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/*
* This file is a part of TTMath Bignum Library
* and is distributed under the 3-Clause 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 headerfilettmathuint_noasm
#define headerfilettmathuint_noasm
/*!
\file ttmathuint_noasm.h
\brief template class UInt<uint> with methods without any assembler code (used for no-asm version of ttmath)
this file is included at the end of ttmathuint.h
*/
#ifdef TTMATH_NOASM
namespace ttmath
{
/*!
returning the string represents the currect type of the library
we have following types:
- 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
*/
template<uint value_size>
const char * UInt<value_size>::LibTypeStr()
{
#ifdef TTMATH_PLATFORM32
static const char info[] = "no_asm_32";
#endif
#ifdef TTMATH_PLATFORM64
static const char info[] = "no_asm_64";
#endif
return info;
}
/*!
returning the currect type of the library
*/
template<uint value_size>
LibTypeCode UInt<value_size>::LibType()
{
#ifdef TTMATH_PLATFORM32
LibTypeCode info = no_asm_32;
#endif
#ifdef TTMATH_PLATFORM64
LibTypeCode info = no_asm_64;
#endif
return info;
}
/*!
this method adds two words together
returns carry
this method is created only when TTMATH_NOASM macro is defined
*/
template<uint value_size>
uint UInt<value_size>::AddTwoWords(uint a, uint b, uint carry, uint * result)
{
uint temp;
if( carry == 0 )
{
temp = a + b;
if( temp < a )
carry = 1;
}
else
{
carry = 1;
temp = a + b + carry;
if( temp > a ) // !(temp<=a)
carry = 0;
}
*result = temp;
return carry;
}
/*!
this method adding ss2 to the this and adding carry if it's defined
(this = this + ss2 + c)
c must be zero or one (might be a bigger value than 1)
function returns carry (1) (if it was)
*/
template<uint value_size>
uint UInt<value_size>::Add(const UInt<value_size> & ss2, uint c)
{
uint i;
for(i=0 ; i<value_size ; ++i)
c = AddTwoWords(table[i], ss2.table[i], c, &table[i]);
TTMATH_LOGC("UInt::Add", c)
return c;
}
/*!
this method adds one word (at a specific position)
and returns a carry (if it was)
if we've got (value_size=3):
table[0] = 10;
table[1] = 30;
table[2] = 5;
and we call:
AddInt(2,1)
then it'll be:
table[0] = 10;
table[1] = 30 + 2;
table[2] = 5;
of course if there was a carry from table[2] it would be returned
*/
template<uint value_size>
uint UInt<value_size>::AddInt(uint value, uint index)
{
uint i, c;
TTMATH_ASSERT( index < value_size )
c = AddTwoWords(table[index], value, 0, &table[index]);
for(i=index+1 ; i<value_size && c ; ++i)
c = AddTwoWords(table[i], 0, c, &table[i]);
TTMATH_LOGC("UInt::AddInt", c)
return c;
}
/*!
this method adds only two unsigned words to the existing value
and these words begin on the 'index' position
(it's used in the multiplication algorithm 2)
index should be equal or smaller than value_size-2 (index <= value_size-2)
x1 - lower word, x2 - higher word
for example if we've got value_size equal 4 and:
table[0] = 3
table[1] = 4
table[2] = 5
table[3] = 6
then let
x1 = 10
x2 = 20
and
index = 1
the result of this method will be:
table[0] = 3
table[1] = 4 + x1 = 14
table[2] = 5 + x2 = 25
table[3] = 6
and no carry at the end of table[3]
(of course if there was a carry in table[2](5+20) then
this carry would be passed to the table[3] etc.)
*/
template<uint value_size>
uint UInt<value_size>::AddTwoInts(uint x2, uint x1, uint index)
{
uint i, c;
TTMATH_ASSERT( index < value_size - 1 )
c = AddTwoWords(table[index], x1, 0, &table[index]);
c = AddTwoWords(table[index+1], x2, c, &table[index+1]);
for(i=index+2 ; i<value_size && c ; ++i)
c = AddTwoWords(table[i], 0, c, &table[i]);
TTMATH_LOGC("UInt::AddTwoInts", c)
return c;
}
/*!
