/*
 * This file is a part of TTMath Bignum Library
 * and is distributed under the (new) BSD licence.
 * Author: Tomasz Sowa <t.sowa@slimaczek.pl>
 */

/* 
 * Copyright (c) 2006-2009, Tomasz Sowa
 * All rights reserved.
 * 
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 * 
 *  * Redistributions of source code must retain the above copyright notice,
 *    this list of conditions and the following disclaimer.
 *    
 *  * Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *    
 *  * Neither the name Tomasz Sowa nor the names of contributors to this
 *    project may be used to endorse or promote products derived
 *    from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
 * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
 * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
 * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
 * THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef headerfilettmathbig
#define headerfilettmathbig

/*!
	\file ttmathbig.h
    \brief A Class for representing floating point numbers
*/

#include "ttmathint.h"

#include <iostream>

namespace ttmath
{


/*!
	\brief Big implements the floating point numbers
*/
template <uint exp,uint man>
class Big
{

/*
	value = mantissa * 2^exponent	

	exponent - an integer value with a sign
	mantissa - an integer value without a sing

	mantissa must be pushed into the left side that is the highest bit from 
	mantissa must be one (of course if there's another value than zero) -- this job
	(pushing bits into the left side) making Standardizing() method

	for example:
	if we want to store value one (1) into our Big object we must:
		set mantissa to 1
		set exponent to 0
		set info to 0
		and call method Standardizing()
*/


public:

Int<exp>  exponent;
UInt<man> mantissa;
unsigned char info;


/*!
	the number of a bit from 'info' which means that a value is with a sign
	(when the bit is set)
*/
#define TTMATH_BIG_SIGN 128


/*!
	Not a number
	if this bit is set that there is no a valid number
*/
#define TTMATH_BIG_NAN  64




	/*!
		this method sets NaN if there was a carry (and returns 1 in such a case)

		c can be 0, 1 or other value different from zero
	*/
	uint CheckCarry(uint c)
	{
		if( c != 0 )
		{
			SetNan();
			return 1;
		}

	return 0;
	}

public:


	/*!
		this method moves all bits from mantissa into its left side
		(suitably changes the exponent) or if the mantissa is zero
		it sets the exponent to zero as well (and clears the sign bit)

		it can return a carry
		the carry will be when we don't have enough space in the exponent

		you don't have to use this method if you don't change the mantissa
		and exponent directly
	*/
	uint Standardizing()
	{
		if( mantissa.IsTheHighestBitSet() )
			return 0;

		if( CorrectZero() )
			return 0;

		uint comp = mantissa.CompensationToLeft();
		uint c    = exponent.Sub( comp );

	return CheckCarry(c);
	}


private:

	/*!
		if the mantissa is equal zero this method sets exponent to zero and
		info without the sign

		it returns true if there was the correction
	*/
	bool CorrectZero()
	{
		if( mantissa.IsZero() )
		{
			Abs();
			exponent.SetZero();

		return true;
		}

	return false;
	}




public:


	/*!
		this method sets zero
	*/
	void SetZero()
	{
		info = 0;
		exponent.SetZero();
		mantissa.SetZero();

		/*
			we don't have to compensate zero
		*/
	}

	
	/*!
		this method sets one
	*/
	void SetOne()
	{
		FromUInt(1);
	}


	/*!
		this method sets value 0.5
	*/
	void Set05()
	{
		FromUInt(1);
		exponent.SubOne();
	}


	/*!
		this method sets NaN flag (Not a Number)
		when this flag is set that means there is no a valid number
	*/
	void SetNan()
	{
		info |= TTMATH_BIG_NAN;	
	}


private:

	/*!
		this method sets the mantissa of the value of pi
	*/
	void SetMantissaPi()
	{
	// this is a static table which represents the value of Pi (mantissa of it)
	// (first is the highest word)
	// we must define this table as 'unsigned int' because 
	// both on 32bit and 64bit platforms this table is 32bit
	static const unsigned int temp_table[] = {
		0xc90fdaa2, 0x2168c234, 0xc4c6628b, 0x80dc1cd1, 0x29024e08, 0x8a67cc74, 0x020bbea6, 0x3b139b22, 
		0x514a0879, 0x8e3404dd, 0xef9519b3, 0xcd3a431b, 0x302b0a6d, 0xf25f1437, 0x4fe1356d, 0x6d51c245, 
		0xe485b576, 0x625e7ec6, 0xf44c42e9, 0xa637ed6b, 0x0bff5cb6, 0xf406b7ed, 0xee386bfb, 0x5a899fa5, 
		0xae9f2411, 0x7c4b1fe6, 0x49286651, 0xece45b3d, 0xc2007cb8, 0xa163bf05, 0x98da4836, 0x1c55d39a, 
		0x69163fa8, 0xfd24cf5f, 0x83655d23, 0xdca3ad96, 0x1c62f356, 0x208552bb, 0x9ed52907, 0x7096966d, 
		0x670c354e, 0x4abc9804, 0xf1746c08, 0xca18217c, 0x32905e46, 0x2e36ce3b, 0xe39e772c, 0x180e8603, 
		0x9b2783a2, 0xec07a28f, 0xb5c55df0, 0x6f4c52c9, 0xde2bcbf6, 0x95581718, 0x3995497c, 0xea956ae5, 
		0x15d22618, 0x98fa0510, 0x15728e5a, 0x8aaac42d, 0xad33170d, 0x04507a33, 0xa85521ab, 0xdf1cba64, 
		0xecfb8504, 0x58dbef0a, 0x8aea7157, 0x5d060c7d, 0xb3970f85, 0xa6e1e4c7, 0xabf5ae8c, 0xdb0933d7, 
		0x1e8c94e0, 0x4a25619d, 0xcee3d226, 0x1ad2ee6b, 0xf12ffa06, 0xd98a0864, 0xd8760273, 0x3ec86a64, 
		0x521f2b18, 0x177b200c, 0xbbe11757, 0x7a615d6c, 0x770988c0, 0xbad946e2, 0x08e24fa0, 0x74e5ab31, 
		0x43db5bfc, 0xe0fd108e, 0x4b82d120, 0xa9210801, 0x1a723c12, 0xa787e6d7, 0x88719a10, 0xbdba5b26, 
		0x99c32718, 0x6af4e23c, 0x1a946834, 0xb6150bda, 0x2583e9ca, 0x2ad44ce8, 0xdbbbc2db, 0x04de8ef9, 
		0x2e8efc14, 0x1fbecaa6, 0x287c5947, 0x4e6bc05d, 0x99b2964f, 0xa090c3a2, 0x233ba186, 0x515be7ed, 
		0x1f612970, 0xcee2d7af, 0xb81bdd76, 0x2170481c, 0xd0069127, 0xd5b05aa9, 0x93b4ea98, 0x8d8fddc1, 
		0x86ffb7dc, 0x90a6c08f, 0x4df435c9, 0x34028492, 0x36c3fab4, 0xd27c7026, 0xc1d4dcb2, 0x602646de, 
		0xc9751e76, 0x3dba37bd, 0xf8ff9406, 0xad9e530e, 0xe5db382f, 0x413001ae, 0xb06a53ed, 0x9027d831, 
		0x179727b0, 0x865a8918, 0xda3edbeb, 0xcf9b14ed, 0x44ce6cba, 0xced4bb1b, 0xdb7f1447, 0xe6cc254b, 
		0x33205151, 0x2bd7af42, 0x6fb8f401, 0x378cd2bf, 0x5983ca01, 0xc64b92ec, 0xf032ea15, 0xd1721d03, 
		0xf482d7ce, 0x6e74fef6, 0xd55e702f, 0x46980c82, 0xb5a84031, 0x900b1c9e, 0x59e7c97f, 0xbec7e8f3, 
		0x23a97a7e, 0x36cc88be, 0x0f1d45b7, 0xff585ac5, 0x4bd407b2, 0x2b4154aa, 0xcc8f6d7e, 0xbf48e1d8, 
		0x14cc5ed2, 0x0f8037e0, 0xa79715ee, 0xf29be328, 0x06a1d58b, 0xb7c5da76, 0xf550aa3d, 0x8a1fbff0, 
		0xeb19ccb1, 0xa313d55c, 0xda56c9ec, 0x2ef29632, 0x387fe8d7, 0x6e3c0468, 0x043e8f66, 0x3f4860ee, 
		0x12bf2d5b, 0x0b7474d6, 0xe694f91e, 0x6dbe1159, 0x74a3926f, 0x12fee5e4, 0x38777cb6, 0xa932df8c, 
		0xd8bec4d0, 0x73b931ba, 0x3bc832b6, 0x8d9dd300, 0x741fa7bf, 0x8afc47ed, 0x2576f693, 0x6ba42466, 
		0x3aab639c, 0x5ae4f568, 0x3423b474, 0x2bf1c978, 0x238f16cb, 0xe39d652d, 0xe3fdb8be, 0xfc848ad9, 
		0x22222e04, 0xa4037c07, 0x13eb57a8, 0x1a23f0c7, 0x3473fc64, 0x6cea306b, 0x4bcbc886, 0x2f8385dd, 
		0xfa9d4b7f, 0xa2c087e8, 0x79683303, 0xed5bdd3a, 0x062b3cf5, 0xb3a278a6, 0x6d2a13f8, 0x3f44f82d, 
		0xdf310ee0, 0x74ab6a36, 0x4597e899, 0xa0255dc1, 0x64f31cc5, 0x0846851d, 0xf9ab4819, 0x5ded7ea1, 
		0xb1d510bd, 0x7ee74d73, 0xfaf36bc3, 0x1ecfa268, 0x359046f4, 0xeb879f92, 0x4009438b, 0x481c6cd7, 
		0x889a002e, 0xd5ee382b, 0xc9190da6, 0xfc026e47, 0x9558e447, 0x5677e9aa, 0x9e3050e2, 0x765694df, 
		0xc81f56e8, 0x80b96e71, 0x60c980dd, 0x98a573ea, 0x4472065a, 0x139cd290, 0x6cd1cb72, 0x9ec52a53 // last one was: 0x9ec52a52
		//0x86d44014, ...
		// (the last word 0x9ec52a52 was rounded up because the next one is 0x86d44014 -- first bit is one 0x8..)
		// 256 32bit words for the mantissa -- about 2464 valid decimal digits
		};
		// the value of PI is comming from the website http://zenwerx.com/pi.php
		// 3101 digits were taken from this website
		//  (later the digits were compared with:
		//   http://www.eveandersson.com/pi/digits/1000000 and http://www.geom.uiuc.edu/~huberty/math5337/groupe/digits.html )
		// and they were set into Big<1,400> type (using operator=(const char*) on a 32bit platform)
		// and then the first 256 words were taken into this table
		// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
		// and on 64bit platform value 128 (256/2=128))
	
		mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
	}

public:


	/*!
		this method sets the value of pi
	*/
	void SetPi()
	{
		SetMantissaPi();
		info = 0;
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 2;
	}


	/*!
		this method sets the value of 0.5 * pi
	*/
	void Set05Pi()
	{
		SetMantissaPi();
		info = 0;
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 1;
	}


	/*!
		this method sets the value of 2 * pi
	*/
	void Set2Pi()
	{
		SetMantissaPi();
		info = 0;
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 3;
	}


	/*!
		this method sets the value of e
		(the base of the natural logarithm)
	*/
	void SetE()
	{
	static const unsigned int temp_table[] = {
		0xadf85458, 0xa2bb4a9a, 0xafdc5620, 0x273d3cf1, 0xd8b9c583, 0xce2d3695, 0xa9e13641, 0x146433fb, 
		0xcc939dce, 0x249b3ef9, 0x7d2fe363, 0x630c75d8, 0xf681b202, 0xaec4617a, 0xd3df1ed5, 0xd5fd6561, 
		0x2433f51f, 0x5f066ed0, 0x85636555, 0x3ded1af3, 0xb557135e, 0x7f57c935, 0x984f0c70, 0xe0e68b77, 
		0xe2a689da, 0xf3efe872, 0x1df158a1, 0x36ade735, 0x30acca4f, 0x483a797a, 0xbc0ab182, 0xb324fb61, 
		0xd108a94b, 0xb2c8e3fb, 0xb96adab7, 0x60d7f468, 0x1d4f42a3, 0xde394df4, 0xae56ede7, 0x6372bb19, 
		0x0b07a7c8, 0xee0a6d70, 0x9e02fce1, 0xcdf7e2ec, 0xc03404cd, 0x28342f61, 0x9172fe9c, 0xe98583ff, 
		0x8e4f1232, 0xeef28183, 0xc3fe3b1b, 0x4c6fad73, 0x3bb5fcbc, 0x2ec22005, 0xc58ef183, 0x7d1683b2, 
		0xc6f34a26, 0xc1b2effa, 0x886b4238, 0x611fcfdc, 0xde355b3b, 0x6519035b, 0xbc34f4de, 0xf99c0238, 
		0x61b46fc9, 0xd6e6c907, 0x7ad91d26, 0x91f7f7ee, 0x598cb0fa, 0xc186d91c, 0xaefe1309, 0x85139270, 
		0xb4130c93, 0xbc437944, 0xf4fd4452, 0xe2d74dd3, 0x64f2e21e, 0x71f54bff, 0x5cae82ab, 0x9c9df69e, 
		0xe86d2bc5, 0x22363a0d, 0xabc52197, 0x9b0deada, 0x1dbf9a42, 0xd5c4484e, 0x0abcd06b, 0xfa53ddef, 
		0x3c1b20ee, 0x3fd59d7c, 0x25e41d2b, 0x669e1ef1, 0x6e6f52c3, 0x164df4fb, 0x7930e9e4, 0xe58857b6, 
		0xac7d5f42, 0xd69f6d18, 0x7763cf1d, 0x55034004, 0x87f55ba5, 0x7e31cc7a, 0x7135c886, 0xefb4318a, 
		0xed6a1e01, 0x2d9e6832, 0xa907600a, 0x918130c4, 0x6dc778f9, 0x71ad0038, 0x092999a3, 0x33cb8b7a, 
		0x1a1db93d, 0x7140003c, 0x2a4ecea9, 0xf98d0acc, 0x0a8291cd, 0xcec97dcf, 0x8ec9b55a, 0x7f88a46b, 
		0x4db5a851, 0xf44182e1, 0xc68a007e, 0x5e0dd902, 0x0bfd64b6, 0x45036c7a, 0x4e677d2c, 0x38532a3a, 
		0x23ba4442, 0xcaf53ea6, 0x3bb45432, 0x9b7624c8, 0x917bdd64, 0xb1c0fd4c, 0xb38e8c33, 0x4c701c3a, 
		0xcdad0657, 0xfccfec71, 0x9b1f5c3e, 0x4e46041f, 0x388147fb, 0x4cfdb477, 0xa52471f7, 0xa9a96910, 
		0xb855322e, 0xdb6340d8, 0xa00ef092, 0x350511e3, 0x0abec1ff, 0xf9e3a26e, 0x7fb29f8c, 0x183023c3, 
		0x587e38da, 0x0077d9b4, 0x763e4e4b, 0x94b2bbc1, 0x94c6651e, 0x77caf992, 0xeeaac023, 0x2a281bf6, 
		0xb3a739c1, 0x22611682, 0x0ae8db58, 0x47a67cbe, 0xf9c9091b, 0x462d538c, 0xd72b0374, 0x6ae77f5e, 
		0x62292c31, 0x1562a846, 0x505dc82d, 0xb854338a, 0xe49f5235, 0xc95b9117, 0x8ccf2dd5, 0xcacef403, 
		0xec9d1810, 0xc6272b04, 0x5b3b71f9, 0xdc6b80d6, 0x3fdd4a8e, 0x9adb1e69, 0x62a69526, 0xd43161c1, 
		0xa41d570d, 0x7938dad4, 0xa40e329c, 0xcff46aaa, 0x36ad004c, 0xf600c838, 0x1e425a31, 0xd951ae64, 
		0xfdb23fce, 0xc9509d43, 0x687feb69, 0xedd1cc5e, 0x0b8cc3bd, 0xf64b10ef, 0x86b63142, 0xa3ab8829, 
		0x555b2f74, 0x7c932665, 0xcb2c0f1c, 0xc01bd702, 0x29388839, 0xd2af05e4, 0x54504ac7, 0x8b758282, 
		0x2846c0ba, 0x35c35f5c, 0x59160cc0, 0x46fd8251, 0x541fc68c, 0x9c86b022, 0xbb709987, 0x6a460e74, 
		0x51a8a931, 0x09703fee, 0x1c217e6c, 0x3826e52c, 0x51aa691e, 0x0e423cfc, 0x99e9e316, 0x50c1217b, 
		0x624816cd, 0xad9a95f9, 0xd5b80194, 0x88d9c0a0, 0xa1fe3075, 0xa577e231, 0x83f81d4a, 0x3f2fa457, 
		0x1efc8ce0, 0xba8a4fe8, 0xb6855dfe, 0x72b0a66e, 0xded2fbab, 0xfbe58a30, 0xfafabe1c, 0x5d71a87e, 
		0x2f741ef8, 0xc1fe86fe, 0xa6bbfde5, 0x30677f0d, 0x97d11d49, 0xf7a8443d, 0x0822e506, 0xa9f4614e, 
		0x011e2a94, 0x838ff88c, 0xd68c8bb7, 0xc51eef6d, 0x49ea8ab4, 0xf2c3df5b, 0xb4e0735a, 0xb0d68749
		// 0x2fe26dd4, ...
		// 256 32bit words for the mantissa -- about 2464 valid decimal digits
		};

		// above value was calculated using Big<1,400> type on a 32bit platform
		// and then the first 256 words were taken,
		// the calculating was made by using ExpSurrounding0(1) method
		// which took 1420 iterations
		// (the result was compared with e taken from http://antwrp.gsfc.nasa.gov/htmltest/gifcity/e.2mil)
		// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
		// and on 64bit platform value 128 (256/2=128))

		mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 2;
		info = 0;
	}


	/*!
		this method sets the value of ln(2)
		the natural logarithm from 2
	*/
	void SetLn2()
	{
	static const unsigned int temp_table[] = {
		0xb17217f7, 0xd1cf79ab, 0xc9e3b398, 0x03f2f6af, 0x40f34326, 0x7298b62d, 0x8a0d175b, 0x8baafa2b, 
		0xe7b87620, 0x6debac98, 0x559552fb, 0x4afa1b10, 0xed2eae35, 0xc1382144, 0x27573b29, 0x1169b825, 
		0x3e96ca16, 0x224ae8c5, 0x1acbda11, 0x317c387e, 0xb9ea9bc3, 0xb136603b, 0x256fa0ec, 0x7657f74b, 
		0x72ce87b1, 0x9d6548ca, 0xf5dfa6bd, 0x38303248, 0x655fa187, 0x2f20e3a2, 0xda2d97c5, 0x0f3fd5c6, 
		0x07f4ca11, 0xfb5bfb90, 0x610d30f8, 0x8fe551a2, 0xee569d6d, 0xfc1efa15, 0x7d2e23de, 0x1400b396, 
		0x17460775, 0xdb8990e5, 0xc943e732, 0xb479cd33, 0xcccc4e65, 0x9393514c, 0x4c1a1e0b, 0xd1d6095d, 
		0x25669b33, 0x3564a337, 0x6a9c7f8a, 0x5e148e82, 0x074db601, 0x5cfe7aa3, 0x0c480a54, 0x17350d2c, 
		0x955d5179, 0xb1e17b9d, 0xae313cdb, 0x6c606cb1, 0x078f735d, 0x1b2db31b, 0x5f50b518, 0x5064c18b, 
		0x4d162db3, 0xb365853d, 0x7598a195, 0x1ae273ee, 0x5570b6c6, 0x8f969834, 0x96d4e6d3, 0x30af889b, 
		0x44a02554, 0x731cdc8e, 0xa17293d1, 0x228a4ef9, 0x8d6f5177, 0xfbcf0755, 0x268a5c1f, 0x9538b982, 
		0x61affd44, 0x6b1ca3cf, 0x5e9222b8, 0x8c66d3c5, 0x422183ed, 0xc9942109, 0x0bbb16fa, 0xf3d949f2, 
		0x36e02b20, 0xcee886b9, 0x05c128d5, 0x3d0bd2f9, 0x62136319, 0x6af50302, 0x0060e499, 0x08391a0c, 
		0x57339ba2, 0xbeba7d05, 0x2ac5b61c, 0xc4e9207c, 0xef2f0ce2, 0xd7373958, 0xd7622658, 0x901e646a, 
		0x95184460, 0xdc4e7487, 0x156e0c29, 0x2413d5e3, 0x61c1696d, 0xd24aaebd, 0x473826fd, 0xa0c238b9, 
		0x0ab111bb, 0xbd67c724, 0x972cd18b, 0xfbbd9d42, 0x6c472096, 0xe76115c0, 0x5f6f7ceb, 0xac9f45ae, 
		0xcecb72f1, 0x9c38339d, 0x8f682625, 0x0dea891e, 0xf07afff3, 0xa892374e, 0x175eb4af, 0xc8daadd8, 
		0x85db6ab0, 0x3a49bd0d, 0xc0b1b31d, 0x8a0e23fa, 0xc5e5767d, 0xf95884e0, 0x6425a415, 0x26fac51c, 
		0x3ea8449f, 0xe8f70edd, 0x062b1a63, 0xa6c4c60c, 0x52ab3316, 0x1e238438, 0x897a39ce, 0x78b63c9f, 
		0x364f5b8a, 0xef22ec2f, 0xee6e0850, 0xeca42d06, 0xfb0c75df, 0x5497e00c, 0x554b03d7, 0xd2874a00, 
		0x0ca8f58d, 0x94f0341c, 0xbe2ec921, 0x56c9f949, 0xdb4a9316, 0xf281501e, 0x53daec3f, 0x64f1b783, 
		0x154c6032, 0x0e2ff793, 0x33ce3573, 0xfacc5fdc, 0xf1178590, 0x3155bbd9, 0x0f023b22, 0x0224fcd8, 
		0x471bf4f4, 0x45f0a88a, 0x14f0cd97, 0x6ea354bb, 0x20cdb5cc, 0xb3db2392, 0x88d58655, 0x4e2a0e8a, 
		0x6fe51a8c, 0xfaa72ef2, 0xad8a43dc, 0x4212b210, 0xb779dfe4, 0x9d7307cc, 0x846532e4, 0xb9694eda, 
		0xd162af05, 0x3b1751f3, 0xa3d091f6, 0x56658154, 0x12b5e8c2, 0x02461069, 0xac14b958, 0x784934b8, 
		0xd6cce1da, 0xa5053701, 0x1aa4fb42, 0xb9a3def4, 0x1bda1f85, 0xef6fdbf2, 0xf2d89d2a, 0x4b183527, 
		0x8fd94057, 0x89f45681, 0x2b552879, 0xa6168695, 0xc12963b0, 0xff01eaab, 0x73e5b5c1, 0x585318e7, 
		0x624f14a5, 0x1a4a026b, 0x68082920, 0x57fd99b6, 0x6dc085a9, 0x8ac8d8ca, 0xf9eeeea9, 0x8a2400ca, 
		0xc95f260f, 0xd10036f9, 0xf91096ac, 0x3195220a, 0x1a356b2a, 0x73b7eaad, 0xaf6d6058, 0x71ef7afb, 
		0x80bc4234, 0x33562e94, 0xb12dfab4, 0x14451579, 0xdf59eae0, 0x51707062, 0x4012a829, 0x62c59cab, 
		0x347f8304, 0xd889659e, 0x5a9139db, 0x14efcc30, 0x852be3e8, 0xfc99f14d, 0x1d822dd6, 0xe2f76797, 
		0xe30219c8, 0xaa9ce884, 0x8a886eb3, 0xc87b7295, 0x988012e8, 0x314186ed, 0xbaf86856, 0xccd3c3b6, 
		0xee94e62f, 0x110a6783, 0xd2aae89c, 0xcc3b76fc, 0x435a0ce1, 0x34c2838f, 0xd571ec6c, 0x1366a993 // last one was: 0x1366a992
		//0xcbb9ac40, ...
		// (the last word 0x1366a992 was rounded up because the next one is 0xcbb9ac40 -- first bit is one 0xc..)
		// 256 32bit words for the mantissa -- about 2464 valid decimal digits
		};	

		// above value was calculated using Big<1,400> type on a 32bit platform
		// and then the first 256 words were taken,
		// the calculating was made by using LnSurrounding1(2) method
		// which took 4035 iterations
		// (the result was compared with ln(2) taken from http://ja0hxv.calico.jp/pai/estart.html)
		// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
		// and on 64bit platform value 128 (256/2=128))

		mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT);
		info = 0;
	}


	/*!
		this method sets the value of ln(10)
		the natural logarithm from 10

		I introduced this constant especially to make the conversion ToString()
		being faster. In fact the method ToString() is keeping values of logarithms
		it has calculated but it must calculate the logarithm at least once.
		If a program, which uses this library, is running for a long time this
		would be ok, but for programs which are running shorter, for example for
		CGI applications which only once are printing values, this would be much
		inconvenience. Then if we're printing with base (radix) 10 and the mantissa
		of our value is smaller than or equal to TTMATH_BUILTIN_VARIABLES_SIZE
		we don't calculate the logarithm but take it from this constant.
	*/
	void SetLn10()
	{
	static const unsigned int temp_table[] = {
		0x935d8ddd, 0xaaa8ac16, 0xea56d62b, 0x82d30a28, 0xe28fecf9, 0xda5df90e, 0x83c61e82, 0x01f02d72, 
		0x962f02d7, 0xb1a8105c, 0xcc70cbc0, 0x2c5f0d68, 0x2c622418, 0x410be2da, 0xfb8f7884, 0x02e516d6, 
		0x782cf8a2, 0x8a8c911e, 0x765aa6c3, 0xb0d831fb, 0xef66ceb0, 0x4ab3c6fa, 0x5161bb49, 0xd219c7bb, 
		0xca67b35b, 0x23605085, 0x8e93368d, 0x44789c4f, 0x5b08b057, 0xd5ede20f, 0x469ea58e, 0x9305e981, 
		0xe2478fca, 0xad3aee98, 0x9cd5b42e, 0x6a271619, 0xa47ecb26, 0x978c5d4f, 0xdb1d28ea, 0x57d4fdc0, 
		0xe40bf3cc, 0x1e14126a, 0x45765cde, 0x268339db, 0xf47fa96d, 0xeb271060, 0xaf88486e, 0xa9b7401e, 
		0x3dfd3c51, 0x748e6d6e, 0x3848c8d2, 0x5faf1bca, 0xe88047f1, 0x7b0d9b50, 0xa949eaaa, 0xdf69e8a5, 
		0xf77e3760, 0x4e943960, 0xe38a5700, 0xffde2db1, 0xad6bfbff, 0xd821ba0a, 0x4cb0466d, 0x61ba648e, 
		0xef99c8e5, 0xf6974f36, 0x3982a78c, 0xa45ddfc8, 0x09426178, 0x19127a6e, 0x3b70fcda, 0x2d732d47, 
		0xb5e4b1c8, 0xc0e5a10a, 0xaa6604a5, 0x324ec3dc, 0xbc64ea80, 0x6e198566, 0x1f1d366c, 0x20663834, 
		0x4d5e843f, 0x20642b97, 0x0a62d18e, 0x478f7bd5, 0x8fcd0832, 0x4a7b32a6, 0xdef85a05, 0xeb56323a, 
		0x421ef5e0, 0xb00410a0, 0xa0d9c260, 0x794a976f, 0xf6ff363d, 0xb00b6b33, 0xf42c58de, 0xf8a3c52d, 
		0xed69b13d, 0xc1a03730, 0xb6524dc1, 0x8c167e86, 0x99d6d20e, 0xa2defd2b, 0xd006f8b4, 0xbe145a2a, 
		0xdf3ccbb3, 0x189da49d, 0xbc1261c8, 0xb3e4daad, 0x6a36cecc, 0xb2d5ae5b, 0x89bf752f, 0xb5dfb353, 
		0xff3065c4, 0x0cfceec8, 0x1be5a9a9, 0x67fddc57, 0xc4b83301, 0x006bf062, 0x4b40ed7a, 0x56c6cdcd, 
		0xa2d6fe91, 0x388e9e3e, 0x48a93f5f, 0x5e3b6eb4, 0xb81c4a5b, 0x53d49ea6, 0x8e668aea, 0xba83c7f8, 
		0xfb5f06c3, 0x58ac8f70, 0xfa9d8c59, 0x8c574502, 0xbaf54c96, 0xc84911f0, 0x0482d095, 0x1a0af022, 
		0xabbab080, 0xec97efd3, 0x671e4e0e, 0x52f166b6, 0xcd5cd226, 0x0dc67795, 0x2e1e34a3, 0xf799677f, 
		0x2c1d48f1, 0x2944b6c5, 0x2ba1307e, 0x704d67f9, 0x1c1035e4, 0x4e927c63, 0x03cf12bf, 0xe2cd2e31, 
		0xf8ee4843, 0x344d51b0, 0xf37da42b, 0x9f0b0fd9, 0x134fb2d9, 0xf815e490, 0xd966283f, 0x23962766, 
		0xeceab1e4, 0xf3b5fc86, 0x468127e2, 0xb606d10d, 0x3a45f4b6, 0xb776102d, 0x2fdbb420, 0x80c8fa84, 
		0xd0ff9f45, 0xc58aef38, 0xdb2410fd, 0x1f1cebad, 0x733b2281, 0x52ca5f36, 0xddf29daa, 0x544334b8, 
		0xdeeaf659, 0x4e462713, 0x1ed485b4, 0x6a0822e1, 0x28db471c, 0xa53938a8, 0x44c3bef7, 0xf35215c8, 
		0xb382bc4e, 0x3e4c6f15, 0x6285f54c, 0x17ab408e, 0xccbf7f5e, 0xd16ab3f6, 0xced2846d, 0xf457e14f, 
		0xbb45d9c5, 0x646ad497, 0xac697494, 0x145de32e, 0x93907128, 0xd263d521, 0x79efb424, 0xd64651d6, 
		0xebc0c9f0, 0xbb583a44, 0xc6412c84, 0x85bb29a6, 0x4d31a2cd, 0x92954469, 0xa32b1abd, 0xf7f5202c, 
		0xa4aa6c93, 0x2e9b53cf, 0x385ab136, 0x2741f356, 0x5de9c065, 0x6009901c, 0x88abbdd8, 0x74efcf73, 
		0x3f761ad4, 0x35f3c083, 0xfd6b8ee0, 0x0bef11c7, 0xc552a89d, 0x58ce4a21, 0xd71e54f2, 0x4157f6c7, 
		0xd4622316, 0xe98956d7, 0x450027de, 0xcbd398d8, 0x4b98b36a, 0x0724c25c, 0xdb237760, 0xe9324b68, 
		0x7523e506, 0x8edad933, 0x92197f00, 0xb853a326, 0xb330c444, 0x65129296, 0x34bc0670, 0xe177806d, 
		0xe338dac4, 0x5537492a, 0xe19add83, 0xcf45000f, 0x5b423bce, 0x6497d209, 0xe30e18a1, 0x3cbf0687, 
		0x67973103, 0xd9485366, 0x81506bba, 0x2e93a9a4, 0x7dd59d3f, 0xf17cd746, 0x8c2075be, 0x552a4348 // last one was: 0x552a4347
		// 0xb4a638ef, ...
		//(the last word 0x552a4347 was rounded up because the next one is 0xb4a638ef -- first bit is one 0xb..)
		// 256 32bit words for the mantissa -- about 2464 valid digits (decimal)
		};	

