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	<html><!-- Created using the cpp_pretty_printer from the dlib C++ library. See http://dlib.net for updates. --><head><title>dlib C++ Library - bigint_kernel_2.cpp</title></head><body bgcolor='white'><pre>
	<font color='#009900'>// Copyright (C) 2003 Davis E. King ([email protected])
	</font><font color='#009900'>// License: Boost Software License See LICENSE.txt for the full license.
	</font><font color='#0000FF'>#ifndef</font> DLIB_BIGINT_KERNEL_2_CPp_
	<font color='#0000FF'>#define</font> DLIB_BIGINT_KERNEL_2_CPp_
	<font color='#0000FF'>#include</font> "<a style='text-decoration:none' href='bigint_kernel_2.h.html'>bigint_kernel_2.h</a>"

	<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>iostream<font color='#5555FF'>></font>
	<font color='#0000FF'>#include</font> <font color='#5555FF'><</font>cmath<font color='#5555FF'>></font>

	<font color='#0000FF'>namespace</font> dlib
	<b>{</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font> <font color='#009900'>// member/friend function definitions
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2::
	<b><a name='bigint_kernel_2'></a>bigint_kernel_2</b> <font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font> :
	slack<font face='Lucida Console'>(</font><font color='#979000'>25</font><font face='Lucida Console'>)</font>,
	data<font face='Lucida Console'>(</font><font color='#0000FF'>new</font> data_record<font face='Lucida Console'>(</font>slack<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b><b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2::
	<b><a name='bigint_kernel_2'></a>bigint_kernel_2</b> <font face='Lucida Console'>(</font>
	uint32 value
	<font face='Lucida Console'>)</font> :
	slack<font face='Lucida Console'>(</font><font color='#979000'>25</font><font face='Lucida Console'>)</font>,
	data<font face='Lucida Console'>(</font><font color='#0000FF'>new</font> data_record<font face='Lucida Console'>(</font>slack<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>value<font color='#5555FF'>&</font><font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font color='#5555FF'>+</font><font color='#979000'>1</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>value<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font><font color='#5555FF'>&</font><font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font color='#5555FF'>+</font><font color='#979000'>1</font><font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>2</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2::
	<b><a name='bigint_kernel_2'></a>bigint_kernel_2</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> item
	<font face='Lucida Console'>)</font> :
	slack<font face='Lucida Console'>(</font><font color='#979000'>25</font><font face='Lucida Console'>)</font>,
	data<font face='Lucida Console'>(</font>item.data<font face='Lucida Console'>)</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2::
	~<b><a name='bigint_kernel_2'></a>bigint_kernel_2</b> <font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>delete</font> data;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font> <font face='Lucida Console'>(</font>
	std::<font color='#BB00BB'>max</font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used,data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font> <font color='#5555FF'>+</font> slack
	<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>long_add</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to our data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>max</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used,rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>long_add</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// if data is not big enough for the result
	</font> <font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>size <font color='#5555FF'><</font><font color='#5555FF'>=</font> std::<font color='#BB00BB'>max</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used,rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>max</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used,rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>long_add</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> data;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// there is enough size and no references
	</font> <font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>long_add</font><font face='Lucida Console'>(</font>data,rhs.data,data<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font> <font face='Lucida Console'>(</font>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> slack
	<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>long_sub</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>long_sub</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>long_sub</font><font face='Lucida Console'>(</font>data,rhs.data,data<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font> <font face='Lucida Console'>(</font>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> slack
	<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>long_mul</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// create a data_record to store the result of the multiplication in
	</font> data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>long_mul</font><font face='Lucida Console'>(</font>data,rhs.data,temp<font face='Lucida Console'>)</font>;

	<font color='#009900'>// if there are other references to data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#0000FF'>delete</font> data;
	<b>}</b>
	data <font color='#5555FF'>=</font> temp;
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data_record<font color='#5555FF'>*</font> remainder;
	<font color='#0000FF'>try</font> <b>{</b>
	remainder <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> temp; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#BB00BB'>long_div</font><font face='Lucida Console'>(</font>data,rhs.data,temp,remainder<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> remainder;


	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>

	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data_record<font color='#5555FF'>*</font> remainder;
	<font color='#0000FF'>try</font> <b>{</b>
	remainder <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> temp; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#BB00BB'>long_div</font><font face='Lucida Console'>(</font>data,rhs.data,temp,remainder<font face='Lucida Console'>)</font>;

	<font color='#009900'>// check if there are other references to data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#009900'>// if there are no references to data then it must be deleted
	</font> <font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#0000FF'>delete</font> data;
	<b>}</b>
	data <font color='#5555FF'>=</font> temp;
	<font color='#0000FF'>delete</font> remainder;


	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data_record<font color='#5555FF'>*</font> remainder;
	<font color='#0000FF'>try</font> <b>{</b>
	remainder <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> temp; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#BB00BB'>long_div</font><font face='Lucida Console'>(</font>data,rhs.data,temp,remainder<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> temp;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>remainder,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>%</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data_record<font color='#5555FF'>*</font> remainder;
	<font color='#0000FF'>try</font> <b>{</b>
	remainder <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> temp; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#BB00BB'>long_div</font><font face='Lucida Console'>(</font>data,rhs.data,temp,remainder<font face='Lucida Console'>)</font>;

	<font color='#009900'>// check if there are other references to data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#009900'>// if there are no references to data then it must be deleted
	</font> <font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#0000FF'>delete</font> data;
	<b>}</b>
	data <font color='#5555FF'>=</font> remainder;
	<font color='#0000FF'>delete</font> temp;
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b> <font color='#5555FF'><</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font color='#BB00BB'>is_less_than</font><font face='Lucida Console'>(</font>data,rhs.data<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font color='#BB00BB'>is_equal_to</font><font face='Lucida Console'>(</font>data,rhs.data<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#0000FF'>this</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#5555FF'>&</font>rhs<font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;

	<font color='#009900'>// if we have the only reference to our data then delete it
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>delete</font> data;
	data <font color='#5555FF'>=</font> rhs.data;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	data <font color='#5555FF'>=</font> rhs.data;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>

	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	std::ostream<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'><</font><font color='#5555FF'><</font> <font face='Lucida Console'>(</font>
	std::ostream<font color='#5555FF'>&</font> out_,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	std::ostream <font color='#BB00BB'>out</font><font face='Lucida Console'>(</font>out_.<font color='#BB00BB'>rdbuf</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;

	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;

	bigint::data_record<font color='#5555FF'></font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font><font color='#5555FF'></font>rhs.data,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;



	<font color='#009900'>// get a char array big enough to hold the number in ascii format
	</font> <font color='#0000FF'><u>char</u></font><font color='#5555FF'>*</font> str;
	<font color='#0000FF'>try</font> <b>{</b>
	str <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#0000FF'><u>char</u></font>[<font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font color='#5555FF'>*</font><font color='#979000'>5</font><font color='#5555FF'>+</font><font color='#979000'>10</font>];
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> temp; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#0000FF'><u>char</u></font><font color='#5555FF'>*</font> str_start <font color='#5555FF'>=</font> str;
	str <font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font color='#5555FF'>*</font><font color='#979000'>5</font><font color='#5555FF'>+</font><font color='#979000'>9</font>;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> <font color='#979000'>0</font>; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;


	uint16 remainder;
	rhs.<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>10000</font>,temp,remainder<font face='Lucida Console'>)</font>;

