919 lines
18 KiB
C++
919 lines
18 KiB
C++
/*
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* This file is a part of TTMath Mathematical Library
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* and is distributed under the (new) BSD licence.
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* Author: Tomasz Sowa <t.sowa@slimaczek.pl>
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*/
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/*
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* Copyright (c) 2006-2008, 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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/*!
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\file ttmathuint.h
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\brief template class UInt<uint> for 64bit processors
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*/
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namespace ttmath
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{
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/*!
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*
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* basic mathematic functions
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*
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*/
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#ifdef TTMATH_PLATFORM64
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/*!
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in 64bit platforms we must define additional operators and contructors
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in order to allow a user initializing the objects in this way:
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UInt<...> type = 20;
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or
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UInt<...> type;
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type = 30;
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decimal constants such as 20, 30 etc. are integer literal of type int,
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if the value is greater it can even be long int,
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0 is an octal integer of type int
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(ISO 14882 p2.13.1 Integer literals)
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*/
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/*!
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this operator converts the unsigned int type to this class
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***this operator is created only on a 64bit platform***
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it takes one argument of 32bit
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*/
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template<uint value_size>
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UInt<value_size> & UInt<value_size>::operator=(unsigned int i)
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{
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FromUInt(uint(i));
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return *this;
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}
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/*!
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a constructor for converting the unsigned int to this class
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***this constructor is created only on a 64bit platform***
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it takes one argument of 32bit
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*/
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template<uint value_size>
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UInt<value_size>::UInt(unsigned int i)
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{
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FromUInt(uint(i));
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}
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/*!
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an operator for converting the signed int to this class
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***this constructor is created only on a 64bit platform***
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it takes one argument of 32bit
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look at the description of UInt::operator=(sint)
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*/
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template<uint value_size>
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UInt<value_size> & UInt<value_size>::operator=(signed int i)
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{
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FromUInt(uint(i));
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return *this;
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}
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/*!
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a constructor for converting the signed int to this class
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***this constructor is created only on a 64bit platform***
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it takes one argument of 32bit
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look at the description of UInt::operator=(sint)
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*/
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template<uint value_size>
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UInt<value_size>::UInt(signed int i)
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{
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FromUInt(uint(i));
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}
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/*!
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this method copies the value stored in an another table
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(warning: first values in temp_table are the highest words -- it's different
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from our table)
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***this method is created only on a 64bit platform***
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we copy as many words as it is possible
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if temp_table_len is bigger than value_size we'll try to round
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the lowest word from table depending on the last not used bit in temp_table
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(this rounding isn't a perfect rounding -- look at the description below)
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and if temp_table_len is smaller than value_size we'll clear the rest words
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in the table
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warning: we're using 'temp_table' as a pointer at 32bit words
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*/
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template<uint value_size>
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void UInt<value_size>::SetFromTable(const unsigned int * temp_table, uint temp_table_len)
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{
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uint temp_table_index = 0;
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sint i; // 'i' with a sign
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for(i=value_size-1 ; i>=0 && temp_table_index<temp_table_len; --i, ++temp_table_index)
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{
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table[i] = uint(temp_table[ temp_table_index ]) << 32;
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++temp_table_index;
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if( temp_table_index<temp_table_len )
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table[i] |= temp_table[ temp_table_index ];
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}
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// rounding mantissa
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if( temp_table_index < temp_table_len )
