mirror of
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1014 lines
21 KiB
C++
1014 lines
21 KiB
C++
/*
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* This file is a part of TTMath Bignum Library
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* and is distributed under the (new) BSD licence.
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* Author: Tomasz Sowa <t.sowa@ttmath.org>
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*/
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/*
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* Copyright (c) 2006-2009, Tomasz Sowa
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* * Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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*
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* * Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* * Neither the name Tomasz Sowa nor the names of contributors to this
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* project may be used to endorse or promote products derived
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* from this software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
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* ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
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* LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
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* CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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* SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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* INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
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* ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
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* THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#ifndef headerfilettmathuint_noasm
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#define headerfilettmathuint_noasm
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#ifdef TTMATH_NOASM
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/*!
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\file ttmathuint_noasm.h
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\brief template class UInt<uint> with methods without any assembler code
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this file is included at the end of ttmathuint.h
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*/
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namespace ttmath
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{
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/*!
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returning the string represents the currect type of the library
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we have following types:
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asm_vc_32 - with asm code designed for Microsoft Visual C++ (32 bits)
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asm_gcc_32 - with asm code designed for GCC (32 bits)
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asm_vc_64 - with asm for VC (64 bit)
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asm_gcc_64 - with asm for GCC (64 bit)
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no_asm_32 - pure C++ version (32 bit) - without any asm code
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no_asm_64 - pure C++ version (64 bit) - without any asm code
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*/
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template<uint value_size>
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const char * UInt<value_size>::LibTypeStr()
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{
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#ifdef TTMATH_PLATFORM32
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static const char info[] = "no_asm_32";
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#endif
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#ifdef TTMATH_PLATFORM64
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static const char info[] = "no_asm_64";
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#endif
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return info;
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}
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/*!
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returning the currect type of the library
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*/
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template<uint value_size>
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LibTypeCode UInt<value_size>::LibType()
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{
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#ifdef TTMATH_PLATFORM32
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LibTypeCode info = no_asm_32;
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#endif
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#ifdef TTMATH_PLATFORM64
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LibTypeCode info = no_asm_64;
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#endif
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return info;
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}
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/*!
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this method adds two words together
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returns carry
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this method is created only when TTMATH_NOASM macro is defined
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*/
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template<uint value_size>
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uint UInt<value_size>::AddTwoWords(uint a, uint b, uint carry, uint * result)
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{
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uint temp;
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if( carry == 0 )
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{
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temp = a + b;
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if( temp < a )
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carry = 1;
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}
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else
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{
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carry = 1;
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temp = a + b + carry;
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if( temp > a ) // !(temp<=a)
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carry = 0;
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}
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*result = temp;
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return carry;
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}
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/*!
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this method adding ss2 to the this and adding carry if it's defined
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(this = this + ss2 + c)
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c must be zero or one (might be a bigger value than 1)
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function returns carry (1) (if it was)
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*/
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template<uint value_size>
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uint UInt<value_size>::Add(const UInt<value_size> & ss2, uint c)
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{
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uint i;
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for(i=0 ; i<value_size ; ++i)
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c = AddTwoWords(table[i], ss2.table[i], c, &table[i]);
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TTMATH_LOGC("UInt::Add", c)
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return c;
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}
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/*!
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this method adds one word (at a specific position)
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and returns a carry (if it was)
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if we've got (value_size=3):
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table[0] = 10;
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table[1] = 30;
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table[2] = 5;
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and we call:
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AddInt(2,1)
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then it'll be:
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table[0] = 10;
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table[1] = 30 + 2;
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table[2] = 5;
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of course if there was a carry from table[2] it would be returned
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*/
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template<uint value_size>
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uint UInt<value_size>::AddInt(uint value, uint index)
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{
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uint i, c;
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TTMATH_ASSERT( index < value_size )
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c = AddTwoWords(table[index], value, 0, &table[index]);
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for(i=index+1 ; i<value_size && c ; ++i)
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c = AddTwoWords(table[i], 0, c, &table[i]);
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TTMATH_LOGC("UInt::AddInt", c)
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return c;
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}
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/*!
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this method adds only two unsigned words to the existing value
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and these words begin on the 'index' position
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(it's used in the multiplication algorithm 2)
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index should be equal or smaller than value_size-2 (index <= value_size-2)
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x1 - lower word, x2 - higher word
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for example if we've got value_size equal 4 and:
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table[0] = 3
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table[1] = 4
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table[2] = 5
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table[3] = 6
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then let
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x1 = 10
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x2 = 20
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and
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index = 1
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the result of this method will be:
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table[0] = 3
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table[1] = 4 + x1 = 14
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table[2] = 5 + x2 = 25
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table[3] = 6
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and no carry at the end of table[3]
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(of course if there was a carry in table[2](5+20) then
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this carry would be passed to the table[3] etc.)