	<font color='#009900'>// pull the digits out of remainder
	</font> <font color='#0000FF'><u>char</u></font> a <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> b <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> c <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> d <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;


	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> a; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> b; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> c; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> d; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;


	<font color='#009900'>// keep looping until temp represents zero
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>\|</font><font color='#5555FF'>\|</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	rhs.<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>10000</font>,temp,remainder<font face='Lucida Console'>)</font>;

	<font color='#009900'>// pull the digits out of remainder
	</font> <font color='#0000FF'><u>char</u></font> a <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> b <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> c <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	<font color='#0000FF'><u>char</u></font> d <font color='#5555FF'>=</font> remainder <font color='#5555FF'>%</font> <font color='#979000'>10</font> <font color='#5555FF'>+</font> '<font color='#FF0000'>0</font>';
	remainder <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;

	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> a; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> b; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> c; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<font color='#5555FF'>*</font>str <font color='#5555FF'>=</font> d; <font color='#5555FF'>-</font><font color='#5555FF'>-</font>str;
	<b>}</b>

	<font color='#009900'>// throw away and extra leading zeros
	</font> <font color='#5555FF'>+</font><font color='#5555FF'>+</font>str;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>str <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>'<font face='Lucida Console'>)</font>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>str;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>str <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>'<font face='Lucida Console'>)</font>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>str;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>str <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>'<font face='Lucida Console'>)</font>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>str;




	out <font color='#5555FF'><</font><font color='#5555FF'><</font> str;
	<font color='#0000FF'>delete</font> [] str_start;
	<font color='#0000FF'>delete</font> temp;
	<font color='#0000FF'>return</font> out_;

	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	std::istream<font color='#5555FF'>&</font> <b><a name='operator'></a>operator</b><font color='#5555FF'>></font><font color='#5555FF'>></font> <font face='Lucida Console'>(</font>
	std::istream<font color='#5555FF'>&</font> in_,
	bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	std::istream <font color='#BB00BB'>in</font><font face='Lucida Console'>(</font>in_.<font color='#BB00BB'>rdbuf</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;

	<font color='#009900'>// ignore any leading whitespaces
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'> </font>' <font color='#5555FF'>\|</font><font color='#5555FF'>\|</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'>\t</font>' <font color='#5555FF'>\|</font><font color='#5555FF'>\|</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> '<font color='#FF0000'>\n</font>'<font face='Lucida Console'>)</font>
	<b>{</b>
	in.<font color='#BB00BB'>get</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// if the first digit is not an integer then this is an error
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font> <font color='#5555FF'>!</font><font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>' <font color='#5555FF'>&</font><font color='#5555FF'>&</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'>=</font> '<font color='#FF0000'>9</font>'<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	in_.<font color='#BB00BB'>clear</font><font face='Lucida Console'>(</font>std::ios::failbit<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> in_;
	<b>}</b>

	<font color='#0000FF'><u>int</u></font> num_read;
	bigint_kernel_2 temp;
	<font color='#0000FF'>do</font>
	<b>{</b>

	<font color='#009900'>// try to get 4 chars from in
	</font> num_read <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'><u>char</u></font> a <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'><u>char</u></font> b <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'><u>char</u></font> c <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'><u>char</u></font> d <font color='#5555FF'>=</font> <font color='#979000'>0</font>;

	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>' <font color='#5555FF'>&</font><font color='#5555FF'>&</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'>=</font> '<font color='#FF0000'>9</font>'<font face='Lucida Console'>)</font>
	<b>{</b>
	num_read <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	a <font color='#5555FF'>=</font> in.<font color='#BB00BB'>get</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>' <font color='#5555FF'>&</font><font color='#5555FF'>&</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'>=</font> '<font color='#FF0000'>9</font>'<font face='Lucida Console'>)</font>
	<b>{</b>
	num_read <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	b <font color='#5555FF'>=</font> in.<font color='#BB00BB'>get</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>' <font color='#5555FF'>&</font><font color='#5555FF'>&</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'>=</font> '<font color='#FF0000'>9</font>'<font face='Lucida Console'>)</font>
	<b>{</b>
	num_read <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	c <font color='#5555FF'>=</font> in.<font color='#BB00BB'>get</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>=</font> '<font color='#FF0000'>0</font>' <font color='#5555FF'>&</font><font color='#5555FF'>&</font> in.<font color='#BB00BB'>peek</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'>=</font> '<font color='#FF0000'>9</font>'<font face='Lucida Console'>)</font>
	<b>{</b>
	num_read <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	d <font color='#5555FF'>=</font> in.<font color='#BB00BB'>get</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// merge the for digits into an uint16
	</font> uint16 num <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>a <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	num <font color='#5555FF'>=</font> a <font color='#5555FF'>-</font> '<font color='#FF0000'>0</font>';
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>b <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	num <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	num <font color='#5555FF'>+</font><font color='#5555FF'>=</font> b <font color='#5555FF'>-</font> '<font color='#FF0000'>0</font>';
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>c <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	num <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	num <font color='#5555FF'>+</font><font color='#5555FF'>=</font> c <font color='#5555FF'>-</font> '<font color='#FF0000'>0</font>';
	<b>}</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>d <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	num <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>10</font>;
	num <font color='#5555FF'>+</font><font color='#5555FF'>=</font> d <font color='#5555FF'>-</font> '<font color='#FF0000'>0</font>';
	<b>}</b>


	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>num_read <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// shift the digits in temp left by the number of new digits we just read
	</font> temp <font color='#5555FF'>*</font><font color='#5555FF'>=</font> num_read;
	<font color='#009900'>// add in new digits
	</font> temp <font color='#5555FF'>+</font><font color='#5555FF'>=</font> num;
	<b>}</b>

	<b>}</b> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>num_read <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>10000</font><font face='Lucida Console'>)</font>;


	rhs <font color='#5555FF'>=</font> temp;
	<font color='#0000FF'>return</font> in_;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>rhs.slack<font face='Lucida Console'>)</font>;

	rhs.<font color='#BB00BB'>short_add</font><font face='Lucida Console'>(</font>rhs.data,lhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>lhs.slack<font face='Lucida Console'>)</font>;

	lhs.<font color='#BB00BB'>short_add</font><font face='Lucida Console'>(</font>lhs.data,rhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>short_add</font><font face='Lucida Console'>(</font>data,rhs,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// or if we need to enlarge data then do so
	</font> <font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>size<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>short_add</font><font face='Lucida Console'>(</font>data,rhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> data;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// or if there is plenty of space and no references
	</font> <font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>short_add</font><font face='Lucida Console'>(</font>data,rhs,data<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>rhs.slack<font face='Lucida Console'>)</font>;

	<font color='#5555FF'></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> lhs <font color='#5555FF'>-</font> <font color='#5555FF'></font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font>;

