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SA-MP/ttmath/ttmathuint.h
RD42 d286182d25 Add ttmath 0.9.1 library
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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 headerfilettmathuint
#define headerfilettmathuint
/*!
\file ttmathuint.h
\brief template class UInt<uint>
*/
#include <iostream>
#include <iomanip>
#include "ttmathtypes.h"
#include "ttmathmisc.h"
/*!
\brief a namespace for the TTMath library
*/
namespace ttmath
{
/*!
\brief UInt implements a big integer value without a sign
value_size - how many bytes specify our value
on 32bit platforms: value_size=1 -> 4 bytes -> 32 bits
on 64bit platforms: value_size=1 -> 8 bytes -> 64 bits
value_size = 1,2,3,4,5,6....
*/
template<uint value_size>
class UInt
{
public:
/*!
buffer for the integer value
table[0] - the lowest word of the value
*/
uint table[value_size];
/*!
some methods used for debugging purposes
*/
/*!
this method is only for debugging purposes or when we want to make
a table of a variable (constant) in ttmathbig.h
it prints the table in a nice form of several columns
*/
template<class ostream_type>
void PrintTable(ostream_type & output) const
{
// how many columns there'll be
const int columns = 8;
int c = 1;
for(int i=value_size-1 ; i>=0 ; --i)
{
output << "0x" << std::setfill('0');
#ifdef TTMATH_PLATFORM32
output << std::setw(8);
#else
output << std::setw(16);
#endif
output << std::hex << table[i];
if( i>0 )
{
output << ", ";
if( ++c > columns )
{
output << std::endl;
c = 1;
}
}
}
output << std::dec << std::endl;
}
/*!
this method is used when macro TTMATH_DEBUG_LOG is defined
*/
template<class char_type, class ostream_type>
static void PrintVectorLog(const char_type * msg, ostream_type & output, const uint * vector, uint vector_len)
{
output << msg << std::endl;
for(uint i=0 ; i<vector_len ; ++i)
output << " table[" << i << "]: " << vector[i] << std::endl;
}
/*!
this method is used when macro TTMATH_DEBUG_LOG is defined
*/
template<class char_type, class ostream_type>
static void PrintVectorLog(const char_type * msg, uint carry, ostream_type & output, const uint * vector, uint vector_len)
{
PrintVectorLog(msg, output, vector, vector_len);
output << " carry: " << carry << std::endl;
}
/*!
this method is used when macro TTMATH_DEBUG_LOG is defined
*/
template<class char_type, class ostream_type>
void PrintLog(const char_type * msg, ostream_type & output) const
{
PrintVectorLog(msg, output, table, value_size);
}
/*!
this method is used when macro TTMATH_DEBUG_LOG is defined
*/
template<class char_type, class ostream_type>
void PrintLog(const char_type * msg, uint carry, ostream_type & output) const
{
PrintVectorLog(msg, output, table, value_size);
output << " carry: " << carry << std::endl;
}
/*!
this method returns the size of the table
*/
uint Size() const
{
return value_size;
}
/*!
this method sets zero
*/
void SetZero()
{
// in the future here can be 'memset'
for(uint i=0 ; i<value_size ; ++i)
table[i] = 0;
TTMATH_LOG("UInt::SetZero")
}
/*!
this method sets one
*/
void SetOne()
{
SetZero();
table[0] = 1;
TTMATH_LOG("UInt::SetOne")
}
/*!
this method sets the max value which this class can hold
(all bits will be one)
*/
void SetMax()
{
for(uint i=0 ; i<value_size ; ++i)
table[i] = TTMATH_UINT_MAX_VALUE;
TTMATH_LOG("UInt::SetMax")
}
/*!
this method sets the min value which this class can hold
(for an unsigned integer value the zero is the smallest value)
*/
void SetMin()
{
SetZero();
TTMATH_LOG("UInt::SetMin")
}
#ifdef TTMATH_PLATFORM32
/*!
this method copies the value stored in an another table
(warning: first values in temp_table are the highest words -- it's different
from our table)
we copy as many words as it is possible
if temp_table_len is bigger than value_size we'll try to round
the lowest word from table depending on the last not used bit in temp_table
(this rounding isn't a perfect rounding -- look at the description below)
and if temp_table_len is smaller than value_size we'll clear the rest words
in the table
*/
void SetFromTable(const uint * temp_table, uint temp_table_len)
{
uint temp_table_index = 0;
sint i; // 'i' with a sign
for(i=value_size-1 ; i>=0 && temp_table_index<temp_table_len; --i, ++temp_table_index)
table[i] = temp_table[ temp_table_index ];
// rounding mantissa
if( temp_table_index < temp_table_len )
{
if( (temp_table[temp_table_index] & TTMATH_UINT_HIGHEST_BIT) != 0 )
{
/*
very simply rounding
if the bit from not used last word from temp_table is set to one
we're rouding the lowest word in the table
in fact there should be a normal addition but
we don't use Add() or AddTwoInts() because these methods
can set a carry and then there'll be a small problem
for optimization
*/
if( table[0] != TTMATH_UINT_MAX_VALUE )
++table[0];
}
}
// cleaning the rest of the mantissa
for( ; i>=0 ; --i)
table[i] = 0;
TTMATH_LOG("UInt::SetFromTable")
}
#endif
#ifdef TTMATH_PLATFORM64
/*!
this method copies the value stored in an another table
(warning: first values in temp_table are the highest words -- it's different
from our table)
***this method is created only on a 64bit platform***
we copy as many words as it is possible
if temp_table_len is bigger than value_size we'll try to round
the lowest word from table depending on the last not used bit in temp_table
(this rounding isn't a perfect rounding -- look at the description below)
and if temp_table_len is smaller than value_size we'll clear the rest words
in the table
warning: we're using 'temp_table' as a pointer at 32bit words
*/
void SetFromTable(const unsigned int * temp_table, uint temp_table_len)
{
uint temp_table_index = 0;
sint i; // 'i' with a sign
for(i=value_size-1 ; i>=0 && temp_table_index<temp_table_len; --i, ++temp_table_index)
{
table[i] = uint(temp_table[ temp_table_index ]) << 32;
++temp_table_index;
if( temp_table_index<temp_table_len )
table[i] |= temp_table[ temp_table_index ];
}
// rounding mantissa
if( temp_table_index < temp_table_len )
{
if( (temp_table[temp_table_index] & TTMATH_UINT_HIGHEST_BIT) != 0 )
{
/*
very simply rounding
if the bit from not used last word from temp_table is set to one
we're rouding the lowest word in the table
in fact there should be a normal addition but
we don't use Add() or AddTwoInts() because these methods
can set a carry and then there'll be a small problem
for optimization
*/
if( table[0] != TTMATH_UINT_MAX_VALUE )
++table[0];
}
}
// cleaning the rest of the mantissa
for( ; i >= 0 ; --i)
table[i] = 0;
TTMATH_LOG("UInt::SetFromTable")
}
#endif
/*!
*
* basic mathematic functions
*
*/
/*!
this method adds one to the existing value
*/
uint AddOne()
{
return AddInt(1);
}
/*!
this method subtracts one from the existing value
*/
uint SubOne()
{
return SubInt(1);
}
private:
/*!
an auxiliary method for moving bits into the left hand side
this method moves only words
*/
void RclMoveAllWords(uint & rest_bits, uint & last_c, uint bits, uint c)
{
rest_bits = bits % TTMATH_BITS_PER_UINT;
uint all_words = bits / TTMATH_BITS_PER_UINT;
uint mask = ( c ) ? TTMATH_UINT_MAX_VALUE : 0;
if( all_words >= value_size )
{
if( all_words == value_size && rest_bits == 0 )
last_c = table[0] & 1;
// else: last_c is default set to 0
// clearing
for(uint i = 0 ; i<value_size ; ++i)
table[i] = mask;
rest_bits = 0;
}
else
if( all_words > 0 )
{
// 0 < all_words < value_size
sint first, second;
last_c = table[value_size - all_words] & 1; // all_words is greater than 0
// copying the first part of the value
for(first = value_size-1, second=first-all_words ; second>=0 ; --first, --second)
table[first] = table[second];
// setting the rest to 'c'
for( ; first>=0 ; --first )
table[first] = mask;
}
TTMATH_LOG("UInt::RclMoveAllWords")
}
public:
/*!
moving all bits into the left side 'bits' times
return value <- this <- C
bits is from a range of <0, man * TTMATH_BITS_PER_UINT>
or it can be even bigger then all bits will be set to 'c'
the value c will be set into the lowest bits
and the method returns state of the last moved bit
*/
uint Rcl(uint bits, uint c=0)
{
uint last_c = 0;
uint rest_bits = bits;
if( bits == 0 )
return 0;
if( bits >= TTMATH_BITS_PER_UINT )
RclMoveAllWords(rest_bits, last_c, bits, c);
if( rest_bits == 0 )
{
TTMATH_LOG("UInt::Rcl")
return last_c;
}
// rest_bits is from 1 to TTMATH_BITS_PER_UINT-1 now
if( rest_bits == 1 )
{
last_c = Rcl2_one(c);
}
else if( rest_bits == 2 )
{
// performance tests showed that for rest_bits==2 it's better to use Rcl2_one twice instead of Rcl2(2,c)
Rcl2_one(c);
last_c = Rcl2_one(c);
}
else
{
last_c = Rcl2(rest_bits, c);
}
TTMATH_LOGC("UInt::Rcl", last_c)
return last_c;
}
private:
/*!
