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 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.

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.

HISTORY

The M_Real structure first appeared in Agar 1.3.4.