Double Complex Functions

Functions for floating-point complex numbers. More...

Functions
dc_complex_double	dc_double_from_doubles (double real, double imag)
	Create a floating-point complex number from real and imaginary parts.
dc_complex_double	dc_double_from_polar (double magnitude, double angle)
	Create a floating-point complex number from polar coordinates.
dc_complex_double	dc_double_zero (void)
	Get the floating-point complex zero (0.0 + 0.0i)
dc_complex_double	dc_double_one (void)
	Get the floating-point complex one (1.0 + 0.0i)
dc_complex_double	dc_double_i (void)
	Get the floating-point complex i (0.0 + 1.0i)
dc_complex_double	dc_double_neg_one (void)
	Get the floating-point complex -1 (-1.0 + 0.0i)
dc_complex_double	dc_double_neg_i (void)
	Get the floating-point complex -i (0.0 + -1.0i)
dc_complex_double	dc_double_retain (dc_complex_double c)
	Increment reference count and return the same object.
void	dc_double_release (dc_complex_double *c)
	Decrement reference count and possibly free memory.
dc_complex_double	dc_double_copy (dc_complex_double c)
	Create a new copy with reference count 1.
dc_complex_double	dc_double_add (dc_complex_double a, dc_complex_double b)
	Add two floating-point complex numbers.
dc_complex_double	dc_double_sub (dc_complex_double a, dc_complex_double b)
	Subtract two floating-point complex numbers.
dc_complex_double	dc_double_mul (dc_complex_double a, dc_complex_double b)
	Multiply two floating-point complex numbers.
dc_complex_double	dc_double_div (dc_complex_double a, dc_complex_double b)
	Divide two floating-point complex numbers.
dc_complex_double	dc_double_negate (dc_complex_double c)
	Negate a floating-point complex number.
dc_complex_double	dc_double_conj (dc_complex_double c)
	Complex conjugate of a floating-point complex number.
dc_complex_double	dc_double_exp (dc_complex_double c)
	Complex exponential function.
dc_complex_double	dc_double_log (dc_complex_double c)
	Complex natural logarithm.
dc_complex_double	dc_double_pow (dc_complex_double a, dc_complex_double b)
	Complex power function.
dc_complex_double	dc_double_sqrt (dc_complex_double c)
	Complex square root.
dc_complex_double	dc_double_sin (dc_complex_double c)
	Complex sine function.
dc_complex_double	dc_double_cos (dc_complex_double c)
	Complex cosine function.
dc_complex_double	dc_double_tan (dc_complex_double c)
	Complex tangent function.
dc_complex_double	dc_double_sinh (dc_complex_double c)
	Complex hyperbolic sine function.
dc_complex_double	dc_double_cosh (dc_complex_double c)
	Complex hyperbolic cosine function.
dc_complex_double	dc_double_tanh (dc_complex_double c)
	Complex hyperbolic tangent function.
double	dc_double_real (dc_complex_double c)
	Get the real part of a floating-point complex number.
double	dc_double_imag (dc_complex_double c)
	Get the imaginary part of a floating-point complex number.
double	dc_double_abs (dc_complex_double c)
	Get the absolute value (magnitude) of a complex number.
double	dc_double_arg (dc_complex_double c)
	Get the argument (phase angle) of a complex number.
bool	dc_double_eq (dc_complex_double a, dc_complex_double b)
	Test if two floating-point complex numbers are equal.
bool	dc_double_is_zero (dc_complex_double c)
	Test if a floating-point complex number is zero.
bool	dc_double_is_real (dc_complex_double c)
	Test if a floating-point complex number is real (imaginary part is zero)
bool	dc_double_is_imag (dc_complex_double c)
	Test if a floating-point complex number is purely imaginary (real part is zero)
bool	dc_double_is_nan (dc_complex_double c)
	Test if a floating-point complex number contains NaN.
bool	dc_double_is_inf (dc_complex_double c)
	Test if a floating-point complex number contains infinity.
char *	dc_double_to_string (dc_complex_double c)
	Convert floating-point complex number to mathematical string representation.

Detailed Description

Functions for floating-point complex numbers.

Function Documentation

dc_double_abs()

double dc_double_abs ( dc_complex_double  c )

extern

Get the absolute value (magnitude) of a complex number.

Parameters

c	The complex number (must not be NULL)

Returns

The magnitude as a double

Note

Uses C99 complex.h cabs() function

Returns sqrt(real² + imag²)

dc_double_add()

dc_complex_double dc_double_add ( dc_complex_double  a, dc_complex_double  b  )

extern

Add two floating-point complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a + b

Note

Result has reference count of 1

Uses IEEE 754 floating-point arithmetic

dc_double_arg()

double dc_double_arg ( dc_complex_double  c )

extern

Get the argument (phase angle) of a complex number.

