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M_REAL(3)		     Library Functions Manual		       M_REAL(3)

NAME
     M_Real -- Agar-Math real number operations

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

DESCRIPTION
     Real  numbers  in Agar-Math are most often described using the M_Real type.
     Depending on which precision mode the library was compiled against (see the
     --with-<mode>-fp configure option), M_Real may  expand  to  float	(32-bit,
     SINGLE_PRECISION  is  defined)  or  double (64-bit, DOUBLE_PRECISION is de-
     fined).

     Most Agar-Math structures use M_Real to represent	floating-point	numbers.
     The  real	and  imaginary parts of M_Complex(3), and the elements of M_Vec-
     tor(3) and M_Matrix(3) are all stored as  M_Real  values.	 Note,	however,
     that   fixed-size	types  such  as  M_Vector2,  M_Vector3,  M_Vector4,  and
     M_Matrix44 may or may not use  a  different  precision  (depending  on  the
     availability  of  SIMD  instructions such as AltiVec and SSE).  The general
     M_Vector and M_Matrix types are always guaranteed to use M_Real.

INITIALIZATION
     M_Real M_ReadReal(AG_DataSource *ds)

     void M_CopyReal(AG_DataSource *ds, M_Real *r)

     void M_WriteReal(AG_DataSource *ds, M_Real r)

     The M_ReadReal() function reads a complex number from  an	AG_DataSource(3)
     and  returns  it.	 The  M_CopyReal()  variant  returns  the  number  in r.
     M_WriteReal() writes a real number to a data source.

CONSTANTS
     The library defines the following fundamental constants:
     M_E	  Euler's constant
     M_LOG2E	  log_2 e
     M_LOG10E	  log_10 e
     M_LN2	  log_e 2
     M_LN10	  log_e 10
     M_PI	  pi
     M_PI_2	  pi/2
     M_PI_4	  pi/4
     M_1_PI	  1/pi
     M_2_PI	  2/pi
     M_2_SQRTPI   2/sqrt(pi)
     M_SQRT2	  sqrt(2)
     M_SQRT1_2	  1/sqrt(2)

     The following constants describe the limitations of the memory  format  for
     the current precision mode:
     M_EXPMIN	     Minimum exponent.
     M_EXPMAX	     Maximum exponent.
     M_PRECISION     Precision of the significand in bits.
     M_PRECISION_2   M_PRECISION/2 (rounded up).
     M_NUMMAX	     Highest representible number.
     M_MACHEP	     Machine epsilon, or unit roundoff.
     M_TINYVAL	     A very small number, close to M_MACHEP.
     M_HUGEVAL	     A very large number.
     M_INFINITY      Representation of infinity.

STANDARD MATH ROUTINES
     M_Real M_Log(M_Real x)

     M_Real M_Exp(M_Real x)

     M_Real M_ExpM1(M_Real x)

     M_Real M_Sqrt(M_Real x)

     M_Real M_Cbrt(M_Real x)

     M_Real M_Sin(M_Real x)

     M_Real M_Cos(M_Real x)

     M_Real M_Tan(M_Real x)

     M_Real M_Sinh(M_Real x)

     M_Real M_Cosh(M_Real x)

     M_Real M_Tanh(M_Real x)

     M_Real M_Cot(M_Real x)

     M_Real M_Sec(M_Real x)

     M_Real M_Csc(M_Real x)

     M_Real M_Asin(M_Real x)

     M_Real M_Acos(M_Real x)

     M_Real M_Atan(M_Real x)

     M_Real M_Asinh(M_Real x)

     M_Real M_Acosh(M_Real x)

     M_Real M_Atanh(M_Real x)

     M_Real M_Atan2(M_Real y, M_Real x)

     M_Real M_Hypot2(M_Real x, M_Real y)

     M_Real M_Fabs(M_Real x)

     M_Real M_Sgn(M_Real x)

     M_Real M_Pow(M_Real x, M_Real y)

     M_Real M_Frexp(M_Real x, int *exp)

     M_Real M_Ldexp(M_Real x, int *exp)

     M_Real M_Ceil(M_Real x)

     M_Real M_Floor(M_Real x)

     int M_IsNaN(M_Real x)

     int M_IsInf(M_Real x)

     M_Log() returns the natural logarithm of x.

     M_Exp() returns the value of e, raised to the power of x.

     The  M_ExpM1()  routine  returns  the  equivalent of M_Exp(x)-1.  Numerical
     roundoff error is prevented in the case of x being near zero.

     M_Sqrt() returns the square root of x.  M_Cbrt() returns the cube	root  of
     x.

     M_Sin(),  M_Cos()	and  M_Tan()  return  the  sine, cosine and tangent of x
     (given in radians).  M_Sinh(), M_Cosh(),  M_Tanh()  return  the  hyperbolic
     sine, cosine and tangent of x.

     M_Cot(),  M_Sec()	and M_Csc() return the cotangent, secant and cosecant of
     x.

     M_Asin(), M_Acos() and M_Atan() return the arc sine,  arc	cosine	and  arc
     tangent of x.  M_Asinh(), M_Acosh() and M_Atanh() return the hyperbolic arc
     sine, arc cosine and arc tangent of x.

     M_Atan2()	returns the equivalent of Atan(y/x), except that the sign of the
     result is determined from the signs of both arguments.

     M_Hypot2() computes the length of the hypotenuse of a right-angle	triangle
     with the right-angle side lengths of x and y.

     M_Fabs() returns the absolute value of x.

     The sign function M_Sgn() returns +1.0 if the sign of x is positive or -1.0
     if the sign is negative.

     M_Pow() returns x raised to the power of y.

     M_Frexp() returns the normalized fraction for x, and writes the exponent to
     exp.

     M_Ldexp() returns the result of multiplication of x by 2 to the power exp.

     M_Ceil()  rounds x up to the nearest integer.  M_Floor() rounds down to the
     nearest integer.

     M_IsNan() evaluates to 1 if x is "not a number".

     M_IsInf() evaluates to 1 if x represents infinity.

SEE ALSO
     AG_DataSource(3), AG_Intro(3),  M_Complex(3),  M_Geometry(3),  M_Matrix(3),
     M_Quaternion(3), M_Vector(3)

HISTORY
     The M_Real structure first appeared in Agar 1.3.4.

Agar 1.7			December 21, 2022		       M_REAL(3)

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