Miscellaneous scalar math functions. More...

Functions
template<class Type >
Type	Abs (Type x)
	Absolute value.
template<class Type >
Type	Mod (Type j, Type k)
	j modulo k.
template<class Type >
Type	PosMod (Type j, Type k)
	Positive wing of j modulo k.
Real	Floor (Real x)
	Floor function.
Real	Ceiling (Real x)
	Ceiling function.
Real	Sqrt (Real x)
	Square root.
Real	Pow (Real x, Real y)
	x to the power of y.
template<class Type >
Type	Log (Type x)
	Log of x to the base E.
template<class Type >
Type	Log10 (Type x)
	Log base 10 of x.
template<class Type >
Type	Atan (Type x)
	Arctangent of x.
template<class Type >
Type	Atan2 (Type x, Type y)
	Arctangent of ratio expressed as numerator x and denominator y.
template<class Type >
Type	Sin (Type x)
	Sine of Type x.
template<class Type >
Type	Cos (Type x)
	Cosine of Type x.
Real	unitInterp (Real f, Integer L, Integer U)
	Unit interpolation.
Real	linearInterpolate (Integer x, Integer xMin, Integer xMax, Integer yMin, Integer yMax)
	Linear interpolation.
Real	Round (Real x)
	Rounding.
Integer	RealToRational (Real f, Integer Reference a, Integer Reference b)
	Convert Real value to rational value.

Detailed Description

Miscellaneous scalar math functions.

Function Documentation

template<class Type >

Type Abs ( Type x ) [inline]

Absolute value.

Parameters:

x Value

Definition at line 35 of file MathFuns.h.

References Return.

{ Return x < 0 ? -x : x; }

template<class Type >

Type Atan ( Type x ) [inline]

Arctangent of x.

Note: Type must be a floating point type.

Parameters:

x Value

Definition at line 94 of file MathFuns.h.

References Return.

{ Return atan( x ); }

template<class Type >

Type Atan2	(	Type	x,
		Type	y
	)		`[inline]`

Arctangent of ratio expressed as numerator x and denominator y.

Note: Type must be a floating point type.

Parameters:

x	Numerator
y	Denominator

Definition at line 100 of file MathFuns.h.

References Return.

{ Return atan2( x, y ); }

Real Ceiling ( Real x ) [inline]

Ceiling function.

Parameters:

x	Real value

Definition at line 70 of file MathFuns.h.

References Return.

{ Return ceil( x ); }

template<class Type >

Type Cos ( Type x ) [inline]

Cosine of Type x.

Note: Type must be a floating point type.

Parameters:

x Value

Definition at line 110 of file MathFuns.h.

References Return.

Referenced by Exp().

{ Return cos( x ); }

Real Floor ( Real x ) [inline]

Floor function.

Parameters:

x	Real value

Definition at line 66 of file MathFuns.h.

References Return.

Referenced by Round().

{ Return floor( x ); }

Real linearInterpolate	(	Integer	x,
		Integer	xMin,
		Integer	xMax,
		Integer	yMin,
		Integer	yMax
	)		`[inline]`

Linear interpolation.

Parameters:

x	Value ranging from xMin to xMax
xMin	Minimum range of x
xMax	Maximum range of x
yMin	Target minimum range
yMax	Target maximum range

Returns:: The interpolated value

Definition at line 128 of file MathFuns.h.

References Return.

Referenced by stretch().

                                                                                                   {
        Real a = Real( x - xMin) / Real(xMax - xMin); // Real division
        Real b = Real( yMax - yMin );
        Return( a * b + yMin );
}

template<class Type >

Type Log ( Type x ) [inline]

Log of x to the base E.

Note: Type must be a floating point type.

Parameters:

x Value

Definition at line 84 of file MathFuns.h.

References Return.

{ Return log( x ); }

template<class Type >

Type Log10 ( Type x ) [inline]

Log base 10 of x.

Note: Type must be a floating point type.

Parameters:

x Value

Definition at line 89 of file MathFuns.h.

References Return.

{ Return log( x ) / log (10.0); }

template<class Type >

Type Mod	(	Type	j,
		Type	k
	)		`[inline]`

j modulo k.

Note: Because of its implementation, Type need not be an integral type.

Parameters:

j	Base of modulo operation
k	Modulus of modulo operation

Definition at line 41 of file MathFuns.h.