this static method addes one vector to the other
'ss1' is larger in size or equal to 'ss2'
- ss1 points to the first (larger) vector
- ss2 points to the second vector
- ss1_size - size of the ss1 (and size of the result too)
- ss2_size - size of the ss2
- result - is the result vector (which has size the same as ss1: ss1_size)
Example: ss1_size is 5, ss2_size is 3
ss1: ss2: result (output):
5 1 5+1
4 3 4+3
2 7 2+7
6 6
9 9
of course the carry is propagated and will be returned from the last item
(this method is used by the Karatsuba multiplication algorithm)
*/
template<uint value_size>
uint UInt<value_size>::AddVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result)
{
uint i, c = 0;
TTMATH_ASSERT( ss1_size >= ss2_size )
for(i=0 ; i<ss2_size ; ++i)
c = AddTwoWords(ss1[i], ss2[i], c, &result[i]);
for( ; i<ss1_size ; ++i)
c = AddTwoWords(ss1[i], 0, c, &result[i]);
TTMATH_VECTOR_LOGC("UInt::AddVector", c, result, ss1_size)
return c;
}
/*!
this method subtractes one word from the other
returns carry
this method is created only when TTMATH_NOASM macro is defined
*/
template<uint value_size>
uint UInt<value_size>::SubTwoWords(uint a, uint b, uint carry, uint * result)
{
if( carry == 0 )
{
*result = a - b;
if( a < b )
carry = 1;
}
else
{
carry = 1;
*result = a - b - carry;
if( a > b ) // !(a <= b )
carry = 0;
}
return carry;
}
/*!
this method's subtracting ss2 from the 'this' and subtracting
carry if it has been defined
(this = this - ss2 - c)
c must be zero or one (might be a bigger value than 1)
function returns carry (1) (if it was)
*/
template<uint value_size>
uint UInt<value_size>::Sub(const UInt<value_size> & ss2, uint c)
{
uint i;
for(i=0 ; i<value_size ; ++i)
c = SubTwoWords(table[i], ss2.table[i], c, &table[i]);
TTMATH_LOGC("UInt::Sub", c)
return c;
}
/*!
this method subtracts one word (at a specific position)
and returns a carry (if it was)
if we've got (value_size=3):
table[0] = 10;
table[1] = 30;
table[2] = 5;
and we call:
SubInt(2,1)
then it'll be:
table[0] = 10;
table[1] = 30 - 2;
table[2] = 5;
of course if there was a carry from table[2] it would be returned
*/
template<uint value_size>
uint UInt<value_size>::SubInt(uint value, uint index)
{
uint i, c;
TTMATH_ASSERT( index < value_size )
c = SubTwoWords(table[index], value, 0, &table[index]);
for(i=index+1 ; i<value_size && c ; ++i)
c = SubTwoWords(table[i], 0, c, &table[i]);
TTMATH_LOGC("UInt::SubInt", c)
return c;
}
/*!
this static method subtractes one vector from the other
'ss1' is larger in size or equal to 'ss2'
- ss1 points to the first (larger) vector
- ss2 points to the second vector
- ss1_size - size of the ss1 (and size of the result too)
- ss2_size - size of the ss2
- result - is the result vector (which has size the same as ss1: ss1_size)
Example: ss1_size is 5, ss2_size is 3
ss1: ss2: result (output):
5 1 5-1
4 3 4-3
2 7 2-7
6 6-1 (the borrow from previous item)
9 9
return (carry): 0
of course the carry (borrow) is propagated and will be returned from the last item
(this method is used by the Karatsuba multiplication algorithm)
*/
template<uint value_size>
uint UInt<value_size>::SubVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result)
{
uint i, c = 0;
TTMATH_ASSERT( ss1_size >= ss2_size )
for(i=0 ; i<ss2_size ; ++i)
c = SubTwoWords(ss1[i], ss2[i], c, &result[i]);
for( ; i<ss1_size ; ++i)
c = SubTwoWords(ss1[i], 0, c, &result[i]);
TTMATH_VECTOR_LOGC("UInt::SubVector", c, result, ss1_size)
return c;
}
/*!
this method moves all bits into the left hand side
return value <- this <- c
the lowest *bit* will be held the 'c' and
the state of one additional bit (on the left hand side)
will be returned
for example:
let this is 001010000
after Rcl2_one(1) there'll be 010100001 and Rcl2_one returns 0
*/
template<uint value_size>
uint UInt<value_size>::Rcl2_one(uint c)
{
uint i, new_c;
if( c != 0 )
c = 1;
for(i=0 ; i<value_size ; ++i)
{
new_c = (table[i] & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0;
table[i] = (table[i] << 1) | c;
c = new_c;
}
TTMATH_LOGC("UInt::Rcl2_one", c)
return c;
}
/*!