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{
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if( (temp_table[temp_table_index] & TTMATH_UINT_HIGHEST_BIT) != 0 )
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{
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/*
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very simply rounding
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if the bit from not used last word from temp_table is set to one
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we're rouding the lowest word in the table
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in fact there should be a normal addition but
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we don't use Add() or AddTwoInts() because these methods
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can set a carry and then there'll be a small problem
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for optimization
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*/
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if( table[0] != TTMATH_UINT_MAX_VALUE )
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++table[0];
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}
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}
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// cleaning the rest of the mantissa
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for( ; i >= 0 ; --i)
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table[i] = 0;
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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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***this method is created only on a 64bit platform***
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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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register uint b = value_size;
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register uint * p1 = table;
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register uint * p2 = const_cast<uint*>(ss2.table);
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#ifndef __GNUC__
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#error "another compiler than GCC is currently not supported in 64bit mode"
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#endif
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#ifdef __GNUC__
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/*
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this part should be compiled with gcc
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*/
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__asm__ __volatile__(
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"push %%rcx \n"
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"xorq %%rax, %%rax \n"
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"movq %%rax, %%rdx \n"
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"subq %%rdi, %%rax \n"
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"1: \n"
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"movq (%%rsi,%%rdx,8),%%rax \n"
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"adcq %%rax, (%%rbx,%%rdx,8) \n"
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"incq %%rdx \n"
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"decq %%rcx \n"
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"jnz 1b \n"
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"setc %%al \n"
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"movzx %%al,%%rdx \n"
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"pop %%rcx \n"
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: "=d" (c)
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: "D" (c), "c" (b), "b" (p1), "S" (p2)
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: "%rax", "cc", "memory" );
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#endif
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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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***this method is created only on a 64bit platform***
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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[3] 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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register uint b = value_size;
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register uint * p1 = table;
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register uint c;
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#ifndef __GNUC__
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#error "another compiler than GCC is currently not supported in 64bit mode"
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#endif
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#ifdef __GNUC__
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__asm__ __volatile__(
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"push %%rax \n"
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"push %%rcx \n"
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"subq %%rdx, %%rcx \n"
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"1: \n"
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"addq %%rax, (%%rbx,%%rdx,8) \n"
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"jnc 2f \n"
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"movq $1, %%rax \n"
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"incq %%rdx \n"
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"decq %%rcx \n"
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"jnz 1b \n"
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"2: \n"
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"setc %%al \n"
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"movzx %%al, %%rdx \n"
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"pop %%rcx \n"
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"pop %%rax \n"
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: "=d" (c)
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: "a" (value), "c" (b), "0" (index), "b" (p1)
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: "cc", "memory" );
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#endif
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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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***this method is created only on a 64bit platform***
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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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register uint b = value_size;
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register uint * p1 = table;
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register uint c;
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#ifndef __GNUC__
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#error "another compiler than GCC is currently not supported in 64bit mode"
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#endif
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#ifdef __GNUC__
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__asm__ __volatile__(
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"push %%rcx \n"
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"push %%rdx \n"
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"subq %%rdx, %%rcx \n"
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"addq %%rsi, (%%rbx,%%rdx,8) \n"
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"incq %%rdx \n"
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"decq %%rcx \n"
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"1: \n"
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"adcq %%rax, (%%rbx,%%rdx,8) \n"
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"jnc 2f \n"
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"mov $0, %%rax \n"
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"incq %%rdx \n"
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"decq %%rcx \n"
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"jnz 1b \n"
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"2: \n"
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"setc %%al \n"
