C complex library

Note

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Powerful C library to easily work with complex numbers, with a variety of complex implementations of some commonly used functions.
All angles are calculated in radians, however you can convert the different units with some built-in functions.

List of all functions

Angle conversion functions

• long double degtorad(long double): Convert degrees to radians.
• long double radtodeg(long double): Convert radians to degrees.

Conversion functions

• char* ctoa(complex_t): Convert complex expression to string, in format $a+bi$ or $a-bi$

Basic complex operations

• complex_t cadd(complex_t, complex_t): Add 2 complex numbers.
• complex_t cdiff(complex_t, complex_t): Substract 2 complex numbers.
• complex_t cmultiply(complex_t, complex_t): Multiply 2 complex numbers.
• complex_t cdivide(complex_t, complex_t): Divide 2 complex numbers.
• complex_t conj(complex_t): Conjugate of a complex number.
• long double carg(complex_t): Complex argument.
• long double cabs(complex_t): Absolute value of a complex number.
• complex_t cvalue(long double, long double): Assign new values to a complex number, and return that value.
• long double imag(complex_t): Get the imaginary part of a complex number.
• long double real(complex_t): Get the real part of a complex number.

Powers and logarithms

• complex_t cexp(complex_t num): Exponential function ($e^{x}$).
• complex_t cpower(complex_t, complex_t): Raise a complex number to a power.
• complex_t csqrt(complex_t): Square root of a complex number.
• complex_t clog(complex_t): Natural logarithm (base e).
• complex_t clogbase(complex_t, complex_t) Logarithm with any base.
• complex_t clog10(complex_t): Common logarithm (base 10).

Trigonometric functions

• complex_t csin(complex_t): Sine.
• complex_t ccos(complex_t): Cosine.
• complex_t ctan(complex_t): Tangent.
• complex_t ccsc(complex_t): Cosecant.
• complex_t csec(complex_t): Secant.
• complex_t ccot(complex_t): Cotangent.

Hyperbolic functions

• complex_t csinh(complex_t): Hyperbolic sine.
• complex_t ccosh(complex_t): Hyperbolic cosine.
• complex_t ctanh(complex_t): Hyperbolic tangent.
• complex_t ccsch(complex_t): Hyperbolic cosecant.
• complex_t csech(complex_t): Hyperbolic secant.
• complex_t ccoth(complex_t): Hyperbolic cotangent.

Example

// Define the 2 complex numbers, 2 + 3i and 3 + 4i respectively
complex_t num1 = {2, 3}, num2 = {3, 4};

// Natural logarithm
printf("ln(%s)=%s\n", ctoa(num1), ctoa(clog(num1))); // Prints 1.2824747+0.98279372i

// Multiplication
printf("(%s)*(%s)=%s", ctoa(num1), ctoa(num2), ctoa(cmultiply(num1, num2))); // Prints -6+17i

// Hyperbolic cosine
printf("cosh(%s)=%s\n", ctoa(num2), ctoa(ccosh(num2))); // Prints -6.580663-7.5815527i

Usage

To use the library, simply include it with the following line:

#include "complex.h"

Furthermore, ctoa() has 2 different output formats:

• Long, which shows the full complex number, including zero-valued parts.
• Short, which trims all the unnecessary data: if a part is zero, it won't be shown.

This behavior can be modified by changing the value of SHORT_CTOA (defined at line 15, complex.c to either 0 (long output) or 1 (short output). Example outputs of both with cpower(cvalue(0, 1), cvalue(0, 1)) ( $i^{i}$ )

Long:

0.20787958+0i

Short:

0.20787958

For simplicity, cvalue() function is the same as j() function, in order to ease the coding process. cpower(cvalue(0, 1), cvalue(0, 1)) --> cpower(j(0, 1), j(0, 1))

Known issues

Due to long double-precision floats limitations, precision loss may happen.

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