an auxiliary method for moving bits into the right hand side
this method moves only words
*/
void RcrMoveAllWords(uint & rest_bits, uint & last_c, uint bits, uint c)
{
rest_bits = bits % TTMATH_BITS_PER_UINT;
uint all_words = bits / TTMATH_BITS_PER_UINT;
uint mask = ( c ) ? TTMATH_UINT_MAX_VALUE : 0;
if( all_words >= value_size )
{
if( all_words == value_size && rest_bits == 0 )
last_c = (table[value_size-1] & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0;
// else: last_c is default set to 0
// clearing
for(uint i = 0 ; i<value_size ; ++i)
table[i] = mask;
rest_bits = 0;
}
else if( all_words > 0 )
{
// 0 < all_words < value_size
uint first, second;
last_c = (table[all_words - 1] & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0; // all_words is > 0
// copying the first part of the value
for(first=0, second=all_words ; second<value_size ; ++first, ++second)
table[first] = table[second];
// setting the rest to 'c'
for( ; first<value_size ; ++first )
table[first] = mask;
}
TTMATH_LOG("UInt::RcrMoveAllWords")
}
public:
/*!
moving all bits into the right side 'bits' times
c -> this -> return value
bits is from a range of <0, man * TTMATH_BITS_PER_UINT>
or it can be even bigger then all bits will be set to 'c'
the value c will be set into the highest bits
and the method returns state of the last moved bit
*/
uint Rcr(uint bits, uint c=0)
{
uint last_c = 0;
uint rest_bits = bits;
if( bits == 0 )
return 0;
if( bits >= TTMATH_BITS_PER_UINT )
RcrMoveAllWords(rest_bits, last_c, bits, c);
if( rest_bits == 0 )
{
TTMATH_LOG("UInt::Rcr")
return last_c;
}
// rest_bits is from 1 to TTMATH_BITS_PER_UINT-1 now
if( rest_bits == 1 )
{
last_c = Rcr2_one(c);
}
else if( rest_bits == 2 )
{
// performance tests showed that for rest_bits==2 it's better to use Rcr2_one twice instead of Rcr2(2,c)
Rcr2_one(c);
last_c = Rcr2_one(c);
}
else
{
last_c = Rcr2(rest_bits, c);
}
TTMATH_LOGC("UInt::Rcr", last_c)
return last_c;
}
/*!
this method moves all bits into the left side
(it returns value how many bits have been moved)
*/
uint CompensationToLeft()
{
uint moving = 0;
// a - index a last word which is different from zero
sint a;
for(a=value_size-1 ; a>=0 && table[a]==0 ; --a);
if( a < 0 )
return moving; // all words in table have zero
if( a != value_size-1 )
{
moving += ( value_size-1 - a ) * TTMATH_BITS_PER_UINT;
// moving all words
sint i;
for(i=value_size-1 ; a>=0 ; --i, --a)
table[i] = table[a];
// setting the rest word to zero
for(; i>=0 ; --i)
table[i] = 0;
}
uint moving2 = FindLeadingBitInWord( table[value_size-1] );
// moving2 is different from -1 because the value table[value_size-1]
// is not zero
moving2 = TTMATH_BITS_PER_UINT - moving2 - 1;
Rcl(moving2);
TTMATH_LOG("UInt::CompensationToLeft")
return moving + moving2;
}
/*!
this method looks for the highest set bit
result:
if 'this' is not zero:
return value - true
'table_id' - the index of a word <0..value_size-1>
'index' - the index of this set bit in the word <0..TTMATH_BITS_PER_UINT)
if 'this' is zero:
return value - false
both 'table_id' and 'index' are zero
*/
bool FindLeadingBit(uint & table_id, uint & index) const
{
for(table_id=value_size-1 ; table_id!=0 && table[table_id]==0 ; --table_id);
if( table_id==0 && table[table_id]==0 )
{
// is zero
index = 0;
return false;
}
// table[table_id] is different from 0
index = FindLeadingBitInWord( table[table_id] );
return true;
}
/*!
this method looks for the smallest set bit
result:
if 'this' is not zero:
return value - true
'table_id' - the index of a word <0..value_size-1>
'index' - the index of this set bit in the word <0..TTMATH_BITS_PER_UINT)
if 'this' is zero:
return value - false
both 'table_id' and 'index' are zero
*/
bool FindLowestBit(uint & table_id, uint & index) const
{
for(table_id=0 ; table_id<value_size && table[table_id]==0 ; ++table_id);
if( table_id >= value_size )
{
// is zero
index = 0;
table_id = 0;
return false;
}
// table[table_id] is different from 0
index = FindLowestBitInWord( table[table_id] );
return true;
}
/*!
getting the 'bit_index' bit
bit_index bigger or equal zero
*/
uint GetBit(uint bit_index) const
{
TTMATH_ASSERT( bit_index < value_size * TTMATH_BITS_PER_UINT )
uint index = bit_index / TTMATH_BITS_PER_UINT;
uint bit = bit_index % TTMATH_BITS_PER_UINT;
uint temp = table[index];
uint res = SetBitInWord(temp, bit);
return res;
}
/*!
setting the 'bit_index' bit
and returning the last state of the bit
bit_index bigger or equal zero
*/
uint SetBit(uint bit_index)
{
TTMATH_ASSERT( bit_index < value_size * TTMATH_BITS_PER_UINT )
uint index = bit_index / TTMATH_BITS_PER_UINT;
uint bit = bit_index % TTMATH_BITS_PER_UINT;
uint res = SetBitInWord(table[index], bit);
TTMATH_LOG("UInt::SetBit")
return res;
}
/*!
this method performs a bitwise operation AND
*/
void BitAnd(const UInt<value_size> & ss2)
{
for(uint x=0 ; x<value_size ; ++x)
table[x] &= ss2.table[x];
TTMATH_LOG("UInt::BitAnd")
}
/*!
this method performs a bitwise operation OR
*/
void BitOr(const UInt<value_size> & ss2)
{
for(uint x=0 ; x<value_size ; ++x)
table[x] |= ss2.table[x];
TTMATH_LOG("UInt::BitOr")
}
/*!
this method performs a bitwise operation XOR
*/
void BitXor(const UInt<value_size> & ss2)
{
for(uint x=0 ; x<value_size ; ++x)
table[x] ^= ss2.table[x];
TTMATH_LOG("UInt::BitXor")
}
/*!
this method performs a bitwise operation NOT
*/
void BitNot()
{
for(uint x=0 ; x<value_size ; ++x)
table[x] = ~table[x];
TTMATH_LOG("UInt::BitNot")
}
/*!
this method performs a bitwise operation NOT but only
on the range of <0, leading_bit>
for example:
BitNot2(8) = BitNot2( 1000(bin) ) = 111(bin) = 7
*/
void BitNot2()
{
uint table_id, index;
if( FindLeadingBit(table_id, index) )
{
for(uint x=0 ; x<table_id ; ++x)
table[x] = ~table[x];
uint mask = TTMATH_UINT_MAX_VALUE;
uint shift = TTMATH_BITS_PER_UINT - index - 1;
if(shift)
mask >>= shift;
table[table_id] ^= mask;
}
else
table[0] = 1;
TTMATH_LOG("UInt::BitNot2")
}
/*!
