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M_COMPLEX(3)		 BSD Library Functions Manual		  M_COMPLEX(3)

NAME
     M_Complex -- Agar-Math complex number

SYNOPSIS
     #include <agar/math.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.

SEE ALSO
     AG_DataSource(3), AG_Intro(3), M_Matrix(3), M_Quaternion(3), M_Real(3),
     M_Vector(3)

HISTORY
     The M_Complex structure first appeared in Agar 1.3.4.

BSD				 July 14, 2009				   BSD
NAME | SYNOPSIS | DESCRIPTION | INITIALIZATION | BASIC OPERATIONS | ARITHMETIC OPERATIONS | TRIGONOMETRIC AND HYPERBOLIC OPERATIONS | SEE ALSO | HISTORY

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