x, double y)
void	a_complex_add_imag_ (a_complex *ctx, double 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, double y)
void	a_complex_sub_real_ (a_complex *ctx, double x)
void	a_complex_sub_imag (a_complex *ctx, a_complex x, double y)
void	a_complex_sub_imag_ (a_complex *ctx, double 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, double y)
void	a_complex_mul_real_ (a_complex *ctx, double x)
void	a_complex_mul_imag (a_complex *ctx, a_complex x, double y)
void	a_complex_mul_imag_ (a_complex *ctx, double 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, double y)
void	a_complex_div_real_ (a_complex *ctx, double x)
void	a_complex_div_imag (a_complex *ctx, a_complex x, double y)
void	a_complex_div_imag_ (a_complex *ctx, double 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, double 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, double a)
	complex number z raised to real power a
void	a_complex_pow_real_ (a_complex *ctx, double 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, double 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, double 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, double 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, double 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, double 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, double 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_C

#define A_COMPLEX_C	(		R,
			I )

Value:

{A_FLOAT_C(R), A_FLOAT_C(I)}

constructs a complex number constant from real and imaginary parts

a_complex_c

#define a_complex_c	(		r,
			i )

Value:

{a_float_c(r), a_float_c(i)}

constructs a complex number from real and imaginary parts

A_COMPLEX_PRI

#define A_COMPLEX_PRI	(		RF,
			RC,
			IF,
			IC )

Value:

"(" A_FLOAT_PRI(RF, RC) "," A_FLOAT_PRI(IF, IC) ")"

format constants for the fprintf family of functions

Function Documentation

a_complex_abs()

double 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()

double 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

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

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

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

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

\[ (a+b i)+(c+d i)=(a+c)+(b+d)i \]

Parameters

ctx	= \( x + y \)
x	complex number on the left
y	complex number on the right

a_complex_arg()

double 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

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

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	= \( (a,-b{i}) \)
z	a complex number

a_complex_cos()

void a_complex_cos	(	a_complex *	ctx,
		a_complex	z )

computes the complex cosine

\[ \cos(z)=\frac{\exp(z{i})+\exp(-z{i})}{2} \]

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

\[ \mathrm{coth}(z)=\frac{1}{\tanh(z)} \]

Parameters

ctx	= \( \mathrm{coth}(z) \)
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

\[ \frac{(a+b i)}{(c+d i)}=\frac{(a+b i)(c-d i)}{(c+d i)(c-d i)}=\frac{a c+b c i-a d i-b d i^{2}}{c^{2}-(d i)^{2}}=\frac{(a c+b d)+(b c-a d) i}{c^{2}+d^{2}}=\left(\frac{a c+b d}{c^{2}+d^{2}}\right)+\left(\frac{b c-a d}{c^{2}+d^{2}}\right) i \]

Parameters

ctx	= \( x \div y \)
x	complex number on the left
y	complex number on the right

a_complex_eq()

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()

double 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

\[ (a+b i)(c+d i)=a c+b c i+a d i+b d i^{2}=(a c-b d)+(b c+a d) i \]

Parameters

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

a_complex_ne()

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	= \( (-a,-b{i}) \)
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,
		double	rho,
		double	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,
		double	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 \( (\inf,\rm{copysign}(0,b)i) \)
z	a complex number

a_complex_rect()

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

inlinestatic

constructs a complex number from real and imaginary parts

Parameters

ctx	= \( (\rm{Re},\rm{Im}) \)
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

\[ \sin(z)=\frac{\exp(z{i})-\exp(-z{i})}{2{i}} \]

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

\[ (a+b i)-(c+d i)=(a-c)+(b-d)i \]

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