arbitraryprecisioncalculation

Arbitrary precision calculation is a library containing trigonometric and other functions of floating point numbers with arbitrary precision using gmp library.

arbitraryprecisioncalculation
Table of Contents
Features
Download
Installation Instructions
- Installation on Windows
- Installation on a Linux operating system
Examples
Documentation
Feedback
License

Features

This library extends the gmp library to use many additional functions.

Trigonometric functions (sin, cos, tan, arccos, ...)
exponential functions (exp, log, ...)
and more (pow, randomize, ...)

Additionally vector wise versions of some functions with two operands and some additional functions only working on vectors (orthogonal projection).

It is recommended to use only this library for calculations because it includes some kind of memory management. Therefore using gmp functions directly on values received from the library or/and the other way around can cause unexpected behaviour!

Download

The source code and all further data can be downloaded from the github-repository.

Installation Instructions

Installation on Windows

Install Cygwin with components gcc, m4 and make
Install the GMP library
- Download and unzip the GMP sources and switch to that folder.
  - For example: download gmp-x.x.x.tar.xz from https://gmplib.org/
  - unzip the file with tar -xJf gmp-x.x.x.tar.xz
  - go to that folder with cd gmp-x.x.x
- Execute ./configure
- Execute make
- Execute make install
- It might be necessary to copy the library libgmp.a and libgmp.la from /usr/local/lib to /lib to ensure that it is recognized.
Download and unzip the High Precision PSO sources and switch to that folder.
Execute make to generate the library file (lib/libarbitraryprecisioncalculation.a).
The library file can be moved to any location.
.h files can be found in the src folder.

Installation on a Linux operating system

Install g++ compiler, and make (if not already present).

On systems like Ubuntu you can install them by the command sudo apt-get install make g++.
Install the GMP library
- On systems like Ubuntu you can install the GMP library by the command sudo apt-get install libgmp-dev.
- Alternatively you can install it as described in the Windows section.
Download and unzip the High Precision PSO sources and switch to that folder.
Execute make to generate the library file (lib/libarbitraryprecisioncalculation.a).
The library file can be moved to any location.
.h files can be found in the src folder.

Examples

In the examples folder some examples can be found.

Example 1

The following code of example1.cpp displays the limitations of double calculations compared to arbitrary precision calculation:

#include <arbitrary_precision_calculation/arbitraryprecisioncalculation.h>
#include <iostream>
#include <string>

int main(){

    double d_1 = 1.0;
    double d_small = 1e-50;

    std::cout << "double calculation:\n";
    std::cout << "((" << d_1 << "+" << d_small << ")-" << d_1 <<")=" << ((d_1 + d_small) -d_1) << "\n";

    arbitraryprecisioncalculation::Configuration::setInitialPrecision(230);
    // 230 is approximately ld(10)*(50+20)
    // 50 decimal digits of needed precision and additional 20 digits to guarantee the precision of the output
    arbitraryprecisioncalculation::Configuration::setPrecisionSafetyMargin(50);
    arbitraryprecisioncalculation::Configuration::setOutputPrecision(20);

    mpf_t* v_1 = arbitraryprecisioncalculation::mpftoperations::ToMpft(d_1);
    mpf_t* v_small = arbitraryprecisioncalculation::mpftoperations::ToMpft(d_small);

    mpf_t* v_sum = arbitraryprecisioncalculation::mpftoperations::Add(v_1, v_small);
    mpf_t* v_result = arbitraryprecisioncalculation::mpftoperations::Subtract(v_sum, v_1);

    std::string s_1 = arbitraryprecisioncalculation::mpftoperations::MpftToString(v_1);
    std::string s_small = arbitraryprecisioncalculation::mpftoperations::MpftToString(v_small);
    std::string s_sum = arbitraryprecisioncalculation::mpftoperations::MpftToString(v_sum);
    std::string s_result = arbitraryprecisioncalculation::mpftoperations::MpftToString(v_result);

    std::cout << "mpf_t calculation:\n";
    std::cout << "(((" << s_1 << ")+(" << s_small << "))-(" << s_1 <<"))=(" << s_sum << ")-(" << s_1 << ")=" << s_result << "\n";
    std::cout << "The non precise value of v_small depends on the non precise conversion from 1e-50 to double not from double to mpf_t!!!\n";

    // After the last use of variable the value should be released.
    // This is actually not really necessary at the end of a program.
    arbitraryprecisioncalculation::mpftoperations::ReleaseValue(v_1);
    arbitraryprecisioncalculation::mpftoperations::ReleaseValue(v_small);
    arbitraryprecisioncalculation::mpftoperations::ReleaseValue(v_sum);
    arbitraryprecisioncalculation::mpftoperations::ReleaseValue(v_result);
}

This file can be compiled by the following command if you are in the examples folder of the downloaded repository:

g++ -I ../src/ -L./../lib example1.cpp -larbitraryprecisioncalculation -lgmp -o example1

To compile your source file you need to need to specify the path to the header files (-I ../src) and the location of the library file (-L./../lib) and specify the used libraries (-larbitraryprecisioncalculation -lgmp). If you are in another current/working directory and/or if you move the library and/or header files to another location then paths may vary or may not be necessary.

The execution of it produces the following output:

$ ./example1 
double calculation:
((1+1e-50)-1)=0
mpf_t calculation:
(((1.00000000000000000000e+00)+(1.00000000000000000762e-50))-(1.00000000000000000000e+00))=(1.00000000000000000000e+00)-(1.00000000000000000000e+00)=1.00000000000000000762e-50
The non precise value of v_small depends on the non precise conversion from 1e-50 to double not from double to mpf_t!!!

Documentation

The documentation including an API can be found on the related github-pages of this repository. It is generated by doxygen. For customizing the output of doxygen some files from the doxygen-bootstrapped repository of Velron are used. It is added as a submodule and has an Apache 2.0 license.

Feedback

Please feel free to contact Alexander Raß (Alexander.Rass@fau.de). Feedback or a notice that you use this program is highly appreciated. We will also support you in case you have problems during installation or usage of this program.

License

The MIT License (MIT)

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

d-hoke/arbitraryprecisioncalculation