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BigInteger, BigDecimal and BigRational for Delphi

These are implementations of the multi-precision BigInteger, BigDecimal and BigRational types, built from scratch.


BigInteger is a multi-precision integer. Its size is only limited by available memory.

BigInteger is built for ease of use, speed and reliability. It is written in plain Object Pascal and x86-32/x86-64 assembler, but every assembler function has a so called "pure Pascal" equivalent as well. It is modelled after the BigInteger type in .NET, but is far more optimized than that and provides an interface that is more in line with Delphi. It uses higher level algorithms like Burnikel-Ziegler, Karatsuba, Toom-Cook, etc. to make things fast even for very large integers. It offers overloaded operators and all the usual functions. More information can be found on the BigIntegers unit page on my website.


BigDecimal is a multi-precision decimal floating point type. It can have an almost unlimited precision.

BigDecimal is equally built for ease of use and reliability. It builds on top of BigInteger: the internal representation is a BigInteger for the significant digits, and a scale to indicate the decimals. It also offers overloaded operators and all the usual functions. This is modelled after the BigDecimal type in Java, but the interface is more in line with Delphi. More information about this type can be found on the BigDecimals unit page on my website.


A type that holds a number as fraction (ratio) of two BigIntegers, a numerator and a denominator, i.e. 1/7 or 100/3. This type is very good at simple arithmetic (+, -, *, /), since it doesn't lose precision or need any rounding. Still a work in progress...


The newest version of BigIntegers has additional overloaded operators and additional constructors that are compatible with C++Builder. So now you simply include:

#include "Velthuis.BigIntegers.hpp"

and then you can do things like:

BigInteger a = 17;
BigInteger b = "123";
BigInteger c = a + b;

Directory structure

         BigDecimalTestDataGenerator /...       --- Test data generator in Java; 
	                                            open with NetBeans 8
         BigIntegerTestGenerator /...           --- Test data generator in C#; open .sln file with 
                                                    Visual Studio 2010 (Express) or newer
	 Java/BigIntegerTestDataGenerator /...  --- Newer test data generator in Java; 
	                                            open with NetBeans 8
         BigRationalTestDataGenerator /...      --- Test data generator in Java, using the Apache 
                                                    Commons-Math library.
                                                    Open with NetBeans 8. Might require installation 
                                                    of the Apache libs.
   Source                                       --- Sources for units and for generator
      BigDecimals /...                          --- Sources for DUnit tests for BigDecimals
      BigIntegers /...                          --- Sources for DUnit tests for BigIntegers
      BigRationals /...                         --- Sources for DUnit tests for BigRationals
   Visualizers                                  --- Sources for IDE debug visualizer DLL and packages for BigInteger 
                                                    and BigDecimal   


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