*
* Multiplication
*
*
*/
public:
/*!
multiplication: this = this * ss2
it can return a carry
*/
uint MulInt(uint ss2)
{
uint r1, r2, x1;
uint c = 0;
UInt<value_size> u(*this);
SetZero();
if( ss2 == 0 )
{
TTMATH_LOGC("UInt::MulInt(uint)", 0)
return 0;
}
for(x1=0 ; x1<value_size-1 ; ++x1)
{
MulTwoWords(u.table[x1], ss2, &r2, &r1);
c += AddTwoInts(r2,r1,x1);
}
// x1 = value_size-1 (last word)
MulTwoWords(u.table[x1], ss2, &r2, &r1);
c += (r2!=0) ? 1 : 0;
c += AddInt(r1, x1);
TTMATH_LOGC("UInt::MulInt(uint)", c)
return (c==0)? 0 : 1;
}
/*!
multiplication: result = this * ss2
we're using this method only when result_size is greater than value_size
if so there will not be a carry
*/
template<uint result_size>
void MulInt(uint ss2, UInt<result_size> & result) const
{
TTMATH_ASSERT( result_size > value_size )
uint r2,r1;
uint x1size=value_size;
uint x1start=0;
result.SetZero();
if( ss2 == 0 )
{
TTMATH_VECTOR_LOG("UInt::MulInt(uint, UInt<>)", result.table, result_size)
return;
}
if( value_size > 2 )
{
// if the value_size is smaller than or equal to 2
// there is no sense to set x1size and x1start to another values
for(x1size=value_size ; x1size>0 && table[x1size-1]==0 ; --x1size);
if( x1size == 0 )
{
TTMATH_VECTOR_LOG("UInt::MulInt(uint, UInt<>)", result.table, result_size)
return;
}
for(x1start=0 ; x1start<x1size && table[x1start]==0 ; ++x1start);
}
for(uint x1=x1start ; x1<x1size ; ++x1)
{
MulTwoWords(table[x1], ss2, &r2, &r1 );
result.AddTwoInts(r2,r1,x1);
}
TTMATH_VECTOR_LOG("UInt::MulInt(uint, UInt<>)", result.table, result_size)
return;
}
/*!
the multiplication 'this' = 'this' * ss2
algorithm: 100 - means automatically choose the fastest algorithm
*/
uint Mul(const UInt<value_size> & ss2, uint algorithm = 100)
{
switch( algorithm )
{
case 1:
return Mul1(ss2);
case 2:
return Mul2(ss2);
case 3:
return Mul3(ss2);
case 100:
default:
return MulFastest(ss2);
}
}
/*!
the multiplication 'result' = 'this' * ss2
since the 'result' is twice bigger than 'this' and 'ss2'
this method never returns a carry
algorithm: 100 - means automatically choose the fastest algorithm
*/
void MulBig(const UInt<value_size> & ss2,
UInt<value_size*2> & result,
uint algorithm = 100)
{
switch( algorithm )
{
case 1:
return Mul1Big(ss2, result);
case 2:
return Mul2Big(ss2, result);
case 3:
return Mul3Big(ss2, result);
case 100:
default:
return MulFastestBig(ss2, result);
}
}
/*!
the first version of the multiplication algorithm
*/
/*!
multiplication: this = this * ss2
it returns carry if it has been
*/
uint Mul1(const UInt<value_size> & ss2)
{
TTMATH_REFERENCE_ASSERT( ss2 )
UInt<value_size> ss1( *this );
SetZero();
for(uint i=0; i < value_size*TTMATH_BITS_PER_UINT ; ++i)
{
if( Add(*this) )
{
TTMATH_LOGC("UInt::Mul1", 1)
return 1;
}
if( ss1.Rcl(1) )
if( Add(ss2) )
{
TTMATH_LOGC("UInt::Mul1", 1)
return 1;
}
}
TTMATH_LOGC("UInt::Mul1", 0)
return 0;
}
/*!
multiplication: result = this * ss2
result is twice bigger than 'this' and 'ss2'
this method never returns carry
*/
void Mul1Big(const UInt<value_size> & ss2_, UInt<value_size*2> & result)
{
UInt<value_size*2> ss2;
uint i;
// copying *this into result and ss2_ into ss2
for(i=0 ; i<value_size ; ++i)
{
result.table[i] = table[i];
ss2.table[i] = ss2_.table[i];
}
// cleaning the highest bytes in result and ss2
for( ; i < value_size*2 ; ++i)
{
result.table[i] = 0;
ss2.table[i] = 0;
}
// multiply
// (there will not be a carry)
result.Mul1( ss2 );
TTMATH_LOG("UInt::Mul1Big")
}
/*!
the second version of the multiplication algorithm
this algorithm is similar to the 'schoolbook method' which is done by hand
*/
/*!
multiplication: this = this * ss2
it returns carry if it has been
*/
uint Mul2(const UInt<value_size> & ss2)
{
UInt<value_size*2> result;
uint i, c = 0;
Mul2Big(ss2, result);
// copying result
for(i=0 ; i<value_size ; ++i)
table[i] = result.table[i];
// testing carry
for( ; i<value_size*2 ; ++i)
if( result.table[i] != 0 )
{
c = 1;
break;
}
TTMATH_LOGC("UInt::Mul2", c)
return c;
}
/*!
multiplication: result = this * ss2
result is twice bigger than this and ss2
this method never returns carry
*/
void Mul2Big(const UInt<value_size> & ss2, UInt<value_size*2> & result)
{
Mul2Big2<value_size>(table, ss2.table, result);
TTMATH_LOG("UInt::Mul2Big")
}
private:
/*!
an auxiliary method for calculating the multiplication
arguments we're taking as pointers (this is to improve the Mul3Big2()- avoiding
unnecessary copying objects), the result should be taken as a pointer too,
but at the moment there is no method AddTwoInts() which can operate on pointers
*/
template<uint ss_size>
void Mul2Big2(const uint * ss1, const uint * ss2, UInt<ss_size*2> & result)
{
uint x1size = ss_size, x2size = ss_size;
uint x1start = 0, x2start = 0;
if( ss_size > 2 )
{
// if the ss_size is smaller than or equal to 2
// there is no sense to set x1size (and others) to another values
for(x1size=ss_size ; x1size>0 && ss1[x1size-1]==0 ; --x1size);
for(x2size=ss_size ; x2size>0 && ss2[x2size-1]==0 ; --x2size);
for(x1start=0 ; x1start<x1size && ss1[x1start]==0 ; ++x1start);
for(x2start=0 ; x2start<x2size && ss2[x2start]==0 ; ++x2start);
}
Mul2Big3<ss_size>(ss1, ss2, result, x1start, x1size, x2start, x2size);
}
/*!
an auxiliary method for calculating the multiplication
*/
template<uint ss_size>
void Mul2Big3(const uint * ss1, const uint * ss2, UInt<ss_size*2> & result, uint x1start, uint x1size, uint x2start, uint x2size)
{
uint r2, r1;
result.SetZero();
if( x1size==0 || x2size==0 )
return;
for(uint x1=x1start ; x1<x1size ; ++x1)
{
for(uint x2=x2start ; x2<x2size ; ++x2)
{
MulTwoWords(ss1[x1], ss2[x2], &r2, &r1);
result.AddTwoInts(r2, r1, x2+x1);
// here will never be a carry
}
}
}
public:
/*!
multiplication: this = this * ss2
This is Karatsuba Multiplication algorithm, we're using it when value_size is greater than
or equal to TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE macro (defined in ttmathuint.h).
If value_size is smaller then we're using Mul2Big() instead.
Karatsuba multiplication:
Assume we have:
this = x = x1*B^m + x0
ss2 = y = y1*B^m + y0
where x0 and y0 are less than B^m
the product from multiplication we can show as:
x*y = (x1*B^m + x0)(y1*B^m + y0) = z2*B^(2m) + z1*B^m + z0
where
z2 = x1*y1
z1 = x1*y0 + x0*y1
z0 = x0*y0
this is standard schoolbook algorithm with O(n^2), Karatsuba observed that z1 can be given in other form:
z1 = (x1 + x0)*(y1 + y0) - z2 - z0 / z1 = (x1*y1 + x1*y0 + x0*y1 + x0*y0) - x1*y1 - x0*y0 = x1*y0 + x0*y1 /
and to calculate the multiplication we need only three multiplications (with some additions and subtractions)
Our objects 'this' and 'ss2' we divide into two parts and by using recurrence we calculate the multiplication.
Karatsuba multiplication has O( n^(ln(3)/ln(2)) )
*/
uint Mul3(const UInt<value_size> & ss2)
{
UInt<value_size*2> result;
uint i, c = 0;
Mul3Big(ss2, result);
// copying result
for(i=0 ; i<value_size ; ++i)
table[i] = result.table[i];
// testing carry
for( ; i<value_size*2 ; ++i)
if( result.table[i] != 0 )
{
c = 1;
break;
}
TTMATH_LOGC("UInt::Mul3", c)
return c;
}
/*!
multiplication: result = this * ss2
result is twice bigger than this and ss2,
this method never returns carry,
(Karatsuba multiplication)
*/
void Mul3Big(const UInt<value_size> & ss2, UInt<value_size*2> & result)
{
Mul3Big2<value_size>(table, ss2.table, result.table);
TTMATH_LOG("UInt::Mul3Big")
}
private:
/*!
an auxiliary method for calculating the Karatsuba multiplication
result_size is equal ss_size*2
*/
template<uint ss_size>
void Mul3Big2(const uint * ss1, const uint * ss2, uint * result)
{
const uint * x1, * x0, * y1, * y0;
if( ss_size>1 && ss_size<TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE )
{
UInt<ss_size*2> res;
Mul2Big2<ss_size>(ss1, ss2, res);
for(uint i=0 ; i<ss_size*2 ; ++i)
result[i] = res.table[i];
return;
}
else
if( ss_size == 1 )
{
return MulTwoWords(*ss1, *ss2, &result[1], &result[0]);
}
if( (ss_size & 1) == 1 )
{
// ss_size is odd
x0 = ss1;
y0 = ss2;
x1 = ss1 + ss_size / 2 + 1;
y1 = ss2 + ss_size / 2 + 1;
// the second vectors (x1 and y1) are smaller about one from the first ones (x0 and y0)
Mul3Big3<ss_size/2 + 1, ss_size/2, ss_size*2>(x1, x0, y1, y0, result);
}
else
{
// ss_size is even
x0 = ss1;
y0 = ss2;
x1 = ss1 + ss_size / 2;
y1 = ss2 + ss_size / 2;
// all four vectors (x0 x1 y0 y1) are equal in size
Mul3Big3<ss_size/2, ss_size/2, ss_size*2>(x1, x0, y1, y0, result);
}
}
#ifdef _MSC_VER
#pragma warning (disable : 4717)
//warning C4717: recursive on all control paths, function will cause runtime stack overflow
//we have the stop point in Mul3Big2() method
#endif
/*!
