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# nim-ttmath
A Nim wrapper for [ttmath library](https://www.ttmath.org/), a c++ template library for operating with
big integers and floats with fixed sizes.

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import ttmath
var a = 2.i256
var b = 2.i256
echo a + b
echo a - b
echo a * b
echo a / b
echo a < b
echo a > b
echo 3.i256 > b
echo a < 3.i256
echo a <= b
echo a >= b
a += b
echo a
a *= b
echo a
a -= b
echo a
a /= b
echo a
echo a mod b
echo a div b
echo a and b
echo a or b
echo a xor b
echo pow(a, 2)
echo a shl 2
echo a shr 2
echo a.getInt
echo -a
echo "02".i256

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--p:"../src"

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Copyright (c) 2006-2012, Tomasz Sowa
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:
* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
* Neither the name Tomasz Sowa nor the names of contributors to this
project may be used to endorse or promote products derived
from this software without specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
THE POSSIBILITY OF SUCH DAMAGE.

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/*
* This file is a part of TTMath Bignum Library
* and is distributed under the (new) BSD licence.
* Author: Tomasz Sowa <t.sowa@ttmath.org>
*/
/*
* Copyright (c) 2012, Tomasz Sowa
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name Tomasz Sowa nor the names of contributors to this
* project may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef headerfilettmathdec
#define headerfilettmathdec
#include "ttmathtypes.h"
#include "ttmaththreads.h"
#include "ttmathuint.h"
namespace ttmath
{
template<uint value_size, uint dec_digits>
class Dec
{
public:
UInt<value_size> value;
unsigned char info;
/*!
Sign
the mask of a bit from 'info' which means that there is a sign
(when the bit is set)
*/
#define TTMATH_DEC_SIGN 128
/*!
Not a number
if this bit is set that there is not a valid number
*/
#define TTMATH_DEC_NAN 64
Dec()
{
info = TTMATH_DEC_NAN;
}
Dec(const char * s)
{
info = TTMATH_DEC_NAN;
FromString(s);
}
Dec<value_size, dec_digits> & operator=(const char * s)
{
FromString(s);
return *this;
}
uint FromString(const char * s, const char ** after_source = 0, bool * value_read = 0)
{
return FromStringBase(s, after_source, value_read);
}
void ToString(std::string & result) const
{
ToStringBase(result);
}
/*!
this method clears a specific bit in the 'info' variable
bit is one of:
*/
void ClearInfoBit(unsigned char bit)
{
info = info & (~bit);
}
/*!
this method sets a specific bit in the 'info' variable
bit is one of:
*/
void SetInfoBit(unsigned char bit)
{
info = info | bit;
}
/*!
this method returns true if a specific bit in the 'info' variable is set
bit is one of:
*/
bool IsInfoBit(unsigned char bit) const
{
return (info & bit) != 0;
}
bool IsNan() const
{
return IsInfoBit(TTMATH_DEC_NAN);
}
bool IsSign() const
{
return IsInfoBit(TTMATH_DEC_SIGN);
}
/*!
this method sets the sign
e.g.
-1 -> -1
2 -> -2
we do not check whether there is a zero or not, if you're using this method
you must be sure that the value is (or will be afterwards) different from zero
*/
void SetSign()
{
SetInfoBit(TTMATH_DEC_SIGN);
}
void SetNaN()
{
SetInfoBit(TTMATH_DEC_NAN);
}
void Abs()
{
ClearInfoBit(TTMATH_DEC_SIGN);
}
uint Add(const Dec<value_size, dec_digits> & arg)
{
uint c = 0;
if( IsSign() == arg.IsSign() )
{
c += value.Add(arg.value);
}
else
{
bool is_sign;
if( value > arg.value )
{
is_sign = IsSign();
value.Sub(arg.value);
}
else
{
is_sign = arg.IsSign();
UInt<value_size> temp(this->value);
value = arg.value;
value.Sub(temp);
}
is_sign ? SetSign() : Abs();
}
if( c )
SetNaN();
return (c==0)? 0 : 1;
}
/*
uint Sub(const Dec<value_size, dec_digits> & arg)
{
}
*/
private:
#ifndef TTMATH_MULTITHREADS
/*!
*/
void SetMultipler(UInt<value_size> & result)
{
// this guardian is initialized before the program runs (static POD type)
static int guardian = 0;
static UInt<value_size> multipler;
if( guardian == 0 )
{
multipler = 10;
multipler.Pow(dec_digits);
guardian = 1;
}
result = multipler;
}
#else
/*!
*/
void SetMultipler(UInt<value_size> & result)
{
// this guardian is initialized before the program runs (static POD type)
volatile static sig_atomic_t guardian = 0;
static UInt<value_size> * pmultipler;
// double-checked locking
if( guardian == 0 )
{
ThreadLock thread_lock;
// locking
if( thread_lock.Lock() )
{
static UInt<value_size> multipler;
if( guardian == 0 )
{
pmultipler = &multipler;
multipler = 10;
multipler.Pow(dec_digits);
guardian = 1;
}
}
else
{
// there was a problem with locking, we store the result directly in 'result' object
result = 10;
result.Pow(dec_digits);
return;
}
// automatically unlocking
}
result = *pmultipler;
}
#endif
/*!
an auxiliary method for converting from a string
*/
template<class char_type>
uint FromStringBase(const char_type * s, const char_type ** after_source = 0, bool * value_read = 0)
{
UInt<value_size> multipler;
const char_type * after;
uint c = 0;
info = 0;
Misc::SkipWhiteCharacters(s);
if( *s == '-' )
{
s += 1;
SetSign();
}
else
if( *s == '+' )
{
s += 1;
}
c += value.FromString(s, 10, &after, value_read);
if( after_source )
*after_source = after;
SetMultipler(multipler);
c += value.Mul(multipler);
if( *after == '.' )
c += FromStringBaseAfterComma(after+1, after_source);
if( c )
SetInfoBit(TTMATH_DEC_NAN);
return (c==0)? 0 : 1;
}
template<class char_type>
uint FromStringBaseAfterComma(const char_type * s, const char_type ** after_source = 0, bool * value_read = 0)
{
UInt<value_size> temp;
UInt<value_size> multipler;
sint z;
uint c = 0;
size_t i = dec_digits;
SetMultipler(multipler);
for( ; i>0 && (z=Misc::CharToDigit(*s, 10)) != -1 ; --i, ++s )
{
multipler.DivInt(10);
temp.SetZero();
if( value_read )
*value_read = true;
if( c == 0 )
{
temp.table[0] = z;
c += temp.Mul(multipler);
c += value.Add(temp);
}
}
if( i == 0 && (z=Misc::CharToDigit(*s, 10)) != -1 && z >= 5 )
c += value.AddOne();
if( after_source )
{
while( (z=Misc::CharToDigit(*s, 10)) != -1 )
s += 1;
*after_source = s;
}
return c;
}
template<class string_type>
void ToStringBase(string_type & result) const
{
if( IsNan() )
{
result = "NaN";
return;
}
value.ToStringBase(result, 10, IsSign());
if( dec_digits > 0 )
{
size_t size = result.size();
if( IsSign() && size > 0 )
size -= 1;
if( dec_digits >= size )
{
size_t zeroes = dec_digits - size + 1;
size_t start = IsSign() ? 1 : 0;
result.insert(start, zeroes, '0');
}
result.insert(result.end() - dec_digits, '.');
}
}
};
} // namespace
#endif

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/*
* This file is a part of TTMath Bignum Library
* and is distributed under the (new) BSD licence.
