I can maybe also provide some comments on capabilities of individual packages (if this is desired), as I took a look at each of them over time.

That would be appreciated.

Here we go - first some additional Pascal implementations I am aware of

BigInt: v1.8 - Franco Milani

http://spazioinwind.libero.it/frm/softwareThough this is a Pascal source >90% are coded as x86-32 Win32 assembler routines - memory served me badly on ths one.

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HugeInt: v5.34 - David J Butler

https://github.com/fundamentalslib/fundamentals5Part of a much larger library but the unit can be used self-contained.

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LongMathForPascal: Zsolt Szakaly

https://github.com/zsoltszakaly/longmathforpascalA quite recent contribution (2021) - unfortunately it does not support any efficient algorithms and becomes slow very fast.

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GInt - Walied Othman

https://github.com/SnakeDoctor/FGIntAgain part of a larger library but can be used self-contained.

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I also promised to provide some comments on the packages. I'll start with BigIntegers and MP-ARITH today and will cover more in the coming days - I have to ressurect some old tools and buried knowledge, so it takes a bit of time. Of course the following is subjective, and I'm explicitely not going into the topic of licenses ...

BigIntegers - Velthuis

- 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

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MPArith - Wolfgang Erhardt

- Functionality

- supports 16/32/64 bit, little- & big-endian

- pure functional implementation

- dynamic sizing

- solid error handling (function results or exceptions)

- extensive set of functions - arith, bitops, comparisons, type conversion, base conversion

- extensive number theory - gcd, modinv, mulmod, pow, powmod, sqrt+remainder, n-root+remainder, and a lot more

- Algorithms

- basecase multiplication only 33% slower than best known pure Pascal

- efficient multiplication: Karatsuba, Toom3

- efficient squaring: Karatsuba, Toom3

- efficient division: Burnikel-Ziegler

- div&cong base conversion (both ways)

- efficient GCD

- efficient modular ops: based on Montgomery & Barrett reductions

- efficient roots: quadratically converging

- Issues

- default thresholds & missing tool for auto detection

- Burnikel-Ziegler efficiency degrades on large sizes

- no class implementation

- Nice things

- simple to activate under FPC

- accompanied by a good manual

- extensive test coverage

- there is also rationals, reals & complex available with large set of functions

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@SymbolicFrank - does the above help you or is there something I should add, take into closer focus, from your perspective?

Regards,

MathMan