this method moves all bits into the right hand side
c -> this -> return value
the highest *bit* will be held the 'c' and
the state of one additional bit (on the right hand side)
will be returned
for example:
let this is 000000010
after Rcr2_one(1) there'll be 100000001 and Rcr2_one returns 0
*/
template<uint value_size>
uint UInt<value_size>::Rcr2_one(uint c)
{
sint i; // signed i
uint new_c;
if( c != 0 )
c = TTMATH_UINT_HIGHEST_BIT;
for(i=sint(value_size)-1 ; i>=0 ; --i)
{
new_c = (table[i] & 1) ? TTMATH_UINT_HIGHEST_BIT : 0;
table[i] = (table[i] >> 1) | c;
c = new_c;
}
c = (c != 0)? 1 : 0;
TTMATH_LOGC("UInt::Rcr2_one", c)
return c;
}
/*!
this method moves all bits into the left hand side
return value <- this <- c
the lowest *bits* will be held the 'c' and
the state of one additional bit (on the left hand side)
will be returned
for example:
let this is 001010000
after Rcl2(3, 1) there'll be 010000111 and Rcl2 returns 1
*/
template<uint value_size>
uint UInt<value_size>::Rcl2(uint bits, uint c)
{
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
uint move = TTMATH_BITS_PER_UINT - bits;
uint i, new_c;
if( c != 0 )
c = TTMATH_UINT_MAX_VALUE >> move;
for(i=0 ; i<value_size ; ++i)
{
new_c = table[i] >> move;
table[i] = (table[i] << bits) | c;
c = new_c;
}
TTMATH_LOGC("UInt::Rcl2", (c & 1))
return (c & 1);
}
/*!
this method moves all bits into the right hand side
C -> this -> return value
the highest *bits* will be held the 'c' and
the state of one additional bit (on the right hand side)
will be returned
for example:
let this is 000000010
after Rcr2(2, 1) there'll be 110000000 and Rcr2 returns 1
*/
template<uint value_size>
uint UInt<value_size>::Rcr2(uint bits, uint c)
{
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
uint move = TTMATH_BITS_PER_UINT - bits;
sint i; // signed
uint new_c;
if( c != 0 )
c = TTMATH_UINT_MAX_VALUE << move;
for(i=value_size-1 ; i>=0 ; --i)
{
new_c = table[i] << move;
table[i] = (table[i] >> bits) | c;
c = new_c;
}
c = (c & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0;
TTMATH_LOGC("UInt::Rcr2", c)
return c;
}
/*!
this method returns the number of the highest set bit in x
if the 'x' is zero this method returns '-1'
*/
template<uint value_size>
sint UInt<value_size>::FindLeadingBitInWord(uint x)
{
if( x == 0 )
return -1;
uint bit = TTMATH_BITS_PER_UINT - 1;
while( (x & TTMATH_UINT_HIGHEST_BIT) == 0 )
{
x = x << 1;
--bit;
}
return bit;
}
/*!
this method returns the number of the highest set bit in x
if the 'x' is zero this method returns '-1'
*/
template<uint value_size>
sint UInt<value_size>::FindLowestBitInWord(uint x)
{
if( x == 0 )
return -1;
uint bit = 0;
while( (x & 1) == 0 )
{
x = x >> 1;
++bit;
}
return bit;
}
/*!
this method sets a special bit in the 'value'
and returns the last state of the bit (zero or one)
bit is from <0,TTMATH_BITS_PER_UINT-1>
e.g.
uint x = 100;
uint bit = SetBitInWord(x, 3);
now: x = 108 and bit = 0
*/
template<uint value_size>
uint UInt<value_size>::SetBitInWord(uint & value, uint bit)
{
TTMATH_ASSERT( bit < TTMATH_BITS_PER_UINT )
uint mask = 1;
if( bit > 0 )
mask = mask << bit;
uint last = value & mask;
value = value | mask;
return (last != 0) ? 1 : 0;
}
/*!