* Author: Tomasz Sowa <t.sowa@ttmath.org>
*/
/*
* Copyright (c) 2006-2010, Tomasz Sowa
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name Tomasz Sowa nor the names of contributors to this
* project may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef headerfilettmathmisc
#define headerfilettmathmisc
/*!
\file ttmathmisc.h
\brief some helpful functions
*/
#include <string>
namespace ttmath
{
/*!
some helpful functions
*/
class Misc
{
public:
/*
*
* AssignString(result, str)
* result = str
*
*/
/*!
result = str
*/
static void AssignString(std::string & result, const char * str)
{
result = str;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
result = str
*/
static void AssignString(std::wstring & result, const char * str)
{
result.clear();
for( ; *str ; ++str )
result += *str;
}
/*!
result = str
*/
static void AssignString(std::wstring & result, const std::string & str)
{
return AssignString(result, str.c_str());
}
/*!
result = str
*/
static void AssignString(std::string & result, const wchar_t * str)
{
result.clear();
for( ; *str ; ++str )
result += static_cast<char>(*str);
}
/*!
result = str
*/
static void AssignString(std::string & result, const std::wstring & str)
{
return AssignString(result, str.c_str());
}
#endif
/*
*
* AddString(result, str)
* result += str
*
*/
/*!
result += str
*/
static void AddString(std::string & result, const char * str)
{
result += str;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
result += str
*/
static void AddString(std::wstring & result, const char * str)
{
for( ; *str ; ++str )
result += *str;
}
#endif
/*
this method omits any white characters from the string
char_type is char or wchar_t
*/
template<class char_type>
static void SkipWhiteCharacters(const char_type * & c)
{
// 13 is at the end in a DOS text file (\r\n)
while( (*c==' ' ) || (*c=='\t') || (*c==13 ) || (*c=='\n') )
++c;
}
/*!
this static method converts one character into its value
for example:
1 -> 1
8 -> 8
A -> 10
f -> 15
this method don't check whether c is correct or not
*/
static uint CharToDigit(uint c)
{
if(c>='0' && c<='9')
return c-'0';
if(c>='a' && c<='z')
return c-'a'+10;
return c-'A'+10;
}
/*!
this method changes a character 'c' into its value
(if there can't be a correct value it returns -1)
for example:
c=2, base=10 -> function returns 2
c=A, base=10 -> function returns -1
c=A, base=16 -> function returns 10
*/
static sint CharToDigit(uint c, uint base)
{
if( c>='0' && c<='9' )
c=c-'0';
else
if( c>='a' && c<='z' )
c=c-'a'+10;
else
if( c>='A' && c<='Z' )
c=c-'A'+10;
else
return -1;
if( c >= base )
return -1;
return sint(c);
}
/*!
this method converts a digit into a char
digit should be from <0,F>
(we don't have to get a base)
for example:
1 -> 1
8 -> 8
10 -> A
15 -> F
*/
static uint DigitToChar(uint digit)
{
if( digit < 10 )
return digit + '0';
return digit - 10 + 'A';
}
}; // struct Misc
}
#endif

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/*
* This file is a part of TTMath Mathematical Library
* and is distributed under the (new) BSD licence.
* Author: Tomasz Sowa <t.sowa@ttmath.org>
*/
/*
* Copyright (c) 2006-2010, Tomasz Sowa
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name Tomasz Sowa nor the names of contributors to this
* project may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef headerfilettmathobject
#define headerfilettmathobject
/*!
\file ttmathobjects.h
\brief Mathematic functions.
*/
#include <string>
#include <vector>
#include <list>
#include <map>
#include "ttmathtypes.h"
#include "ttmathmisc.h"
namespace ttmath
{
/*!
objects of this class are used with the mathematical parser
they hold variables or functions defined by a user
each object has its own table in which we're keeping variables or functions
*/
class Objects
{
public:
/*!
one item (variable or function)
'items' will be on the table
*/
struct Item
{
// name of a variable of a function
// internally we store variables and funcions as std::string (not std::wstring even when wide characters are used)
std::string value;
// number of parameters required by the function
// (if there's a variable this 'param' is ignored)
int param;
Item() {}
Item(const std::string & v, int p) : value(v), param(p) {}
};
// 'Table' is the type of our table
typedef std::map<std::string, Item> Table;
typedef Table::iterator Iterator;
typedef Table::const_iterator CIterator;
/*!
this method returns true if a character 'c' is a character
which can be in a name
if 'can_be_digit' is true that means when the 'c' is a digit this
method returns true otherwise it returns false
*/
static bool CorrectCharacter(int c, bool can_be_digit)
{
if( (c>='a' && c<='z') || (c>='A' && c<='Z') )
return true;
if( can_be_digit && ((c>='0' && c<='9') || c=='_') )
return true;
return false;
}
/*!
this method returns true if the name can be as a name of an object
*/
template<class string_type>
static bool IsNameCorrect(const string_type & name)
{
if( name.empty() )
return false;
if( !CorrectCharacter(name[0], false) )
return false;
typename string_type::const_iterator i = name.begin();
for(++i ; i!=name.end() ; ++i)
if( !CorrectCharacter(*i, true) )
return false;
return true;
}
/*!
this method returns true if such an object is defined (name exists)
*/
bool IsDefined(const std::string & name)
{
Iterator i = table.find(name);
if( i != table.end() )
// we have this object in our table
return true;
return false;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method returns true if such an object is defined (name exists)
*/
bool IsDefined(const std::wstring & name)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return false;
Misc::AssignString(str_tmp1, name);
return IsDefined(str_tmp1);
}
#endif
/*!