		// above value was calculated using Big<1,400> type on a 32bit platform
		// and then the first 256 32bit words were taken,
		// the calculating was made by using LnSurrounding1(10) method
		// which took 22080 iterations
		// (the result was compared with ln(10) taken from http://ja0hxv.calico.jp/pai/estart.html)
		// (the formula used in LnSurrounding1(x) converges badly when
	    // the x is greater than one but in fact we can use it, only the
		// number of iterations will be greater)
		// (TTMATH_BUILTIN_VARIABLES_SIZE on 32bit platform should have the value 256,
		// and on 64bit platform value 128 (256/2=128))

		mantissa.SetFromTable(temp_table, sizeof(temp_table) / sizeof(int));
		exponent = -sint(man)*sint(TTMATH_BITS_PER_UINT) + 2;
		info = 0;
	}


	/*!
		this method sets the maximum value which can be held in this type
	*/
	void SetMax()
	{
		info = 0;
		mantissa.SetMax();
		exponent.SetMax();

		// we don't have to use 'Standardizing()' because the last bit from
		// the mantissa is set
	}


	/*!
		this method sets the minimum value which can be held in this type
	*/
	void SetMin()
	{
		info = 0;

		mantissa.SetMax();
		exponent.SetMax();
		SetSign();

		// we don't have to use 'Standardizing()' because the last bit from
		// the mantissa is set
	}


	/*!
		testing whether there is a value zero or not
	*/
	bool IsZero() const
	{
		/*
			we only have to test the mantissa
			also we don't check the NaN flag
		*/
		return mantissa.IsZero();
	}


	/*!
		this method returns true when there's the sign set
		also we don't check the NaN flag
	*/
	bool IsSign() const
	{
		return (info & TTMATH_BIG_SIGN) == TTMATH_BIG_SIGN;
	}


	/*!
		this method returns true when there is not a valid number
	*/
	bool IsNan() const
	{
		return (info & TTMATH_BIG_NAN) == TTMATH_BIG_NAN;
	}



	/*!
		this method clears the sign
		(there'll be an absolute value)

			e.g.
			-1 -> 1
			2  -> 2
	*/
	void Abs()
	{
		info &= ~TTMATH_BIG_SIGN;
	}


	/*!
		this method remains the 'sign' of the value
		e.g.  -2 = -1 
		       0 = 0
		      10 = 1
	*/
	void Sgn()
	{
		if( IsNan() )
			return;

		if( IsSign() )
		{
			SetOne();
			SetSign();
		}
		else
		if( IsZero() )
			SetZero();
		else
			SetOne();
	}



	/*!
		this method sets the sign

			e.g.
			-1 -> -1
			2  -> -2

		we do not check whether there is a zero or not, if you're using this method
		you must be sure that the value is (or will be afterwards) different from zero
	*/
	void SetSign()
	{
		info |= TTMATH_BIG_SIGN;
	}


	/*!
		this method changes the sign

			e.g.
			-1 -> 1
			2  -> -2
	*/
	void ChangeSign()
	{
		if( info & TTMATH_BIG_SIGN )
		{
			info &= ~TTMATH_BIG_SIGN;
			return;
		}

		if( IsZero() )
			return;

		info |= TTMATH_BIG_SIGN;
	}





	/*!
	*
	*	basic mathematic functions
	*
	*/


	/*!
		Addition this = this + ss2

		it returns carry if the sum is too big
	*/
	uint Add(Big<exp, man> ss2)
	{
	Int<exp> exp_offset( exponent );
	Int<exp> mantissa_size_in_bits( man * TTMATH_BITS_PER_UINT );

	uint c = 0;

		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		exp_offset.Sub( ss2.exponent );
		exp_offset.Abs();

		// (1) abs(this) will be >= abs(ss2)
		if( SmallerWithoutSignThan(ss2) )
		{
			Big<exp, man> temp(ss2);

			ss2   = *this;
			*this = temp;
		}
	

		if( exp_offset >= mantissa_size_in_bits )
		{
			// the second value is too small for taking into consideration in the sum
			return 0;
		}
		else
		if( exp_offset < mantissa_size_in_bits )
		{
			// (2) moving 'exp_offset' times
			ss2.mantissa.Rcr( exp_offset.ToInt(), 0 );
		}


		if( IsSign() == ss2.IsSign() )
		{
			// values have the same signs
			if( mantissa.Add(ss2.mantissa) )
			{
				mantissa.Rcr(1,1);
				c = exponent.AddOne();
			}
		}
		else
		{
			// values have different signs
			// there shouldn't be a carry here because
			// (1) (2) guarantee that the mantissa of this
			// is greater than or equal to the mantissa of the ss2
			uint c_temp = mantissa.Sub(ss2.mantissa);

			TTMATH_ASSERT( c_temp == 0 )
		}

		c += Standardizing();

	return CheckCarry(c);
	}


	/*!
		Subtraction this = this - ss2

		it returns carry if the result is too big
	*/
	uint Sub(Big<exp, man> ss2)
	{
		ss2.ChangeSign();

	return Add(ss2);
	}
		

	/*!
		bitwise AND

		this and ss2 must be >= 0
		return values:
			0 - ok
			1 - carry
			2 - this or ss2 was negative
	*/
	uint BitAnd(Big<exp, man> ss2)
	{
		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		if( IsSign() || ss2.IsSign() )
			return 2;

		Int<exp> exp_offset( exponent );
		Int<exp> mantissa_size_in_bits( man * TTMATH_BITS_PER_UINT );

		uint c = 0;

		exp_offset.Sub( ss2.exponent );
		exp_offset.Abs();

		// abs(this) will be >= abs(ss2)
		if( SmallerWithoutSignThan(ss2) )
		{
			Big<exp, man> temp(ss2);

			ss2   = *this;
			*this = temp;
		}

		if( exp_offset >= mantissa_size_in_bits )
		{
			// the second value is too small
			SetZero();
			return 0;
		}

		// exp_offset < mantissa_size_in_bits, moving 'exp_offset' times
		ss2.mantissa.Rcr( exp_offset.ToInt(), 0 );
		mantissa.BitAnd(ss2.mantissa);

		c += Standardizing();

	return CheckCarry(c);
	}


	/*!
		bitwise OR

		this and ss2 must be >= 0
		return values:
			0 - ok
			1 - carry
			2 - this or ss2 was negative
	*/
	uint BitOr(Big<exp, man> ss2)
	{
		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		if( IsSign() || ss2.IsSign() )
			return 2;
		
		Int<exp> exp_offset( exponent );
		Int<exp> mantissa_size_in_bits( man * TTMATH_BITS_PER_UINT );

		uint c = 0;

		exp_offset.Sub( ss2.exponent );
		exp_offset.Abs();

		// abs(this) will be >= abs(ss2)
		if( SmallerWithoutSignThan(ss2) )
		{
			Big<exp, man> temp(ss2);

			ss2   = *this;
			*this = temp;
		}

		if( exp_offset >= mantissa_size_in_bits )
			// the second value is too small
			return 0;

		// exp_offset < mantissa_size_in_bits, moving 'exp_offset' times
		ss2.mantissa.Rcr( exp_offset.ToInt(), 0 );
		mantissa.BitOr(ss2.mantissa);

		c += Standardizing();

	return CheckCarry(c);
	}


	/*!
		bitwise XOR

		this and ss2 must be >= 0
		return values:
			0 - ok
			1 - carry
			2 - this or ss2 was negative
	*/
	uint BitXor(Big<exp, man> ss2)
	{
		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		if( IsSign() || ss2.IsSign() )
			return 2;
		
		Int<exp> exp_offset( exponent );
		Int<exp> mantissa_size_in_bits( man * TTMATH_BITS_PER_UINT );

		uint c = 0;

		exp_offset.Sub( ss2.exponent );
		exp_offset.Abs();

		// abs(this) will be >= abs(ss2)
		if( SmallerWithoutSignThan(ss2) )
		{
			Big<exp, man> temp(ss2);

			ss2   = *this;
			*this = temp;
		}

		if( exp_offset >= mantissa_size_in_bits )
			// the second value is too small
			return 0;

		// exp_offset < mantissa_size_in_bits, moving 'exp_offset' times
		ss2.mantissa.Rcr( exp_offset.ToInt(), 0 );
		mantissa.BitXor(ss2.mantissa);

		c += Standardizing();

	return CheckCarry(c);
	}



	/*!
		Multiplication this = this * ss2 (ss2 is uint)

		ss2 without a sign
	*/
	uint MulUInt(uint ss2)
	{
	UInt<man+1> man_result;
	uint i,c = 0;

		if( IsNan() )
			return 1;