Parameters

c	The complex number (must not be NULL)

Returns

The angle in radians (-π to π)

Note

Uses C99 complex.h carg() function

Returns atan2(imag, real)

dc_double_conj()

dc_complex_double dc_double_conj ( dc_complex_double  c )

extern

Complex conjugate of a floating-point complex number.

Parameters

c	The operand (must not be NULL)

Returns

New complex number with imaginary part negated

Note

Result has reference count of 1

For a+bi, returns a-bi

Uses C99 complex.h conj() function

dc_double_copy()

dc_complex_double dc_double_copy ( dc_complex_double  c )

extern

Create a new copy with reference count 1.

Parameters

c	The complex number to copy (must not be NULL)

Returns

New complex number with same value

Note

Result has reference count of 1

dc_double_cos()

dc_complex_double dc_double_cos ( dc_complex_double  c )

extern

Complex cosine function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number cos(c)

Note

Result has reference count of 1

Uses C99 complex.h ccos() function

dc_double_cosh()

dc_complex_double dc_double_cosh ( dc_complex_double  c )

extern

Complex hyperbolic cosine function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number cosh(c)

Note

Result has reference count of 1

Uses C99 complex.h ccosh() function

dc_double_div()

dc_complex_double dc_double_div ( dc_complex_double  a, dc_complex_double  b  )

extern

Divide two floating-point complex numbers.

Parameters

a	Dividend (must not be NULL)
b	Divisor (must not be NULL and not zero)

Returns

New complex number a / b

Note

Result has reference count of 1

Uses C99 complex.h division

dc_double_eq()

bool dc_double_eq ( dc_complex_double  a, dc_complex_double  b  )

extern

Test if two floating-point complex numbers are equal.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

true if a == b (exact equality), false otherwise

Note

Uses exact floating-point comparison

Consider using epsilon comparison for numerical stability

dc_double_exp()

dc_complex_double dc_double_exp ( dc_complex_double  c )

extern

Complex exponential function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number e^c

Note

Result has reference count of 1

Uses C99 complex.h cexp() function

dc_double_from_doubles()

dc_complex_double dc_double_from_doubles ( double  real, double  imag  )

extern

Create a floating-point complex number from real and imaginary parts.

Parameters

real	The real part
imag	The imaginary part

Returns

New floating-point complex number (must be released)

Note

Result has reference count of 1

dc_double_from_polar()

dc_complex_double dc_double_from_polar ( double  magnitude, double  angle  )

extern

Create a floating-point complex number from polar coordinates.

Parameters

magnitude	The magnitude (radius)
angle	The angle in radians

Returns

New floating-point complex number (must be released)

Note

Result has reference count of 1

Uses formula: magnitude * e^(i*angle)

dc_double_i()

dc_complex_double dc_double_i ( void  )

extern

Get the floating-point complex i (0.0 + 1.0i)

Returns

Singleton imaginary unit

Note

This is a singleton with high reference count

dc_double_imag()

double dc_double_imag ( dc_complex_double  c )

extern

Get the imaginary part of a floating-point complex number.

Parameters

c	The complex number (must not be NULL)

Returns

The imaginary part as a double

Note

Uses C99 complex.h cimag() function

dc_double_is_imag()

bool dc_double_is_imag ( dc_complex_double  c )

extern

Test if a floating-point complex number is purely imaginary (real part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if real part is 0.0, false otherwise

dc_double_is_inf()

bool dc_double_is_inf ( dc_complex_double  c )

extern

Test if a floating-point complex number contains infinity.

Parameters

c	The complex number (must not be NULL)

Returns

true if either component is infinite, false otherwise

Note

Uses isinf() for both real and imaginary parts

dc_double_is_nan()

bool dc_double_is_nan ( dc_complex_double  c )

extern

Test if a floating-point complex number contains NaN.

Parameters

c	The complex number (must not be NULL)

Returns

true if either component is NaN, false otherwise

Note

Uses isnan() for both real and imaginary parts

dc_double_is_real()

bool dc_double_is_real ( dc_complex_double  c )

extern

Test if a floating-point complex number is real (imaginary part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if imaginary part is 0.0, false otherwise

dc_double_is_zero()

bool dc_double_is_zero ( dc_complex_double  c )

extern

Test if a floating-point complex number is zero.

Parameters

c	The complex number (must not be NULL)

Returns

true if c == 0.0+0.0i, false otherwise

dc_double_log()

dc_complex_double dc_double_log ( dc_complex_double  c )

extern

Complex natural logarithm.