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"movzx %%al, %%rax \n"
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"pop %%rdx \n"
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"pop %%rcx \n"
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: "=a" (c)
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: "c" (b), "d" (index), "b" (p1), "S" (x1), "0" (x2)
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: "cc", "memory" );
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#endif
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return c;
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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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***this method is created only on a 64bit platform***
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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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register uint b = value_size;
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register uint * p1 = table;
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register uint * p2 = const_cast<uint*>(ss2.table);
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#ifndef __GNUC__
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#error "another compiler than GCC is currently not supported in 64bit mode"
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#endif
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#ifdef __GNUC__
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__asm__ __volatile__(
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"push %%rbx \n"
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"push %%rcx \n"
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"push %%rdx \n"
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"movq $0, %%rax \n"
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"subq %%rsi, %%rax \n"
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"1: \n"
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"movq (%%rbx),%%rax \n"
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"sbbq (%%rdx),%%rax \n"
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"movq %%rax,(%%rbx) \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rbx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"inc %%rdx \n"
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"loop 1b \n"
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"movq $0, %%rax \n"
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"adcq %%rax,%%rax \n"
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"movq %%rax, %%rsi \n"
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"pop %%rdx \n"
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"pop %%rcx \n"
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"pop %%rbx \n"
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: "=S" (c)
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: "0" (c), "c" (b), "b" (p1), "d" (p2)
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: "%rax", "cc", "memory" );
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#endif
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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)
|
|
and returns a carry (if it was)
|
|
|
|
***this method is created only on a 64bit platform***
|
|
|
|
if we've got (value_size=3):
|
|
table[0] = 10;
|
|
table[1] = 30;
|
|
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[3] 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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register uint b = value_size;
|
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register uint * p1 = table;
|
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register uint c;
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
__asm__ __volatile__(
|
|
|
|
"push %%rbx \n"
|
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"push %%rcx \n"
|
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"push %%rdx \n"
|
|
|
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"subq %%rdx, %%rcx \n"
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|
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"leaq (%%rbx,%%rdx,8), %%rbx \n"
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|
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"movq %%rsi, %%rdx \n"
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"clc \n"
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|
"1: \n"
|
|
|
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"movq (%%rbx), %%rax \n"
|
|
"sbbq %%rdx, %%rax \n"
|
|
"movq %%rax, (%%rbx) \n"
|
|
|
|
"jnc 2f \n"
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|
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"movq $0, %%rdx \n"
|
|
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
"inc %%rbx \n"
|
|
|
|
"loop 1b \n"
|
|
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|
"2: \n"
|
|
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|
"movq $0, %%rax \n"
|
|
"adcq %%rax,%%rax \n"
|
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|
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"pop %%rdx \n"
|
|
"pop %%rcx \n"
|
|
"pop %%rbx \n"
|
|
|
|
: "=a" (c)
|
|
: "c" (b), "d" (index), "b" (p1), "S" (value)
|
|
: "cc", "memory" );
|
|
|
|
#endif
|
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|
|
|
|
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
|
|
|
|
***this method is created only on a 64bit platform***
|
|
*/
|
|
template<uint value_size>
|
|
uint UInt<value_size>::Rcl2(uint bits, uint c)
|
|
{
|
|
if( bits == 0 )
|
|
return 0;
|
|
|
|
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
|
|
|
|
register sint b = value_size;
|
|
register uint * p1 = table;
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
__asm__ __volatile__(
|
|
|
|
"push %%rsi \n"
|
|
|
|
|
|
"2: \n"
|
|
|
|
"xorq %%rax,%%rax \n"
|
|
"subq %%rdx,%%rax \n"
|
|
|
|
"push %%rbx \n"
|
|
"push %%rcx \n"
|
|
|
|
//"lahf \n"
|
|
".byte 0x9f \n"
|
|
"1: \n"
|
|
//"sahf \n"
|
|
".byte 0x9e \n"
|
|
"rclq $1,(%%rbx) \n"
|
|
//"lahf \n"
|
|
".byte 0x9f \n"
|
|
|
|
"addq $8,%%rbx \n"
|
|
|
|
"subq $1,%%rcx \n"
|
|
"loop 1b \n"
|
|
|
|
"pop %%rcx \n"
|
|
"pop %%rbx \n"
|
|
|
|
"subq $1,%%rsi \n"
|
|
"jnz 2b \n"
|
|
|
|
"xor %%rdx,%%rdx \n"
|
|
//"sahf \n"
|
|
".byte 0x9e \n"
|
|
"setc %%dl \n"
|
|
|
|
"pop %%rsi \n"
|
|
|
|
: "=d" (c)
|
|
: "0" (c), "c" (b), "b" (p1), "S" (bits)
|
|
: "%rax", "cc", "memory" );
|
|
|
|
#endif
|
|
|
|
|
|
return c;
|
|
}
|
|
|
|
|
|
/*!
|
|
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
|
|
|
|
***this method is created only on a 64bit platform***
|
|
*/
|
|
template<uint value_size>
|
|
uint UInt<value_size>::Rcr2(uint bits, uint c)
|
|
{
|
|
if( bits == 0 )
|
|
return 0;
|
|
|
|
TTMATH_ASSERT( bits>0 && bits<TTMATH_BITS_PER_UINT )
|
|
|
|
register sint b = value_size;
|
|
register uint * p1 = table;
|
|
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
|
|
#ifdef __GNUC__
|
|
__asm__ __volatile__(
|
|
|
|
"push %%rsi \n"
|
|
|
|
|
|
"2: \n"
|
|
|
|
|
|
"push %%rbx \n"
|
|
"push %%rcx \n"
|
|
|
|
"leaq (%%rbx,%%rcx,8),%%rbx \n"
|
|
|
|
"xorq %%rax, %%rax \n"
|
|
"subq %%rdx, %%rax \n"
|
|
|
|
//"lahf \n"
|
|
".byte 0x9f \n"
|
|
"1: \n"
|
|
"subq $8, %%rbx \n"
|
|
|
|
//"sahf \n"
|
|
".byte 0x9e \n"
|
|
|
|
"rcrq $1,(%%rbx) \n"
|
|
//"lahf \n"
|
|
".byte 0x9f \n"
|
|
|
|
"subq $1,%%rcx \n"
|
|
"jnz 1b \n"
|
|
|
|
"pop %%rcx \n"
|
|
"pop %%rbx \n"
|
|
|
|
"subq $1,%%rsi \n"
|
|
|
|
"jnz 2b \n"
|
|
|
|
"xor %%rdx,%%rdx \n"
|
|
//"sahf \n"
|
|
".byte 0x9e \n"
|
|
"setc %%dl \n"
|
|
|
|
"pop %%rsi \n"
|
|
|
|
: "=d" (c)
|
|
: "0" (c), "c" (b), "b" (p1), "S" (bits)
|
|
: "%rax", "cc", "memory" );
|
|
|
|
#endif
|
|
|
|
|
|
return c;
|
|
}
|
|
|
|
|
|
/*
|
|
this method returns the number of the highest set bit in one 32-bit word
|
|
if the 'x' is zero this method returns '-1'
|
|
|
|
***this method is created only on a 64bit platform***
|
|
*/
|
|
template<uint value_size>
|
|
sint UInt<value_size>::FindLeadingBitInWord(uint x)
|
|
{
|
|
register sint result;
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
__asm__ __volatile__(
|
|
|
|
"push %%rdx \n"
|
|
"andq $-1,%%rdx \n"
|
|
"bsrq %%rbx, %%rax \n"
|
|
"cmovz %%rdx,%%rax \n"
|
|
"pop %%rdx \n"
|
|
|
|
: "=a" (result)
|
|
: "b" (x)
|
|
: "cc" );
|
|
|
|
#endif
|
|
|
|
|
|
return result;
|
|
}
|
|
|
|
|
|
/*!