an auxiliary method for calculating the Karatsuba multiplication
x = x1*B^m + x0
y = y1*B^m + y0
first_size - is the size of vectors: x0 and y0
second_size - is the size of vectors: x1 and y1 (can be either equal first_size or smaller about one from first_size)
x*y = (x1*B^m + x0)(y1*B^m + y0) = z2*B^(2m) + z1*B^m + z0
where
z0 = x0*y0
z2 = x1*y1
z1 = (x1 + x0)*(y1 + y0) - z2 - z0
*/
template<uint first_size, uint second_size, uint result_size>
void Mul3Big3(const uint * x1, const uint * x0, const uint * y1, const uint * y0, uint * result)
{
uint i, c, xc, yc;
UInt<first_size> temp, temp2;
UInt<first_size*3> z1;
// z0 and z2 we store directly in the result (we don't use any temporary variables)
Mul3Big2<first_size>(x0, y0, result); // z0
Mul3Big2<second_size>(x1, y1, result+first_size*2); // z2
// now we calculate z1
// temp = (x0 + x1)
// temp2 = (y0 + y1)
// we're using temp and temp2 with UInt<first_size>, although there can be a carry but
// we simple remember it in xc and yc (xc and yc can be either 0 or 1),
// and (x0 + x1)*(y0 + y1) we calculate in this way (schoolbook algorithm):
//
// xc | temp
// yc | temp2
// --------------------
// (temp * temp2)
// xc*temp2 |
// yc*temp |
// xc*yc |
// ---------- z1 --------
//
// and the result is never larger in size than 3*first_size
xc = AddVector(x0, x1, first_size, second_size, temp.table);
yc = AddVector(y0, y1, first_size, second_size, temp2.table);
Mul3Big2<first_size>(temp.table, temp2.table, z1.table);
// clearing the rest of z1
for(i=first_size*2 ; i<first_size*3 ; ++i)
z1.table[i] = 0;
if( xc )
{
c = AddVector(z1.table+first_size, temp2.table, first_size*3-first_size, first_size, z1.table+first_size);
TTMATH_ASSERT( c==0 )
}
if( yc )
{
c = AddVector(z1.table+first_size, temp.table, first_size*3-first_size, first_size, z1.table+first_size);
TTMATH_ASSERT( c==0 )
}
if( xc && yc )
{
for( i=first_size*2 ; i<first_size*3 ; ++i )
if( ++z1.table[i] != 0 )
break; // break if there was no carry
}
// z1 = z1 - z2
c = SubVector(z1.table, result+first_size*2, first_size*3, second_size*2, z1.table);
TTMATH_ASSERT(c==0)
// z1 = z1 - z0
c = SubVector(z1.table, result, first_size*3, first_size*2, z1.table);
TTMATH_ASSERT(c==0)
// here we've calculated the z1
// now we're adding it to the result
if( first_size > second_size )
{
uint z1_size = result_size - first_size;
TTMATH_ASSERT( z1_size <= first_size*3 )
for(i=z1_size ; i<first_size*3 ; ++i)
TTMATH_ASSERT( z1.table[i] == 0 )
;
c = AddVector(result+first_size, z1.table, result_size-first_size, z1_size, result+first_size);
TTMATH_ASSERT(c==0)
}
else
{
c = AddVector(result+first_size, z1.table, result_size-first_size, first_size*3, result+first_size);
TTMATH_ASSERT(c==0)
}
}
#ifdef _MSC_VER
#pragma warning (default : 4717)
#endif
public:
/*!
multiplication this = this * ss2
*/
uint MulFastest(const UInt<value_size> & ss2)
{
UInt<value_size*2> result;
uint i, c = 0;
MulFastestBig(ss2, result);
// copying result
for(i=0 ; i<value_size ; ++i)
table[i] = result.table[i];
// testing carry
for( ; i<value_size*2 ; ++i)
if( result.table[i] != 0 )
{
c = 1;
break;
}
TTMATH_LOGC("UInt::MulFastest", c)
return c;
}
/*!
multiplication result = this * ss2
this method is trying to select the fastest algorithm
(in the future this method can be improved)
*/
void MulFastestBig(const UInt<value_size> & ss2, UInt<value_size*2> & result)
{
if( value_size < TTMATH_USE_KARATSUBA_MULTIPLICATION_FROM_SIZE )
return Mul2Big(ss2, result);
uint x1size = value_size, x2size = value_size;
uint x1start = 0, x2start = 0;
for(x1size=value_size ; x1size>0 && table[x1size-1]==0 ; --x1size);
for(x2size=value_size ; x2size>0 && ss2.table[x2size-1]==0 ; --x2size);
if( x1size==0 || x2size==0 )
{
// either 'this' or 'ss2' is equal zero - the result is zero too
result.SetZero();
return;
}
for(x1start=0 ; x1start<x1size && table[x1start]==0 ; ++x1start);
for(x2start=0 ; x2start<x2size && ss2.table[x2start]==0 ; ++x2start);
uint distancex1 = x1size - x1start;
uint distancex2 = x2size - x2start;
if( distancex1 < 3 || distancex2 < 3 )
// either 'this' or 'ss2' have only 2 (or 1) items different from zero (side by side)
// (this condition in the future can be improved)
return Mul2Big3<value_size>(table, ss2.table, result, x1start, x1size, x2start, x2size);
// Karatsuba multiplication
Mul3Big(ss2, result);
TTMATH_LOG("UInt::MulFastestBig")
}
/*!
*
* Division
*
*
*/
public:
/*!
division by one unsigned word
returns 1 when divisor is zero
*/
uint DivInt(uint divisor, uint * remainder = 0)
{
if( divisor == 0 )
{
if( remainder )
*remainder = 0; // this is for convenience, without it the compiler can report that 'remainder' is uninitialized
TTMATH_LOG("UInt::DivInt")
return 1;
}
if( divisor == 1 )
{
if( remainder )
*remainder = 0;
TTMATH_LOG("UInt::DivInt")
return 0;
}
UInt<value_size> dividend(*this);
SetZero();
sint i; // i must be with a sign
uint r = 0;
// we're looking for the last word in ss1
for(i=value_size-1 ; i>0 && dividend.table[i]==0 ; --i);
for( ; i>=0 ; --i)
DivTwoWords(r, dividend.table[i], divisor, &table[i], &r);
if( remainder )
*remainder = r;
TTMATH_LOG("UInt::DivInt")
return 0;
}
uint DivInt(uint divisor, uint & remainder)
{
return DivInt(divisor, &remainder);
}
/*!
division this = this / ss2
return values:
0 - ok
1 - division by zero
'this' will be the quotient
'remainder' - remainder
*/
uint Div( const UInt<value_size> & divisor,
UInt<value_size> * remainder = 0,
uint algorithm = 3)
{
switch( algorithm )
{
case 1:
return Div1(divisor, remainder);
case 2:
return Div2(divisor, remainder);
case 3:
default:
return Div3(divisor, remainder);
}
}
uint Div(const UInt<value_size> & divisor, UInt<value_size> & remainder, uint algorithm = 3)
{
return Div(divisor, &remainder, algorithm);
}
private:
/*!
return values:
0 - none has to be done
1 - division by zero
2 - division should be made
*/
uint Div_StandardTest( const UInt<value_size> & v,
uint & m, uint & n,
UInt<value_size> * remainder = 0)
{
switch( Div_CalculatingSize(v, m, n) )
{
case 4: // 'this' is equal v
if( remainder )
remainder->SetZero();
SetOne();
TTMATH_LOG("UInt::Div_StandardTest")
return 0;
case 3: // 'this' is smaller than v
if( remainder )
*remainder = *this;
SetZero();
TTMATH_LOG("UInt::Div_StandardTest")
return 0;
case 2: // 'this' is zero
if( remainder )
remainder->SetZero();
SetZero();
TTMATH_LOG("UInt::Div_StandardTest")
return 0;
case 1: // v is zero
TTMATH_LOG("UInt::Div_StandardTest")
return 1;
}
TTMATH_LOG("UInt::Div_StandardTest")
return 2;
}
/*!