		// man_result = mantissa * ss2.mantissa
		mantissa.MulInt(ss2, man_result);

		int bit = UInt<man>::FindLeadingBitInWord(man_result.table[man]); // man - last word
		
		if( bit!=-1 && uint(bit) > (TTMATH_BITS_PER_UINT/2) )
		{
			// 'i' will be from 0 to TTMATH_BITS_PER_UINT
			i = man_result.CompensationToLeft();
			c = exponent.Add( TTMATH_BITS_PER_UINT - i );

			for(i=0 ; i<man ; ++i)
				mantissa.table[i] = man_result.table[i+1];
		}
		else
		{
			if( bit != -1 )
			{
				man_result.Rcr(bit+1, 0);
				c += exponent.Add(bit+1);
			}

			for(i=0 ; i<man ; ++i)
				mantissa.table[i] = man_result.table[i];
		}

		c += Standardizing();

	return CheckCarry(c);
	}


	/*!
		Multiplication this = this * ss2 (ss2 is sint)

		ss2 with a sign
	*/
	uint MulInt(sint ss2)
	{
		if( IsNan() )
			return 1;

		if( ss2 == 0 )
		{
			SetZero();
			return 0;
		}

		if( IsZero() )
			return 0;

		if( IsSign() == (ss2<0) )
		{
			// the signs are the same (both are either - or +), the result is positive
			Abs();
		}
		else
		{
			// the signs are different, the result is negative
			SetSign();
		}

		if( ss2<0 )
			ss2 = -ss2;


	return MulUInt( uint(ss2) );
	}


	/*!
		multiplication this = this * ss2
		this method returns a carry
	*/
	uint Mul(const Big<exp, man> & ss2)
	{
	TTMATH_REFERENCE_ASSERT( ss2 )

	UInt<man*2> man_result;
	uint i,c;

		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		// man_result = mantissa * ss2.mantissa
		mantissa.MulBig(ss2.mantissa, man_result);

		// 'i' will be from 0 to man*TTMATH_BITS_PER_UINT
		// because mantissa and ss2.mantissa are standardized 
		// (the highest bit in man_result is set to 1 or
		// if there is a zero value in man_result the method CompensationToLeft()
		// returns 0 but we'll correct this at the end in Standardizing() method)
		i = man_result.CompensationToLeft();
		
		c  = exponent.Add( man * TTMATH_BITS_PER_UINT - i );
		c += exponent.Add( ss2.exponent );

		for(i=0 ; i<man ; ++i)
			mantissa.table[i] = man_result.table[i+man];

		if( IsSign() == ss2.IsSign() )
		{
			// the signs are the same, the result is positive
			Abs();
		}
		else
		{
			// the signs are different, the result is negative
			// if the value is zero it will be corrected later in Standardizing method
			SetSign();
		}

		c += Standardizing();

	return CheckCarry(c);
	}
	

	/*!
		division this = this / ss2
		this method returns carry (in a division carry can be as well)

		(it also returns 0 if ss2 is zero)
	*/
	uint Div(const Big<exp, man> & ss2)
	{
	TTMATH_REFERENCE_ASSERT( ss2 )

	UInt<man*2> man1;
	UInt<man*2> man2;
	uint i,c = 0;
		
		if( IsNan() || ss2.IsNan() || ss2.IsZero() )
			return CheckCarry(1);

		for(i=0 ; i<man ; ++i)
		{
			man1.table[i+man] = mantissa.table[i];
			man2.table[i]     = ss2.mantissa.table[i];
		}

		for(i=0 ; i<man ; ++i)
		{
			man1.table[i] = 0;
			man2.table[i+man] = 0;
		}

		man1.Div(man2);

		i = man1.CompensationToLeft();

		if( i )
			c += exponent.Sub(i);

		c += exponent.Sub(ss2.exponent);
		
		for(i=0 ; i<man ; ++i)
			mantissa.table[i] = man1.table[i+man];

		if( IsSign() == ss2.IsSign() )
			Abs();
		else
			SetSign(); // if there is a zero it will be corrected in Standardizing()

		c += Standardizing();

	return CheckCarry(c);
	}


	/*!
		the remainder from a division

		e.g.
		 12.6 mod  3 =  0.6   because  12.6 = 3*4 + 0.6
		-12.6 mod  3 = -0.6   bacause -12.6 = 3*(-4) + (-0.6)
		 12.6 mod -3 =  0.6
		-12.6 mod -3 = -0.6

		it means:
		in other words: this(old) = ss2 * q + this(new)
	*/
	uint Mod(const Big<exp, man> & ss2)
	{
	TTMATH_REFERENCE_ASSERT( ss2 )

	uint c = 0;

		if( IsNan() || ss2.IsNan() )
			return CheckCarry(1);

		if( !SmallerWithoutSignThan(ss2) )
		{
			Big<exp, man> temp(*this);

			c = temp.Div(ss2);
			temp.SkipFraction();
			c += temp.Mul(ss2);
			c += Sub(temp);

			if( !SmallerWithoutSignThan( ss2 ) )
				c += 1;
		}

	return CheckCarry(c);
	}




	/*!
		power this = this ^ pow
		(pow without a sign)

		binary algorithm (r-to-l)

		return values:
		0 - ok
		1 - carry
		2 - incorrect arguments (0^0)
	*/
	template<uint pow_size>
	uint Pow(UInt<pow_size> pow)
	{
		if( IsNan() )
			return 1;

		if( pow.IsZero() && IsZero() )
		{
			// we don't define zero^zero
			SetNan();
			return 2;
		}

		Big<exp, man> start(*this), start_temp;
		Big<exp, man> result;
		result.SetOne();
		uint c = 0;

		while( !c && !pow.IsZero() )
		{
			if( pow.table[0] & 1 )
				c += result.Mul(start);

			start_temp = start;
			c += start.Mul(start_temp);

			pow.Rcr(1);
		}

		*this = result;

	return CheckCarry(c);
	}


	/*!
		power this = this ^ pow
		p can be negative

		return values:
		0 - ok
		1 - carry
		2 - incorrect arguments 0^0 or 0^(-something)
	*/
	template<uint pow_size>
	uint Pow(Int<pow_size> pow)
	{
		if( IsNan() )
			return 1;

		if( !pow.IsSign() )
			return Pow( UInt<pow_size>(pow) );

		if( IsZero() )
		{
			// if 'p' is negative then
			// 'this' must be different from zero
			SetNan();
			return 2;
		}

		uint c = pow.ChangeSign();

		Big<exp, man> t(*this);
		c += t.Pow( UInt<pow_size>(pow) ); // here can only be a carry (return:1)

		SetOne();
		c += Div(t);

	return CheckCarry(c);
	}


	/*!
		this method returns: 'this' mod 2
		(either zero or one)

		this method is much faster than using Mod( object_with_value_two )
	*/
	uint Mod2() const
	{
		if( exponent>sint(0) || exponent<=-sint(man*TTMATH_BITS_PER_UINT) )
			return 0;

		sint exp_int = exponent.ToInt();
		// 'exp_int' is negative (or zero), we set it as positive
		exp_int = -exp_int;

	return mantissa.GetBit(exp_int);
	}



	/*!
		power this = this ^ abs([pow])
		pow is treated as a value without a sign and without a fraction
		 if pow has a sign then the method pow.Abs() is used
		 if pow has a fraction the fraction is skipped (not used in calculation)

		return values:
		0 - ok
		1 - carry
		2 - incorrect arguments (0^0)
	*/
	uint PowUInt(Big<exp, man> pow)
	{
		if( IsNan() || pow.IsNan() )
			return CheckCarry(1);

		if( pow.IsZero() && IsZero() )
		{
			SetNan();
			return 2;
		}

		if( pow.IsSign() )
			pow.Abs();

		Big<exp, man> start(*this), start_temp;
		Big<exp, man> result;
		Big<exp, man> one;
		Int<exp> e_one;
		uint c = 0;

		e_one.SetOne();
		one.SetOne();
		result = one;

		while( !c && pow >= one )
		{
			if( pow.Mod2() )
				c += result.Mul(start);

			start_temp = start;
			c += start.Mul(start_temp);

			c += pow.exponent.Sub( e_one );
		}

		*this = result;

	return CheckCarry(c);
	}


	/*!
		power this = this ^ [pow]
		pow is treated as a value without a fraction
		pow can be negative

		return values:
		0 - ok
		1 - carry
		2 - incorrect arguments 0^0 or 0^(-something)
	*/
	uint PowInt(const Big<exp, man> & pow)
	{
		TTMATH_REFERENCE_ASSERT( pow )
	
		if( IsNan() || pow.IsNan() )
			return CheckCarry(1);

		if( !pow.IsSign() )
			return PowUInt(pow);

		if( IsZero() )
		{
			// if 'pow' is negative then
			// 'this' must be different from zero
			SetNan();
			return 2;
		}

		Big<exp, man> temp(*this);
		uint c = temp.PowUInt(pow); // here can only be a carry (result:1)

		SetOne();
		c += Div(temp);

	return CheckCarry(c);
	}


	/*!
		power this = this ^ pow
		this must be greater than zero (this > 0)
		pow can be negative and with fraction

		return values:
		0 - ok
		1 - carry
		2 - incorrect argument ('this' <= 0)
	*/
	uint PowFrac(const Big<exp, man> & pow)
	{
		TTMATH_REFERENCE_ASSERT( pow )

		if( IsNan() || pow.IsNan() )
			return CheckCarry(1);

		Big<exp, man> temp;
		uint c = temp.Ln(*this);

		if( c != 0 ) // can be 2 from Ln()
		{
			SetNan();
			return c;
		}

		c += temp.Mul(pow);
		c += Exp(temp);

	return CheckCarry(c);
	}



	/*!
		power this = this ^ pow
		pow can be negative and with fraction

		return values:
		0 - ok
		1 - carry
		2 - incorrect argument ('this' or 'pow')
	*/
	uint Pow(const Big<exp, man> & pow)
	{
		TTMATH_REFERENCE_ASSERT( pow )

		if( IsNan() || pow.IsNan() )
			return CheckCarry(1);

		if( IsZero() )
		{
			// 0^pow will be 0 only for pow>0
			if( pow.IsSign() || pow.IsZero() )
			{
				SetNan();
				return 2;
			}

			SetZero();

		return 0;
		}

		if( pow.exponent>-int(man*TTMATH_BITS_PER_UINT) && pow.exponent<=0 )
		{
			Big<exp, man> pow_frac( pow );
			pow_frac.RemainFraction();

			if( pow_frac.IsZero() )
				return PowInt( pow );
		}

	return PowFrac(pow);
	}


private:

#ifdef TTMATH_CONSTANTSGENERATOR
public:
#endif

	/*!
		Exponent this = exp(x) = e^x where x is in (-1,1)

		we're using the formula exp(x) = 1 + (x)/(1!) + (x^2)/(2!) + (x^3)/(3!) + ...
	*/
	void ExpSurrounding0(const Big<exp,man> & x, uint * steps = 0)
	{
		TTMATH_REFERENCE_ASSERT( x )