this method adds one object (variable of function) into the table
*/
ErrorCode Add(const std::string & name, const std::string & value, int param = 0)
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
Iterator i = table.find(name);
if( i != table.end() )
// we have this object in our table
return err_object_exists;
table.insert( std::make_pair(name, Item(value, param)) );
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method adds one object (variable of function) into the table
*/
ErrorCode Add(const std::wstring & name, const std::wstring & value, int param = 0)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
Misc::AssignString(str_tmp2, value);
return Add(str_tmp1, str_tmp2, param);
}
#endif
/*!
this method returns 'true' if the table is empty
*/
bool Empty() const
{
return table.empty();
}
/*!
this method clears the table
*/
void Clear()
{
return table.clear();
}
/*!
this method returns 'const_iterator' on the first item on the table
*/
CIterator Begin() const
{
return table.begin();
}
/*!
this method returns 'const_iterator' pointing at the space after last item
(returns table.end())
*/
CIterator End() const
{
return table.end();
}
/*!
this method changes the value and the number of parameters for a specific object
*/
ErrorCode EditValue(const std::string & name, const std::string & value, int param = 0)
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
Iterator i = table.find(name);
if( i == table.end() )
return err_unknown_object;
i->second.value = value;
i->second.param = param;
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method changes the value and the number of parameters for a specific object
*/
ErrorCode EditValue(const std::wstring & name, const std::wstring & value, int param = 0)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
Misc::AssignString(str_tmp2, value);
return EditValue(str_tmp1, str_tmp2, param);
}
#endif
/*!
this method changes the name of a specific object
*/
ErrorCode EditName(const std::string & old_name, const std::string & new_name)
{
if( !IsNameCorrect(old_name) || !IsNameCorrect(new_name) )
return err_incorrect_name;
Iterator old_i = table.find(old_name);
if( old_i == table.end() )
return err_unknown_object;
if( old_name == new_name )
// the new name is the same as the old one
// we treat it as a normal situation
return err_ok;
ErrorCode err = Add(new_name, old_i->second.value, old_i->second.param);
if( err == err_ok )
{
old_i = table.find(old_name);
TTMATH_ASSERT( old_i != table.end() )
table.erase(old_i);
}
return err;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method changes the name of a specific object
*/
ErrorCode EditName(const std::wstring & old_name, const std::wstring & new_name)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(old_name) || !IsNameCorrect(new_name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, old_name);
Misc::AssignString(str_tmp2, new_name);
return EditName(str_tmp1, str_tmp2);
}
#endif
/*!
this method deletes an object
*/
ErrorCode Delete(const std::string & name)
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
Iterator i = table.find(name);
if( i == table.end() )
return err_unknown_object;
table.erase( i );
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method deletes an object
*/
ErrorCode Delete(const std::wstring & name)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
return Delete(str_tmp1);
}
#endif
/*!
this method gets the value of a specific object
*/
ErrorCode GetValue(const std::string & name, std::string & value) const
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
CIterator i = table.find(name);
if( i == table.end() )
{
value.clear();
return err_unknown_object;
}
value = i->second.value;
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method gets the value of a specific object
*/
ErrorCode GetValue(const std::wstring & name, std::wstring & value)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
ErrorCode err = GetValue(str_tmp1, str_tmp2);
Misc::AssignString(value, str_tmp2);
return err;
}
#endif
/*!
this method gets the value of a specific object
(this version is used for not copying the whole string)
*/
ErrorCode GetValue(const std::string & name, const char ** value) const
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
CIterator i = table.find(name);
if( i == table.end() )
{
*value = 0;
return err_unknown_object;
}
*value = i->second.value.c_str();
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method gets the value of a specific object
(this version is used for not copying the whole string)
*/
ErrorCode GetValue(const std::wstring & name, const char ** value)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
return GetValue(str_tmp1, value);
}
#endif
/*!
this method gets the value and the number of parameters
of a specific object
*/
ErrorCode GetValueAndParam(const std::string & name, std::string & value, int * param) const
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
CIterator i = table.find(name);
if( i == table.end() )
{
value.empty();
*param = 0;
return err_unknown_object;
}
value = i->second.value;
*param = i->second.param;
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method gets the value and the number of parameters
of a specific object
*/
ErrorCode GetValueAndParam(const std::wstring & name, std::wstring & value, int * param)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
ErrorCode err = GetValueAndParam(str_tmp1, str_tmp2, param);
Misc::AssignString(value, str_tmp2);
return err;
}
#endif
/*!
this method sets the value and the number of parameters
of a specific object
(this version is used for not copying the whole string)
*/
ErrorCode GetValueAndParam(const std::string & name, const char ** value, int * param) const
{
if( !IsNameCorrect(name) )
return err_incorrect_name;
CIterator i = table.find(name);
if( i == table.end() )
{
*value = 0;
*param = 0;
return err_unknown_object;
}
*value = i->second.value.c_str();
*param = i->second.param;
return err_ok;
}
#ifndef TTMATH_DONT_USE_WCHAR
/*!
this method sets the value and the number of parameters
of a specific object
(this version is used for not copying the whole string
but in fact we make one copying during AssignString())
*/
ErrorCode GetValueAndParam(const std::wstring & name, const char ** value, int * param)
{
// we should check whether the name (in wide characters) are correct
// before calling AssignString() function
if( !IsNameCorrect(name) )
return err_incorrect_name;
Misc::AssignString(str_tmp1, name);
return GetValueAndParam(str_tmp1, value, param);
}
#endif
/*!
this method returns a pointer into the table
*/
Table * GetTable()
{
return &table;
}
private:
Table table;
std::string str_tmp1, str_tmp2;
}; // end of class Objects
/*!
objects of the class History are used to keep values in functions
which take a lot of time during calculating, for instance in the
function Factorial(x)
it means that when we're calculating e.g. Factorial(1000) and the
Factorial finds that we have calculated it before, the value (result)
is taken from the history
*/
template<class ValueType>
class History
{
/*!
one item in the History's object holds a key, a value for the key
and a corresponding error code
*/
struct Item
{
ValueType key, value;
ErrorCode err;
};
/*!
we use std::list for simply deleting the first item
but because we're searching through the whole container
(in the method Get) the container should not be too big
(linear time of searching)
*/
typedef std::list<Item> buffer_type;
buffer_type buffer;
typename buffer_type::size_type buffer_max_size;
public:
/*!
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

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/*
* This file is a part of TTMath Bignum Library
* and is distributed under the (new) BSD licence.
* Author: Tomasz Sowa <t.sowa@ttmath.org>
*/
/*
* Copyright (c) 2006-2009, Tomasz Sowa
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name Tomasz Sowa nor the names of contributors to this
* project may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef headerfilettmaththreads
#define headerfilettmaththreads
#include "ttmathtypes.h"
#ifdef TTMATH_WIN32_THREADS
#include <windows.h>
#include <cstdio>
#endif
#ifdef TTMATH_POSIX_THREADS
#include <pthread.h>
#endif
/*!