	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>lhs.slack<font face='Lucida Console'>)</font>;

	lhs.<font color='#BB00BB'>short_sub</font><font face='Lucida Console'>(</font>lhs.data,rhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>short_sub</font><font face='Lucida Console'>(</font>data,rhs,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>short_sub</font><font face='Lucida Console'>(</font>data,rhs,data<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>rhs.slack<font face='Lucida Console'>)</font>;

	rhs.<font color='#BB00BB'>short_mul</font><font face='Lucida Console'>(</font>rhs.data,lhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>*</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>lhs.slack<font face='Lucida Console'>)</font>;

	lhs.<font color='#BB00BB'>short_mul</font><font face='Lucida Console'>(</font>lhs.data,rhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>short_mul</font><font face='Lucida Console'>(</font>data,rhs,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// or if we need to enlarge data
	</font> <font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>size<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>short_mul</font><font face='Lucida Console'>(</font>data,rhs,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> data;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>short_mul</font><font face='Lucida Console'>(</font>data,rhs,data<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>rhs.slack<font face='Lucida Console'>)</font>;

	<font color='#009900'>// if rhs might not be bigger than lhs
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> lhs<font color='#5555FF'>/</font> <font color='#5555FF'></font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>/</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font>
	<font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>lhs.slack<font face='Lucida Console'>)</font>;

	uint16 remainder;
	lhs.<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>lhs.data,rhs,temp,remainder<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	uint16 remainder;
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>data,rhs,temp,remainder<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>data,rhs,data,remainder<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	<font color='#009900'>// temp is zero by default
	</font> bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>rhs.slack<font face='Lucida Console'>)</font>;

	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if rhs is just an uint16 inside then perform the modulus
	</font> <font color='#5555FF'></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> lhs <font color='#5555FF'>%</font> <font color='#5555FF'></font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#009900'>// if rhs is bigger than lhs then the answer is lhs
	</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> lhs;
	<b>}</b>

	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 <b><a name='operator'></a>operator</b><font color='#5555FF'>%</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>typedef</font> bigint_kernel_2 bigint;
	bigint::data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> bigint::<font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>lhs.slack<font face='Lucida Console'>)</font>;

	uint16 remainder;

	lhs.<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>lhs.data,rhs,temp,remainder<font face='Lucida Console'>)</font>;
	temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> remainder;
	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>%</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	uint16 remainder;
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>data,rhs,temp,remainder<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>short_div</font><font face='Lucida Console'>(</font>data,rhs,data,remainder<font face='Lucida Console'>)</font>;
	<b>}</b>

	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> remainder;
	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'><</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>></font> <font color='#979000'>1</font> <font color='#5555FF'>\|</font><font color='#5555FF'>\|</font> lhs <font color='#5555FF'><</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'><</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>&</font><font color='#5555FF'>&</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'><</font> rhs<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> lhs,
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>&</font><font color='#5555FF'>&</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>lhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> rhs<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> <b><a name='operator'></a>operator</b> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 lhs,
	<font color='#0000FF'>const</font> bigint_kernel_2<font color='#5555FF'>&</font> rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font> <font color='#5555FF'>&</font><font color='#5555FF'>&</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>rhs.data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> lhs<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>
	uint16 rhs
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// check if there are other references to our data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>try</font> <b>{</b>
	data <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>slack<font face='Lucida Console'>)</font>;
	<b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>+</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>; <font color='#0000FF'>throw</font>; <b>}</b>
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>

	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> rhs;

	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data then make a copy of it
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>increment</font><font face='Lucida Console'>(</font>data,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#009900'>// or if we need to enlarge data then do so
	</font> <font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>size<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>increment</font><font face='Lucida Console'>(</font>data,temp<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>delete</font> data;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>increment</font><font face='Lucida Console'>(</font>data,data<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>+</font><font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'><u>int</u></font>
	<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp; <font color='#009900'>// this is the copy of temp we will return in the end
	</font>
	data_record<font color='#5555FF'>*</font> temp2 <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>increment</font><font face='Lucida Console'>(</font>data,temp2<font face='Lucida Console'>)</font>;

	temp <font color='#5555FF'>=</font> data;
	data <font color='#5555FF'>=</font> temp2;

	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	bigint_kernel_2<font color='#5555FF'>&</font> bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
	<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if there are other references to this data
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	data<font color='#5555FF'>-</font><font color='#5555FF'>></font>references <font color='#5555FF'>-</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#BB00BB'>decrement</font><font face='Lucida Console'>(</font>data,temp<font face='Lucida Console'>)</font>;
	data <font color='#5555FF'>=</font> temp;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#BB00BB'>decrement</font><font face='Lucida Console'>(</font>data,data<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#0000FF'>return</font> <font color='#5555FF'>*</font><font color='#0000FF'>this</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'>const</font> bigint_kernel_2 bigint_kernel_2::
	<b><a name='operator'></a>operator</b><font color='#5555FF'>-</font><font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>
	<font color='#0000FF'><u>int</u></font>
	<font face='Lucida Console'>)</font>
	<b>{</b>
	data_record<font color='#5555FF'>*</font> temp; <font color='#009900'>// this is the copy of temp we will return in the end
	</font>
	data_record<font color='#5555FF'>*</font> temp2 <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> <font color='#BB00BB'>data_record</font><font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>decrement</font><font face='Lucida Console'>(</font>data,temp2<font face='Lucida Console'>)</font>;

	temp <font color='#5555FF'>=</font> data;
	data <font color='#5555FF'>=</font> temp2;

	<font color='#0000FF'>return</font> <font color='#BB00BB'>bigint_kernel_2</font><font face='Lucida Console'>(</font>temp,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font> <font color='#009900'>// private member function definitions
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font><font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='short_add'></a>short_add</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	uint16 value,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#009900'>// put value into the carry part of temp
	</font> uint32 temp <font color='#5555FF'>=</font> value;
	temp <font color='#5555FF'><</font><font color='#5555FF'><</font><font color='#5555FF'>=</font> <font color='#979000'>16</font>;


	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> number <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used; <font color='#009900'>// one past the end of number
	</font> uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;

	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>number <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// add *number and the current carry
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>number <font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	<font color='#009900'>// if there is a final carry
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> <font color='#979000'>1</font>;
	<font color='#009900'>// store the carry in the most significant digit of the result
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='short_sub'></a>short_sub</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	uint16 value,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>


	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> number <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;

	uint32 temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>number <font color='#5555FF'>-</font> value;

	<font color='#009900'>// put the low word of temp into *data
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;


	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>number <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;

	<font color='#009900'>// subtract the carry from *number
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>number <font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>31</font><font face='Lucida Console'>)</font>;

	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// if we lost a digit in the subtraction
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>else</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>


	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='short_mul'></a>short_mul</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	uint16 value,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>

	uint32 temp <font color='#5555FF'>=</font> <font color='#979000'>0</font>;


	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> r <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;



	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font> r <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>

	<font color='#009900'>// multiply *data and value and add in the carry
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'></font>number<font color='#5555FF'></font><font face='Lucida Console'>(</font>uint32<font face='Lucida Console'>)</font>value <font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;