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*/
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template<uint value_size>
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uint UInt<value_size>::AddTwoInts(uint x2, uint x1, uint index)
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{
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uint i, c;
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TTMATH_ASSERT( index < value_size - 1 )
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c = AddTwoWords(table[index], x1, 0, &table[index]);
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c = AddTwoWords(table[index+1], x2, c, &table[index+1]);
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for(i=index+2 ; i<value_size && c ; ++i)
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c = AddTwoWords(table[i], 0, c, &table[i]);
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TTMATH_LOGC("UInt::AddTwoInts", c)
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return c;
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}
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/*!
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this static method addes one vector to the other
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'ss1' is larger in size or equal to 'ss2'
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ss1 points to the first (larger) vector
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ss2 points to the second vector
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ss1_size - size of the ss1 (and size of the result too)
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ss2_size - size of the ss2
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result - is the result vector (which has size the same as ss1: ss1_size)
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Example: ss1_size is 5, ss2_size is 3
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ss1: ss2: result (output):
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5 1 5+1
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4 3 4+3
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2 7 2+7
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6 6
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9 9
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of course the carry is propagated and will be returned from the last item
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(this method is used by the Karatsuba multiplication algorithm)
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*/
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template<uint value_size>
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uint UInt<value_size>::AddVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result)
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{
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uint i, c = 0;
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TTMATH_ASSERT( ss1_size >= ss2_size )
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for(i=0 ; i<ss2_size ; ++i)
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c = AddTwoWords(ss1[i], ss2[i], c, &result[i]);
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for( ; i<ss1_size ; ++i)
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c = AddTwoWords(ss1[i], 0, c, &result[i]);
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TTMATH_VECTOR_LOGC("UInt::AddVector", c, result, ss1_size)
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return c;
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}
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/*!
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this method subtractes one word from the other
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returns carry
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this method is created only when TTMATH_NOASM macro is defined
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*/
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template<uint value_size>
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uint UInt<value_size>::SubTwoWords(uint a, uint b, uint carry, uint * result)
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{
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if( carry == 0 )
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{
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*result = a - b;
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if( a < b )
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carry = 1;
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}
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else
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{
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carry = 1;
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*result = a - b - carry;
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if( a > b ) // !(a <= b )
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carry = 0;
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}
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return carry;
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}
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/*!
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this method's subtracting ss2 from the 'this' and subtracting
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carry if it has been defined
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(this = this - ss2 - c)
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c must be zero or one (might be a bigger value than 1)
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function returns carry (1) (if it was)
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*/
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template<uint value_size>
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uint UInt<value_size>::Sub(const UInt<value_size> & ss2, uint c)
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{
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uint i;
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for(i=0 ; i<value_size ; ++i)
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c = SubTwoWords(table[i], ss2.table[i], c, &table[i]);
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TTMATH_LOGC("UInt::Sub", c)
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return c;
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}
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/*!
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this method subtracts one word (at a specific position)
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and returns a carry (if it was)
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if we've got (value_size=3):
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table[0] = 10;
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table[1] = 30;
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table[2] = 5;
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and we call:
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SubInt(2,1)
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then it'll be:
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table[0] = 10;
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table[1] = 30 - 2;
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table[2] = 5;
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of course if there was a carry from table[2] it would be returned
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*/
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template<uint value_size>
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uint UInt<value_size>::SubInt(uint value, uint index)
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{
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uint i, c;
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TTMATH_ASSERT( index < value_size )
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c = SubTwoWords(table[index], value, 0, &table[index]);
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for(i=index+1 ; i<value_size && c ; ++i)
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c = SubTwoWords(table[i], 0, c, &table[i]);
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TTMATH_LOGC("UInt::SubInt", c)
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return c;
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}
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/*!