\file ttmaththreads.h
\brief Some objects used in multithreads environment
*/
/*
this is a simple skeleton of a program in multithreads environment:
#define TTMATH_MULTITHREADS
#include<ttmath/ttmath.h>
TTMATH_MULTITHREADS_HELPER
int main()
{
[...]
}
make sure that macro TTMATH_MULTITHREADS is defined and (somewhere in *.cpp file)
use TTMATH_MULTITHREADS_HELPER macro (outside of any classes/functions/namespaces scope)
*/
namespace ttmath
{
#ifdef TTMATH_WIN32_THREADS
/*
we use win32 threads
*/
/*!
in multithreads environment you should use TTMATH_MULTITHREADS_HELPER macro
somewhere in *.cpp file
(at the moment in win32 this macro does nothing)
*/
#define TTMATH_MULTITHREADS_HELPER
/*!
objects of this class are used to synchronize
*/
class ThreadLock
{
HANDLE mutex_handle;
void CreateName(char * buffer) const
{
#ifdef _MSC_VER
#pragma warning (disable : 4996)
// warning C4996: 'sprintf': This function or variable may be unsafe. Consider using sprintf_s instead.
#endif
sprintf(buffer, "TTMATH_LOCK_%ul", (unsigned long)GetCurrentProcessId());
#ifdef _MSC_VER
#pragma warning (default : 4996)
#endif
}
public:
bool Lock()
{
char buffer[50];
CreateName(buffer);
mutex_handle = CreateMutexA(0, false, buffer);
if( mutex_handle == 0 )
return false;
WaitForSingleObject(mutex_handle, INFINITE);
return true;
}
ThreadLock()
{
mutex_handle = 0;
}
~ThreadLock()
{
if( mutex_handle != 0 )
{
ReleaseMutex(mutex_handle);
CloseHandle(mutex_handle);
}
}
};
#endif // #ifdef TTMATH_WIN32_THREADS
#ifdef TTMATH_POSIX_THREADS
/*
we use posix threads
*/
/*!
in multithreads environment you should use TTMATH_MULTITHREADS_HELPER macro
somewhere in *.cpp file
(this macro defines a pthread_mutex_t object used by TTMath library)
*/
#define TTMATH_MULTITHREADS_HELPER \
namespace ttmath \
{ \
pthread_mutex_t ttmath_mutex = PTHREAD_MUTEX_INITIALIZER; \
}
/*!
ttmath_mutex will be defined by TTMATH_MULTITHREADS_HELPER macro
*/
extern pthread_mutex_t ttmath_mutex;
/*!
objects of this class are used to synchronize
*/
class ThreadLock
{
public:
bool Lock()
{
if( pthread_mutex_lock(&ttmath_mutex) != 0 )
return false;
return true;
}
~ThreadLock()
{
pthread_mutex_unlock(&ttmath_mutex);
}
};
#endif // #ifdef TTMATH_POSIX_THREADS
#if !defined(TTMATH_POSIX_THREADS) && !defined(TTMATH_WIN32_THREADS)
/*!
we don't use win32 and pthreads
*/
/*!
*/
#define TTMATH_MULTITHREADS_HELPER
/*!
objects of this class are used to synchronize
actually we don't synchronize, the method Lock() returns always 'false'
*/
class ThreadLock
{
public:
bool Lock()
{
return false;
}
};
#endif // #if !defined(TTMATH_POSIX_THREADS) && !defined(TTMATH_WIN32_THREADS)
} // namespace
#endif

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/*
* This file is a part of TTMath Bignum Library
* and is distributed under the (new) BSD licence.
* Author: Tomasz Sowa <t.sowa@ttmath.org>
*/
/*
* Copyright (c) 2006-2012, Tomasz Sowa
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice,
* this list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
*
* * Neither the name Tomasz Sowa nor the names of contributors to this
* project may be used to endorse or promote products derived
* from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
* THE POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef headerfilettmathtypes
#define headerfilettmathtypes
/*!
\file ttmathtypes.h
\brief constants used in the library
As our library is written in header files (templates) we cannot use
constants like 'const int' etc. because we should have some source files
*.cpp to define this variables. Only what we can have are constants
defined by #define preprocessor macros.
All macros are preceded by TTMATH_ prefix
*/
#include <stdexcept>
#include <sstream>
#include <vector>
#ifndef _MSC_VER
#include <stdint.h>
// for uint64_t and int64_t on a 32 bit platform
#endif
/*!
the version of the library
TTMATH_PRERELEASE_VER is either zero or one
zero means that this is the release version of the library
(one means something like beta)
*/
#define TTMATH_MAJOR_VER 0
#define TTMATH_MINOR_VER 9
#define TTMATH_REVISION_VER 3
#define TTMATH_PRERELEASE_VER 0
/*!
you can define a platform explicitly by defining either
TTMATH_PLATFORM32 or TTMATH_PLATFORM64 macro
*/
#if !defined TTMATH_PLATFORM32 && !defined TTMATH_PLATFORM64
#if !defined _M_X64 && !defined __x86_64__
/*
other platforms than x86 and amd64 are not recognized at the moment
so you should set TTMATH_PLATFORMxx manually
*/
// we're using a 32bit platform
#define TTMATH_PLATFORM32
#else
// we're using a 64bit platform
#define TTMATH_PLATFORM64
#endif
#endif
/*!
asm version of the library is available by default only for:
x86 and amd64 platforms and for Microsoft Visual and GCC compilers
but you can force using asm version (the same asm as for Microsoft Visual)
by defining TTMATH_FORCEASM macro
you have to be sure that your compiler accept such an asm format
*/
#ifndef TTMATH_FORCEASM
#if !defined __i386__ && !defined _X86_ && !defined _M_IX86 && !defined __x86_64__ && !defined _M_X64
/*!
x86 architecture:
__i386__ defined by GNU C
_X86_ defined by MinGW32
_M_IX86 defined by Visual Studio, Intel C/C++, Digital Mars and Watcom C/C++
amd64 architecture:
__x86_64__ defined by GNU C, CLANG (LLVM) and Sun Studio
_M_X64 defined by Visual Studio
asm version is available only for x86 or amd64 platforms
*/
#define TTMATH_NOASM
#endif
#if !defined _MSC_VER && !defined __GNUC__
/*!