	<font color='#009900'>// put the low word of temp into *data
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	<font color='#009900'>// if there is a final carry
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> <font color='#979000'>1</font>;
	<font color='#009900'>// put the final carry into the most significant digit of the result
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>


	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='short_div'></a>short_div</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	uint16 value,
	data_record<font color='#5555FF'>*</font> result,
	uint16<font color='#5555FF'>&</font> rem
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>

	uint16 remainder <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	uint32 temp;



	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> number <font color='#5555FF'>-</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;


	<font color='#009900'>// if we are losing a digit in this division
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>number <font color='#5555FF'><</font> value<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>else</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>


	<font color='#009900'>// perform the actual division
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>number <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>

	temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>number <font color='#5555FF'>+</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>uint32<font face='Lucida Console'>)</font>remainder<font face='Lucida Console'>)</font><font color='#5555FF'><</font><font color='#5555FF'><</font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>/</font>value<font face='Lucida Console'>)</font>;
	remainder <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>%</font>value<font face='Lucida Console'>)</font>;

	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>number;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;
	<b>}</b>

	rem <font color='#5555FF'>=</font> remainder;
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='long_add'></a>long_add</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#009900'>// put value into the carry part of temp
	</font> uint32 temp<font color='#5555FF'>=</font><font color='#979000'>0</font>;

	uint16<font color='#5555FF'>*</font> min_num; <font color='#009900'>// the number with the least digits used
	</font> uint16<font color='#5555FF'>*</font> max_num; <font color='#009900'>// the number with the most digits used
	</font> uint16<font color='#5555FF'>*</font> min_end; <font color='#009900'>// one past the end of min_num
	</font> uint16<font color='#5555FF'>*</font> max_end; <font color='#009900'>// one past the end of max_num
	</font> uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;

	uint32 max_digits_used;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'><</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font>
	<b>{</b>
	max_digits_used <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	min_num <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	max_num <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	min_end <font color='#5555FF'>=</font> min_num <font color='#5555FF'>+</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	max_end <font color='#5555FF'>=</font> max_num <font color='#5555FF'>+</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	max_digits_used <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	min_num <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	max_num <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	min_end <font color='#5555FF'>=</font> min_num <font color='#5555FF'>+</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	max_end <font color='#5555FF'>=</font> max_num <font color='#5555FF'>+</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>




	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>min_num <font color='#5555FF'>!</font><font color='#5555FF'>=</font> min_end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// add min_num, max_num and the current carry
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'></font>min_num <font color='#5555FF'>+</font> <font color='#5555FF'></font>max_num <font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>min_num;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>max_num;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>


	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>max_num <font color='#5555FF'>!</font><font color='#5555FF'>=</font> max_end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// add *max_num and the current carry
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>max_num <font color='#5555FF'>+</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>max_num;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	<font color='#009900'>// check if there was a final carry
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> max_digits_used <font color='#5555FF'>+</font> <font color='#979000'>1</font>;
	<font color='#009900'>// put the carry into the most significant digit in the result
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>16</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> max_digits_used;
	<b>}</b>


	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='long_sub'></a>long_sub</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>


	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number1 <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> number2 <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>const</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> number2 <font color='#5555FF'>+</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;



	uint32 temp <font color='#5555FF'>=</font><font color='#979000'>0</font>;


	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>number2 <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>

	<font color='#009900'>// subtract number2 from number1 and then subtract any carry
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'></font>number1 <font color='#5555FF'>-</font> <font color='#5555FF'></font>number2 <font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>31</font><font face='Lucida Console'>)</font>;

	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number1;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number2;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	end <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number <font color='#5555FF'>+</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>number1 <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>

	<font color='#009900'>// subtract the carry from *number1
	</font> temp <font color='#5555FF'>=</font> <font color='#5555FF'>*</font>number1 <font color='#5555FF'>-</font> <font face='Lucida Console'>(</font>temp<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>31</font><font face='Lucida Console'>)</font>;

	<font color='#009900'>// put the low word of temp into *r
	</font> <font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>temp <font color='#5555FF'>&</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>number1;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#009900'>// adjust the number of digits used appropriately
	</font> <font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font> <font color='#5555FF'>&</font><font color='#5555FF'>&</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>></font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='long_div'></a>long_div</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs,
	data_record<font color='#5555FF'>*</font> result,
	data_record<font color='#5555FF'>*</font> remainder
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#009900'>// zero result
	</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#979000'>0</font>;

	uint16<font color='#5555FF'>*</font> a;
	uint16<font color='#5555FF'>*</font> b;
	uint16<font color='#5555FF'>*</font> end;

	<font color='#009900'>// copy lhs into remainder
	</font> remainder<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	a <font color='#5555FF'>=</font> remainder<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	end <font color='#5555FF'>=</font> a <font color='#5555FF'>+</font> remainder<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	b <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>a <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>a <font color='#5555FF'>=</font> <font color='#5555FF'></font>b;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>a;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>b;
	<b>}</b>


	<font color='#009900'>// if rhs is bigger than lhs then result == 0 and remainder == lhs
	</font> <font color='#009900'>// so then we can quit right now
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#BB00BB'>is_less_than</font><font face='Lucida Console'>(</font>lhs,rhs<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font>;
	<b>}</b>


	<font color='#009900'>// make a temporary number
	</font> data_record <font color='#BB00BB'>temp</font><font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> slack<font face='Lucida Console'>)</font>;


	<font color='#009900'>// shift rhs left until it is one shift away from being larger than lhs and
	</font> <font color='#009900'>// put the number of left shifts necessary into shifts
	</font> uint32 shifts;
	shifts <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font> <font color='#5555FF'>*</font> <font color='#979000'>16</font>;

	<font color='#BB00BB'>shift_left</font><font face='Lucida Console'>(</font>rhs,<font color='#5555FF'>&</font>temp,shifts<font face='Lucida Console'>)</font>;


	<font color='#009900'>// while (lhs > temp)
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#BB00BB'>is_less_than</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>temp,lhs<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#BB00BB'>shift_left</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>temp,<font color='#5555FF'>&</font>temp,<font color='#979000'>1</font><font face='Lucida Console'>)</font>;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>shifts;
	<b>}</b>
	<font color='#009900'>// make sure lhs isn't smaller than temp
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#BB00BB'>is_less_than</font><font face='Lucida Console'>(</font>lhs,<font color='#5555FF'>&</font>temp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#BB00BB'>shift_right</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>temp,<font color='#5555FF'>&</font>temp<font face='Lucida Console'>)</font>;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>shifts;
	<b>}</b>



	<font color='#009900'>// we want to execute the loop shifts +1 times
	</font> <font color='#5555FF'>+</font><font color='#5555FF'>+</font>shifts;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>shifts <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#BB00BB'>shift_left</font><font face='Lucida Console'>(</font>result,result,<font color='#979000'>1</font><font face='Lucida Console'>)</font>;
	<font color='#009900'>// if (temp <= remainder)
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>!</font><font color='#BB00BB'>is_less_than</font><font face='Lucida Console'>(</font>remainder,<font color='#5555FF'>&</font>temp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#BB00BB'>long_sub</font><font face='Lucida Console'>(</font>remainder,<font color='#5555FF'>&</font>temp,remainder<font face='Lucida Console'>)</font>;