return values:
0 - ok
'm' - is the index (from 0) of last non-zero word in table ('this')
'n' - is the index (from 0) of last non-zero word in v.table
1 - v is zero
2 - 'this' is zero
3 - 'this' is smaller than v
4 - 'this' is equal v
if the return value is different than zero the 'm' and 'n' are undefined
*/
uint Div_CalculatingSize(const UInt<value_size> & v, uint & m, uint & n)
{
m = n = value_size-1;
for( ; n!=0 && v.table[n]==0 ; --n);
if( n==0 && v.table[n]==0 )
return 1;
for( ; m!=0 && table[m]==0 ; --m);
if( m==0 && table[m]==0 )
return 2;
if( m < n )
return 3;
else
if( m == n )
{
uint i;
for(i = n ; i!=0 && table[i]==v.table[i] ; --i);
if( table[i] < v.table[i] )
return 3;
else
if (table[i] == v.table[i] )
return 4;
}
return 0;
}
public:
/*!
the first division algorithm
radix 2
*/
uint Div1(const UInt<value_size> & divisor, UInt<value_size> * remainder = 0)
{
uint m,n, test;
test = Div_StandardTest(divisor, m, n, remainder);
if( test < 2 )
return test;
if( !remainder )
{
UInt<value_size> rem;
return Div1_Calculate(divisor, rem);
}
return Div1_Calculate(divisor, *remainder);
}
private:
uint Div1_Calculate(const UInt<value_size> & divisor, UInt<value_size> & rest)
{
TTMATH_REFERENCE_ASSERT( divisor )
sint loop;
sint c;
rest.SetZero();
loop = value_size * TTMATH_BITS_PER_UINT;
c = 0;
div_a:
c = Rcl(1, c);
c = rest.Add(rest,c);
c = rest.Sub(divisor,c);
c = !c;
if(!c)
goto div_d;
div_b:
--loop;
if(loop)
goto div_a;
c = Rcl(1, c);
TTMATH_LOG("UInt::Div1_Calculate")
return 0;
div_c:
c = Rcl(1, c);
c = rest.Add(rest,c);
c = rest.Add(divisor);
if(c)
goto div_b;
div_d:
--loop;
if(loop)
goto div_c;
c = Rcl(1, c);
c = rest.Add(divisor);
TTMATH_LOG("UInt::Div1_Calculate")
return 0;
}
public:
/*!
the second division algorithm
return values:
0 - ok
1 - division by zero
*/
uint Div2(const UInt<value_size> & divisor, UInt<value_size> * remainder = 0)
{
TTMATH_REFERENCE_ASSERT( divisor )
uint bits_diff;
uint status = Div2_Calculate(divisor, remainder, bits_diff);
if( status < 2 )
return status;
if( CmpBiggerEqual(divisor) )
{
Div2(divisor, remainder);
SetBit(bits_diff);
}
else
{
if( remainder )
*remainder = *this;
SetZero();
SetBit(bits_diff);
}
TTMATH_LOG("UInt::Div2")
return 0;
}
uint Div2(const UInt<value_size> & divisor, UInt<value_size> & remainder)
{
return Div2(divisor, &remainder);
}
private:
/*!
return values:
0 - we've calculated the division
1 - division by zero
2 - we have to still calculate
*/
uint Div2_Calculate(const UInt<value_size> & divisor, UInt<value_size> * remainder,
uint & bits_diff)
{
uint table_id, index;
uint divisor_table_id, divisor_index;
uint status = Div2_FindLeadingBitsAndCheck( divisor, remainder,
table_id, index,
divisor_table_id, divisor_index);
if( status < 2 )
{
TTMATH_LOG("UInt::Div2_Calculate")
return status;
}
// here we know that 'this' is greater than divisor
// then 'index' is greater or equal 'divisor_index'
bits_diff = index - divisor_index;
UInt<value_size> divisor_copy(divisor);
divisor_copy.Rcl(bits_diff, 0);
if( CmpSmaller(divisor_copy, table_id) )
{
divisor_copy.Rcr(1);
--bits_diff;
}
Sub(divisor_copy, 0);
TTMATH_LOG("UInt::Div2_Calculate")
return 2;
}
/*!
return values:
0 - we've calculated the division
1 - division by zero
2 - we have to still calculate
*/
uint Div2_FindLeadingBitsAndCheck( const UInt<value_size> & divisor,
UInt<value_size> * remainder,
uint & table_id, uint & index,
uint & divisor_table_id, uint & divisor_index)
{
if( !divisor.FindLeadingBit(divisor_table_id, divisor_index) )
{
// division by zero
TTMATH_LOG("UInt::Div2_FindLeadingBitsAndCheck")
return 1;
}
if( !FindLeadingBit(table_id, index) )
{
// zero is divided by something
SetZero();
if( remainder )
remainder->SetZero();
TTMATH_LOG("UInt::Div2_FindLeadingBitsAndCheck")
return 0;
}
divisor_index += divisor_table_id * TTMATH_BITS_PER_UINT;
index += table_id * TTMATH_BITS_PER_UINT;
if( divisor_table_id == 0 )
{
// dividor has only one 32-bit word
uint r;
DivInt(divisor.table[0], &r);
if( remainder )
{
remainder->SetZero();
remainder->table[0] = r;
}
TTMATH_LOG("UInt::Div2_FindLeadingBitsAndCheck")
return 0;
}
if( Div2_DivisorGreaterOrEqual( divisor, remainder,
table_id, index,
divisor_index) )
{
TTMATH_LOG("UInt::Div2_FindLeadingBitsAndCheck")
return 0;
}
TTMATH_LOG("UInt::Div2_FindLeadingBitsAndCheck")
return 2;
}
/*!
return values:
true if divisor is equal or greater than 'this'
*/
bool Div2_DivisorGreaterOrEqual( const UInt<value_size> & divisor,
UInt<value_size> * remainder,
uint table_id, uint index,
uint divisor_index )
{
if( divisor_index > index )
{
// divisor is greater than this
if( remainder )
*remainder = *this;
SetZero();
TTMATH_LOG("UInt::Div2_DivisorGreaterOrEqual")
return true;
}
if( divisor_index == index )
{
// table_id == divisor_table_id as well
uint i;
for(i = table_id ; i!=0 && table[i]==divisor.table[i] ; --i);
if( table[i] < divisor.table[i] )
{
// divisor is greater than 'this'
if( remainder )
*remainder = *this;
SetZero();
TTMATH_LOG("UInt::Div2_DivisorGreaterOrEqual")
return true;
}
else
if( table[i] == divisor.table[i] )
{
// divisor is equal 'this'
if( remainder )
remainder->SetZero();
SetOne();
TTMATH_LOG("UInt::Div2_DivisorGreaterOrEqual")
return true;
}
}
TTMATH_LOG("UInt::Div2_DivisorGreaterOrEqual")
return false;
}
public:
/*!
the third division algorithm
this algorithm is described in the following book:
"The art of computer programming 2" (4.3.1 page 272)
Donald E. Knuth
*/
uint Div3(const UInt<value_size> & v, UInt<value_size> * remainder = 0)
{
TTMATH_REFERENCE_ASSERT( v )
uint m,n, test;
test = Div_StandardTest(v, m, n, remainder);
if( test < 2 )
return test;
if( n == 0 )
{
uint r;
DivInt( v.table[0], &r );
if( remainder )
{
remainder->SetZero();
remainder->table[0] = r;
}
TTMATH_LOG("UInt::Div3")
return 0;
}
// we can only use the third division algorithm when
// the divisor is greater or equal 2^32 (has more than one 32-bit word)
++m;
++n;
m = m - n;
Div3_Division(v, remainder, m, n);
TTMATH_LOG("UInt::Div3")
return 0;
}
private:
void Div3_Division(UInt<value_size> v, UInt<value_size> * remainder, uint m, uint n)
{
TTMATH_ASSERT( n>=2 )
UInt<value_size+1> uu, vv;
UInt<value_size> q;
uint d, u_value_size, u0, u1, u2, v1, v0, j=m;
u_value_size = Div3_Normalize(v, n, d);
if( j+n == value_size )
u2 = u_value_size;
else
u2 = table[j+n];
Div3_MakeBiggerV(v, vv);
for(uint i = j+1 ; i<value_size ; ++i)
q.table[i] = 0;
while( true )
{
u1 = table[j+n-1];
u0 = table[j+n-2];
v1 = v.table[n-1];
v0 = v.table[n-2];
uint qp = Div3_Calculate(u2,u1,u0, v1,v0);
Div3_MakeNewU(uu, j, n, u2);
Div3_MultiplySubtract(uu, vv, qp);
Div3_CopyNewU(uu, j, n);
q.table[j] = qp;
// the next loop
if( j-- == 0 )
break;
u2 = table[j+n];
}
if( remainder )
Div3_Unnormalize(remainder, n, d);
*this = q;
TTMATH_LOG("UInt::Div3_Division")
}
void Div3_MakeNewU(UInt<value_size+1> & uu, uint j, uint n, uint u_max)
{
uint i;
for(i=0 ; i<n ; ++i, ++j)
uu.table[i] = table[j];
// 'n' is from <1..value_size> so and 'i' is from <0..value_size>
// then table[i] is always correct (look at the declaration of 'uu')
uu.table[i] = u_max;
for( ++i ; i<value_size+1 ; ++i)
uu.table[i] = 0;
TTMATH_LOG("UInt::Div3_MakeNewU")
}
void Div3_CopyNewU(const UInt<value_size+1> & uu, uint j, uint n)
{
uint i;
for(i=0 ; i<n ; ++i)
table[i+j] = uu.table[i];
if( i+j < value_size )
table[i+j] = uu.table[i];
TTMATH_LOG("UInt::Div3_CopyNewU")
}
/*!
