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OpenPFGW is software that is designed to perform PRP and primality tests on numbers of specific forms. This software currently run on any x86 hardware with the support of George Woltman's gwnum library, the same library behind GIMPS and Prime95.
Precise Calculator has arbitrary precision and can calculate with complex numbers, fractions, vectors and matrices. Has more than 150 mathematical functions and statistical functions and is programmable (if, goto, print, return, for).
Aleph One is a highly sophisticated program for generating fractals. Some major features are: A built-in expression generator, 32-bit colouring schemes for the fractals, multi-threaded and multi-server rendering! WOW! And lots, lots more...
The source code has moved to GitLab: https://gitlab.com/jmmcg/alephone
Freemat is an interpreted, matrix-oriented development environment for engineering and scientific applications, similar to the commercial package MATLAB. Freemat provides visualization, image manipulation, and plotting as well as parallel programming.
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A simple sieve/prefactor program for Eisenstein-Mersenne Primes
A simple sieve/prefactor program for the so-called Eisenstein-Mersenne Primes: 3^p +- 3^((p + 1)/2) + 1. See http://oeis.org/A125738, A125739 and [1] for a good introduction. Some easily established properties are: p must be prime; sign is minus for p=+-1 (mod 12), plus otherwise; composites only have factors of form 6kp+1 (integer k).
Related probable primes (3^p -+ 3^((p + 1)/2) + 1)/7 are sieved at the same time. See http://oeis.org/A125743, A125744.
After sieving, the Berrizbeitia-Iskra or a Proth test can be run; this is best implemented with FFT mod (3^3p+1) using GWNUM library. A sample implementation (a patch to the LLR program) is available from Batalov...
Iterate function viewer for Windows and Linux. It has built in 14 different iterate {Mandelbrot) functions. Many possibilities for changing parameters, saving as bitmap or small file. windows-32. Linux 32 - 64bit. Low level written in assembler.
libNT is a Number Theory Library which is based on a BigInteger Class. It will contain several algorithms for solving Number Theory Problems. Written in the IDE Code::Blocks
A strong, yet minimalistic Math-oriented Programming Language (MML) providing an easy-to-use console and a command-line script interpreter, targetted towards fast calculations for extremely big numbers, and bundled with a number of math libraries.
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Magneticle is a 3D OpenGL physical simulation that applies the Biot-Savart law to charged particles operating inside a magnetic field produced by a current-carrying wire modeled as an arbitrary space curve.
Fractal explorer with movie recording, deep zoom, multicore and more
Fractice is a fractal explorer/renderer for Windows. It supports navigation, thumbnails, previews, deep zoom, printing, posters, palettes, multicore and distributed processing, movie recording, undo/redo, job control, VJ mixing, dual-monitor, & MIDI.
Matho is a OS Independant Application and API for mathematical operations, features include curve sketching, calculus, iterative formulae, algebra solver, 2d/3d geometry and mechanical and statistical functionality.
x86mph is an optimized library with vector, matrix, and vertex helpers (including an own TnL) It also contains memory helpers, and other stuff such as image processing (color inverting, changing bpp) taking advantage of x86's 3DNow!, MMX, and SSE
JellyMark is a next-generation OpenGL and CPU benchmarking program.
Features:
Realtime Physics simulation of non rigid body bouncing in a rotating cube.
100% Assembly optimized FPU spring calculation routine.
Cube environment mapping for reflections.
Improving the speed of the signal analysis code for Seti@home. Leveraging modern processors advanced features such as SIMD and parallel execution units, as well as identifying better methods to code existing functions.
This STL-like C++ library contains classes for long integer numbers processing with using of assembler functions as a backend. Lazy evaluation is also used for optimization. It also contains generic implementation of classical number-theory algorithms.