Fractions

What is Fractions?

Fractions is a unit for doing calculations with fractions.
The unit was inspired by a discussion on the Lazarus forum.

Subversion

You can get a copy of fractions on

svn https://lazarus-ccr.svn.sourceforge.net/svnroot/lazarus-ccr/components/fractions

Or you can use viewcv to preview the files:

http://sourceforge.net/p/lazarus-ccr/svn/HEAD/tree/components/fractions/

Features

The TFraction type

TFraction is an "advanced record": a record with methods and properties.

Porperties of TFraction

• property Numerator: Int64;
  • Gets and sets the Numerator part of the fraction
• property Denominator: Int64;
  • Gets and sets the Denominator part of the fraction.
  • Trying to assign 0 (zero) to TFraction.Denomiator will raise an EZeroDivide exception

Methods of TFraction

• procedure Normalize;
  • Normalizes the fraction by dividing the Numerator and Dominatr by their greatest common divisor, e.g. 10/5 becomes 2/1
• function ToString: String;
  • returns the string representation of the fraction (no normalizaltion is done), e.g. when Numerator = 10 and Denominator = 5, the function retruns '10/5'
• function Resolve: String;
  • retruns the string representation of the fraction after normalization, e.g. when Numerator = 4 and Denominator = 3, the function returns '1 1/3'
• function ToFloat: Double;
  • returns the floating point representation of the fraction, e.g. when Numerator = 1 and Denominator = 3, the function returns 0.3333333333333

Assigning and creating Fractions

• function Fraction(ANumerator, ADenominator: Int64): TFraction;
  • creates the fraction ANumerator/ADenominator, e.g. Fraction(1,2) gives 1/2 (one half).
• function Fraction(AIntPart, ANumerator, ADenominator: Int64): TFraction;
  • creates the fraction ANumerator/ADenominator, e.g. Fraction(1,1,2) gives 1 1/2 (one and one half).

Supported calculations

Overloaded operators

• = (equals)
• < (less than)
• > (greater than)
• <= (less than or equal)
• >= (greater than or equal)
• := (assign): this operator allows an Int64 or a String on the right hand side
• + (add)
• - (subtract)
• * (multiply): overloaded for fractions and Int64
• / (divide): overloaded for fractions and Int64
• ** (power): only allowed for Integers (on right hand side)

Mathematical functions

• function Min(a, b: TFraction): TFraction; inline; overload;
  • returns a if (a <= b), otherwise retruns b
• function Max(a, b: TFraction): TFraction; inline; overload;
  • returns a if (a >= b), otherwise returns b
• function InRange(const AValue, AMin, AMax: TFraction): Boolean; inline; overload;
  • returns True if (AValue >= AMin) and (AValue <= AMax), otherwise returns False
• function EnsureRange(const AValue, AMin, AMax: TFraction): TFraction; inline; overload;
  • returns AMin if (AValue < AMin), otherwise returns AMax if (AValue > AMax), otherwise returns AValue
• function Sign(const AValue: TFraction): TValueSign; inline; overload;
  • retruns NegativeValue if (AValue < 0), otherwise returns PositiveValue if (AValue >0), otherwise returns ZeroValue
• function IsZero(const AValue: TFraction): Boolean; overload;
  • returns True if (AValue = 0), otherwise returns False
• function Abs(const AValue: TFraction): TFraction; overload;
  • return AValue if (AValue >= 0), otherwise returns -AValue;

General purpose functions

• function GreatestCommonDivisor(a, b: Int64): Int64;
  • returns the greates common divisor of a and b
• function Floor(D: Double): Int64; overload;
  • returns the integer part of D (subtracted with 1, if (D < 0))

Conversion routines

• function FloatToFraction(Value, Precision: Double): TFraction;
  • returns an approximation of Value in the form of a fraction, e.g. FloatTofraction(0.5,0.01) returns 1/2 (one half)
  • Precision defines the acceptable value for which (Abs(Result) - Abs(Value) <= Precision.
  • Precision is bound to Value by a magnitude of 15 at most
  • FloatToFraction in fact is a function varable which is initialized to the MF_FloatTofraction() function. You can assign your own function to it if wanted.
• function TryFloatToFraction(Value, Precision: Double; out F: TFraction; AcceptPrecisionError: Boolean): Boolean;
  • return value depends on AcceptPrecisionError value:
    • if (AcceptPrecisionError = True) then the function retruns True if an approxiamtion can be found
    • if (AcceptPrecisionError = False) the functions returns True if an approximation can be found AND Abs(Abs(Result)-Abs(Value)) <= Precision
  • the value of F only makes sense if the function returns True
• function FloatToFractionDef(Value, Precision: Double; Def: TFraction; AcceptPrecisionError: Boolean): TFraction;
  • returns the found approximation (F) if TryFloatToFraction(Value, Precision, F, AcceptPrecisionError: Boolean) succeeds, otherwise returns Def
• function StrToFraction(const S: String): TFraction;
  • returns fraction that is represented in S, raises an EConvertError upon failure
• function TryStrToFraction(const S: String; out F: TFraction): Boolean;
  • retruns True if S can be converted to a fraction, otherwise returns False
  • the value of F only makes sense f the function returns True
• function StrToFractionDef(const S: String; Def: TFraction): TFraction;
  • returns the fraction represented in S if conversion succeeds, otherwise returns Def