another compilers than MS VC or GCC or CLANG (LLVM) by default use no asm version
(CLANG defines __GNUC__ too)
*/
#define TTMATH_NOASM
#endif
#endif
namespace ttmath
{
#ifdef TTMATH_PLATFORM32
/*!
on 32bit platforms one word (uint, sint) will be equal 32bits
*/
typedef unsigned int uint;
typedef signed int sint;
/*!
on 32 bit platform ulint and slint will be equal 64 bits
*/
#ifdef _MSC_VER
// long long on MS Windows (Visual and GCC mingw compilers) have 64 bits
// stdint.h is not available on Visual Studio prior to VS 2010 version
typedef unsigned long long int ulint;
typedef signed long long int slint;
#else
// we do not use 'long' here because there is a difference in unix and windows
// environments: in unix 'long' has 64 bits but in windows it has only 32 bits
typedef uint64_t ulint;
typedef int64_t slint;
#endif
/*!
how many bits there are in the uint type
*/
#define TTMATH_BITS_PER_UINT 32u
/*!
the mask for the highest bit in the unsigned 32bit word (2^31)
*/
#define TTMATH_UINT_HIGHEST_BIT 2147483648u
/*!
the max value of the unsigned 32bit word (2^32 - 1)
(all bits equal one)
*/
#define TTMATH_UINT_MAX_VALUE 4294967295u
/*!
the number of words (32bit words on 32bit platform)
which are kept in built-in variables for a Big<> type
(these variables are defined in ttmathbig.h)
*/
#define TTMATH_BUILTIN_VARIABLES_SIZE 256u
/*!
this macro returns the number of machine words
capable to hold min_bits bits
e.g. TTMATH_BITS(128) returns 4
*/
#define TTMATH_BITS(min_bits) ((min_bits-1)/32 + 1)
#else
/*!
on 64bit platforms one word (uint, sint) will be equal 64bits
*/
#ifdef _MSC_VER
/* in VC 'long' type has 32 bits, __int64 is VC extension */
typedef unsigned __int64 uint;
typedef signed __int64 sint;
#else
typedef unsigned long uint;
typedef signed long sint;
#endif
/*!
on 64bit platforms we do not define ulint and slint
*/
/*!
how many bits there are in the uint type
*/
#define TTMATH_BITS_PER_UINT 64ul
/*!
the mask for the highest bit in the unsigned 64bit word (2^63)
*/
#define TTMATH_UINT_HIGHEST_BIT 9223372036854775808ul
/*!
the max value of the unsigned 64bit word (2^64 - 1)
(all bits equal one)
*/
#define TTMATH_UINT_MAX_VALUE 18446744073709551615ul
/*!
the number of words (64bit words on 64bit platforms)
which are kept in built-in variables for a Big<> type
(these variables are defined in ttmathbig.h)
*/
#define TTMATH_BUILTIN_VARIABLES_SIZE 128ul
/*!
this macro returns the number of machine words
capable to hold min_bits bits
e.g. TTMATH_BITS(128) returns 2
*/
#define TTMATH_BITS(min_bits) ((min_bits-1)/64 + 1)
#endif
}
#if defined(TTMATH_MULTITHREADS) && !defined(TTMATH_MULTITHREADS_NOSYNC)
#if !defined(TTMATH_POSIX_THREADS) && !defined(TTMATH_WIN32_THREADS)
#if defined(_WIN32)
#define TTMATH_WIN32_THREADS
#elif defined(unix) || defined(__unix__) || defined(__unix)
#define TTMATH_POSIX_THREADS
#endif
#endif
#endif
/*!
this variable defines how many iterations are performed
during some kind of calculating when we're making any long formulas
(for example Taylor series)
it's used in ExpSurrounding0(...), LnSurrounding1(...), Sin0pi05(...), etc.
note! there'll not be so many iterations, iterations are stopped when
there is no sense to continue calculating (for example when the result
still remains unchanged after adding next series and we know that the next
series are smaller than previous ones)
*/
#define TTMATH_ARITHMETIC_MAX_LOOP 10000
/*!
this is a limit when calculating Karatsuba multiplication
if the size of a vector is smaller than TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE
the Karatsuba algorithm will use standard schoolbook multiplication
*/
#ifdef TTMATH_DEBUG_LOG
// if TTMATH_DEBUG_LOG is defined then we should use the same size regardless of the compiler
#define TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE 3
#else
#ifdef __GNUC__
#define TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE 3
#else
#define TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE 5
#endif
#endif
/*!
this is a special value used when calculating the Gamma(x) function
if x is greater than this value then the Gamma(x) will be calculated using
some kind of series
don't use smaller values than about 100
*/
#define TTMATH_GAMMA_BOUNDARY 2000
namespace ttmath
{
/*!
lib type codes:
asm_vc_32 - with asm code designed for Microsoft Visual C++ (32 bits)
asm_gcc_32 - with asm code designed for GCC (32 bits)
asm_vc_64 - with asm for VC (64 bit)
asm_gcc_64 - with asm for GCC (64 bit)
no_asm_32 - pure C++ version (32 bit) - without any asm code
no_asm_64 - pure C++ version (64 bit) - without any asm code
*/
enum LibTypeCode
{
asm_vc_32 = 0,
asm_gcc_32,
asm_vc_64,
asm_gcc_64,
no_asm_32,
no_asm_64
};
/*!
error codes
*/
enum ErrorCode
{
err_ok = 0,
err_nothing_has_read,
err_unknown_character,
err_unexpected_final_bracket,
err_stack_not_clear,
err_unknown_variable,
err_division_by_zero,
err_interrupt,
err_overflow,
err_unknown_function,
err_unknown_operator,
err_unexpected_semicolon_operator,
err_improper_amount_of_arguments,
err_improper_argument,
err_unexpected_end,
err_internal_error,
err_incorrect_name,
err_incorrect_value,
err_variable_exists,
err_variable_loop,
err_functions_loop,
err_must_be_only_one_value,
err_object_exists,
err_unknown_object,
err_still_calculating,
err_in_short_form_used_function,
err_percent_from
};
/*!
this struct is used when converting to/from a string
/temporarily only in Big::ToString() and Big::FromString()/
*/
struct Conv
{
/*!
base (radix) on which the value will be shown (or read)
default: 10
*/
uint base;
/*!
used only in Big::ToString()
if true the value will be always shown in the scientific mode, e.g: 123e+30
default: false
*/
bool scient;
/*!
used only in Big::ToString()
if scient is false then the value will be printed in the scientific mode
only if the exponent is greater than scien_from
default: 15
*/
sint scient_from;
/*!
if 'base_round' is true and 'base' is different from 2, 4, 8, or 16
and the result value is not an integer then we make an additional rounding
(after converting the last digit from the result is skipped)
default: true
e.g.