|
|
this method sets a special bit in the 'value'
|
|
and returns the result
|
|
|
|
***this method is created only on a 64bit platform***
|
|
|
|
bit is from <0,31>
|
|
|
|
e.g.
|
|
SetBitInWord(0,0) = 1
|
|
SetBitInWord(0,2) = 4
|
|
SetBitInWord(10, 8) = 266
|
|
*/
|
|
template<uint value_size>
|
|
uint UInt<value_size>::SetBitInWord(uint value, uint bit)
|
|
{
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
__asm__ __volatile__(
|
|
|
|
"btsq %%rbx,%%rax \n"
|
|
|
|
: "=a" (value)
|
|
: "0" (value), "b" (bit)
|
|
: "cc" );
|
|
|
|
#endif
|
|
|
|
return value;
|
|
}
|
|
|
|
|
|
/*!
|
|
*
|
|
* Multiplication
|
|
*
|
|
*
|
|
*/
|
|
|
|
|
|
/*!
|
|
multiplication: result2:result1 = a * b
|
|
result2 - higher word
|
|
result1 - lower word of the result
|
|
|
|
this methos never returns a carry
|
|
|
|
***this method is created only on a 64bit platform***
|
|
|
|
it is an auxiliary method for version two of the multiplication algorithm
|
|
*/
|
|
template<uint value_size>
|
|
void UInt<value_size>::MulTwoWords(uint a, uint b, uint * result2, uint * result1)
|
|
{
|
|
/*
|
|
we must use these temporary variables in order to inform the compilator
|
|
that value pointed with result1 and result2 has changed
|
|
|
|
this has no effect in visual studio but it's usefull when
|
|
using gcc and options like -O
|
|
*/
|
|
register uint result1_;
|
|
register uint result2_;
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
|
|
__asm__ __volatile__(
|
|
|
|
"mulq %%rdx \n"
|
|
|
|
: "=a" (result1_), "=d" (result2_)
|
|
: "0" (a), "1" (b)
|
|
: "cc" );
|
|
|
|
#endif
|
|
|
|
|
|
*result1 = result1_;
|
|
*result2 = result2_;
|
|
}
|
|
|
|
|
|
|
|
|
|
/*!
|
|
*
|
|
* Division
|
|
*
|
|
*
|
|
*/
|
|
|
|
|
|
/*!
|
|
this method calculates 64bits word a:b / 32bits c (a higher, b lower word)
|
|
r = a:b / c and rest - remainder
|
|
|
|
***this method is created only on a 64bit platform***
|
|
|
|
*
|
|
* WARNING:
|
|
* if r (one word) is too small for the result or 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)
|
|
{
|
|
register uint r_;
|
|
register uint rest_;
|
|
/*
|
|
these variables have similar meaning like those in
|
|
the multiplication algorithm MulTwoWords
|
|
*/
|
|
|
|
#ifndef __GNUC__
|
|
#error "another compiler than GCC is currently not supported in 64bit mode"
|
|
#endif
|
|
|
|
#ifdef __GNUC__
|
|
|
|
__asm__ __volatile__(
|
|
|
|
"divq %%rcx \n"
|
|
|
|
: "=a" (r_), "=d" (rest_)
|
|
: "d" (a), "a" (b), "c" (c)
|
|
: "cc" );
|
|
|
|
#endif
|
|
|
|
|
|
*r = r_;
|
|
*rest = rest_;
|
|
}
|
|
|
|
#endif
|
|
|
|
} //namespace
|