		Big<exp,man> denominator, denominator_i;
		Big<exp,man> one, old_value, next_part;
		Big<exp,man> numerator = x;
		
		SetOne();
		one.SetOne();
		denominator.SetOne();
		denominator_i.SetOne();

		// every 'step_test' times we make a test
		const uint step_test = 5;
		uint i;
		old_value = *this;

		// we begin from 1 in order to not testing at the beginning
	#ifdef TTMATH_CONSTANTSGENERATOR
		for(i=1 ; true ; ++i)
	#else
		for(i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
	#endif
		{
			bool testing = ((i % step_test) == 0);

			next_part = numerator;

			if( next_part.Div( denominator ) )
				// if there is a carry here we only break the loop 
				// however the result we return as good
				// it means there are too many parts of the formula
				break;

			// there shouldn't be a carry here
			Add( next_part );

			if( testing && old_value==*this )
				// we've added next few parts of the formula but the result
				// is still the same then we break the loop
				break;
			else
				old_value = *this;


			// we set the denominator and the numerator for a next part of the formula
			if( denominator_i.Add(one) )
				// if there is a carry here the result we return as good
				break;

			if( denominator.Mul(denominator_i) )
				break;

			if( numerator.Mul(x) )
				break;
		}

		if( steps )
			*steps = i;
	}

public:


	/*!
		Exponent this = exp(x) = e^x

		we're using the fact that our value is stored in form of:
			x = mantissa * 2^exponent
		then
			e^x = e^(mantissa* 2^exponent) or
			e^x = (e^mantissa)^(2^exponent)

		'Exp' returns a carry if we can't count the result ('x' is too big)
	*/
	uint Exp(const Big<exp,man> & x)
	{
	uint c = 0;
		
		if( x.IsNan() )
			return CheckCarry(1);

		if( x.IsZero() )
		{
			SetOne();
		return 0;
		}

		// m will be the value of the mantissa in range (-1,1)
		Big<exp,man> m(x);
		m.exponent = -sint(man*TTMATH_BITS_PER_UINT);

		// 'e_' will be the value of '2^exponent'
		//   e_.mantissa.table[man-1] = TTMATH_UINT_HIGHEST_BIT;  and
		//   e_.exponent.Add(1) mean:
		//     e_.mantissa.table[0] = 1;
		//     e_.Standardizing();
		//     e_.exponent.Add(man*TTMATH_BITS_PER_UINT)
		//     (we must add 'man*TTMATH_BITS_PER_UINT' because we've taken it from the mantissa)
		Big<exp,man> e_(x);
		e_.mantissa.SetZero();
		e_.mantissa.table[man-1] = TTMATH_UINT_HIGHEST_BIT;
		c += e_.exponent.Add(1);
		e_.Abs();

		/*
			now we've got:
			m - the value of the mantissa in range (-1,1)
			e_ - 2^exponent

			e_ can be as:
			...2^-2, 2^-1, 2^0, 2^1, 2^2 ...
			...1/4 , 1/2 , 1  , 2  , 4   ...

			above one e_ is integer

			if e_ is greater than 1 we calculate the exponent as:
				e^(m * e_) = ExpSurrounding0(m) ^ e_
			and if e_ is smaller or equal one we calculate the exponent in this way:
				e^(m * e_) = ExpSurrounding0(m* e_)
			because if e_ is smaller or equal 1 then the product of m*e_ is smaller or equal m
		*/

		if( e_ <= 1 )
		{
			m.Mul(e_);
			ExpSurrounding0(m);
		}
		else
		{
			ExpSurrounding0(m);
			c += PowUInt(e_);
		}
	
	return CheckCarry(c);
	}




private:

#ifdef TTMATH_CONSTANTSGENERATOR
public:
#endif

	/*!
		Natural logarithm this = ln(x) where x in range <1,2)

		we're using the formula:
		ln x = 2 * [ (x-1)/(x+1) + (1/3)((x-1)/(x+1))^3 + (1/5)((x-1)/(x+1))^5 + ... ]
	*/
	void LnSurrounding1(const Big<exp,man> & x, uint * steps = 0)
	{
		Big<exp,man> old_value, next_part, denominator, one, two, x1(x), x2(x);

		one.SetOne();

		if( x == one )
		{
			// LnSurrounding1(1) is 0
			SetZero();
			return;
		}

		two = 2;

		x1.Sub(one);
		x2.Add(one);

		x1.Div(x2);
		x2 = x1;
		x2.Mul(x1);

		denominator.SetOne();
		SetZero();

		old_value = *this;
		
		// every 'step_test' times we make a test
		const uint step_test = 5;
		uint i;


	#ifdef TTMATH_CONSTANTSGENERATOR
		for(i=1 ; true ; ++i)
	#else
		// we begin from 1 in order to not testing at the beginning
		for(i=1 ; i<=TTMATH_ARITHMETIC_MAX_LOOP ; ++i)
	#endif
		{
			bool testing = ((i % step_test) == 0);

			next_part = x1;

			if( next_part.Div(denominator) )
				// if there is a carry here we only break the loop 
				// however the result we return as good
				// it means there are too many parts of the formula
				break;

			// there shouldn't be a carry here
			Add(next_part);

			if( testing && old_value == *this )
				// we've added next (step_test) parts of the formula but the result
				// is still the same then we break the loop
				break;
			else
				old_value = *this;

			if( x1.Mul(x2) )
				// if there is a carry here the result we return as good
				break;

			if( denominator.Add(two) )
				break;
		}

		// this = this * 2
		// ( there can't be a carry here because we calculate the logarithm between <1,2) )
		exponent.AddOne();

		if( steps )
			*steps = i;
	}




public:


	/*!
		Natural logarithm this = ln(x)
		(a logarithm with the base equal 'e')

		we're using the fact that our value is stored in form of:
			x = mantissa * 2^exponent
		then
			ln(x) = ln (mantissa * 2^exponent) = ln (mantissa) + (exponent * ln (2))

		the mantissa we'll show as a value from range <1,2) because the logarithm
		is decreasing too fast when 'x' is going to 0

		return values:
			0 - ok
			1 - overflow (carry)
			2 - incorrect argument (x<=0)
	*/
	uint Ln(const Big<exp,man> & x)
	{
		TTMATH_REFERENCE_ASSERT( x )

		if( x.IsNan() )
			return CheckCarry(1);

		if( x.IsSign() || x.IsZero() )
		{
			SetNan();
			return 2;
		}

		// m will be the value of the mantissa in range <1,2)
		Big<exp,man> m(x);
		m.exponent = -sint(man*TTMATH_BITS_PER_UINT - 1);

	    LnSurrounding1(m);

		Big<exp,man> exponent_temp;
		exponent_temp.FromInt( x.exponent );

		// we must add 'man*TTMATH_BITS_PER_UINT-1' because we've taken it from the mantissa
		uint c = exponent_temp.Add(man*TTMATH_BITS_PER_UINT-1);

		Big<exp,man> ln2;
		ln2.SetLn2();
		c += exponent_temp.Mul(ln2);
		c += Add(exponent_temp);

	return CheckCarry(c);
	}



	/*!
		Logarithm from 'x' with a 'base'

		we're using the formula:
			Log(x) with 'base' = ln(x) / ln(base)

		return values:
			0 - ok
			1 - overflow
			2 - incorrect argument (x<=0)
			3 - incorrect base (a<=0 lub a=1)
	*/
	uint Log(const Big<exp,man> & x, const Big<exp,man> & base)
	{
		TTMATH_REFERENCE_ASSERT( base )
		TTMATH_REFERENCE_ASSERT( x )

		if( x.IsNan() || base.IsNan() )
			return CheckCarry(1);

		if( x.IsSign() || x.IsZero() )
		{
			SetNan();
			return 2;
		}

		Big<exp,man> denominator;;
		denominator.SetOne();

		if( base.IsSign() || base.IsZero() || base==denominator )
		{
			SetNan();
			return 3;
		}
		
		if( x == denominator ) // (this is: if x == 1)
		{
			// log(1) is 0
			SetZero();
			return 0;
		}

		// another error values we've tested at the beginning
		// there can only be a carry
		uint c = Ln(x);

		c += denominator.Ln(base);
		c += Div(denominator);

	return CheckCarry(c);
	}




	/*!
	*
	*	converting methods
	*
	*/


	/*!
		converting from another type of a Big object
	*/
	template<uint another_exp, uint another_man>
	uint FromBig(const Big<another_exp, another_man> & another)
	{
		info = another.info;

		if( IsNan() )
			return 1;

		if( exponent.FromInt(another.exponent) )
		{
			SetNan();
			return 1;
		}

		uint man_len_min = (man < another_man)? man : another_man;
		uint i;
		uint c = 0;

		for( i = 0 ; i<man_len_min ; ++i )
			mantissa.table[man-1-i] = another.mantissa.table[another_man-1-i];
	
		for( ; i<man ; ++i )
			mantissa.table[man-1-i] = 0;


		// MS Visual Express 2005 reports a warning (in the lines with 'uint man_diff = ...'):
		// warning C4307: '*' : integral constant overflow
		// but we're using 'if( man > another_man )' and 'if( man < another_man )' and there'll be no such situation here
		#ifdef _MSC_VER
		#pragma warning( disable: 4307 )
		#endif

		if( man > another_man )
		{
			uint man_diff = (man - another_man) * TTMATH_BITS_PER_UINT;
			c += exponent.SubInt(man_diff, 0);
		}
		else
		if( man < another_man )
		{
			uint man_diff = (another_man - man) * TTMATH_BITS_PER_UINT;
			c += exponent.AddInt(man_diff, 0);
		}
		
		#ifdef _MSC_VER
		#pragma warning( default: 4307 )
		#endif

		// mantissa doesn't have to be standardized (either the highest bit is set or all bits are equal zero)
		CorrectZero();

	return CheckCarry(c);
	}


	/*!
		this method converts 'this' into 'result'

		if the value is too big this method returns a carry (1)
	*/
	uint ToUInt(uint & result, bool test_sign = true) const
	{
		result = 0;

		if( IsZero() )
			return 0;

		if( test_sign && IsSign() )
			// the result should be positive
			return 1;

		sint maxbit = -sint(man*TTMATH_BITS_PER_UINT);

		if( exponent > maxbit + sint(TTMATH_BITS_PER_UINT) )
			// if exponent > (maxbit + sint(TTMATH_BITS_PER_UINT)) the value can't be passed
			// into the 'sint' type (it's too big)
			return 1;

		if( exponent <= maxbit )
			// our value is from the range of (-1,1) and we return zero
			return 0;

