Number Factory

Number Factory is a collection of mini-programs that can compute various numbers to extremely large sizes.
It's essentially a souped up version of Mini-Pi that is powered by the same backend as y-cruncher.

Examples include:

• Large integer power
• Factorial and Binomial Coefficient
• Square Root
• Logarithms
• e - Binary Splitting of exp(1).
• Pi - Chudnovsky, Ramanujan, AGM, Machin-like formulas.
• Catalan's Constant - Lupas, Huvent formulas
• Zeta(3), Zeta(5) - various formulas
• Lemniscate, Gamma(1/4)

Number Factory's current goals are:

• Test the feasibility of maintaining a public interface to the y-cruncher's internals.
• Serve as a research infrastructure for the y-cruncher project.
• Show-and-tell some basic, but efficient and parallel implementations of various constants and functions.

Number Factory uses the YMP library which is an experimental public interface to y-cruncher's internals.

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Performance:

Number Factory has access to parallel large arithmetic whereas most other programs do not. For this reason alone, it is often faster than other programs by sheer force of parallelization.

For most constants, the overall performance comes within a factor of 2 of y-cruncher. This is actually pretty good considering that most of Number Factory's implementations are relatively unoptimized.

That said, squeezing out the remaining factor of 2 will probably be difficult. y-cruncher does some pretty crazy things to get to where it is now. And it uses internal functionality that isn't exposed through the YMP interface.

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Requirements:

Compilation:

• Visual Studio 2015

A Visual Studio project has been provided with various configurations that target different processors. It should be fairly straight-forward to compile and run the app through the IDE. (Though it will be faster to run from outside the IDE since it bypasses the debug heap.)

The DLL interface with the YMP library is "supposed to" be portable across different compilers. But this is untested. Number Factory is the first program to dynamically link with YMP. (y-cruncher statically links.)

Run-Time:

• 64-bit Windows Vista or later. (Windows 7 SP1 required for AVX)
• A processor with SSE4.1. (Intel Penryn or later. Or AMD Bulldozer or later.)

Number Factory itself can be compiled for older processors. But for all practical purposes, the underlying YMP library needs a minimum of SSE4.1 to be competitive with existing libraries. That said, the real performance gains will require AVX2.

There is currently no support for Linux yet. The Number Factory/YMP project is still experimental and will be tested in Windows first. Only if it is massively successful will a Linux version be considered.

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Configurations:

The Visual Studio project currently supports the following build configurations:

Configuration	Target Processor	YMP Binary	Notes
Debug		SSE4.1	No Optimizations
Release		SSE4.1	Same as "08-Nehalem"
08-Nehalem	Intel Nehalem	SSE4.1
11-SandyBridge	Intel Sandy Bridge	AVX
11-Bulldozer	AMD Bulldozer	FMA4/XOP
13-Haswell	Intel Haswell	FMA3/AVX2

Upon building a configuration through the IDE, the appropriate DLLs are copied into the same directory as the output binary. They will be needed to run the binary.

All ymp.dll binaries of the same YMP release will have the same ABI. So any Number Factory binary (or any other client app) will be able to link with any of them. This may make it slightly easier to do CPU dispatching.

However, ymp.dll binaries from different releases are not guaranteed to be compatible. Backwards incompatible changes may require recompilation of the client app. Maintaining a static ABI is currently not a feasible commitment.

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Source Directories:

• NumberFactory/ - The main Number Factory directory.
• ymp/ - Headers for the YMP library.
• PublicLibs/ - Public shared libraries. Also used by the Digit Viewer.
• PrivateLibs/, Objects/, and Modules/ - Internal components. Don't use directly.

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Documentation:

• YMP Library (v1.0): http://www.numberworld.org/ymp/v1.0/

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Licensing:

• The source code for Number Factory is opened-sourced and licensed under BSD-3.
• The binary cilkrts20.dll is Intel's Cilk Run-Time library. It is licensed under BSD-3.
• The binary ymp.dll is the YMP library. It is free for non-commercial use only.