Parameters

c	The operand (must not be NULL and not zero)

Returns

New complex number log(c)

Note

Result has reference count of 1

Uses C99 complex.h clog() function

Principal branch of logarithm

dc_double_mul()

dc_complex_double dc_double_mul ( dc_complex_double  a, dc_complex_double  b  )

extern

Multiply two floating-point complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a * b

Note

Result has reference count of 1

Uses C99 complex.h multiplication

dc_double_neg_i()

dc_complex_double dc_double_neg_i ( void  )

extern

Get the floating-point complex -i (0.0 + -1.0i)

Returns

Singleton negative imaginary unit

Note

This is a singleton with high reference count

dc_double_neg_one()

dc_complex_double dc_double_neg_one ( void  )

extern

Get the floating-point complex -1 (-1.0 + 0.0i)

Returns

Singleton negative one complex number

Note

This is a singleton with high reference count

dc_double_negate()

dc_complex_double dc_double_negate ( dc_complex_double  c )

extern

Negate a floating-point complex number.

Parameters

c	The operand (must not be NULL)

Returns

New complex number -c

Note

Result has reference count of 1

dc_double_one()

dc_complex_double dc_double_one ( void  )

extern

Get the floating-point complex one (1.0 + 0.0i)

Returns

Singleton one complex number

Note

This is a singleton with high reference count

dc_double_pow()

dc_complex_double dc_double_pow ( dc_complex_double  a, dc_complex_double  b  )

extern

Complex power function.

Parameters

a	Base (must not be NULL)
b	Exponent (must not be NULL)

Returns

New complex number a^b

Note

Result has reference count of 1

Uses C99 complex.h cpow() function

Principal branch for multi-valued functions

dc_double_real()

double dc_double_real ( dc_complex_double  c )

extern

Get the real part of a floating-point complex number.

Parameters

c	The complex number (must not be NULL)

Returns

The real part as a double

Note

Uses C99 complex.h creal() function

dc_double_release()

void dc_double_release ( dc_complex_double *  c )

extern

Decrement reference count and possibly free memory.

Parameters

c	Pointer to complex number pointer (gracefully handles NULL)

Note

Sets *c to NULL after release

Only frees memory when reference count reaches 0

Singletons are never freed

dc_double_retain()

dc_complex_double dc_double_retain ( dc_complex_double  c )

extern

Increment reference count and return the same object.

Parameters

c	The complex number to retain (must not be NULL)

Returns

The same object passed in

Note

Increases reference count by 1

dc_double_sin()

dc_complex_double dc_double_sin ( dc_complex_double  c )

extern

Complex sine function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number sin(c)

Note

Result has reference count of 1

Uses C99 complex.h csin() function

dc_double_sinh()

dc_complex_double dc_double_sinh ( dc_complex_double  c )

extern

Complex hyperbolic sine function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number sinh(c)

Note

Result has reference count of 1

Uses C99 complex.h csinh() function

dc_double_sqrt()

dc_complex_double dc_double_sqrt ( dc_complex_double  c )

extern

Complex square root.

Parameters

c	The operand (must not be NULL)

Returns

New complex number sqrt(c)

Note

Result has reference count of 1

Uses C99 complex.h csqrt() function

Principal branch with Re(sqrt(c)) >= 0

dc_double_sub()

dc_complex_double dc_double_sub ( dc_complex_double  a, dc_complex_double  b  )

extern

Subtract two floating-point complex numbers.

Parameters

a	First operand (must not be NULL)
b	Second operand (must not be NULL)

Returns

New complex number a - b

Note

Result has reference count of 1

Uses IEEE 754 floating-point arithmetic

dc_double_tan()

dc_complex_double dc_double_tan ( dc_complex_double  c )

extern

Complex tangent function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number tan(c)

Note

Result has reference count of 1

Uses C99 complex.h ctan() function

dc_double_tanh()

dc_complex_double dc_double_tanh ( dc_complex_double  c )

extern

Complex hyperbolic tangent function.

Parameters

c	The operand (must not be NULL)

Returns

New complex number tanh(c)

Note

Result has reference count of 1

Uses C99 complex.h ctanh() function

dc_double_to_string()

char * dc_double_to_string ( dc_complex_double  c )

extern

Convert floating-point complex number to mathematical string representation.

Parameters

c	The complex number (must not be NULL)

Returns

Newly allocated string (must be freed with free())

Note

Format examples: "3.14+2.71i", "1.5-2.3i", "2.71i", "-i", "3.14", "0"

Uses mathematical notation with 'i' for imaginary unit

Uses g format for compact representation

dc_double_zero()

dc_complex_double dc_double_zero ( void  )

extern

Get the floating-point complex zero (0.0 + 0.0i)

Returns

Singleton zero complex number

Note

This is a singleton with high reference count