we're making the new 'vv'
the value is actually the same but the 'table' is bigger (value_size+1)
*/
void Div3_MakeBiggerV(const UInt<value_size> & v, UInt<value_size+1> & vv)
{
for(uint i=0 ; i<value_size ; ++i)
vv.table[i] = v.table[i];
vv.table[value_size] = 0;
TTMATH_LOG("UInt::Div3_MakeBiggerV")
}
/*!
we're moving all bits from 'v' into the left side of the n-1 word
(the highest bit at v.table[n-1] will be equal one,
the bits from 'this' we're moving the same times as 'v')
return values:
d - how many times we've moved
return - the next-left value from 'this' (that after table[value_size-1])
*/
uint Div3_Normalize(UInt<value_size> & v, uint n, uint & d)
{
// v.table[n-1] is != 0
uint bit = (uint)FindLeadingBitInWord(v.table[n-1]);
uint move = (TTMATH_BITS_PER_UINT - bit - 1);
uint res = table[value_size-1];
d = move;
if( move > 0 )
{
v.Rcl(move, 0);
Rcl(move, 0);
res = res >> (bit + 1);
}
else
{
res = 0;
}
TTMATH_LOG("UInt::Div3_Normalize")
return res;
}
void Div3_Unnormalize(UInt<value_size> * remainder, uint n, uint d)
{
for(uint i=n ; i<value_size ; ++i)
table[i] = 0;
Rcr(d,0);
*remainder = *this;
TTMATH_LOG("UInt::Div3_Unnormalize")
}
uint Div3_Calculate(uint u2, uint u1, uint u0, uint v1, uint v0)
{
UInt<2> u_temp;
uint rp;
bool next_test;
TTMATH_ASSERT( v1 != 0 )
u_temp.table[1] = u2;
u_temp.table[0] = u1;
u_temp.DivInt(v1, &rp);
TTMATH_ASSERT( u_temp.table[1]==0 || u_temp.table[1]==1 )
do
{
bool decrease = false;
if( u_temp.table[1] == 1 )
decrease = true;
else
{
UInt<2> temp1, temp2;
UInt<2>::MulTwoWords(u_temp.table[0], v0, temp1.table+1, temp1.table);
temp2.table[1] = rp;
temp2.table[0] = u0;
if( temp1 > temp2 )
decrease = true;
}
next_test = false;
if( decrease )
{
u_temp.SubOne();
rp += v1;
if( rp >= v1 ) // it means that there wasn't a carry (r<b from the book)
next_test = true;
}
}
while( next_test );
TTMATH_LOG("UInt::Div3_Calculate")
return u_temp.table[0];
}
void Div3_MultiplySubtract( UInt<value_size+1> & uu,
const UInt<value_size+1> & vv, uint & qp)
{
// D4 (in the book)
UInt<value_size+1> vv_temp(vv);
vv_temp.MulInt(qp);
if( uu.Sub(vv_temp) )
{
// there was a carry
//
// !!! this part of code was not tested
//
--qp;
uu.Add(vv);
// can be a carry from this additions but it should be ignored
// because it cancels with the borrow from uu.Sub(vv_temp)
}
TTMATH_LOG("UInt::Div3_MultiplySubtract")
}
public:
/*!
power this = this ^ pow
binary algorithm (r-to-l)
return values:
0 - ok
1 - carry
2 - incorrect argument (0^0)
*/
uint Pow(UInt<value_size> pow)
{
if(pow.IsZero() && IsZero())
// we don't define zero^zero
return 2;
UInt<value_size> start(*this), start_temp;
UInt<value_size> result;
result.SetOne();
uint c = 0;
while( !c )
{
if( pow.table[0] & 1 )
c += result.Mul(start);
pow.Rcr2_one(0);
if( pow.IsZero() )
break;
start_temp = start;
// in the second Mul algorithm we can use start.Mul(start) directly (there is no TTMATH_ASSERT_REFERENCE there)
c += start.Mul(start_temp);
}
*this = result;
TTMATH_LOGC("UInt::Pow(UInt<>)", c)
return (c==0)? 0 : 1;
}
/*!
square root
e.g. Sqrt(9) = 3
('digit-by-digit' algorithm)
*/
void Sqrt()
{
UInt<value_size> bit, temp;
if( IsZero() )
return;
UInt<value_size> value(*this);
SetZero();
bit.SetZero();
bit.table[value_size-1] = (TTMATH_UINT_HIGHEST_BIT >> 1);
while( bit > value )
bit.Rcr(2);
while( !bit.IsZero() )
{
temp = *this;
temp.Add(bit);
if( value >= temp )
{
value.Sub(temp);
Rcr(1);
Add(bit);
}
else
{
Rcr(1);
}
bit.Rcr(2);
}
TTMATH_LOG("UInt::Sqrt")
}
/*!
this method sets n first bits to value zero
For example:
let n=2 then if there's a value 111 (bin) there'll be '100' (bin)
*/
void ClearFirstBits(uint n)
{
if( n >= value_size*TTMATH_BITS_PER_UINT )
{
SetZero();
TTMATH_LOG("UInt::ClearFirstBits")
return;
}
uint * p = table;
// first we're clearing the whole words
while( n >= TTMATH_BITS_PER_UINT )
{
*p++ = 0;
n -= TTMATH_BITS_PER_UINT;
}
if( n == 0 )
{
TTMATH_LOG("UInt::ClearFirstBits")
return;
}
// and then we're clearing one word which has left
// mask -- all bits are set to one
uint mask = TTMATH_UINT_MAX_VALUE;
mask = mask << n;
(*p) &= mask;
TTMATH_LOG("UInt::ClearFirstBits")
}
/*!
this method returns true if the highest bit of the value is set
*/
bool IsTheHighestBitSet() const
{
return (table[value_size-1] & TTMATH_UINT_HIGHEST_BIT) != 0;
}
/*!
this method returns true if the lowest bit of the value is set
*/
bool IsTheLowestBitSet() const
{
return (*table & 1) != 0;
}
/*!
this method returns true if the value is equal zero
*/
bool IsZero() const
{
for(uint i=0 ; i<value_size ; ++i)
if(table[i] != 0)
return false;
return true;
}
/*!
returning true if first 'bits' bits are equal zero
*/
bool AreFirstBitsZero(uint bits) const
{
TTMATH_ASSERT( bits <= value_size * TTMATH_BITS_PER_UINT )
uint index = bits / TTMATH_BITS_PER_UINT;
uint rest = bits % TTMATH_BITS_PER_UINT;
uint i;
for(i=0 ; i<index ; ++i)
if(table[i] != 0 )
return false;
if( rest == 0 )
return true;
uint mask = TTMATH_UINT_MAX_VALUE >> (TTMATH_BITS_PER_UINT - rest);
return (table[i] & mask) == 0;
}
/*!
*
* conversion methods
*
*/
/*!
this method converts an UInt<another_size> type to this class
this operation has mainly sense if the value from p is
equal or smaller than that one which is returned from UInt<value_size>::SetMax()
it returns a carry if the value 'p' is too big
*/
template<uint argument_size>
uint FromUInt(const UInt<argument_size> & p)
{
uint min_size = (value_size < argument_size)? value_size : argument_size;
uint i;
for(i=0 ; i<min_size ; ++i)
table[i] = p.table[i];
if( value_size > argument_size )
{
// 'this' is longer than 'p'
for( ; i<value_size ; ++i)
table[i] = 0;
}
else
{
for( ; i<argument_size ; ++i)
if( p.table[i] != 0 )
{
TTMATH_LOGC("UInt::FromUInt(UInt<>)", 1)
return 1;
}
}
TTMATH_LOGC("UInt::FromUInt(UInt<>)", 0)
return 0;
}
/*!
this method converts the uint type to this class
*/
void FromUInt(uint value)
{
for(uint i=1 ; i<value_size ; ++i)
table[i] = 0;
table[0] = value;
TTMATH_LOG("UInt::FromUInt(uint)")
}
/*!
this operator converts an UInt<another_size> type to this class
it doesn't return a carry
*/
template<uint argument_size>
UInt<value_size> & operator=(const UInt<argument_size> & p)
{
FromUInt(p);
return *this;
}
/*!
the assignment operator
*/
UInt<value_size> & operator=(const UInt<value_size> & p)
{
for(uint i=0 ; i<value_size ; ++i)
table[i] = p.table[i];
TTMATH_LOG("UInt::operator=(UInt<>)")
return *this;
}
/*!
this method converts the uint type to this class
*/
UInt<value_size> & operator=(uint i)
{
FromUInt(i);
return *this;
}
/*!
a constructor for converting the uint to this class
*/
UInt(uint i)
{
FromUInt(i);
}
/*!
this method converts the sint type to this class
we provide operator(sint) and the constructor(sint) in order to allow
the programmer do that:
UInt<..> type = 10;
above "10" constant has the int type (signed int), if we don't give such
operators and constructors the compiler will not compile the program,
because it has to make a conversion and doesn't know into which type
(the UInt class has operator=(const char*), operator=(uint) etc.)