*
* Multiplication
*
*
*/
/*!
multiplication: result_high:result_low = a * b
- result_high - higher word of the result
- result_low - lower word of the result
this methos never returns a carry
this method is used in the second version of the multiplication algorithms
*/
template<uint value_size>
void UInt<value_size>::MulTwoWords(uint a, uint b, uint * result_high, uint * result_low)
{
#ifdef TTMATH_PLATFORM32
/*
on 32bit platforms we have defined 'unsigned long long int' type known as 'ulint' in ttmath namespace
this type has 64 bits, then we're using only one multiplication: 32bit * 32bit = 64bit
*/
union uint_
{
struct
{
uint low; // 32 bits
uint high; // 32 bits
} u_;
ulint u; // 64 bits
} res;
res.u = ulint(a) * ulint(b); // multiply two 32bit words, the result has 64 bits
*result_high = res.u_.high;
*result_low = res.u_.low;
#else
/*
64 bits platforms
we don't have a native type which has 128 bits
then we're splitting 'a' and 'b' to 4 parts (high and low halves)
and using 4 multiplications (with additions and carry correctness)
*/
uint_ a_;
uint_ b_;
uint_ res_high1, res_high2;
uint_ res_low1, res_low2;
a_.u = a;
b_.u = b;
/*
the multiplication is as follows (schoolbook algorithm with O(n^2) ):
32 bits 32 bits
+--------------------------------+
| a_.u_.high | a_.u_.low |
+--------------------------------+
| b_.u_.high | b_.u_.low |
+--------------------------------+--------------------------------+
| res_high1.u | res_low1.u |
+--------------------------------+--------------------------------+
| res_high2.u | res_low2.u |
+--------------------------------+--------------------------------+
64 bits 64 bits
*/
uint_ temp;
res_low1.u = uint(b_.u_.low) * uint(a_.u_.low);
temp.u = uint(res_low1.u_.high) + uint(b_.u_.low) * uint(a_.u_.high);
res_low1.u_.high = temp.u_.low;
res_high1.u_.low = temp.u_.high;
res_high1.u_.high = 0;
res_low2.u_.low = 0;
temp.u = uint(b_.u_.high) * uint(a_.u_.low);
res_low2.u_.high = temp.u_.low;
res_high2.u = uint(b_.u_.high) * uint(a_.u_.high) + uint(temp.u_.high);
uint c = AddTwoWords(res_low1.u, res_low2.u, 0, &res_low2.u);
AddTwoWords(res_high1.u, res_high2.u, c, &res_high2.u); // there is no carry from here
*result_high = res_high2.u;
*result_low = res_low2.u;
#endif
}
/*!
*
* Division
*
*
*/
/*!
this method calculates 64bits word a:b / 32bits c (a higher, b lower word)
r = a:b / c and rest - remainder
*
* WARNING:
* the c has to be suitably large for the result being keeped in one word,
* if c is equal zero there'll be a hardware interruption (0)
* and probably the end of your program
*
*/
template<uint value_size>
void UInt<value_size>::DivTwoWords(uint a, uint b, uint c, uint * r, uint * rest)
{
// (a < c ) for the result to be one word
TTMATH_ASSERT( c != 0 && a < c )
#ifdef TTMATH_PLATFORM32
union
{
struct
{
uint low; // 32 bits
uint high; // 32 bits
} u_;
ulint u; // 64 bits
} ab;
ab.u_.high = a;
ab.u_.low = b;
*r = uint(ab.u / c);
*rest = uint(ab.u % c);
#else
uint_ c_;
c_.u = c;
if( a == 0 )
{
*r = b / c;
*rest = b % c;
}
else
if( c_.u_.high == 0 )
{
// higher half of 'c' is zero
// then higher half of 'a' is zero too (look at the asserts at the beginning - 'a' is smaller than 'c')
uint_ a_, b_, res_, temp1, temp2;
a_.u = a;
b_.u = b;
temp1.u_.high = a_.u_.low;
temp1.u_.low = b_.u_.high;
res_.u_.high = (unsigned int)(temp1.u / c);
temp2.u_.high = (unsigned int)(temp1.u % c);
temp2.u_.low = b_.u_.low;
res_.u_.low = (unsigned int)(temp2.u / c);
*rest = temp2.u % c;
*r = res_.u;
}
else
{
return DivTwoWords2(a, b, c, r, rest);
}
#endif
}
#ifdef TTMATH_PLATFORM64
/*!
