BigInteger

There are several (free) Pascal libraries for BigInteger (and sometimes Big Decimals like 1.23) functionality. Note: the C-based GMP library can also be used in Free Pascal, it's not listed here.

TForge

• By: Sergey Kasandrov
• Homepage: https://github.com/Alexey-T/TForge-Pascal

Modern cryptographic library for Delphi and Lazarus/FPC implemented as a set of runtime packages. Project development was stopped, the last found snapshot v0.76 was put to GitHub.

Big Decimal Math

• By: Benito van der Zander
• Homepage: https://benibela.de/sources_en.html#bigdecimalmath

This unit provides a BigDecimal-Type which stores arbitrary precision (BCD) decimal numbers and can be used like any native numeric type.

FNX

• By: Marcel Martin
• Homepage: https://www.ellipsa.eu/public/fnx/fnx.html

Library of multi-precision numbers (currently, only big integers) written for Free Pascal and Linux. The assembler code that can be enabled with a compiler directive, is for x86-64 processors only.

MPArith

• By: Wolfgang Ehrhardt
• Homepage: https://github.com/Alexey-T/Wolfgang_Ehrhardt_codes/tree/master/Misc/MPArith

Project development was stopped in about 2018. The last found snapshot was put to GitHub.

BigInt

• By: Franco Milani
• Homepage: http://spazioinwind.libero.it/frm/software

Though this is a Pascal source >90% are coded as x86-32 Win32 assembler routines.

HugeInt

• By: David J Butler
• Homepage: https://github.com/fundamentalslib/fundamentals5

Part of a much larger library but the unit can be used self-contained.

LongMathForPascal

• By: Zsolt Szakaly
• Homepage: https://github.com/zsoltszakaly/longmathforpascal

A quite recent contribution (2021) - unfortunately it does not support any efficient algorithms and becomes slow very fast.

GInt

• By: Walied Othman
• Homepage: https://github.com/SnakeDoctor/FGInt

Again part of a larger library but can be used self-contained.

BigIntegers for Delphi

• By: Rudy Velthuis
• Homepage: https://github.com/rvelthuis/DelphiBigNumbers

Code can be adapted for Free Pascal with a little effort.

Comment by forum user MathMan:

• Functionality
  • supports 32/64 bit, little- & big-endian
  • class implementation with operators & functional replicants
  • dynamic sizing and immutability
  • late binding
  • solid error handling
  • solid set of operators - arith, bitops, comparisons, expl & impl conversions
  • some number theory - gcd, modinv, mulmod, pow, powmod, sqrt+remainder, n-root+remainder
• Algorithms
  • basecase multiplication only 33% slower than best known pure Pascal
  • efficient multiplication: Karatsuba, Toom3
  • efficient squaring: Karatsuba
  • efficient division: Burnikel-Ziegler
  • div&cong base conversion (from binary to arb base only)
  • euclidean GCD
• Issues
  • tricky to convert to FPC
  • memory management degrades efficient algs on larger sizes (speed reduced by 5)
  • default thresholds & missing tool for auto detection
  • sqr-schoolbook = mul-schoolbook
  • missing efficient GCD algorithm
  • missing efficient mod algorithms (Montgomery, Barrett)
  • the way asm-enhancements are integrated could be improved (subjective)
  • testing depth & breadth could be improved (subjective)
• Nice things
  • there is also BigDecimals, BigRationals & BigFloats