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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 defined). Most Agar-Math structures use M_Real to represent floating-point num- bers. 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 tri- angle 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 expo- nent 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)
NAME | SYNOPSIS | DESCRIPTION | INITIALIZATION | CONSTANTS | STANDARD MATH ROUTINES | SEE ALSO | HISTORY
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