	<font color='#009900'>// increment result
	</font> uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> r <font color='#5555FF'>+</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#979000'>true</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font><font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r<font face='Lucida Console'>)</font>;
	<font color='#009900'>// if there was no carry then we are done
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<font color='#0000FF'>break</font>;

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;

	<font color='#009900'>// if we hit the end of r and there is still a carry then
	</font> <font color='#009900'>// the next digit of r is 1 and there is one more digit used
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>r <font color='#5555FF'>=</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>*</font>r <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font><font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font>;
	<font color='#0000FF'>break</font>;
	<b>}</b>
	<b>}</b>
	<b>}</b>
	<font color='#BB00BB'>shift_right</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>temp,<font color='#5555FF'>&</font>temp<font face='Lucida Console'>)</font>;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>shifts;
	<b>}</b>


	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='long_mul'></a>long_mul</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#009900'>// if one of the numbers is small then use this simple but O(n^2) algorithm
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>std::<font color='#BB00BB'>min</font><font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used, rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font> <font color='#5555FF'><</font> <font color='#979000'>10</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// make result be zero
	</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#979000'>0</font>;


	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> aa;
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> bb;

	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'><</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// make copies of lhs and rhs and give them an appropriate amount of
	</font> <font color='#009900'>// extra memory so there won't be any overflows
	</font> aa <font color='#5555FF'>=</font> lhs;
	bb <font color='#5555FF'>=</font> rhs;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#009900'>// make copies of lhs and rhs and give them an appropriate amount of
	</font> <font color='#009900'>// extra memory so there won't be any overflows
	</font> aa <font color='#5555FF'>=</font> rhs;
	bb <font color='#5555FF'>=</font> lhs;
	<b>}</b>

	<font color='#009900'>// copy the larger(approximately) of lhs and rhs into b
	</font> data_record <font color='#BB00BB'>b</font><font face='Lucida Console'>(</font><font color='#5555FF'>*</font>bb,aa<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>+</font>slack<font face='Lucida Console'>)</font>;


	uint32 shift_value <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	uint16<font color='#5555FF'>*</font> anum <font color='#5555FF'>=</font> aa<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> anum <font color='#5555FF'>+</font> aa<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>anum <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end <font face='Lucida Console'>)</font>
	<b>{</b>
	uint16 bit <font color='#5555FF'>=</font> <font color='#979000'>0x0001</font>;

	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>int</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> <font color='#979000'>16</font>; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if the specified bit of a is 1
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font><font color='#5555FF'>*</font>anum <font color='#5555FF'>&</font> bit<font face='Lucida Console'>)</font> <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#BB00BB'>shift_left</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>b,<font color='#5555FF'>&</font>b,shift_value<font face='Lucida Console'>)</font>;
	shift_value <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#BB00BB'>long_add</font><font face='Lucida Console'>(</font><font color='#5555FF'>&</font>b,result,result<font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>shift_value;
	bit <font color='#5555FF'><</font><font color='#5555FF'><</font><font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>anum;
	<b>}</b>
	<b>}</b>
	<font color='#0000FF'>else</font> <font color='#009900'>// else if both lhs and rhs are large then use the more complex
	</font> <font color='#009900'>// O(n*logn) algorithm
	</font> <b>{</b>
	uint32 size <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#009900'>// make size a power of 2
	</font> <font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>size <font color='#5555FF'><</font> <font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font><font color='#5555FF'>*</font><font color='#979000'>2</font><font face='Lucida Console'>)</font>
	<b>{</b>
	size <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>2</font>;
	<b>}</b>

	<font color='#009900'>// allocate some temporary space so we can do the FFT
	</font> ct<font color='#5555FF'>*</font> a <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> ct[size];
	ct<font color='#5555FF'>*</font> b; <font color='#0000FF'>try</font> <b>{</b>b <font color='#5555FF'>=</font> <font color='#0000FF'>new</font> ct[size]; <b>}</b> <font color='#0000FF'>catch</font> <font face='Lucida Console'>(</font>...<font face='Lucida Console'>)</font> <b>{</b> <font color='#0000FF'>delete</font> [] a; <font color='#0000FF'>throw</font>; <b>}</b>

	<font color='#009900'>// load lhs into the a array. We are breaking the input number into
	</font> <font color='#009900'>// 8bit chunks for the purpose of using this fft algorithm. The reason
	</font> <font color='#009900'>// for this is so that we have smaller numbers coming out of the final
	</font> <font color='#009900'>// ifft. This helps avoid overflow.
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>uint32 i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	a[i<font color='#5555FF'>*</font><font color='#979000'>2</font>] <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>t<font face='Lucida Console'>)</font><font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number[i]<font color='#5555FF'>&</font><font color='#979000'>0xFF</font><font face='Lucida Console'>)</font>,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	a[i<font color='#5555FF'>*</font><font color='#979000'>2</font><font color='#5555FF'>+</font><font color='#979000'>1</font>] <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>t<font face='Lucida Console'>)</font><font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number[i]<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>8</font><font face='Lucida Console'>)</font>,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>uint32 i <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>*</font><font color='#979000'>2</font>; i <font color='#5555FF'><</font> size; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	a[i] <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<b>}</b>

	<font color='#009900'>// load rhs into the b array
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>uint32 i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	b[i<font color='#5555FF'>*</font><font color='#979000'>2</font>] <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>t<font face='Lucida Console'>)</font><font face='Lucida Console'>(</font>rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number[i]<font color='#5555FF'>&</font><font color='#979000'>0xFF</font><font face='Lucida Console'>)</font>,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	b[i<font color='#5555FF'>*</font><font color='#979000'>2</font><font color='#5555FF'>+</font><font color='#979000'>1</font>] <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font><font face='Lucida Console'>(</font>t<font face='Lucida Console'>)</font><font face='Lucida Console'>(</font>rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number[i]<font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#979000'>8</font><font face='Lucida Console'>)</font>,<font color='#979000'>0</font><font face='Lucida Console'>)</font>;
	<b>}</b>
	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>uint32 i <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font color='#5555FF'>*</font><font color='#979000'>2</font>; i <font color='#5555FF'><</font> size; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	b[i] <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<b>}</b>

	<font color='#009900'>// perform the forward fft of a and b
	</font> <font color='#BB00BB'>fft</font><font face='Lucida Console'>(</font>a,size<font face='Lucida Console'>)</font>;
	<font color='#BB00BB'>fft</font><font face='Lucida Console'>(</font>b,size<font face='Lucida Console'>)</font>;

	<font color='#0000FF'>const</font> <font color='#0000FF'><u>double</u></font> l <font color='#5555FF'>=</font> <font color='#979000'>1.0</font><font color='#5555FF'>/</font>size;

	<font color='#009900'>// do the pointwise multiply of a and b and also apply the scale
	</font> <font color='#009900'>// factor in this loop too.
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> size; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	a[i] <font color='#5555FF'>=</font> l<font color='#5555FF'></font>a[i]<font color='#5555FF'></font>b[i];
	<b>}</b>

