Complex number library

Complex

Mathematical complex number manipulation library written in and for C.

This C library introduces a complex number data type to C that comes along a wide range of functions that help to manipulate this data type and perform various mathematical operations with it.

Features

Elementary operations with complex numbers (addition, substraction, multiplication, division)
Exponentiation of complex numbers
Square root function
Degrees to radians conversion and viceversa
Conjugate of a complex number
Real and imaginary part of a complex number
Convert a complex number type (complex_t) to a displayable string.
Modulus of a complex number (absolute value)
Polar coordinates of a complex number
Trigonometric functions of a complex number
Hyperbolic trigonometric functions of a complex number

Usage

To import the library, simply add #include "complex.h" to the file. All functions will be imported and you'll now be able to use the library.
The complex number data type is defined as complex_t, which is a struct with two long double data types: the real part and the imaginary part. Although it is possible to change the individual values of the complex_t data type, it is recommended to use the built-in functions.

In this documentation, complex_t means the complex data type, long double is a real number, and char* is a C null-terminated string. These are all the functions with the corresponding description and arguments:

Conversion functions

char* ctoa(complex_t cnum)
Convert complex number to a string, in format a+bi or a-bi.
long double degtorad(long double num)
Convert degrees to radians.
long double radtodeg(long double num)
Convert radians to degrees.

Basic complex operations

long double cabs(complex_t cnum)
Absolute value (modulus) of a complex number.
complex_t cadd(complex_t cnum1, complex_t cnum2)
Add 2 complex numbers.
complex_t cdiff(complex_t cnum1, complex_t cnum1)
Substract 2 complex numbers.
complex_t cdivide(complex_t cnum1, complex_t cnum2)
Divide 2 complex numbers.
complex_t cmultiply(complex_t cnum1, complex_t cnum2)
Multiply 2 complex numbers.
complex_t conj(complex_t cnum)
Conjugate of a complex number (a-bi).
complex_t cpower(complex_t base, complex_t power)
Raise a complex number to a complex power.
complex_t csqrt(complex_t) num
Square root of a complex number

Logarithms & exponentials

complex_t
            cexp(complex_t
            num)

Exponential function for complex numbers (e^z)

complex_t
            clogbase(complex_t
            base, complex_t num)

Complex logarithm of any base

complex_t
            clog10(complex_t
            num)

Complex natural logarithm

Trigonometric functions


            complex_t
            csin(complex_t
            num)

Sine of a complex number.


            complex_t
            ccos(complex_t
            num)

Cosine of a complex number.


            complex_t
            ctan(complex_t
            num)

Tangent of a complex number.


            complex_t
            ccsc(complex_t
            num)

Cosecant of a complex number.


            complex_t
            csec(complex_t
            num)

Secant of a complex number.


            complex_t
            ccot(complex_t
            num)

Cotangent of a complex number.

Hyperbolic functions


            complex_t
            csinh(complex_t
            num)

Hyperbolic sine of a complex number.


            complex_t
            ccosh(complex_t
            num)

Hyperbolic cosine of a complex number.


            complex_t
            ctanh(complex_t
            num)

Hyperbolic tangent of a complex number.


            complex_t
            csch(complex_t
            num)

Hyperbolic cosecant of a complex number.


            complex_t
            csech(complex_t
            num)

Hyperbolic secant of a complex number.


            complex_t
            ccoth(complex_t
            num)

Hyperbolic cotangent of a complex number.

Other functions

long double imag(complex_t)
Get the imaginary part of a complex number, returns 0 if no imaginary part exists.
long double real(complex_t)
Get the real part of a complex number, returns 0 if no real part exists.
complex_t cvalue(long double, long double)
Assign new values to a complex number, and return that value.
There is equally the shorthand alias j(long double, long double)

Complex number to string

The ctoa() function takes a complex number in the complex_t format and transforms it into a null-pointed string, in the form of a+bi or a-bi. This function automatically allocates the required memory for the output but does not free it afterwards, which should be handled by the user to avoid memory leaks.
There are two possible output formats of ctoa():

Full number representation: This is the default mode. It always prints numbers in its full form a+bi even if one of the two parts is zero.
Short number representation: Must be activated by changing SHORT_CTOA option to one. This format will print the result in the shortest possible way, removing zero-valued parts of the complex number.

This function will print a part of the complex number as zero if it is smaller than 10^-15, automatically handling rounding errors inherent to 64-bit floating-point numbers.