*/
UInt<value_size> & operator=(sint i)
{
FromUInt(uint(i));
return *this;
}
/*!
a constructor for converting the sint to this class
look at the description of UInt::operator=(sint)
*/
UInt(sint i)
{
FromUInt(uint(i));
}
#ifdef TTMATH_PLATFORM64
/*!
in 64bit platforms we must define additional operators and contructors
in order to allow a user initializing the objects in this way:
UInt<...> type = 20;
or
UInt<...> type;
type = 30;
decimal constants such as 20, 30 etc. are integer literal of type int,
if the value is greater it can even be long int,
0 is an octal integer of type int
(ISO 14882 p2.13.1 Integer literals)
*/
/*!
this operator converts the unsigned int type to this class
***this operator is created only on a 64bit platform***
it takes one argument of 32bit
*/
UInt<value_size> & operator=(unsigned int i)
{
FromUInt(uint(i));
return *this;
}
/*!
a constructor for converting the unsigned int to this class
***this constructor is created only on a 64bit platform***
it takes one argument of 32bit
*/
UInt(unsigned int i)
{
FromUInt(uint(i));
}
/*!
an operator for converting the signed int to this class
***this constructor is created only on a 64bit platform***
it takes one argument of 32bit
look at the description of UInt::operator=(sint)
*/
UInt<value_size> & operator=(signed int i)
{
FromUInt(uint(i));
return *this;
}
/*!
a constructor for converting the signed int to this class
***this constructor is created only on a 64bit platform***
it takes one argument of 32bit
look at the description of UInt::operator=(sint)
*/
UInt(signed int i)
{
FromUInt(uint(i));
}
#endif
/*!
a constructor for converting a string to this class (with the base=10)
*/
UInt(const char * s)
{
FromString(s);
}
/*!
a constructor for converting a string to this class (with the base=10)
*/
UInt(const wchar_t * s)
{
FromString(s);
}
/*!
a constructor for converting a string to this class (with the base=10)
*/
UInt(const std::string & s)
{
FromString( s.c_str() );
}
/*!
a constructor for converting a string to this class (with the base=10)
*/
UInt(const std::wstring & s)
{
FromString( s.c_str() );
}
/*!
a default constructor
we don't clear the table
*/
UInt()
{
// when macro TTMATH_DEBUG_LOG is defined
// we set special values to the table
// in order to be everywhere the same value of the UInt object
// without this it would be difficult to analyse the log file
#ifdef TTMATH_DEBUG_LOG
#ifdef TTMATH_PLATFORM32
for(uint i=0 ; i<value_size ; ++i)
table[i] = 0xc1c1c1c1;
#else
for(uint i=0 ; i<value_size ; ++i)
table[i] = 0xc1c1c1c1c1c1c1c1;
#endif
#endif
}
/*!
a copy constructor
*/
UInt(const UInt<value_size> & u)
{
for(uint i=0 ; i<value_size ; ++i)
table[i] = u.table[i];
TTMATH_LOG("UInt::UInt(UInt<>)")
}
/*!
a template for producting constructors for copying from another types
*/
template<uint argument_size>
UInt(const UInt<argument_size> & u)
{
// look that 'size' we still set as 'value_size' and not as u.value_size
FromUInt(u);
}
/*!
a destructor
*/
~UInt()
{
}
/*!
this method returns the lowest value from table
we must be sure when we using this method whether the value
will hold in an uint type or not (the rest value from the table must be zero)
*/
uint ToUInt() const
{
return table[0];
}
private:
/*!
an auxiliary method for converting to a string
*/
template<class string_type>
void ToStringBase(string_type & result, uint b = 10) const
{
UInt<value_size> temp( *this );
char character;
uint rem;
result.clear();
if( b<2 || b>16 )
return;
do
{
temp.DivInt(b, &rem);
character = static_cast<char>( Misc::DigitToChar(rem) );
result.insert(result.begin(), character);
}
while( !temp.IsZero() );
return;
}
public:
/*!
this method converts the value to a string with a base equal 'b'
*/
void ToString(std::string & result, uint b = 10) const
{
return ToStringBase(result, b);
}
void ToString(std::wstring & result, uint b = 10) const
{
return ToStringBase(result, b);
}
std::string ToString(uint b = 10) const
{
std::string result;
ToStringBase(result, b);
return result;
}
std::wstring ToWString(uint b = 10) const
{
std::wstring result;
ToStringBase(result, b);
return result;
}
private:
/*!
an auxiliary method for converting from a string
*/
template<class char_type>
uint FromStringBase(const char_type * s, uint b = 10, const char_type ** after_source = 0, bool * value_read = 0)
{
UInt<value_size> base( b );
UInt<value_size> temp;
sint z;
uint c = 0;
SetZero();
temp.SetZero();
Misc::SkipWhiteCharacters(s);
if( after_source )
*after_source = s;
if( value_read )
*value_read = false;
if( b<2 || b>16 )
return 1;
for( ; (z=Misc::CharToDigit(*s, b)) != -1 ; ++s)
{
if( value_read )
*value_read = true;
if( c == 0 )
{
temp.table[0] = z;
c += Mul(base);
c += Add(temp);
}
}
if( after_source )
*after_source = s;
TTMATH_LOGC("UInt::FromString", c)
return (c==0)? 0 : 1;
}
public:
/*!
this method converts a string into its value
it returns carry=1 if the value will be too big or an incorrect base 'b' is given
string is ended with a non-digit value, for example:
"12" will be translated to 12
as well as:
"12foo" will be translated to 12 too
existing first white characters will be ommited
if the value from s is too large the rest digits will be skipped
after_source (if exists) is pointing at the end of the parsed string
value_read (if exists) tells whether something has actually been read (at least one digit)
*/
uint FromString(const char * s, uint b = 10, const char ** after_source = 0, bool * value_read = 0)
{
return FromStringBase(s, b, after_source, value_read);
}
/*!
this method converts a string into its value
*/
uint FromString(const wchar_t * s, uint b = 10, const wchar_t ** after_source = 0, bool * value_read = 0)
{
return FromStringBase(s, b, after_source, value_read);
}
/*!
this method converts a string into its value
(it returns carry=1 if the value will be too big or an incorrect base 'b' is given)
*/
uint FromString(const std::string & s, uint b = 10)
{
return FromString( s.c_str(), b );
}
/*!
this method converts a string into its value
(it returns carry=1 if the value will be too big or an incorrect base 'b' is given)
*/
uint FromString(const std::wstring & s, uint b = 10)
{
return FromString( s.c_str(), b );
}
/*!
this operator converts a string into its value (with base = 10)
*/
UInt<value_size> & operator=(const char * s)
{
FromString(s);
return *this;
}
/*!
this operator converts a string into its value (with base = 10)
*/
UInt<value_size> & operator=(const wchar_t * s)
{
FromString(s);
return *this;
}
/*!
this operator converts a string into its value (with base = 10)
*/
UInt<value_size> & operator=(const std::string & s)
{
FromString( s.c_str() );
return *this;
}
/*!
this operator converts a string into its value (with base = 10)
*/
UInt<value_size> & operator=(const std::wstring & s)
{
FromString( s.c_str() );
return *this;
}
/*!