this method is available only on 64bit platforms
the same algorithm like the third division algorithm in ttmathuint.h
but now with the radix=2^32
*/
template<uint value_size>
void UInt<value_size>::DivTwoWords2(uint a, uint b, uint c, uint * r, uint * rest)
{
// a is not zero
// c_.u_.high is not zero
uint_ a_, b_, c_, u_, q_;
unsigned int u3; // 32 bit
a_.u = a;
b_.u = b;
c_.u = c;
// normalizing
uint d = DivTwoWordsNormalize(a_, b_, c_);
// loop from j=1 to j=0
// the first step (for j=2) is skipped because our result is only in one word,
// (first 'q' were 0 and nothing would be changed)
u_.u_.high = a_.u_.high;
u_.u_.low = a_.u_.low;
u3 = b_.u_.high;
q_.u_.high = DivTwoWordsCalculate(u_, u3, c_);
MultiplySubtract(u_, u3, q_.u_.high, c_);
u_.u_.high = u_.u_.low;
u_.u_.low = u3;
u3 = b_.u_.low;
q_.u_.low = DivTwoWordsCalculate(u_, u3, c_);
MultiplySubtract(u_, u3, q_.u_.low, c_);
*r = q_.u;
// unnormalizing for the remainder
u_.u_.high = u_.u_.low;
u_.u_.low = u3;
*rest = DivTwoWordsUnnormalize(u_.u, d);
}
template<uint value_size>
uint UInt<value_size>::DivTwoWordsNormalize(uint_ & a_, uint_ & b_, uint_ & c_)
{
uint d = 0;
for( ; (c_.u & TTMATH_UINT_HIGHEST_BIT) == 0 ; ++d )
{
c_.u = c_.u << 1;
uint bc = b_.u & TTMATH_UINT_HIGHEST_BIT; // carry from 'b'
b_.u = b_.u << 1;
a_.u = a_.u << 1; // carry bits from 'a' are simply skipped
if( bc )
a_.u = a_.u | 1;
}
return d;
}
template<uint value_size>
uint UInt<value_size>::DivTwoWordsUnnormalize(uint u, uint d)
{
if( d == 0 )
return u;
u = u >> d;
return u;
}
template<uint value_size>
unsigned int UInt<value_size>::DivTwoWordsCalculate(uint_ u_, unsigned int u3, uint_ v_)
{
bool next_test;
uint_ qp_, rp_, temp_;
qp_.u = u_.u / uint(v_.u_.high);
rp_.u = u_.u % uint(v_.u_.high);
TTMATH_ASSERT( qp_.u_.high==0 || qp_.u_.high==1 )
do
{
bool decrease = false;
if( qp_.u_.high == 1 )
decrease = true;
else
{
temp_.u_.high = rp_.u_.low;
temp_.u_.low = u3;
if( qp_.u * uint(v_.u_.low) > temp_.u )
decrease = true;
}
next_test = false;
if( decrease )
{
--qp_.u;
rp_.u += v_.u_.high;
if( rp_.u_.high == 0 )
next_test = true;
}
}
while( next_test );
return qp_.u_.low;
}
template<uint value_size>
void UInt<value_size>::MultiplySubtract(uint_ & u_, unsigned int & u3, unsigned int & q, uint_ v_)
{
uint_ temp_;
uint res_high;
uint res_low;
MulTwoWords(v_.u, q, &res_high, &res_low);
uint_ sub_res_high_;
uint_ sub_res_low_;
temp_.u_.high = u_.u_.low;
temp_.u_.low = u3;
uint c = SubTwoWords(temp_.u, res_low, 0, &sub_res_low_.u);
temp_.u_.high = 0;
temp_.u_.low = u_.u_.high;
c = SubTwoWords(temp_.u, res_high, c, &sub_res_high_.u);
if( c )
{
--q;
c = AddTwoWords(sub_res_low_.u, v_.u, 0, &sub_res_low_.u);
AddTwoWords(sub_res_high_.u, 0, c, &sub_res_high_.u);
}
u_.u_.high = sub_res_high_.u_.low;
u_.u_.low = sub_res_low_.u_.high;
u3 = sub_res_low_.u_.low;
}
#endif // #ifdef TTMATH_PLATFORM64
} //namespace
#endif //ifdef TTMATH_NOASM
#endif
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