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this static method subtractes one vector from the other
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|
'ss1' is larger in size or equal to 'ss2'
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|
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|
ss1 points to the first (larger) vector
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|
ss2 points to the second vector
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ss1_size - size of the ss1 (and size of the result too)
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ss2_size - size of the ss2
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result - is the result vector (which has size the same as ss1: ss1_size)
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Example: ss1_size is 5, ss2_size is 3
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ss1: ss2: result (output):
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5 1 5-1
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4 3 4-3
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2 7 2-7
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6 6-1 (the borrow from previous item)
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9 9
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return (carry): 0
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of course the carry (borrow) is propagated and will be returned from the last item
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(this method is used by the Karatsuba multiplication algorithm)
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*/
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template<uint value_size>
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uint UInt<value_size>::SubVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result)
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{
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uint i, c = 0;
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TTMATH_ASSERT( ss1_size >= ss2_size )
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for(i=0 ; i<ss2_size ; ++i)
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c = SubTwoWords(ss1[i], ss2[i], c, &result[i]);
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for( ; i<ss1_size ; ++i)
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c = SubTwoWords(ss1[i], 0, c, &result[i]);
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TTMATH_VECTOR_LOGC("UInt::SubVector", c, result, ss1_size)
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return c;
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}
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/*!
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this method moves all bits into the left hand side
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return value <- this <- c
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the lowest *bit* will be held the 'c' and
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the state of one additional bit (on the left hand side)
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will be returned
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for example:
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let this is 001010000
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after Rcl2_one(1) there'll be 010100001 and Rcl2_one returns 0
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*/
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template<uint value_size>
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uint UInt<value_size>::Rcl2_one(uint c)
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{
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uint i, new_c;
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if( c != 0 )
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c = 1;
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for(i=0 ; i<value_size ; ++i)
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{
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new_c = (table[i] & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0;
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table[i] = (table[i] << 1) | c;
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c = new_c;
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}
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TTMATH_LOGC("UInt::Rcl2_one", c)
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return c;
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}
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/*!
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|
this method moves all bits into the right hand side
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|
c -> this -> return value
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|
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the highest *bit* will be held the 'c' and
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|
the state of one additional bit (on the right hand side)
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|
will be returned
|
|
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for example:
|
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let this is 000000010
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after Rcr2_one(1) there'll be 100000001 and Rcr2_one returns 0
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*/
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template<uint value_size>
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uint UInt<value_size>::Rcr2_one(uint c)
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{
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sint i; // signed i
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uint new_c;
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if( c != 0 )
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c = TTMATH_UINT_HIGHEST_BIT;
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for(i=sint(value_size)-1 ; i>=0 ; --i)
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{
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new_c = (table[i] & 1) ? TTMATH_UINT_HIGHEST_BIT : 0;
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table[i] = (table[i] >> 1) | c;
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c = new_c;
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}
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TTMATH_LOGC("UInt::Rcr2_one", c)
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return c;
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}
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|
/*!
|
|
this method moves all bits into the left hand side
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|
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
|
|
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|
for example:
|
|
let this is 001010000
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|
after Rcl2(3, 1) there'll be 010000111 and Rcl2 returns 1
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*/
|
|
template<uint value_size>
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|
uint UInt<value_size>::Rcl2(uint bits, uint c)
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{
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|
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
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|
uint move = TTMATH_BITS_PER_UINT - bits;
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uint i, new_c;
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if( c != 0 )
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c = TTMATH_UINT_MAX_VALUE >> move;
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for(i=0 ; i<value_size ; ++i)
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{
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new_c = table[i] >> move;
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table[i] = (table[i] << bits) | c;
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c = new_c;
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}
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TTMATH_LOGC("UInt::Rcl2", c)
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return (c & 1);
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}
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|
|
|
/*!
|
|
this method moves all bits into the right hand side
|
|
C -> this -> return value
|
|
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|
the highest *bits* will be held the 'c' and
|
|
the state of one additional bit (on the right hand side)
|
|
will be returned
|
|
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|
for example:
|
|
let this is 000000010
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|
after Rcr2(2, 1) there'll be 110000000 and Rcr2 returns 1
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*/
|
|
template<uint value_size>
|
|
uint UInt<value_size>::Rcr2(uint bits, uint c)
|
|
{
|
|
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
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|
|
|
uint move = TTMATH_BITS_PER_UINT - bits;
|
|
sint i; // signed
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|
uint new_c;
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|
|
if( c != 0 )
|
|
c = TTMATH_UINT_MAX_VALUE << move;
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|
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|
for(i=value_size-1 ; i>=0 ; --i)
|
|
{
|
|
new_c = table[i] << move;
|
|
table[i] = (table[i] >> bits) | c;
|
|
c = new_c;
|
|
}
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|
TTMATH_LOGC("UInt::Rcr2", c)
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return (c & TTMATH_UINT_HIGHEST_BIT) ? 1 : 0;
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}
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|
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|
|
|
/*!
|
|
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
|
|
|
|
|
|
|
|
|