# Berta Danilo

## Big Number C++ library

This article - or better the downloadable attachments - describe the behavior of a BigNumber C++ library – called bn.h that is an acronym for Big Number - developed by myself, performing the standard four operations: sum, subtraction, multiplication and division between two BIG NUMBERS (in the following B.N.) using the standard well-know-lower-school-teached-algorithms. The definition of B.N. is: number with a quantity of digits that it's impossible and/or difficult to deal with them as usual C++ - signed or unsigned -  long double number, bigger than LDBL_MAX and/or lesser than LDBL_MIN.

Now,  considering  that  LDBL_MAX/MIN  are  platform  dependent  –  the  values  are  different  for different machines architecture – as a rule of thumbs those values are about: LDBL_MIN=3.3621e-4932 and LDBL_MAX=1.18973e+4932; in practical problems this is not an issue. Some problems start to come up when you consider the precision; for a  C++ long double type the precision – that is always platform dependent – has usually the value of 18. This value is the “number  of  digits  (in  decimal  base)  that  can  be  represented  without  change”   (from http://www.cplusplus.com/reference/limits/numeric_limits/).  In  more  technical  words,  the  C++ code:

#include <climits>
std::cout << "long double minimum   = " << std::numeric_limits<long double>::min() << std::endl;
std::cout << "long double maximum   = " << std::numeric_limits<long double>::max() << std::endl;
std::cout << "long double precision = " << std::numeric_limits<long double>::digits10 << std::endl;

Produces:

long double minimum   = 3.3621e-4932
long double maximum   = 1.18973e+4932
long double precision = 18

So, rephrasing, the following B.N. definition should be used: is a B.N. any number that has to be used in calculations requiring a precision greater than the precision of a C++ long double type.

Functions  in  bn.h library  are  NOT  THREAD  SAFE,  because  they  use  variables  passed  by reference. It will not be difficult to “transform” those functions in “thread-safe”, replacing the return value of each function with a C++ structs; should be this behavior will be adjusted –time allowing– in a next release.

All the  primary functions  - that are: SumB(), SubB(), MulB(), InvB(), DivB() -  are located in the core module “bn.h”; in the module “functions.h” are located secondary functions- in this release just one function  PowB() -  that are considered secondary because functions that call primary functions to operate.

Just to give you a taste of the library usage, the following is a call to MulB() function performing product between two B.N.

strNum1       = "1234567890";
strNum2       = "1234567890.1010";
bolSignNum1   = true;
bolSignNum2   = false;
bolSignResult = false;
isError       = false;
strSeparator  = ".";

strResult = MulB(strNum1,strNum2,bolSignNum1,bolSignNum2,bolSignResult,isError,strSeparator);
cout << strNum1 << " * (-" << strNum2 << ") = " << strResult << endl;
cout << "bolSignResult = " << bolSignResult << endl;
cout << "isError       = " << isError       << endl;

Results is:

1234567890 * (-1234567890.1010) = 1524157875143743456.89
bolSignResult = 0
isError       = 0

Library (source code) and User/Reference Manual should be downloaded at the bottom of current article. The project was developed using Code::Block and the source code include the CodeBlock complete project.

This code is released under GPL version 3 - Copyright (C) 2015 Berta Danilo

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.

See the GNU General Public License for more details.

Attachments:
FileDescriptionFile sizeDownloadsCreated
U-RMC++ Big Number Library User & Reference Manual238 kB8822015-09-11 12:24
BNC++ Big Number Library source code (basic four operations)908 kB2852015-09-11 12:22

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