810 lines
17 KiB
C++
810 lines
17 KiB
C++
/*
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* This file is a part of TTMath Mathematical Library
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* and is distributed under the 3-Clause BSD Licence.
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* Author: Tomasz Sowa <t.sowa@ttmath.org>
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*/
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/*
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* Copyright (c) 2006-2017, Tomasz Sowa
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* * Neither the name Tomasz Sowa nor the names of contributors to this
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* project may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
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* THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef headerfilettmathobject
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#define headerfilettmathobject
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/*!
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\file ttmathobjects.h
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\brief Mathematic functions.
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*/
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#include <string>
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#include <vector>
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#include <list>
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#include <map>
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#include "ttmathtypes.h"
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#include "ttmathmisc.h"
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namespace ttmath
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{
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/*!
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objects of this class are used with the mathematical parser
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they hold variables or functions defined by a user
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each object has its own table in which we're keeping variables or functions
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*/
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class Objects
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{
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public:
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/*!
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one item (variable or function)
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'items' will be on the table
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*/
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struct Item
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{
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// name of a variable of a function
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// internally we store variables and funcions as std::string (not std::wstring even when wide characters are used)
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std::string value;
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// number of parameters required by the function
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// (if there's a variable this 'param' is ignored)
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int param;
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Item() {}
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Item(const std::string & v, int p) : value(v), param(p) {}
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};
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// 'Table' is the type of our table
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typedef std::map<std::string, Item> Table;
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typedef Table::iterator Iterator;
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typedef Table::const_iterator CIterator;
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/*!
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this method returns true if a character 'c' is a character
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which can be in a name
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if 'can_be_digit' is true that means when the 'c' is a digit this
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method returns true otherwise it returns false
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*/
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static bool CorrectCharacter(int c, bool can_be_digit)
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{
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if( (c>='a' && c<='z') || (c>='A' && c<='Z') )
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return true;
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if( can_be_digit && ((c>='0' && c<='9') || c=='_') )
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return true;
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return false;
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}
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/*!
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this method returns true if the name can be as a name of an object
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*/
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template<class string_type>
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static bool IsNameCorrect(const string_type & name)
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{
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if( name.empty() )
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return false;
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if( !CorrectCharacter(name[0], false) )
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return false;
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typename string_type::const_iterator i = name.begin();
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for(++i ; i!=name.end() ; ++i)
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if( !CorrectCharacter(*i, true) )
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return false;
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return true;
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}
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/*!
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this method returns true if such an object is defined (name exists)
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*/
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bool IsDefined(const std::string & name)
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{
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Iterator i = table.find(name);
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if( i != table.end() )
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// we have this object in our table
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return true;
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return false;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method returns true if such an object is defined (name exists)
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*/
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bool IsDefined(const std::wstring & name)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return false;
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Misc::AssignString(str_tmp1, name);
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return IsDefined(str_tmp1);
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}
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#endif
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/*!
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this method adds one object (variable of function) into the table
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*/
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ErrorCode Add(const std::string & name, const std::string & value, int param = 0)
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Iterator i = table.find(name);
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if( i != table.end() )
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// we have this object in our table
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return err_object_exists;
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table.insert( std::make_pair(name, Item(value, param)) );
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method adds one object (variable of function) into the table
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*/
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ErrorCode Add(const std::wstring & name, const std::wstring & value, int param = 0)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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Misc::AssignString(str_tmp2, value);
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return Add(str_tmp1, str_tmp2, param);
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}
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#endif
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/*!
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this method returns 'true' if the table is empty
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*/
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bool Empty() const
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{
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return table.empty();
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}
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/*!
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this method clears the table
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*/
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void Clear()
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{
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return table.clear();
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}
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/*!
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this method returns 'const_iterator' on the first item on the table
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*/
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CIterator Begin() const
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{
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return table.begin();
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}
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/*!
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this method returns 'const_iterator' pointing at the space after last item
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(returns table.end())
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*/
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CIterator End() const
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{
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return table.end();
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}
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/*!
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this method changes the value and the number of parameters for a specific object
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*/
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ErrorCode EditValue(const std::string & name, const std::string & value, int param = 0)
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Iterator i = table.find(name);
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if( i == table.end() )
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return err_unknown_object;
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i->second.value = value;
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i->second.param = param;
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method changes the value and the number of parameters for a specific object
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*/
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ErrorCode EditValue(const std::wstring & name, const std::wstring & value, int param = 0)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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Misc::AssignString(str_tmp2, value);
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return EditValue(str_tmp1, str_tmp2, param);
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}
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#endif
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/*!