	<font color='#009900'>// Now compute the inverse fft of the pointwise multiplication of a and b.
	</font> <font color='#009900'>// This is basically the result. We just have to take care of any carries
	</font> <font color='#009900'>// that should happen.
	</font> <font color='#BB00BB'>ifft</font><font face='Lucida Console'>(</font>a,size<font face='Lucida Console'>)</font>;

	<font color='#009900'>// loop over the result and propagate any carries that need to take place.
	</font> <font color='#009900'>// We will also be moving the resulting numbers into result->number at
	</font> <font color='#009900'>// the same time.
	</font> uint64 carry <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'><u>int</u></font> zeros <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'>const</font> uint32 len <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> i <font color='#5555FF'>=</font> <font color='#979000'>0</font>; i <font color='#5555FF'><</font> len; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>i<font face='Lucida Console'>)</font>
	<b>{</b>
	uint64 num1 <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint64<font color='#5555FF'>></font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>floor</font><font face='Lucida Console'>(</font>a[i<font color='#5555FF'>*</font><font color='#979000'>2</font>].<font color='#BB00BB'>real</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font color='#5555FF'>+</font><font color='#979000'>0.5</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;
	num1 <font color='#5555FF'>+</font><font color='#5555FF'>=</font> carry;
	carry <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>num1 <font color='#5555FF'>></font> <font color='#979000'>255</font><font face='Lucida Console'>)</font>
	<b>{</b>
	carry <font color='#5555FF'>=</font> num1 <font color='#5555FF'>></font><font color='#5555FF'>></font> <font color='#979000'>8</font>;
	num1 <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>num1<font color='#5555FF'>&</font><font color='#979000'>0xFF</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	uint64 num2 <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint64<font color='#5555FF'>></font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>floor</font><font face='Lucida Console'>(</font>a[i<font color='#5555FF'>*</font><font color='#979000'>2</font><font color='#5555FF'>+</font><font color='#979000'>1</font>].<font color='#BB00BB'>real</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font><font color='#5555FF'>+</font><font color='#979000'>0.5</font><font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;
	num2 <font color='#5555FF'>+</font><font color='#5555FF'>=</font> carry;
	carry <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>num2 <font color='#5555FF'>></font> <font color='#979000'>255</font><font face='Lucida Console'>)</font>
	<b>{</b>
	carry <font color='#5555FF'>=</font> num2 <font color='#5555FF'>></font><font color='#5555FF'>></font> <font color='#979000'>8</font>;
	num2 <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>num2<font color='#5555FF'>&</font><font color='#979000'>0xFF</font><font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// put the new number into its final place
	</font> num1 <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>num2<font color='#5555FF'><</font><font color='#5555FF'><</font><font color='#979000'>8</font><font face='Lucida Console'>)</font> <font color='#5555FF'>\|</font> num1;
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number[i] <font color='#5555FF'>=</font> <font color='#0000FF'>static_cast</font><font color='#5555FF'><</font>uint16<font color='#5555FF'>></font><font face='Lucida Console'>(</font>num1<font face='Lucida Console'>)</font>;

	<font color='#009900'>// keep track of the number of leading zeros
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>num1 <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>zeros;
	<font color='#0000FF'>else</font>
	zeros <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font><font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used<font face='Lucida Console'>)</font>;
	<b>}</b>

	<font color='#009900'>// adjust digits_used so that it reflects the actual number
	</font> <font color='#009900'>// of non-zero digits in our representation.
	</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font><font color='#5555FF'>=</font> zeros;

	<font color='#009900'>// if the result was zero then adjust the result accordingly
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// make result be zero
	</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font>result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#979000'>0</font>;
	<b>}</b>

	<font color='#009900'>// free all the temporary buffers
	</font> <font color='#0000FF'>delete</font> [] a;
	<font color='#0000FF'>delete</font> [] b;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='shift_left'></a>shift_left</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	data_record<font color='#5555FF'>*</font> result,
	uint32 shift_amount
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	uint32 offset <font color='#5555FF'>=</font> shift_amount<font color='#5555FF'>/</font><font color='#979000'>16</font>;
	shift_amount <font color='#5555FF'>&</font><font color='#5555FF'>=</font> <font color='#979000'>0xf</font>; <font color='#009900'>// same as shift_amount %= 16;
	</font>
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> offset; <font color='#009900'>// result
	</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> s <font color='#5555FF'>=</font> end <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used; <font color='#009900'>// source
	</font> <font color='#0000FF'>const</font> uint32 temp <font color='#5555FF'>=</font> <font color='#979000'>16</font> <font color='#5555FF'>-</font> shift_amount;

	<font color='#5555FF'></font>r <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font color='#5555FF'></font><font face='Lucida Console'>(</font><font color='#5555FF'>-</font><font color='#5555FF'>-</font>s<font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>></font> temp<font face='Lucida Console'>)</font>;
	<font color='#009900'>// set the number of digits used in the result
	</font> <font color='#009900'>// if the upper bits from *s were zero then don't count this first word
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> offset;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> offset <font color='#5555FF'>+</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;

	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>s <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>r <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font face='Lucida Console'>(</font><font color='#5555FF'></font>s <font color='#5555FF'><</font><font color='#5555FF'><</font> shift_amount<font face='Lucida Console'>)</font> <font color='#5555FF'>\|</font> <font face='Lucida Console'>(</font> <font color='#5555FF'>*</font><font face='Lucida Console'>(</font>s<font color='#5555FF'>-</font><font color='#979000'>1</font><font face='Lucida Console'>)</font> <font color='#5555FF'>></font><font color='#5555FF'>></font> temp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>s;
	<b>}</b>
	<font color='#5555FF'></font>r <font color='#5555FF'>=</font> <font color='#5555FF'></font>s <font color='#5555FF'><</font><font color='#5555FF'><</font> shift_amount;

	<font color='#009900'>// now zero the rest of the result
	</font> end <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>r <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<font color='#5555FF'>*</font><font face='Lucida Console'>(</font><font color='#5555FF'>-</font><font color='#5555FF'>-</font>r<font face='Lucida Console'>)</font> <font color='#5555FF'>=</font> <font color='#979000'>0</font>;

	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='shift_right'></a>shift_right</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> data,
	data_record<font color='#5555FF'>*</font> result
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>

	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> result<font color='#5555FF'>-</font><font color='#5555FF'>></font>number; <font color='#009900'>// result
	</font> uint16<font color='#5555FF'>*</font> s <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>number; <font color='#009900'>// source
	</font> uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> s <font color='#5555FF'>+</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;

	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>s <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>r <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font><font color='#5555FF'></font>s <font color='#5555FF'>></font><font color='#5555FF'>></font> <font color='#979000'>1</font><font face='Lucida Console'>)</font> <font color='#5555FF'>\|</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font><font face='Lucida Console'>(</font>s<font color='#5555FF'>+</font><font color='#979000'>1</font><font face='Lucida Console'>)</font> <font color='#5555FF'><</font><font color='#5555FF'><</font> <font color='#979000'>15</font><font face='Lucida Console'>)</font>;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<b>}</b>
	<font color='#5555FF'></font>r <font color='#5555FF'>=</font> <font color='#5555FF'></font>s <font color='#5555FF'>></font><font color='#5555FF'>></font> <font color='#979000'>1</font>;


