NAME

M_Complex — Agar-Math complex number

SYNOPSIS

#include <agar/core.h>
#include <agar/gui.h>
#include <agar/math/m.h>

DESCRIPTION

The M_Complex object describes a complex number (without requiring an ISO C90 compiler). It is a simple structure defined as:

typedef struct m_complex {
	M_Real r;    /* Real part */
	M_Real i;    /* "Imaginary" part */
} M_Complex;

INITIALIZATION

M_Complex
M_ComplexGet(M_Real r, M_Real i);

M_Complex
M_ReadComplex(AG_DataSource *ds);

void
M_CopyComplex(AG_DataSource *ds, M_Complex *z);

void
M_WriteComplex(AG_DataSource *ds, M_Complex z);

The M_ComplexGet() routine returns a M_Complex structure describing a complex number with real part r and imaginary part i.

M_ComplexI() returns the complex number for i. M_ComplexMinusI() returns the complex number for -i.

The M_ReadComplex() function reads a complex number from an AG_DataSource(3) and returns it. M_CopyComplex() returns the number in z. M_WriteComplex() writes a complex number to a data source.

BASIC OPERATIONS

M_Real
M_ComplexReal(M_Complex z);

M_Real
M_ComplexImag(M_Complex z);

M_Real
M_ComplexModulus(M_Complex z);

M_Real
M_ComplexArg(M_Complex z);

M_Complex
M_ComplexAdditiveInverse(M_Complex z);

M_Complex
M_ComplexMultiplicativeInverse(M_Complex z);

void
M_ComplexPolar(M_Complex z, M_Real *r, M_Real *theta);

The M_ComplexReal() routine extracts and return the real part of complex number z. M_ComplexImag() returns the imaginary part.

M_ComplexModulus() returns the modulus of z, which is computed as sqrt(r^2 + i^2). M_ComplexArg() returns the argument of z, computed as atan2(i,r);

M_ComplexAdditiveInverse() returns the additive inverse of z.

M_ComplexMultiplicativeInverse() returns the multiplicative inverse of z.

M_ComplexPolar() returns the polar form of z into r (corresponding to the modulus) and theta (corresponding to the argument).

ARITHMETIC OPERATIONS

M_Complex
M_ComplexAdd(M_Complex a, M_Complex b);

M_Complex
M_ComplexSub(M_Complex a, M_Complex b);

M_Complex
M_ComplexMult(M_Complex a, M_Complex b);

M_Complex
M_ComplexDiv(M_Complex a, M_Complex b);

M_Real
M_ComplexAbs(M_Complex z);

The M_ComplexAdd() routine returns the sum of complex numbers a and b. M_ComplexSub() returns the difference.

M_ComplexMult() computes the product of complex numbers a and b. M_ComplexDiv() divides a by b and returns the result.

The M_ComplexAbs() function computes the complex absolute value (i.e., sqrt(r^2 + i^2)). If the magnitude of either real or imaginary parts differs with zero up to 50% of machine precision, both parts are rescaled prior to squaring.

M_ComplexSqrt() computes the complex square root of z.

M_ComplexLog() computes the complex natural logarithm of z.

M_ComplexExp() computes the exponential of z.

M_ComplexPow() returns a raised to the complex power z.

TRIGONOMETRIC AND HYPERBOLIC OPERATIONS

M_Complex
M_ComplexSin(M_Complex z);

M_Complex
M_ComplexCos(M_Complex z);

M_Complex
M_ComplexTan(M_Complex z);

M_Complex
M_ComplexCot(M_Complex z);

M_Complex
M_ComplexAsin(M_Complex z);

M_Complex
M_ComplexAcos(M_Complex z);

M_Complex
M_ComplexAtan(M_Complex z);

M_Complex
M_ComplexSinh(M_Complex z);

M_Complex
M_ComplexAsinh(M_Complex z);

M_Complex
M_ComplexCosh(M_Complex z);

M_Complex
M_ComplexAcosh(M_Complex z);

M_Complex
M_ComplexTanh(M_Complex z);

M_Complex
M_ComplexAtanh(M_Complex z);

The M_ComplexSin() function returns the complex sine of z. M_ComplexCos() returns the complex cosine, M_ComplexTan() returns the complex tangent and M_ComplexCot() returns the complex cotangent.

M_ComplexAsin(), M_ComplexAcos() and M_ComplexAtan() compute the complex arc sine, arc cosine and arc tangent of z, respectively.

M_ComplexSinh(), M_ComplexAsinh(), M_ComplexCosh(), M_ComplexAcosh(), M_ComplexTanh(), M_ComplexAtanh() compute the complex hyperbolic sine, arc sine, cosine, arc cosine, tangent and arc tangent of z, respectively.

HISTORY

The M_Complex structure first appeared in Agar 1.3.4.