Conv c;
c.base_round = false;
Big<1, 1> a = "0.1"; // decimal input
std::cout << a.ToString(c) << std::endl; // the result is: 0.099999999
*/
bool base_round;
/*!
used only in Big::ToString()
tells how many digits after comma are possible
default: -1 which means all digits are printed
set it to zero if you want integer value only
for example when the value is:
12.345678 and 'round' is 4
then the result will be
12.3457 (the last digit was rounded)
*/
sint round;
/*!
if true that not mattered digits in the mantissa will be cut off
(zero characters at the end -- after the comma operator)
e.g. 1234,78000 will be: 1234,78
default: true
*/
bool trim_zeroes;
/*!
the main comma operator (used when reading and writing)
default is a dot '.'
*/
uint comma;
/*!
additional comma operator (used only when reading)
if you don't want it just set it to zero
default is a comma ','
this allowes you to convert from a value:
123.45 as well as from 123,45
*/
uint comma2;
/*!
it sets the character which is used for grouping
if group=' ' then: 1234,56789 will be printed as: 1 234,567 89
if you don't want grouping just set it to zero (which is default)
*/
uint group;
/*!
how many digits should be grouped (it is used if 'group' is non zero)
default: 3
*/
uint group_digits;
/*!
*/
uint group_exp; // not implemented yet
Conv()
{
// default values
base = 10;
scient = false;
scient_from = 15;
base_round = true;
round = -1;
trim_zeroes = true;
comma = '.';
comma2 = ',';
group = 0;
group_digits = 3;
group_exp = 0;
}
};
/*!
this simple class can be used in multithreading model
(you can write your own class derived from this one)
for example: in some functions like Factorial()
/at the moment only Factorial/ you can give a pointer to
the 'stop object', if the method WasStopSignal() of this
object returns true that means we should break the calculating
and return
*/
class StopCalculating
{
public:
virtual bool WasStopSignal() const volatile { return false; }
virtual ~StopCalculating(){}
};
/*!
a small class which is useful when compiling with gcc
object of this type holds the name and the line of a file
in which the macro TTMATH_ASSERT or TTMATH_REFERENCE_ASSERT was used
*/
class ExceptionInfo
{
const char * file;
int line;
public:
ExceptionInfo() : file(0), line(0) {}
ExceptionInfo(const char * f, int l) : file(f), line(l) {}
std::string Where() const
{
if( !file )
return "unknown";
std::ostringstream result;
result << file << ":" << line;
return result.str();
}
};
/*!
A small class used for reporting 'reference' errors
In the library is used macro TTMATH_REFERENCE_ASSERT which
can throw an exception of this type
** from version 0.9.2 this macro is removed from all methods
in public interface so you don't have to worry about it **
If you compile with gcc you can get a small benefit
from using method Where() (it returns std::string) with
the name and the line of a file where the macro TTMATH_REFERENCE_ASSERT
was used)
*/
class ReferenceError : public std::logic_error, public ExceptionInfo
{
public:
ReferenceError() : std::logic_error("reference error")
{
}
ReferenceError(const char * f, int l) :
std::logic_error("reference error"), ExceptionInfo(f,l)
{
}
std::string Where() const
{
return ExceptionInfo::Where();
}
};
/*!
a small class used for reporting errors
in the library is used macro TTMATH_ASSERT which
(if the condition in it is false) throw an exception
of this type
if you compile with gcc you can get a small benefit
from using method Where() (it returns std::string) with
the name and the line of a file where the macro TTMATH_ASSERT
was used)
*/
class RuntimeError : public std::runtime_error, public ExceptionInfo
{
public:
RuntimeError() : std::runtime_error("internal error")
{
}
RuntimeError(const char * f, int l) :
std::runtime_error("internal error"), ExceptionInfo(f,l)
{
}
std::string Where() const
{
return ExceptionInfo::Where();
}
};
/*!
TTMATH_DEBUG
this macro enables further testing during writing your code
you don't have to define it in a release mode
if this macro is set then macros TTMATH_ASSERT and TTMATH_REFERENCE_ASSERT
are set as well and these macros can throw an exception if a condition in it
is not fulfilled (look at the definition of TTMATH_ASSERT and TTMATH_REFERENCE_ASSERT)
TTMATH_DEBUG is set automatically if DEBUG or _DEBUG are defined
*/
#if defined DEBUG || defined _DEBUG
#define TTMATH_DEBUG
#endif
#ifdef TTMATH_DEBUG
#if defined(__FILE__) && defined(__LINE__)
#define TTMATH_REFERENCE_ASSERT(expression) \
if( &(expression) == this ) throw ttmath::ReferenceError(__FILE__, __LINE__);
#define TTMATH_ASSERT(expression) \
if( !(expression) ) throw ttmath::RuntimeError(__FILE__, __LINE__);
#else
#define TTMATH_REFERENCE_ASSERT(expression) \
if( &(expression) == this ) throw ReferenceError();
#define TTMATH_ASSERT(expression) \
if( !(expression) ) throw RuntimeError();
#endif
#else
#define TTMATH_REFERENCE_ASSERT(expression)
#define TTMATH_ASSERT(expression)
#endif
#ifdef TTMATH_DEBUG_LOG
#define TTMATH_LOG(msg) PrintLog(msg, std::cout);
#define TTMATH_LOGC(msg, carry) PrintLog(msg, carry, std::cout);
#define TTMATH_VECTOR_LOG(msg, vector, len) PrintVectorLog(msg, std::cout, vector, len);
#define TTMATH_VECTOR_LOGC(msg, carry, vector, len) PrintVectorLog(msg, carry, std::cout, vector, len);
#else
#define TTMATH_LOG(msg)
#define TTMATH_LOGC(msg, carry)
#define TTMATH_VECTOR_LOG(msg, vector, len)
#define TTMATH_VECTOR_LOGC(msg, carry, vector, len)
#endif
} // namespace
#endif

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;
; This file is a part of TTMath Bignum Library
; and is distributed under the (new) BSD licence.
; Author: Christian Kaiser <chk@online.de>
;
;
; Copyright (c) 2009, Christian Kaiser
; All rights reserved.
;
; Redistribution and use in source and binary forms, with or without
; modification, are permitted provided that the following conditions are met:
;
; * Redistributions of source code must retain the above copyright notice,
; this list of conditions and the following disclaimer.
;
; * Redistributions in binary form must reproduce the above copyright
; notice, this list of conditions and the following disclaimer in the
; documentation and/or other materials provided with the distribution.
;
; * Neither the name Christian Kaiser nor the names of contributors to this
; project may be used to endorse or promote products derived
; from this software without specific prior written permission.