		UInt<man> mantissa_temp(mantissa);
		// exponent is from a range of (maxbit, maxbit + sint(TTMATH_BITS_PER_UINT) >
		sint how_many_bits = exponent.ToInt();

		// how_many_bits is negative, we'll make it positive
		how_many_bits = -how_many_bits;
	
		// we're taking into account only the last word in a mantissa table
		mantissa_temp.Rcr( how_many_bits % TTMATH_BITS_PER_UINT, 0 );
		result = mantissa_temp.table[ man-1 ];

	return 0;
	}



	/*!
		this method converts 'this' into 'result'

		if the value is too big this method returns a carry (1)
	*/
	uint ToInt(sint & result) const
	{
		result = 0;
		uint result_uint;

		if( ToUInt(result_uint, false) )
			return 1;

		result = static_cast<sint>( result_uint );

		// the exception for the minimal value
		if( IsSign() && result_uint == TTMATH_UINT_HIGHEST_BIT )
			return 0;

		if( (result_uint & TTMATH_UINT_HIGHEST_BIT) != 0 )
			// the value is too big
			return 1;

		if( IsSign() )
			result = -result;

	return 0;
	}


	/*!
		this method converts 'this' into 'result'

		if the value is too big this method returns a carry (1)
	*/
	template<uint int_size>
	uint ToInt(Int<int_size> & result) const
	{
		result.SetZero();

		if( IsZero() )
			return 0;
		
		sint maxbit = -sint(man*TTMATH_BITS_PER_UINT);

		if( exponent > maxbit + sint(int_size*TTMATH_BITS_PER_UINT) )
			// if exponent > (maxbit + sint(int_size*TTMATH_BITS_PER_UINT)) the value can't be passed
			// into the 'Int<int_size>' type (it's too big)

		if( exponent <= maxbit )
			// our value is from range (-1,1) and we return zero
			return 0;

		UInt<man> mantissa_temp(mantissa);
		sint how_many_bits = exponent.ToInt();

		if( how_many_bits < 0 )
		{
			how_many_bits = -how_many_bits;
			uint index    = how_many_bits / TTMATH_BITS_PER_UINT;
			mantissa_temp.Rcr( how_many_bits % TTMATH_BITS_PER_UINT, 0 );

			for(uint i=index, a=0 ; i<man ; ++i,++a)
				result.table[a] = mantissa_temp.table[i];
		}
		else
		{
			uint index = how_many_bits / TTMATH_BITS_PER_UINT;

			for(uint i=0 ; i<man ; ++i)
				result.table[index+i] = mantissa_temp.table[i];

			result.Rcl( how_many_bits % TTMATH_BITS_PER_UINT, 0 );
		}

		// the exception for the minimal value
		if( IsSign() )
		{
			Int<int_size> min;
			min.SetMin();

			if( result == min )
				return 0;
		}

		if( (result.table[int_size-1] & TTMATH_UINT_HIGHEST_BIT) != 0 )
			// the value is too big
			return 1;

		if( IsSign() )
			result.ChangeSign();

	return 0;
	}


	/*!
		a method for converting 'uint' to this class
	*/
	void FromUInt(uint value)
	{
		info = 0;

		for(uint i=0 ; i<man-1 ; ++i)
			mantissa.table[i] = 0;

		mantissa.table[man-1] = value;
		exponent = -sint(man-1) * sint(TTMATH_BITS_PER_UINT);

		// there shouldn't be a carry because 'value' has the 'uint' type 
		Standardizing();
	}


	/*!
		a method for converting 'sint' to this class
	*/
	void FromInt(sint value)
	{
	bool is_sign = false;

		if( value < 0 )
		{
			value   = -value;
			is_sign = true;
		}

		FromUInt(uint(value));

		if( is_sign )
			SetSign();
	}



	/*!
		this method converts from standard double into this class

		standard double means IEEE-754 floating point value with 64 bits
		it is as follows (from http://www.psc.edu/general/software/packages/ieee/ieee.html):

		The IEEE double precision floating point standard representation requires
		a 64 bit word, which may be represented as numbered from 0 to 63, left to
		right. The first bit is the sign bit, S, the next eleven bits are the
		exponent bits, 'E', and the final 52 bits are the fraction 'F':

		S EEEEEEEEEEE FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF
		0 1        11 12                                                63

		The value V represented by the word may be determined as follows:

		* If E=2047 and F is nonzero, then V=NaN ("Not a number")
		* If E=2047 and F is zero and S is 1, then V=-Infinity
		* If E=2047 and F is zero and S is 0, then V=Infinity
		* If 0<E<2047 then V=(-1)**S * 2 ** (E-1023) * (1.F) where "1.F" is intended
		  to represent the binary number created by prefixing F with an implicit
		  leading 1 and a binary point.
		* If E=0 and F is nonzero, then V=(-1)**S * 2 ** (-1022) * (0.F) These are
		  "unnormalized" values.
		* If E=0 and F is zero and S is 1, then V=-0
		* If E=0 and F is zero and S is 0, then V=0 
	*/

#ifdef TTMATH_PLATFORM32

	void FromDouble(double value)
	{
		// sizeof(double) should be 8 (64 bits), this is actually not a runtime
		// error but I leave it at the moment as is
		TTMATH_ASSERT( sizeof(double) == 8 )

		// I am not sure what will be on a platform which has 
		// a different endianness... but we use this library only
		// on x86 and amd (intel) 64 bits (as there's a lot of assembler code)
		union 
		{
			double d;
			uint u[2]; // two 32bit words
		} temp;

		temp.d = value;

		sint e  = ( temp.u[1] & 0x7FF00000u) >> 20;
		uint m1 = ((temp.u[1] &    0xFFFFFu) << 11) | (temp.u[0] >> 21);
		uint m2 = temp.u[0] << 11;
		
		if( e == 2047 )
		{
			// If E=2047 and F is nonzero, then V=NaN ("Not a number")
			// If E=2047 and F is zero and S is 1, then V=-Infinity
			// If E=2047 and F is zero and S is 0, then V=Infinity

			// at the moment we do not support NaN, -Infinity and +Infinity

			SetZero();
		}
		else
		if( e > 0 )
		{
			// If 0<E<2047 then
			// V=(-1)**S * 2 ** (E-1023) * (1.F)
			// where "1.F" is intended to represent the binary number
			// created by prefixing F with an implicit leading 1 and a binary point.
			
			FromDouble_SetExpAndMan((temp.u[1] & 0x80000000u) != 0,
									e - 1023 - man*TTMATH_BITS_PER_UINT + 1, 0x80000000u,
									m1, m2);

			// we do not have to call Standardizing() here
			// because the mantissa will have the highest bit set
		}
		else
		{
			// e == 0

			if( m1 != 0 || m2 != 0 )
			{
				// If E=0 and F is nonzero,
				// then V=(-1)**S * 2 ** (-1022) * (0.F)
				// These are "unnormalized" values.

				UInt<2> m;
				m.table[1] = m1;
				m.table[0] = m2;
				uint moved = m.CompensationToLeft();

				FromDouble_SetExpAndMan((temp.u[1] & 0x80000000u) != 0,
										e - 1022 - man*TTMATH_BITS_PER_UINT + 1 - moved, 0,
										m.table[1], m.table[2]);
			}
			else
			{
				// If E=0 and F is zero and S is 1, then V=-0
				// If E=0 and F is zero and S is 0, then V=0 

				// we do not support -0 or 0, only is one 0
				SetZero();
			}
		}
	}


private:

	void FromDouble_SetExpAndMan(bool is_sign, int e, uint mhighest, uint m1, uint m2)
	{
		exponent = e;

		if( man > 1 )
		{
			mantissa.table[man-1] = m1 | mhighest;
			mantissa.table[sint(man-2)] = m2;
			// although man>1 we're using casting into sint
			// to get rid from a warning which generates Microsoft Visual:
			// warning C4307: '*' : integral constant overflow

			for(uint i=0 ; i<man-2 ; ++i)
				mantissa.table[i] = 0;
		}
		else
		{
			mantissa.table[0] = m1 | mhighest;
		}

		info = 0;
	
		// the value should be different from zero
		TTMATH_ASSERT( mantissa.IsZero() == false )

		if( is_sign )
			SetSign();
	}


#else

public:

	// 64bit platforms
	void FromDouble(double value)
	{
		// sizeof(double) should be 8 (64 bits), this is actually not a runtime
		// error but I leave it at the moment as is
		TTMATH_ASSERT( sizeof(double) == 8 )

		// I am not sure what will be on a plaltform which has 
		// a different endianness... but we use this library only
		// on x86 and amd (intel) 64 bits (as there's a lot of assembler code)
		union 
		{
			double d;
			uint u; // one 64bit word
		} temp;

		temp.d = value;
                          
		sint e = (temp.u & 0x7FF0000000000000ul) >> 52;
		uint m = (temp.u &    0xFFFFFFFFFFFFFul) << 11;
		
		if( e == 2047 )
		{
			// If E=2047 and F is nonzero, then V=NaN ("Not a number")
			// If E=2047 and F is zero and S is 1, then V=-Infinity
			// If E=2047 and F is zero and S is 0, then V=Infinity

			// at the moment we do not support NaN, -Infinity and +Infinity

			SetZero();
		}
		else
		if( e > 0 )
		{
			// If 0<E<2047 then
			// V=(-1)**S * 2 ** (E-1023) * (1.F)
			// where "1.F" is intended to represent the binary number
			// created by prefixing F with an implicit leading 1 and a binary point.
			
			FromDouble_SetExpAndMan((temp.u & 0x8000000000000000ul) != 0,
									e - 1023 - man*TTMATH_BITS_PER_UINT + 1,
									0x8000000000000000ul, m);

			// we do not have to call Standardizing() here
			// because the mantissa will have the highest bit set
		}
		else
		{
			// e == 0

			if( m != 0 )
			{
				// If E=0 and F is nonzero,
				// then V=(-1)**S * 2 ** (-1022) * (0.F)
				// These are "unnormalized" values.