References Return, and While.

Referenced by Pitch::invert(), Pitch::operator%(), PitchClass(), List< Type >::rotate(), and SetComplex().

                                                     {
        While ( j >= k ) { j = j - k; }
        While ( j <= -k ) { j = j + k; }
        Return( j );
}

template<class Type >

Type PosMod	(	Type	j,
		Type	k
	)		`[inline]`

Positive wing of j modulo k.

PosMod performs modulus arithmetic but returns only the positive wing of modulus values. Note: Because of its implementation, Type need not be an integral type.

Parameters:

j	Base of modulo operation
k	Modulus of modulo operation Note, the result will always be positive.

Definition at line 53 of file MathFuns.h.

References Return, and While.

Referenced by cycle(), List< Type >::rotate(), and List< Type >::transpose().

{
        While ( j >= k ) {
                j = j - k; 
        }
        While ( j < 0 ) {
                j = j + k; 
        }
        Return( j );
}

Real Pow	(	Real	x,
		Real	y
	)		`[inline]`

x to the power of y.

Parameters:

x	Base
y	Exponent

Definition at line 79 of file MathFuns.h.

References Return.

Referenced by Pitch::hertz().

{ Return pow( x, y ); }

Integer RealToRational	(	Real	f,
		Integer Reference	a,
		Integer Reference	b
	)

Convert Real value to rational value.

Parameters:

f	Real value
a	Numerator of resulting rational value
b	Denominator of resulting rational value

Convert Real value to rational value.

Parameters:

f	Real value to convert
a	Integer numerator of rational fraction
b	Integer denominator of rational fraction

Returns:: The number of attempts to determine the rational fraction. If the return value equals the internal count value, then the method did not converge. The values for the numerator and denominator returned are nonetheless the best estimates given the limits. Internal tuning values count and limit are used to control the amount of effort this routine puts into finding the best estimate of the rational fractional equivalent.

Definition at line 34 of file Musimat.cpp.

References Abs(), Const, Else, For, If, and Return.

Referenced by Rational::Rational(), and Rhythm::Rhythm().

                                                                           {
        If (f == 0.0) {
                a = 0;
                b = 1;
                Return( 0 );
        } Else If (f == 1.0) {
                a = b = 1;
                Return( 0 );
        }

        Const Integer count = 3000000;
        Const Real limit = 0.0000001 /* or try: LDBL_EPSILON * 10000 */;

        If (f < limit) {
                a = 1;
                b = count;
                Return( 0 );
        }

        a = b = 1;      // start off with a ratio of 1/1
        Integer i;
        For (i = 0; i < count; i++) {
                If ( Abs(Real(a)/Real(b) - f) < limit )
                        Return i;
                Else {
                        Real x = Abs( Real(a+1)/Real(b) - f ); 
                        Real y = Abs( Real(a)/Real(b+1) - f );
                        If (x < y)
                                a++;
                        Else
                                b++;
                }
        }
        Return i; // If we get here, we've not converged in the number of cycles available
}

Real Round ( Real x ) [inline]

Rounding.

Parameters:

x	Value to round

Returns:: Rounded value

Definition at line 137 of file MathFuns.h.

References Floor(), and Return.

Referenced by InterpTendency().

                            { 
        Return( Floor( x + 0.5 ) );
}

template<class Type >

Type Sin ( Type x ) [inline]

Sine of Type x.

Note: Type must be a floating point type.

Parameters:

x Value

Definition at line 105 of file MathFuns.h.

References Return.

Referenced by Exp().

{ Return sin( x ); }

Real Sqrt ( Real x ) [inline]

Square root.

Parameters:

x	Real value

Definition at line 74 of file MathFuns.h.

References Return.

{ Return sqrt( x ); }

Real unitInterp	(	Real	f,
		Integer	L,
		Integer	U
	)		`[inline]`

Unit interpolation.

Parameters:

f	Fraction, in the range 0<=f<=1.0
L	Lower bound of unit interpolation
U	Upper bound of unit interpolation

Returns:: The interpolated value

Definition at line 117 of file MathFuns.h.

References Return.

Referenced by InterpTendency().

                                                       {
        Return( f * ( U - L ) + L );
}

Miscellaneous Math Functions

Functions

Detailed Description

Function Documentation