;
; THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
; AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
; IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
; ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
; LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
; CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
; SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
; INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
; CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
; ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
; THE POSSIBILITY OF SUCH DAMAGE.
;
;
; compile with debug info: ml64.exe /c /Zd /Zi ttmathuint_x86_64_msvc.asm
; compile without debug info: ml64.exe /c ttmathuint_x86_64_msvc.asm
; this creates ttmathuint_x86_64_msvc.obj file which can be linked with your program
;
PUBLIC ttmath_adc_x64
PUBLIC ttmath_addindexed_x64
PUBLIC ttmath_addindexed2_x64
PUBLIC ttmath_addvector_x64
PUBLIC ttmath_sbb_x64
PUBLIC ttmath_subindexed_x64
PUBLIC ttmath_subvector_x64
PUBLIC ttmath_rcl_x64
PUBLIC ttmath_rcr_x64
PUBLIC ttmath_rcl2_x64
PUBLIC ttmath_rcr2_x64
PUBLIC ttmath_div_x64
;
; Microsoft x86_64 convention: http://msdn.microsoft.com/en-us/library/9b372w95.aspx
;
; "rax, rcx, rdx, r8-r11 are volatile."
; "rbx, rbp, rdi, rsi, r12-r15 are nonvolatile."
;
.CODE
ALIGN 8
;----------------------------------------
ttmath_adc_x64 PROC
; rcx = p1
; rdx = p2
; r8 = nSize
; r9 = nCarry
xor rax, rax
xor r11, r11
sub rax, r9 ; sets CARRY if r9 != 0
ALIGN 16
loop1:
mov rax,qword ptr [rdx + r11 * 8]
adc qword ptr [rcx + r11 * 8], rax
lea r11, [r11+1]
dec r8
jnz loop1
setc al
movzx rax, al
ret
ttmath_adc_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_addindexed_x64 PROC
; rcx = p1
; rdx = nSize
; r8 = nPos
; r9 = nValue
xor rax, rax ; rax = result
sub rdx, r8 ; rdx = remaining count of uints
add qword ptr [rcx + r8 * 8], r9
jc next1
ret
next1:
mov r9, 1
ALIGN 16
loop1:
dec rdx
jz done_with_cy
lea r8, [r8+1]
add qword ptr [rcx + r8 * 8], r9
jc loop1
ret
done_with_cy:
lea rax, [rax+1] ; rax = 1
ret
ttmath_addindexed_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_addindexed2_x64 PROC
; rcx = p1 (pointer)
; rdx = b (value size)
; r8 = nPos
; r9 = nValue1
; [esp+0x28] = nValue2
xor rax, rax ; return value
mov r11, rcx ; table
sub rdx, r8 ; rdx = remaining count of uints
mov r10, [esp+028h] ; r10 = nValue2
add qword ptr [r11 + r8 * 8], r9
lea r8, [r8+1]
lea rdx, [rdx-1]
adc qword ptr [r11 + r8 * 8], r10
jc next
ret
ALIGN 16
loop1:
lea r8, [r8+1]
add qword ptr [r11 + r8 * 8], 1
jc next
ret
next:
dec rdx ; does not modify CY too...
jnz loop1
lea rax, [rax+1]
ret
ttmath_addindexed2_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_addvector_x64 PROC
; rcx = ss1
; rdx = ss2
; r8 = ss1_size
; r9 = ss2_size
; [esp+0x28] = result
mov r10, [esp+028h]
sub r8, r9
xor r11, r11 ; r11=0, cf=0
ALIGN 16
loop1:
mov rax, qword ptr [rcx + r11 * 8]
adc rax, qword ptr [rdx + r11 * 8]
mov qword ptr [r10 + r11 * 8], rax
inc r11
dec r9
jnz loop1
adc r9, r9 ; r9 has the cf state
or r8, r8
jz done
neg r9 ; setting cf from r9
mov r9, 0 ; don't use xor here (cf is used)
loop2:
mov rax, qword ptr [rcx + r11 * 8]
adc rax, r9
mov qword ptr [r10 + r11 * 8], rax
inc r11
dec r8
jnz loop2
adc r8, r8
mov rax, r8
ret
done:
mov rax, r9
ret
ttmath_addvector_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_sbb_x64 PROC
; rcx = p1
; rdx = p2
; r8 = nCount
; r9 = nCarry
xor rax, rax
xor r11, r11
sub rax, r9 ; sets CARRY if r9 != 0
ALIGN 16
loop1:
mov rax,qword ptr [rdx + r11 * 8]
sbb qword ptr [rcx + r11 * 8], rax
lea r11, [r11+1]
dec r8
jnz loop1
setc al
movzx rax, al
ret
ttmath_sbb_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_subindexed_x64 PROC
; rcx = p1
; rdx = nSize
; r8 = nPos
; r9 = nValue
sub rdx, r8 ; rdx = remaining count of uints
ALIGN 16
loop1:
sub qword ptr [rcx + r8 * 8], r9
jnc done
lea r8, [r8+1]
mov r9, 1
dec rdx
jnz loop1
mov rax, 1
ret
done:
xor rax, rax
ret
ttmath_subindexed_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
; the same asm code as in addvector_x64 only two instructions 'adc' changed to 'sbb'
ttmath_subvector_x64 PROC
; rcx = ss1
; rdx = ss2
; r8 = ss1_size
; r9 = ss2_size
; [esp+0x28] = result
mov r10, [esp+028h]
sub r8, r9
xor r11, r11 ; r11=0, cf=0
ALIGN 16
loop1:
mov rax, qword ptr [rcx + r11 * 8]
sbb rax, qword ptr [rdx + r11 * 8]
mov qword ptr [r10 + r11 * 8], rax
inc r11
dec r9
jnz loop1
adc r9, r9 ; r9 has the cf state
or r8, r8
jz done
neg r9 ; setting cf from r9
mov r9, 0 ; don't use xor here (cf is used)
loop2:
mov rax, qword ptr [rcx + r11 * 8]
sbb rax, r9
mov qword ptr [r10 + r11 * 8], rax
inc r11
dec r8
jnz loop2
adc r8, r8
mov rax, r8
ret
done:
mov rax, r9
ret
ttmath_subvector_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_rcl_x64 PROC
; rcx = p1
; rdx = b
; r8 = nLowestBit
mov r11, rcx ; table
xor r10, r10
neg r8 ; CY set if r8 <> 0
ALIGN 16
loop1:
