Integer Complex Functions

Functions for Gaussian integers (complex numbers with integer components) More...

Functions
dc_complex_int	dc_int_from_ints (int64_t real, int64_t imag)
	Create a Gaussian integer from int64_t real and imaginary parts.
dc_complex_int	dc_int_from_di (di_int real, di_int imag)
	Create a Gaussian integer from dynamic integer components.
dc_complex_int	dc_int_zero (void)
	Get the Gaussian integer zero (0 + 0i)
dc_complex_int	dc_int_one (void)
	Get the Gaussian integer one (1 + 0i)
dc_complex_int	dc_int_i (void)
	Get the Gaussian integer i (0 + 1i)
dc_complex_int	dc_int_neg_one (void)
	Get the Gaussian integer -1 (-1 + 0i)
dc_complex_int	dc_int_neg_i (void)
	Get the Gaussian integer -i (0 - 1i)
dc_complex_int	dc_int_retain (dc_complex_int c)
	Increment reference count and return the same object.
void	dc_int_release (dc_complex_int *c)
	Decrement reference count and possibly free memory.
dc_complex_int	dc_int_copy (dc_complex_int c)
	Create a new copy with reference count 1.
dc_complex_int	dc_int_add (dc_complex_int a, dc_complex_int b)
	Add two Gaussian integers.
dc_complex_int	dc_int_sub (dc_complex_int a, dc_complex_int b)
	Subtract two Gaussian integers.
dc_complex_int	dc_int_mul (dc_complex_int a, dc_complex_int b)
	Multiply two Gaussian integers.
dc_complex_frac	dc_int_div (dc_complex_int a, dc_complex_int b)
	Divide two Gaussian integers (returns exact rational result)
dc_complex_int	dc_int_negate (dc_complex_int c)
	Negate a Gaussian integer.
dc_complex_int	dc_int_conj (dc_complex_int c)
	Complex conjugate of a Gaussian integer.
di_int	dc_int_real (dc_complex_int c)
	Get the real part of a Gaussian integer.
di_int	dc_int_imag (dc_complex_int c)
	Get the imaginary part of a Gaussian integer.
bool	dc_int_eq (dc_complex_int a, dc_complex_int b)
	Test if two Gaussian integers are equal.
bool	dc_int_is_zero (dc_complex_int c)
	Test if a Gaussian integer is zero.
bool	dc_int_is_real (dc_complex_int c)
	Test if a Gaussian integer is real (imaginary part is zero)
bool	dc_int_is_imag (dc_complex_int c)
	Test if a Gaussian integer is purely imaginary (real part is zero)
char *	dc_int_to_string (dc_complex_int c)
	Convert Gaussian integer to mathematical string representation.

Detailed Description

Functions for Gaussian integers (complex numbers with integer components)

Function Documentation

dc_int_add()

dc_complex_int dc_int_add ( dc_complex_int  a, dc_complex_int  b  )

extern

Add two Gaussian integers.

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

dc_int_conj()

dc_complex_int dc_int_conj ( dc_complex_int  c )

extern

Complex conjugate of a Gaussian integer.

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

dc_int_copy()

dc_complex_int dc_int_copy ( dc_complex_int  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_int_div()

dc_complex_frac dc_int_div ( dc_complex_int  a, dc_complex_int  b  )

extern

Divide two Gaussian integers (returns exact rational result)

Parameters

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

Returns

New rational complex number a / b

Note

Returns dc_complex_frac for exact division

Result has reference count of 1

Use dc_frac_is_gaussian_int() to check if result is still integer

dc_int_eq()

bool dc_int_eq ( dc_complex_int  a, dc_complex_int  b  )

extern

Test if two Gaussian integers are equal.

Parameters

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

Returns

true if a == b, false otherwise

dc_int_from_di()

dc_complex_int dc_int_from_di ( di_int  real, di_int  imag  )

extern

Create a Gaussian integer from dynamic integer components.

Parameters

real	The real part (must not be NULL)
imag	The imaginary part (must not be NULL)

Returns

New Gaussian integer complex number (must be released)

Note

Result has reference count of 1

Input integers are retained

dc_int_from_ints()

dc_complex_int dc_int_from_ints ( int64_t  real, int64_t  imag  )

extern

Create a Gaussian integer from int64_t real and imaginary parts.

Parameters

real	The real part
imag	The imaginary part

Returns

New Gaussian integer complex number (must be released)

Note

Result has reference count of 1

dc_int_i()

dc_complex_int dc_int_i ( void  )

extern

Get the Gaussian integer i (0 + 1i)

Returns

Singleton imaginary unit

Note

This is a singleton with high reference count

dc_int_imag()

di_int dc_int_imag ( dc_complex_int  c )

extern

Get the imaginary part of a Gaussian integer.

Parameters

c	The complex number (must not be NULL)

Returns

New dynamic integer (must be released)

Note

Result has reference count of 1

dc_int_is_imag()

bool dc_int_is_imag ( dc_complex_int  c )

extern

Test if a Gaussian integer is purely imaginary (real part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if real part is zero, false otherwise

dc_int_is_real()

bool dc_int_is_real ( dc_complex_int  c )

extern

Test if a Gaussian integer is real (imaginary part is zero)

Parameters

c	The complex number (must not be NULL)

Returns

true if imaginary part is zero, false otherwise

dc_int_is_zero()

bool dc_int_is_zero ( dc_complex_int  c )

extern

Test if a Gaussian integer is zero.

Parameters

c	The complex number (must not be NULL)

Returns

true if c == 0+0i, false otherwise

dc_int_mul()

dc_complex_int dc_int_mul ( dc_complex_int  a, dc_complex_int  b  )

extern

Multiply two Gaussian integers.

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 formula: (a+bi)(c+di) = (ac-bd) + (ad+bc)i

dc_int_neg_i()

dc_complex_int dc_int_neg_i ( void  )

extern

Get the Gaussian integer -i (0 - 1i)

Returns

Singleton negative imaginary unit

Note

This is a singleton with high reference count

dc_int_neg_one()

dc_complex_int dc_int_neg_one ( void  )

extern

Get the Gaussian integer -1 (-1 + 0i)

Returns

Singleton negative one complex number

Note

This is a singleton with high reference count

dc_int_negate()

dc_complex_int dc_int_negate ( dc_complex_int  c )

extern

Negate a Gaussian integer.

Parameters

c	The operand (must not be NULL)

Returns

New complex number -c

Note

Result has reference count of 1

dc_int_one()

dc_complex_int dc_int_one ( void  )

extern

Get the Gaussian integer one (1 + 0i)

Returns

Singleton one complex number

Note

This is a singleton with high reference count

dc_int_real()

di_int dc_int_real ( dc_complex_int  c )

extern

Get the real part of a Gaussian integer.

Parameters

c	The complex number (must not be NULL)

Returns

New dynamic integer (must be released)

Note

Result has reference count of 1

dc_int_release()

void dc_int_release ( dc_complex_int *  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_int_retain()

dc_complex_int dc_int_retain ( dc_complex_int  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_int_sub()

dc_complex_int dc_int_sub ( dc_complex_int  a, dc_complex_int  b  )

extern

Subtract two Gaussian integers.

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

dc_int_to_string()

char * dc_int_to_string ( dc_complex_int  c )

extern

Convert Gaussian integer 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+4i", "2-3i", "i", "-i", "5", "0"

Uses mathematical notation with 'i' for imaginary unit

dc_int_zero()

dc_complex_int dc_int_zero ( void  )

extern

Get the Gaussian integer zero (0 + 0i)

Returns

Singleton zero complex number

Note

This is a singleton with high reference count