	<font color='#009900'>// calculate the new number for digits_used
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>r <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>else</font>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	result<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> data<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>


	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> bigint_kernel_2::
	<b><a name='is_less_than'></a>is_less_than</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	uint32 lhs_digits_used <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	uint32 rhs_digits_used <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;

	<font color='#009900'>// if lhs is definitely less than rhs
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>lhs_digits_used <font color='#5555FF'><</font> rhs_digits_used <font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#979000'>true</font>;
	<font color='#009900'>// if lhs is definitely greater than rhs
	</font> <font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>lhs_digits_used <font color='#5555FF'>></font> rhs_digits_used<font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#979000'>false</font>;
	<font color='#0000FF'>else</font>
	<b>{</b>
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> l <font color='#5555FF'>=</font> end <font color='#5555FF'>+</font> lhs_digits_used;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number <font color='#5555FF'>+</font> rhs_digits_used;

	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>l <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>l;
	<font color='#5555FF'>-</font><font color='#5555FF'>-</font>r;
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'></font>l <font color='#5555FF'><</font> <font color='#5555FF'></font>r<font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#979000'>true</font>;
	<font color='#0000FF'>else</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'></font>l <font color='#5555FF'>></font> <font color='#5555FF'></font>r<font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#979000'>false</font>;
	<b>}</b>

	<font color='#009900'>// at this point we know that they are equal
	</font> <font color='#0000FF'>return</font> <font color='#979000'>false</font>;
	<b>}</b>

	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>bool</u></font> bigint_kernel_2::
	<b><a name='is_equal_to'></a>is_equal_to</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> lhs,
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> rhs
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#009900'>// if lhs and rhs are definitely not equal
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>!</font><font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>return</font> <font color='#979000'>false</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	uint16<font color='#5555FF'>*</font> l <font color='#5555FF'>=</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> r <font color='#5555FF'>=</font> rhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> l <font color='#5555FF'>+</font> lhs<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;

	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>l <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'></font>l <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#5555FF'></font>r<font face='Lucida Console'>)</font>
	<font color='#0000FF'>return</font> <font color='#979000'>false</font>;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>l;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>r;
	<b>}</b>

	<font color='#009900'>// at this point we know that they are equal
	</font> <font color='#0000FF'>return</font> <font color='#979000'>true</font>;
	<b>}</b>

	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='increment'></a>increment</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> source,
	data_record<font color='#5555FF'>*</font> dest
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	uint16<font color='#5555FF'>*</font> s <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> d <font color='#5555FF'>=</font> dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> s <font color='#5555FF'>+</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#979000'>true</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>d <font color='#5555FF'>=</font> <font color='#5555FF'></font>s <font color='#5555FF'>+</font> <font color='#979000'>1</font>;

	<font color='#009900'>// if there was no carry then break out of the loop
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>d <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font><font face='Lucida Console'>)</font>
	<b>{</b>
	dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;

	<font color='#009900'>// copy the rest of the digits over to d
	</font> <font color='#5555FF'>+</font><font color='#5555FF'>+</font>d; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>s <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>d <font color='#5555FF'>=</font> <font color='#5555FF'></font>s;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<b>}</b>

	<font color='#0000FF'>break</font>;
	<b>}</b>


	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;

	<font color='#009900'>// if we have hit the end of s and there was a carry up to this point
	</font> <font color='#009900'>// then just make the next digit 1 and add one to the digits used
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>s <font color='#5555FF'>=</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>+</font> <font color='#979000'>1</font>;
	<font color='#5555FF'>*</font>d <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>break</font>;
	<b>}</b>

	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='decrement'></a>decrement</b> <font face='Lucida Console'>(</font>
	<font color='#0000FF'>const</font> data_record<font color='#5555FF'>*</font> source,
	data_record<font color='#5555FF'>*</font> dest
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	uint16<font color='#5555FF'>*</font> s <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> d <font color='#5555FF'>=</font> dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>number;
	uint16<font color='#5555FF'>*</font> end <font color='#5555FF'>=</font> s <font color='#5555FF'>+</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font><font color='#979000'>true</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>d <font color='#5555FF'>=</font> <font color='#5555FF'></font>s <font color='#5555FF'>-</font> <font color='#979000'>1</font>;

	<font color='#009900'>// if there was no carry then break out of the loop
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>d <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0xFFFF</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// if we lost a digit in the subtraction
	</font> <font color='#0000FF'>if</font> <font face='Lucida Console'>(</font><font color='#5555FF'>*</font>d <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>0</font> <font color='#5555FF'>&</font><font color='#5555FF'>&</font> s<font color='#5555FF'>+</font><font color='#979000'>1</font> <font color='#5555FF'>=</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>if</font> <font face='Lucida Console'>(</font>source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>else</font>
	dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>-</font> <font color='#979000'>1</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	dest<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used <font color='#5555FF'>=</font> source<font color='#5555FF'>-</font><font color='#5555FF'>></font>digits_used;
	<b>}</b>
	<font color='#0000FF'>break</font>;
	<b>}</b>
	<font color='#0000FF'>else</font>
	<b>{</b>
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<b>}</b>

	<b>}</b>

	<font color='#009900'>// copy the rest of the digits over to d
	</font> <font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<font color='#0000FF'>while</font> <font face='Lucida Console'>(</font>s <font color='#5555FF'>!</font><font color='#5555FF'>=</font> end<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#5555FF'></font>d <font color='#5555FF'>=</font> <font color='#5555FF'></font>s;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>d;
	<font color='#5555FF'>+</font><font color='#5555FF'>+</font>s;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='fft'></a>fft</b> <font face='Lucida Console'>(</font>
	ct<font color='#5555FF'>*</font> data,
	<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> len
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#0000FF'>const</font> t pi2 <font color='#5555FF'>=</font> <font color='#5555FF'>-</font><font color='#979000'>2.0</font><font color='#5555FF'>*</font><font color='#979000'>3.1415926535897932384626433832795028841971693993751</font>;

	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> half <font color='#5555FF'>=</font> len<font color='#5555FF'>/</font><font color='#979000'>2</font>;

	std::vector<font color='#5555FF'><</font>ct<font color='#5555FF'>></font> twiddle_factors;
	twiddle_factors.<font color='#BB00BB'>resize</font><font face='Lucida Console'>(</font>half<font face='Lucida Console'>)</font>;

	<font color='#009900'>// compute the complex root of unity w
	</font> <font color='#0000FF'>const</font> t temp <font color='#5555FF'>=</font> pi2<font color='#5555FF'>/</font>len;
	ct w <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>cos</font><font face='Lucida Console'>(</font>temp<font face='Lucida Console'>)</font>,std::<font color='#BB00BB'>sin</font><font face='Lucida Console'>(</font>temp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;

	ct w_pow <font color='#5555FF'>=</font> <font color='#979000'>1</font>;

