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 defined).

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_Vector(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.

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.

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.

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.

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

The M_Real structure first appeared in Agar 1.3.4.