*
* methods for comparing
*
*/
/*!
this method returns true if 'this' is smaller than 'l'
'index' is an index of the first word from will be the comparison performed
(note: we start the comparison from back - from the last word, when index is -1 /default/
it is automatically set into the last word)
I introduced it for some kind of optimization made in the second division algorithm (Div2)
*/
bool CmpSmaller(const UInt<value_size> & l, sint index = -1) const
{
sint i;
if( index==-1 || index>=sint(value_size) )
i = value_size - 1;
else
i = index;
for( ; i>=0 ; --i)
{
if( table[i] != l.table[i] )
return table[i] < l.table[i];
}
// they're equal
return false;
}
/*!
this method returns true if 'this' is bigger than 'l'
'index' is an index of the first word from will be the comparison performed
(note: we start the comparison from back - from the last word, when index is -1 /default/
it is automatically set into the last word)
I introduced it for some kind of optimization made in the second division algorithm (Div2)
*/
bool CmpBigger(const UInt<value_size> & l, sint index = -1) const
{
sint i;
if( index==-1 || index>=sint(value_size) )
i = value_size - 1;
else
i = index;
for( ; i>=0 ; --i)
{
if( table[i] != l.table[i] )
return table[i] > l.table[i];
}
// they're equal
return false;
}
/*!
this method returns true if 'this' is equal 'l'
'index' is an index of the first word from will be the comparison performed
(note: we start the comparison from back - from the last word, when index is -1 /default/
it is automatically set into the last word)
*/
bool CmpEqual(const UInt<value_size> & l, sint index = -1) const
{
sint i;
if( index==-1 || index>=sint(value_size) )
i = value_size - 1;
else
i = index;
for( ; i>=0 ; --i)
if( table[i] != l.table[i] )
return false;
return true;
}
/*!
this method returns true if 'this' is smaller than or equal 'l'
'index' is an index of the first word from will be the comparison performed
(note: we start the comparison from back - from the last word, when index is -1 /default/
it is automatically set into the last word)
*/
bool CmpSmallerEqual(const UInt<value_size> & l, sint index=-1) const
{
sint i;
if( index==-1 || index>=sint(value_size) )
i = value_size - 1;
else
i = index;
for( ; i>=0 ; --i)
{
if( table[i] != l.table[i] )
return table[i] < l.table[i];
}
// they're equal
return true;
}
/*!
this method returns true if 'this' is bigger than or equal 'l'
'index' is an index of the first word from will be the comparison performed
(note: we start the comparison from back - from the last word, when index is -1 /default/
it is automatically set into the last word)
*/
bool CmpBiggerEqual(const UInt<value_size> & l, sint index=-1) const
{
sint i;
if( index==-1 || index>=sint(value_size) )
i = value_size - 1;
else
i = index;
for( ; i>=0 ; --i)
{
if( table[i] != l.table[i] )
return table[i] > l.table[i];
}
// they're equal
return true;
}
/*
operators for comparising
*/
bool operator<(const UInt<value_size> & l) const
{
return CmpSmaller(l);
}
bool operator>(const UInt<value_size> & l) const
{
return CmpBigger(l);
}
bool operator==(const UInt<value_size> & l) const
{
return CmpEqual(l);
}
bool operator!=(const UInt<value_size> & l) const
{
return !operator==(l);
}
bool operator<=(const UInt<value_size> & l) const
{
return CmpSmallerEqual(l);
}
bool operator>=(const UInt<value_size> & l) const
{
return CmpBiggerEqual(l);
}
/*!
*
* standard mathematical operators
*
*/
UInt<value_size> operator-(const UInt<value_size> & p2) const
{
UInt<value_size> temp(*this);
temp.Sub(p2);
return temp;
}
UInt<value_size> & operator-=(const UInt<value_size> & p2)
{
Sub(p2);
return *this;
}
UInt<value_size> operator+(const UInt<value_size> & p2) const
{
UInt<value_size> temp(*this);
temp.Add(p2);
return temp;
}
UInt<value_size> & operator+=(const UInt<value_size> & p2)
{
Add(p2);
return *this;
}
UInt<value_size> operator*(const UInt<value_size> & p2) const
{
UInt<value_size> temp(*this);
temp.Mul(p2);
return temp;
}
UInt<value_size> & operator*=(const UInt<value_size> & p2)
{
Mul(p2);
return *this;
}
UInt<value_size> operator/(const UInt<value_size> & p2) const
{
UInt<value_size> temp(*this);
temp.Div(p2);
return temp;
}
UInt<value_size> & operator/=(const UInt<value_size> & p2)
{
Div(p2);
return *this;
}
UInt<value_size> operator%(const UInt<value_size> & p2) const
{
UInt<value_size> temp(*this);
UInt<value_size> remainder;
temp.Div( p2, remainder );
return remainder;
}
UInt<value_size> & operator%=(const UInt<value_size> & p2)
{
UInt<value_size> temp(*this);
UInt<value_size> remainder;
temp.Div( p2, remainder );
operator=(remainder);
return *this;
}
/*!
Prefix operator e.g ++variable
*/
UInt<value_size> & operator++()
{
AddOne();
return *this;
}
/*!
Postfix operator e.g variable++
*/
UInt<value_size> operator++(int)
{
UInt<value_size> temp( *this );
AddOne();
return temp;
}
UInt<value_size> & operator--()
{
SubOne();
return *this;
}
UInt<value_size> operator--(int)
{
UInt<value_size> temp( *this );
SubOne();
return temp;
}
UInt<value_size> operator>>(int move)
{
UInt<value_size> temp( *this );
temp.Rcr(move);
return temp;
}
UInt<value_size> & operator>>=(int move)
{
Rcr(move);
return *this;
}
UInt<value_size> operator<<(int move)
{
UInt<value_size> temp( *this );
temp.Rcl(move);
return temp;
}
UInt<value_size> & operator<<=(int move)
{
Rcl(move);
return *this;
}
/*!
*
* input/output operators for standard streams
*
* (they are very simple, in the future they should be changed)
*
*/
private:
/*!
an auxiliary method for outputing to standard streams
*/
template<class ostream_type, class string_type>
static ostream_type & OutputToStream(ostream_type & s, const UInt<value_size> & l)
{
string_type ss;
l.ToString(ss);
s << ss;
return s;
}
public:
/*!
output to standard streams
*/
friend std::ostream & operator<<(std::ostream & s, const UInt<value_size> & l)
{
return OutputToStream<std::ostream, std::string>(s, l);
}
/*!
output to standard streams
*/
friend std::wostream & operator<<(std::wostream & s, const UInt<value_size> & l)
{
return OutputToStream<std::wostream, std::wstring>(s, l);
}
private:
/*!
an auxiliary method for reading from standard streams
*/
template<class istream_type, class string_type, class char_type>
static istream_type & InputFromStream(istream_type & s, UInt<value_size> & l)
{
string_type ss;
// char or wchar_t for operator>>
char_type z;
// operator>> omits white characters if they're set for ommiting
s >> z;
// we're reading only digits (base=10)
while( s.good() && Misc::CharToDigit(z, 10)>=0 )
{
ss += z;
z = static_cast<char_type>(s.get());
}
// we're leaving the last read character
// (it's not belonging to the value)
s.unget();
l.FromString(ss);
return s;
}
public:
/*!
input from standard streams
*/
friend std::istream & operator>>(std::istream & s, UInt<value_size> & l)
{
return InputFromStream<std::istream, std::string, char>(s, l);
}
/*!
input from standard streams
*/
friend std::wistream & operator>>(std::wistream & s, UInt<value_size> & l)
{
return InputFromStream<std::wistream, std::wstring, wchar_t>(s, l);
}
/*
following methods are defined in:
ttmathuint_x86.h
ttmathuint_x86_64.h
ttmathuint_noasm.h
*/
#ifdef TTMATH_NOASM
static uint AddTwoWords(uint a, uint b, uint carry, uint * result);
static uint SubTwoWords(uint a, uint b, uint carry, uint * result);
#ifdef TTMATH_PLATFORM64
union uint_
{
struct
{
unsigned int low; // 32 bit
unsigned int high; // 32 bit
} u_;
uint u; // 64 bit
};
static void DivTwoWords2(uint a,uint b, uint c, uint * r, uint * rest);
static uint DivTwoWordsNormalize(uint_ & a_, uint_ & b_, uint_ & c_);
static uint DivTwoWordsUnnormalize(uint u, uint d);
static unsigned int DivTwoWordsCalculate(uint_ u_, unsigned int u3, uint_ v_);
static void MultiplySubtract(uint_ & u_, unsigned int & u3, unsigned int & q, uint_ v_);
#endif // TTMATH_PLATFORM64
#endif // TTMATH_NOASM
private:
uint Rcl2_one(uint c);
uint Rcr2_one(uint c);
uint Rcl2(uint bits, uint c);
uint Rcr2(uint bits, uint c);
public:
static const char * LibTypeStr();
static LibTypeCode LibType();
uint Add(const UInt<value_size> & ss2, uint c=0);
uint AddInt(uint value, uint index = 0);
uint AddTwoInts(uint x2, uint x1, uint index);
static uint AddVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result);
uint Sub(const UInt<value_size> & ss2, uint c=0);
uint SubInt(uint value, uint index = 0);
static uint SubVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result);
static sint FindLeadingBitInWord(uint x);
static sint FindLowestBitInWord(uint x);
static uint SetBitInWord(uint & value, uint bit);
static void MulTwoWords(uint a, uint b, uint * result_high, uint * result_low);
static void DivTwoWords(uint a,uint b, uint c, uint * r, uint * rest);
};
/*!
this specialization is needed in order to not confused the compiler "error: ISO C++ forbids zero-size array"
when compiling Mul3Big2() method
*/
template<>
class UInt<0>
{
public:
uint table[1];
void Mul2Big(const UInt<0> &, UInt<0> &) { TTMATH_ASSERT(false) };
void SetZero() { TTMATH_ASSERT(false) };
uint AddTwoInts(uint, uint, uint) { TTMATH_ASSERT(false) return 0; };
};
} //namespace
#include "ttmathuint_x86.h"
#include "ttmathuint_x86_64.h"
#include "ttmathuint_noasm.h"
#endif
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