	<font color='#009900'>// compute the twiddle factors
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>std::vector<font color='#5555FF'><</font>ct<font color='#5555FF'>></font>::size_type j <font color='#5555FF'>=</font> <font color='#979000'>0</font>; j <font color='#5555FF'><</font> twiddle_factors.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>j<font face='Lucida Console'>)</font>
	<b>{</b>
	twiddle_factors[j] <font color='#5555FF'>=</font> w_pow;
	w_pow <font color='#5555FF'>*</font><font color='#5555FF'>=</font> w;
	<b>}</b>

	ct a, b;

	<font color='#009900'>// now compute the decimation in frequency. This first
	</font> <font color='#009900'>// outer loop loops log2(len) number of times
	</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> skip <font color='#5555FF'>=</font> <font color='#979000'>1</font>;
	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> step <font color='#5555FF'>=</font> half; step <font color='#5555FF'>!</font><font color='#5555FF'>=</font> <font color='#979000'>0</font>; step <font color='#5555FF'>></font><font color='#5555FF'>></font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// do blocks of butterflies in this loop
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> j <font color='#5555FF'>=</font> <font color='#979000'>0</font>; j <font color='#5555FF'><</font> len; j <font color='#5555FF'>+</font><font color='#5555FF'>=</font> step<font color='#5555FF'>*</font><font color='#979000'>2</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// do step butterflies
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> k <font color='#5555FF'>=</font> <font color='#979000'>0</font>; k <font color='#5555FF'><</font> step; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>k<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> a_idx <font color='#5555FF'>=</font> j<font color='#5555FF'>+</font>k;
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> b_idx <font color='#5555FF'>=</font> j<font color='#5555FF'>+</font>k<font color='#5555FF'>+</font>step;
	a <font color='#5555FF'>=</font> data[a_idx] <font color='#5555FF'>+</font> data[b_idx];
	b <font color='#5555FF'>=</font> <font face='Lucida Console'>(</font>data[a_idx] <font color='#5555FF'>-</font> data[b_idx]<font face='Lucida Console'>)</font><font color='#5555FF'></font>twiddle_factors[k<font color='#5555FF'></font>skip];
	data[a_idx] <font color='#5555FF'>=</font> a;
	data[b_idx] <font color='#5555FF'>=</font> b;
	<b>}</b>
	<b>}</b>
	skip <font color='#5555FF'>*</font><font color='#5555FF'>=</font> <font color='#979000'>2</font>;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<font color='#0000FF'><u>void</u></font> bigint_kernel_2::
	<b><a name='ifft'></a>ifft</b><font face='Lucida Console'>(</font>
	ct<font color='#5555FF'>*</font> data,
	<font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> len
	<font face='Lucida Console'>)</font> <font color='#0000FF'>const</font>
	<b>{</b>
	<font color='#0000FF'>const</font> t pi2 <font color='#5555FF'>=</font> <font color='#979000'>2.0</font><font color='#5555FF'>*</font><font color='#979000'>3.1415926535897932384626433832795028841971693993751</font>;

	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> half <font color='#5555FF'>=</font> len<font color='#5555FF'>/</font><font color='#979000'>2</font>;

	std::vector<font color='#5555FF'><</font>ct<font color='#5555FF'>></font> twiddle_factors;
	twiddle_factors.<font color='#BB00BB'>resize</font><font face='Lucida Console'>(</font>half<font face='Lucida Console'>)</font>;

	<font color='#009900'>// compute the complex root of unity w
	</font> <font color='#0000FF'>const</font> t temp <font color='#5555FF'>=</font> pi2<font color='#5555FF'>/</font>len;
	ct w <font color='#5555FF'>=</font> <font color='#BB00BB'>ct</font><font face='Lucida Console'>(</font>std::<font color='#BB00BB'>cos</font><font face='Lucida Console'>(</font>temp<font face='Lucida Console'>)</font>,std::<font color='#BB00BB'>sin</font><font face='Lucida Console'>(</font>temp<font face='Lucida Console'>)</font><font face='Lucida Console'>)</font>;

	ct w_pow <font color='#5555FF'>=</font> <font color='#979000'>1</font>;

	<font color='#009900'>// compute the twiddle factors
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font>std::vector<font color='#5555FF'><</font>ct<font color='#5555FF'>></font>::size_type j <font color='#5555FF'>=</font> <font color='#979000'>0</font>; j <font color='#5555FF'><</font> twiddle_factors.<font color='#BB00BB'>size</font><font face='Lucida Console'>(</font><font face='Lucida Console'>)</font>; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>j<font face='Lucida Console'>)</font>
	<b>{</b>
	twiddle_factors[j] <font color='#5555FF'>=</font> w_pow;
	w_pow <font color='#5555FF'>*</font><font color='#5555FF'>=</font> w;
	<b>}</b>

	ct a, b;

	<font color='#009900'>// now compute the inverse decimation in frequency. This first
	</font> <font color='#009900'>// outer loop loops log2(len) number of times
	</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> skip <font color='#5555FF'>=</font> half;
	<font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> step <font color='#5555FF'>=</font> <font color='#979000'>1</font>; step <font color='#5555FF'><</font><font color='#5555FF'>=</font> half; step <font color='#5555FF'><</font><font color='#5555FF'><</font><font color='#5555FF'>=</font> <font color='#979000'>1</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// do blocks of butterflies in this loop
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> j <font color='#5555FF'>=</font> <font color='#979000'>0</font>; j <font color='#5555FF'><</font> len; j <font color='#5555FF'>+</font><font color='#5555FF'>=</font> step<font color='#5555FF'>*</font><font color='#979000'>2</font><font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#009900'>// do step butterflies
	</font> <font color='#0000FF'>for</font> <font face='Lucida Console'>(</font><font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> k <font color='#5555FF'>=</font> <font color='#979000'>0</font>; k <font color='#5555FF'><</font> step; <font color='#5555FF'>+</font><font color='#5555FF'>+</font>k<font face='Lucida Console'>)</font>
	<b>{</b>
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> a_idx <font color='#5555FF'>=</font> j<font color='#5555FF'>+</font>k;
	<font color='#0000FF'>const</font> <font color='#0000FF'><u>unsigned</u></font> <font color='#0000FF'><u>long</u></font> b_idx <font color='#5555FF'>=</font> j<font color='#5555FF'>+</font>k<font color='#5555FF'>+</font>step;
	data[b_idx] <font color='#5555FF'></font><font color='#5555FF'>=</font> twiddle_factors[k<font color='#5555FF'></font>skip];
	a <font color='#5555FF'>=</font> data[a_idx] <font color='#5555FF'>+</font> data[b_idx];
	b <font color='#5555FF'>=</font> data[a_idx] <font color='#5555FF'>-</font> data[b_idx];
	data[a_idx] <font color='#5555FF'>=</font> a;
	data[b_idx] <font color='#5555FF'>=</font> b;
	<b>}</b>
	<b>}</b>
	skip <font color='#5555FF'>/</font><font color='#5555FF'>=</font> <font color='#979000'>2</font>;
	<b>}</b>
	<b>}</b>

	<font color='#009900'>// ----------------------------------------------------------------------------------------
	</font>
	<b>}</b>
	<font color='#0000FF'>#endif</font> <font color='#009900'>// DLIB_BIGINT_KERNEL_2_CPp_
	</font>

	</pre></body></html>