rcl qword ptr [r11 + r10 * 8], 1
lea r10, [r10+1]
dec rdx
jnz loop1
setc al
movzx rax, al
ret
ttmath_rcl_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_rcr_x64 PROC
; rcx = p1
; rdx = nSize
; r8 = nLowestBit
xor r10, r10
neg r8 ; CY set if r8 <> 0
ALIGN 16
loop1:
rcr qword ptr -8[rcx + rdx * 8], 1
dec rdx
jnz loop1
setc al
movzx rax, al
ret
ttmath_rcr_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_div_x64 PROC
; rcx = &Hi
; rdx = &Lo
; r8 = nDiv
mov r11, rcx
mov r10, rdx
mov rdx, qword ptr [r11]
mov rax, qword ptr [r10]
div r8
mov qword ptr [r10], rdx ; remainder
mov qword ptr [r11], rax ; value
ret
ttmath_div_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_rcl2_x64 PROC
; rcx = p1
; rdx = nSize
; r8 = bits
; r9 = c
push rbx
mov r10, rcx ; r10 = p1
xor rax, rax
mov rcx, 64
sub rcx, r8
mov r11, -1
shr r11, cl ; r11 = mask
mov rcx, r8 ; rcx = count of bits
mov rbx, rax ; rbx = old value = 0
or r9, r9
cmovnz rbx, r11 ; if (c) then old value = mask
mov r9, rax ; r9 = index (0..nSize-1)
ALIGN 16
loop1:
rol qword ptr [r10+r9*8], cl
mov rax, qword ptr [r10+r9*8]
and rax, r11
xor qword ptr [r10+r9*8], rax
or qword ptr [r10+r9*8], rbx
mov rbx, rax
lea r9, [r9+1]
dec rdx
jnz loop1
and rax, 1
pop rbx
ret
ttmath_rcl2_x64 ENDP
;----------------------------------------
ALIGN 8
;----------------------------------------
ttmath_rcr2_x64 PROC
; rcx = p1
; rdx = nSize
; r8 = bits
; r9 = c
push rbx
mov r10, rcx ; r10 = p1
xor rax, rax
mov rcx, 64
sub rcx, r8
mov r11, -1
shl r11, cl ; r11 = mask
mov rcx, r8 ; rcx = count of bits
mov rbx, rax ; rbx = old value = 0
or r9, r9
cmovnz rbx, r11 ; if (c) then old value = mask
mov r9, rdx ; r9 = index (0..nSize-1)
lea r9, [r9-1]
ALIGN 16
loop1:
ror qword ptr [r10+r9*8], cl
mov rax, qword ptr [r10+r9*8]
and rax, r11
xor qword ptr [r10+r9*8], rax
or qword ptr [r10+r9*8], rbx
mov rbx, rax
lea r9, [r9-1]
dec rdx
jnz loop1
rol rax, 1
and rax, 1
pop rbx
ret
ttmath_rcr2_x64 ENDP
END

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const TTMATH_HEADER = "headers/ttmath.h"
type
Int256* {.importc: "ttmath::Int<4>", header: TTMATH_HEADER.} = object
table: array[4, int]
stdString {.importc: "std::string", header: "<string.h>".} = object
#var tmp256* {.exportc: "tmp256".}: Int256
# var tmpString256* {.exportc: "tmpString256", importcpp: "(char*)malloc(sizeof(char) * 256)".}: cstring
proc `+`*(a: Int256, b: Int256): Int256 {.importcpp: "(# + #)".}
proc `-`*(a: Int256, b: Int256): Int256 {.importcpp: "(# - #)".}
proc `*`*(a: Int256, b: Int256): Int256 {.importcpp: "(# * #)".}
proc `/`*(a: Int256, b: Int256): Int256 {.importcpp: "(# / #)".}
proc `div`*(a: Int256, b: Int256): Int256 {.importcpp: "(# / #)".}
proc `==`*(a: Int256, b: Int256): bool {.importcpp: "(# == #)".}
proc `<`*(a: Int256, b: Int256): bool {.importcpp: "(# < #)".}
proc `<=`*(a: Int256, b: Int256): bool {.importcpp: "(# <= #)".}
proc `+=`*(a: var Int256, b: Int256) {.importcpp: "# += #".}
proc `-=`*(a: var Int256, b: Int256) {.importcpp: "# -= #".}
proc `*=`*(a: var Int256, b: Int256) {.importcpp: "# *= #".}
proc `/=`*(a: var Int256, b: Int256) {.importcpp: "# /= #".}
template `-`*(a: Int256): Int256 =
0.i256 - a
proc `and`*(a: Int256, b: Int256): Int256 {.importcpp: "(# & #)".}
proc `or`*(a: Int256, b: Int256): Int256 {.importcpp: "(# | #)".}
proc `xor`*(a: Int256, b: Int256): Int256 {.importcpp: "(# ^ #)".}
proc i256*(a: int): Int256 {.importcpp: "ttmath::Int<4>((int)#)".}
proc i256*(a: cstring): Int256 {.importcpp: "ttmath::Int<4>(#)".}
proc i256*(a: string): Int256 =
cstring(a).i256
proc inplacePow(a: var Int256, b: Int256) {.importcpp: "(#.Pow(#))".}
proc inplaceDiv(a: var Int256, b: Int256, c: var Int256) {.importcpp: "(#.Div(#, #))".}
proc pow*(a: Int256, b: int): Int256 =
var tmp = a
tmp.inplacePow(b.i256)
result = tmp
proc `mod`*(a: Int256, b: Int256): Int256 =
var tmp = a
tmp.inplaceDiv(b, result)
proc ToString(a: Int256, s: stdString | cstring) {.importcpp: "#.ToString(#)", header: TTMATH_HEADER.}
proc strcpy(c: cstring, s: cstring) {.importc: "strcpy", header: "<cstring>".}
proc c_str(s: stdString): cstring {.importcpp: "#.c_str()", header: "<string.h>".}
#proc toCString*(a: Int256): cstring =
proc `shl`*(a: Int256, b: int): Int256 {.importcpp: "(# << #)".}
proc `shr`*(a: Int256, b: int): Int256 {.importcpp: "(# >> #)".}
proc getInt*(a: Int256): int =
a.table[0]
proc `$`*(a: Int256): string =
var tmp: stdString
# TODO: something smarter
{.emit: "tmp = \" \";".}
var s: cstring
{.emit: "s = new char[256];".}
a.ToString(tmp)
strcpy(s, tmp.c_str())
result = $s
{.emit: "delete[] s;".}

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ttmath.nimble Normal file
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packageName = "ttmath"
version = "0.1.0"
author = "Status Research & Development GmbH"
description = "A Nim wrapper for ttmath: big numbers with fixed size"
license = "Apache License 2.0"
srcDir = "src"
### Dependencies
requires "nim >= 0.17.2"