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this method changes the name of a specific object
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*/
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ErrorCode EditName(const std::string & old_name, const std::string & new_name)
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{
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if( !IsNameCorrect(old_name) || !IsNameCorrect(new_name) )
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return err_incorrect_name;
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Iterator old_i = table.find(old_name);
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if( old_i == table.end() )
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return err_unknown_object;
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if( old_name == new_name )
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// the new name is the same as the old one
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// we treat it as a normal situation
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return err_ok;
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ErrorCode err = Add(new_name, old_i->second.value, old_i->second.param);
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if( err == err_ok )
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{
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old_i = table.find(old_name);
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TTMATH_ASSERT( old_i != table.end() )
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table.erase(old_i);
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}
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return err;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method changes the name of a specific object
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*/
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ErrorCode EditName(const std::wstring & old_name, const std::wstring & new_name)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(old_name) || !IsNameCorrect(new_name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, old_name);
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Misc::AssignString(str_tmp2, new_name);
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return EditName(str_tmp1, str_tmp2);
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}
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#endif
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/*!
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this method deletes an object
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*/
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ErrorCode Delete(const std::string & name)
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Iterator i = table.find(name);
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if( i == table.end() )
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return err_unknown_object;
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table.erase( i );
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method deletes an object
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*/
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ErrorCode Delete(const std::wstring & name)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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return Delete(str_tmp1);
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}
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#endif
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/*!
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this method gets the value of a specific object
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*/
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ErrorCode GetValue(const std::string & name, std::string & value) const
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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CIterator i = table.find(name);
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if( i == table.end() )
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{
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value.clear();
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return err_unknown_object;
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}
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value = i->second.value;
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method gets the value of a specific object
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*/
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ErrorCode GetValue(const std::wstring & name, std::wstring & value)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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ErrorCode err = GetValue(str_tmp1, str_tmp2);
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Misc::AssignString(value, str_tmp2);
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return err;
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}
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#endif
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/*!
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this method gets the value of a specific object
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(this version is used for not copying the whole string)
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*/
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ErrorCode GetValue(const std::string & name, const char ** value) const
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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CIterator i = table.find(name);
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if( i == table.end() )
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{
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*value = 0;
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return err_unknown_object;
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}
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*value = i->second.value.c_str();
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method gets the value of a specific object
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(this version is used for not copying the whole string)
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*/
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ErrorCode GetValue(const std::wstring & name, const char ** value)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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return GetValue(str_tmp1, value);
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}
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#endif
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/*!
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this method gets the value and the number of parameters
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of a specific object
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*/
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ErrorCode GetValueAndParam(const std::string & name, std::string & value, int * param) const
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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CIterator i = table.find(name);
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if( i == table.end() )
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{
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value.clear();
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*param = 0;
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return err_unknown_object;
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}
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value = i->second.value;
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*param = i->second.param;
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method gets the value and the number of parameters
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of a specific object
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*/
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ErrorCode GetValueAndParam(const std::wstring & name, std::wstring & value, int * param)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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ErrorCode err = GetValueAndParam(str_tmp1, str_tmp2, param);
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Misc::AssignString(value, str_tmp2);
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return err;
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}
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#endif
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/*!
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this method sets the value and the number of parameters
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of a specific object
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(this version is used for not copying the whole string)
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*/
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ErrorCode GetValueAndParam(const std::string & name, const char ** value, int * param) const
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{
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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CIterator i = table.find(name);
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if( i == table.end() )
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{
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*value = 0;
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*param = 0;
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return err_unknown_object;
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}
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*value = i->second.value.c_str();
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*param = i->second.param;
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return err_ok;
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}
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#ifndef TTMATH_DONT_USE_WCHAR
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/*!
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this method sets the value and the number of parameters
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of a specific object
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(this version is used for not copying the whole string
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but in fact we make one copying during AssignString())
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*/
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ErrorCode GetValueAndParam(const std::wstring & name, const char ** value, int * param)
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{
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// we should check whether the name (in wide characters) are correct
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// before calling AssignString() function
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if( !IsNameCorrect(name) )
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return err_incorrect_name;
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Misc::AssignString(str_tmp1, name);
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return GetValueAndParam(str_tmp1, value, param);
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}
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#endif
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/*!
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this method returns a pointer into the table
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*/
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Table * GetTable()
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{
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return &table;
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}
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private:
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Table table;
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std::string str_tmp1, str_tmp2;
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}; // end of class Objects
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/*!
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objects of the class History are used to keep values in functions
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which take a lot of time during calculating, for instance in the
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function Factorial(x)
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it means that when we're calculating e.g. Factorial(1000) and the
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Factorial finds that we have calculated it before, the value (result)
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is taken from the history
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*/
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template<class ValueType>
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class History
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{
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/*!
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one item in the History's object holds a key, a value for the key
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and a corresponding error code
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*/
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struct Item
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{
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ValueType key, value;
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ErrorCode err;
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};
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/*!
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we use std::list for simply deleting the first item
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but because we're searching through the whole container
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(in the method Get) the container should not be too big
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(linear time of searching)
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*/
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typedef std::list<Item> buffer_type;
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buffer_type buffer;
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typename buffer_type::size_type buffer_max_size;
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public:
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/*!
