BigNumberXLib
BigNumberXLib is a Delphi Big Number Library with support for Integer and Floating Point Computations.
It consists of three custom types namely
-
TIntegerXwhich provides support for Integer Computations and is based on ClojureCLR BigInteger Class -
TDecimalXwhich provides support for Floating Point Computations and is based on ClojureCLR BigDecimal Class. -
TContextwhich defines the precision and rounding mode for Floating Point Computations.
Hints about the code:
1. Multi-condition "for" loops and loops where iterator gets changed inside
the loop were converted to while loops.
2. This Library is written with (Delphi XE7 Update 1).
This Library have been tested to work properly with Delphi (XE7 Update 1).
This Library might work with other Unicode versions of Delphi (at least XE3
upwards) with little or no modifications but have not been tested by me.
3. Finally, Mobile Compilers are Supported.
4. This Library is Locale-Aware but it's Unit Tests are not.
Usage Hints
1. This Library supports Operator Overloading as well as "Chaining Mode".
2. When Performing Floating Point Arithmetics, especially Division, it
is advisable to use the "Chaining Mode" so we can specify the "TContext"
in order to avoid issues with "Non-terminating decimal expansion" like (1/3)
since this Library is an "Unlimited" Precision Library.
When using the "Chaining Mode", do note that it uses Left to Right precedence
rather than "PEMDAS" or "BODMAS".
In order to use "PEMDAS" or "BODMAS" precedence in Chaining Mode, you have
to group the preferred operations in Parenthesis.
3. Note that when using the Double Constructor of "TDecimalX",
TDecimalX.Create(0.1) <> TDecimalX.Create('0.1');
This is as a result of Computers being unable to store floating point values
exactly Internally.
4. Note that the "=" operator or ".Equals" of TDecimalX compares both precision, not
just coefficients and exponents, so assertions
like 1.0 = 1.00 will return false.
for such comparisons, use the "CompareTo" method.
Examples
var
a, b: TDecimalX;
result: Boolean;
begin
a:= TDecimalX.Create('1.0');
b:= TDecimalX.Create('1.00');
result := a = b; // returns false
result := a.CompareTo(b) = 0; // returns true
end;
Code Examples
To Perform Operations with TIntegerX and TDecimalX:
Using Operator Overloading Method;
uses
SysUtils, IntegerX, DecimalX;
procedure Calc();
var
int1, int2, intans: TIntegerX;
dec1, dec2, decans: TDecimalX;
begin
int1 := TIntegerX.Create(4);
int2 := TIntegerX.Create('8');
intans := int1 * int2 + int1 - int2 div int1;
ShowMessage(intans.ToString());
dec1 := TDecimalX.Create(8.97);
dec2 := TDecimalX.Create('6.2');
decans := dec1 * dec2 + dec1 - dec2 / dec1;
ShowMessage(decans.ToString());
end;
Using Chaining Method;
uses
SysUtils, IntegerX, DecimalX;
procedure Calc();
var
int1, int2, intans: TIntegerX;
dec1, dec2, decans: TDecimalX;
c: TContext;
begin
int1 := TIntegerX.Create(4);
int2 := TIntegerX.Create('8');
// left to right
intans := int1.Multiply(int2).Add(int1).Subtract(int2).Divide(int1);
ShowMessage(intans.ToString());
c:= TContext.Create(5, TRoundingMode.HalfUp);
dec1 := TDecimalX.Create(8.97);
dec2 := TDecimalX.Create('6.2');
// left to right
decans := dec1.Multiply(dec2, c).Add(dec1, c).Subtract(dec2, c).Divide(dec1, c);
ShowMessage(decans.ToString());
end;
Unit Tests
Unit Tests can be found in BigNumberXLib.Test Folder.
The Unit tests makes use of DUnitX and TestInsight.
License
This Program is Licensed Under Mozilla Public License v. 2.0
Conclusion
Special Thanks to the makers of ClojureCLR and Leo Aso.