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default constructor
|
|
default max size of the History's container is 15 items
|
|
*/
|
|
History()
|
|
{
|
|
buffer_max_size = 15;
|
|
}
|
|
|
|
|
|
/*!
|
|
a constructor which takes another value of the max size
|
|
of the History's container
|
|
*/
|
|
History(typename buffer_type::size_type new_size)
|
|
{
|
|
buffer_max_size = new_size;
|
|
}
|
|
|
|
|
|
/*!
|
|
this method adds one item into the History
|
|
if the size of the container is greater than buffer_max_size
|
|
the first item will be removed
|
|
*/
|
|
void Add(const ValueType & key, const ValueType & value, ErrorCode err)
|
|
{
|
|
Item item;
|
|
item.key = key;
|
|
item.value = value;
|
|
item.err = err;
|
|
|
|
buffer.insert( buffer.end(), item );
|
|
|
|
if( buffer.size() > buffer_max_size )
|
|
buffer.erase(buffer.begin());
|
|
}
|
|
|
|
|
|
/*!
|
|
this method checks whether we have an item which has the key equal 'key'
|
|
|
|
if there's such item the method sets the 'value' and the 'err'
|
|
and returns true otherwise it returns false and 'value' and 'err'
|
|
remain unchanged
|
|
*/
|
|
bool Get(const ValueType & key, ValueType & value, ErrorCode & err)
|
|
{
|
|
typename buffer_type::iterator i = buffer.begin();
|
|
|
|
for( ; i != buffer.end() ; ++i )
|
|
{
|
|
if( i->key == key )
|
|
{
|
|
value = i->value;
|
|
err = i->err;
|
|
return true;
|
|
}
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
|
|
/*!
|
|
this methods deletes an item
|
|
|
|
we assume that there is only one item with the 'key'
|
|
(this methods removes the first one)
|
|
*/
|
|
bool Remove(const ValueType & key)
|
|
{
|
|
typename buffer_type::iterator i = buffer.begin();
|
|
|
|
for( ; i != buffer.end() ; ++i )
|
|
{
|
|
if( i->key == key )
|
|
{
|
|
buffer.erase(i);
|
|
return true;
|
|
}
|
|
}
|
|
|
|
return false;
|
|
}
|
|
|
|
|
|
}; // end of class History
|
|
|
|
|
|
|
|
/*!
|
|
this is an auxiliary class used when calculating Gamma() or Factorial()
|
|
|
|
in multithreaded environment you can provide an object of this class to
|
|
the Gamma() or Factorial() function, e.g;
|
|
typedef Big<1, 3> MyBig;
|
|
MyBig x = 123456;
|
|
CGamma<MyBig> cgamma;
|
|
std::cout << Gamma(x, cgamma);
|
|
each thread should have its own CGamma<> object
|
|
|
|
in a single-thread environment a CGamma<> object is a static variable
|
|
in a second version of Gamma() and you don't have to explicitly use it, e.g.
|
|
typedef Big<1, 3> MyBig;
|
|
MyBig x = 123456;
|
|
std::cout << Gamma(x);
|
|
*/
|
|
template<class ValueType>
|
|
struct CGamma
|
|
{
|
|
/*!
|
|
this table holds factorials
|
|
1
|
|
1
|
|
2
|
|
6
|
|
24
|
|
120
|
|
720
|
|
.......
|
|
*/
|
|
std::vector<ValueType> fact;
|
|
|
|
|
|
/*!
|
|
this table holds Bernoulli numbers
|
|
1
|
|
-0.5
|
|
0.166666666666666666666666667
|
|
0
|
|
-0.0333333333333333333333333333
|
|
0
|
|
0.0238095238095238095238095238
|
|
0
|
|
-0.0333333333333333333333333333
|
|
0
|
|
0.075757575757575757575757576
|
|
.....
|
|
*/
|
|
std::vector<ValueType> bern;
|
|
|
|
|
|
/*!
|
|
here we store some calculated values
|
|
(this is for speeding up, if the next argument of Gamma() or Factorial()
|
|
is in the 'history' then the result we are not calculating but simply
|
|
return from the 'history' object)
|
|
*/
|
|
History<ValueType> history;
|
|
|
|
|
|
/*!
|
|
this method prepares some coefficients: factorials and Bernoulli numbers
|
|
stored in 'fact' and 'bern' objects
|
|
|
|
how many values should be depends on the size of the mantissa - if
|
|
the mantissa is larger then we must calculate more values
|
|
for a mantissa which consists of 256 bits (8 words on a 32bit platform)
|
|
we have to calculate about 30 values (the size of fact and bern will be 30),
|
|
and for a 2048 bits mantissa we have to calculate 306 coefficients
|
|
|
|
you don't have to call this method, these coefficients will be automatically calculated
|
|
when they are needed
|
|
|
|
you must note that calculating these coefficients is a little time-consuming operation,
|
|
(especially when the mantissa is large) and first call to Gamma() or Factorial()
|
|
can take more time than next calls, and in the end this is the point when InitAll()
|
|
comes in handy: you can call this method somewhere at the beginning of your program
|
|
*/
|
|
void InitAll();
|
|
// definition is in ttmath.h
|
|
};
|
|
|
|
|
|
|
|
|
|
} // namespace
|
|
|
|
#endif
|