				FromDouble_SetExpAndMan(bool(temp.u & 0x8000000000000000ul),
										e - 1022 - man*TTMATH_BITS_PER_UINT + 1, 0, m);
				Standardizing();
			}
			else
			{
				// If E=0 and F is zero and S is 1, then V=-0
				// If E=0 and F is zero and S is 0, then V=0 

				// we do not support -0 or 0, only is one 0
				SetZero();
			}
		}
	}

private:

	void FromDouble_SetExpAndMan(bool is_sign, sint e, uint mhighest, uint m)
	{
		exponent = e;
		mantissa.table[man-1] = m | mhighest;

		for(uint i=0 ; i<man-1 ; ++i)
			mantissa.table[i] = 0;

		info = 0;

		// the value should be different from zero
		TTMATH_ASSERT( mantissa.IsZero() == false )

		if( is_sign )
			SetSign();
	}

#endif


public:



	/*!
		this method converts from this class into the 'double'

		if the value is too big:
			'result' will be +/-infinity (depending on the sign)
			and the method returns 1
		if the value is too small:
			'result' will be 0
			and the method returns 1
	*/
	uint ToDouble(double & result) const
	{
		// sizeof(double) should be 8 (64 bits), this is actually not a runtime
		// error but I leave it at the moment as is
		TTMATH_ASSERT( sizeof(double) == 8 )

		if( IsZero() )
		{
			result = 0.0;
			return 0;
		}

		sint e_correction = sint(man*TTMATH_BITS_PER_UINT) - 1;

		if( exponent >= 1024 - e_correction )
		{
			// +/- infinity
			result = ToDouble_SetDouble( IsSign(), 2047, 0, true);

		return 1;
		}
		else
		if( exponent <= -1023 - 52 - e_correction )
		{
			// too small value - we assume that there'll be a zero
			result = 0;

			// and return a carry
		return 1;
		}
		
		sint e = exponent.ToInt() + e_correction;

		if( e <= -1023 )
		{
			// -1023-52 < e <= -1023  (unnormalized value)
			result = ToDouble_SetDouble( IsSign(), 0, -(e + 1023));
		}
		else
		{
			// -1023 < e < 1024
			result = ToDouble_SetDouble( IsSign(), e + 1023, -1);
		}

	return 0;
	}

private:

#ifdef TTMATH_PLATFORM32

	// 32bit platforms
	double ToDouble_SetDouble(bool is_sign, uint e, sint move, bool infinity = false) const
	{
		union 
		{
			double d;
			uint u[2]; // two 32bit words
		} temp;

		temp.u[0] = temp.u[1] = 0;

		if( is_sign )
			temp.u[1] |= 0x80000000u;

		temp.u[1] |= (e << 20) & 0x7FF00000u;

		if( infinity )
			return temp.d;

		UInt<2> m;
		m.table[1] = mantissa.table[man-1];
		m.table[0] = ( man > 1 ) ? mantissa.table[sint(man-2)] : 0;
		// although man>1 we're using casting into sint
		// to get rid from a warning which generates Microsoft Visual:
		// warning C4307: '*' : integral constant overflow

		m.Rcr( 12 + move );
		m.table[1] &= 0xFFFFFu; // cutting the 20 bit (when 'move' was -1)

		temp.u[1] |= m.table[1];
		temp.u[0] |= m.table[0];

	return temp.d;
	}

#else

	// 64bit platforms
	double ToDouble_SetDouble(bool is_sign, uint e, sint move, bool infinity = false) const
	{
		union 
		{
			double d;
			uint u; // 64bit word
		} temp;

		temp.u = 0;
		
		if( is_sign )
			temp.u |= 0x8000000000000000ul;
		                
		temp.u |= (e << 52) & 0x7FF0000000000000ul;

		if( infinity )
			return temp.d;

		uint m = mantissa.table[man-1];

		m >>= ( 12 + move );
		m &= 0xFFFFFFFFFFFFFul; // cutting the 20 bit (when 'move' was -1)
		temp.u |= m;

	return temp.d;
	}

#endif


public:


	/*!
		an operator= for converting 'sint' to this class
	*/
	Big<exp, man> & operator=(sint value)
	{
		FromInt(value);

	return *this;
	}


	/*!
		an operator= for converting 'uint' to this class
	*/
	Big<exp, man> & operator=(uint value)
	{
		FromUInt(value);

	return *this;
	}


	/*!
		an operator= for converting 'double' to this class
	*/
	Big<exp, man> & operator=(double value)
	{
		FromDouble(value);

	return *this;
	}


	/*!
		a constructor for converting 'sint' to this class
	*/
	Big(sint value)
	{
		FromInt(value);
	}

	/*!
		a constructor for converting 'uint' to this class
	*/
	Big(uint value)
	{	
		FromUInt(value);
	}
	

	/*!
		a constructor for converting 'double' to this class
	*/
	Big(double value)
	{
		FromDouble(value);
	}


#ifdef TTMATH_PLATFORM64

	/*!
		in 64bit platforms we must define additional operators and contructors
		in order to allow a user initializing the objects in this way:
			Big<...> type = 20;
		or
			Big<...> type; 
			type = 30;

		decimal constants such as 20, 30 etc. are integer literal of type int,
		if the value is greater it can even be long int,
		0 is an octal integer of type int
		(ISO 14882 p2.13.1 Integer literals)
	*/

	/*!
		an operator= for converting 'signed int' to this class
		***this operator is created only on a 64bit platform***
		it takes one argument of 32bit

		
	*/
	Big<exp, man> & operator=(signed int value)
	{
		FromInt(sint(value));

	return *this;
	}


	/*!
		an operator= for converting 'unsigned int' to this class
		***this operator is created only on a 64bit platform***
		it takes one argument of 32bit
	*/
	Big<exp, man> & operator=(unsigned int value)
	{
		FromUInt(uint(value));

	return *this;
	}


	/*!
		a constructor for converting 'signed int' to this class
		***this constructor is created only on a 64bit platform***
		it takes one argument of 32bit
	*/
	Big(signed int value)
	{
		FromInt(sint(value));
	}

	/*!
		a constructor for converting 'unsigned int' to this class
		***this constructor is created only on a 64bit platform***
		it takes one argument of 32bit
	*/
	Big(unsigned int value)
	{
		FromUInt(uint(value));
	}

#endif

private:

	/*!
		an auxiliary method for converting from UInt and Int

		we assume that there'll never be a carry here
		(we have an exponent and the value in Big can be bigger than
		that one from the UInt)
	*/
	template<uint int_size>
	void FromUIntOrInt(const UInt<int_size> & value, sint compensation)
	{
		uint minimum_size = (int_size < man)? int_size : man;
		exponent          = (sint(int_size)-sint(man)) * sint(TTMATH_BITS_PER_UINT) - compensation;

		// copying the highest words
		uint i;
		for(i=1 ; i<=minimum_size ; ++i)
			mantissa.table[man-i] = value.table[int_size-i];

		// setting the rest of mantissa.table into zero (if some has left)
		for( ; i<=man ; ++i)
			mantissa.table[man-i] = 0;
	}


public:


	/*!
		a method for converting from 'UInt<int_size>' to this class
	*/
	template<uint int_size>
	void FromUInt(UInt<int_size> value)
	{
		info = 0;
		sint compensation = (sint)value.CompensationToLeft();
	
	return FromUIntOrInt(value, compensation);
	}


	/*!
		a method for converting from 'Int<int_size>' to this class
	*/
	template<uint int_size>
	void FromInt(Int<int_size> value)
	{
		info = 0;
		bool is_sign = false;

		if( value.IsSign() )
		{
			value.ChangeSign();
			is_sign = true;
		}
		
		sint compensation = (sint)value.CompensationToLeft();
		FromUIntOrInt(value, compensation);

		if( is_sign )
			SetSign();
	}


	/*!
		an operator= for converting from 'Int<int_size>' to this class
	*/
	template<uint int_size>
	Big<exp,man> & operator=(const Int<int_size> & value)
	{
		FromInt(value);

	return *this;
	}


	/*!
		a constructor for converting from 'Int<int_size>' to this class
	*/
	template<uint int_size>
	Big(const Int<int_size> & value)
	{
		FromInt(value);
	}


	/*!
		an operator= for converting from 'UInt<int_size>' to this class
	*/
	template<uint int_size>
	Big<exp,man> & operator=(const UInt<int_size> & value)
	{
		FromUInt(value);

	return *this;
	}


	/*!
		a constructor for converting from 'UInt<int_size>' to this class
	*/
	template<uint int_size>
	Big(const UInt<int_size> & value)
	{
		FromUInt(value);
	}


	/*!
		an operator= for converting from 'Big<another_exp, another_man>' to this class
	*/
	template<uint another_exp, uint another_man>
	Big<exp,man> & operator=(const Big<another_exp, another_man> & value)
	{
		FromBig(value);

	return *this;
	}


	/*!
		a constructor for converting from 'Big<another_exp, another_man>' to this class
	*/
	template<uint another_exp, uint another_man>
	Big(const Big<another_exp, another_man> & value)
	{
		FromBig(value);
	}


	/*!
		a default constructor

		we don't set any of the members to zero
		only NaN flag is set
	*/
	Big()
	{
		SetNan();
	}


	/*!
		a destructor
	*/
	~Big()
	{
	}


	/*!
		the default assignment operator
	*/
	Big<exp,man> & operator=(const Big<exp,man> & value)
	{
		info     = value.info;
		exponent = value.exponent;
		mantissa = value.mantissa;

	return *this;
	}
	

	/*!
		a constructor for copying from another object of this class
	*/
	
	Big(const Big<exp,man> & value)
	{
		operator=(value);
	}
	

	/*!
		a method for converting the value into a string with a base equal 'base'

		input:
		*	base - a base (radix) on which the value will be shown

		*	if 'always_scientific' is true the result will be shown in 'scientific' mode
			if 'always_scientific' is false the result will be shown
			either as 'scientific' or 'normal' mode, it depends whether the abs(exponent)
			is greater than 'when_scientific' or not, if it's greater the value
			will be printed as 'scientific'

		*   'max_digit_after_comma' - rounding
			if 'max_digit_after_comma' is equal -1 that all digits in the mantissa
			will be printed
			if 'max_digit_after_comma' is equal or greater than zero
			that only 'max_digit_after_comma' after the comma operator will be shown
			(if 'max_digit_after_comma' is equal zero there'll be shown only 
			integer value without the comma)
				for example when the value is:
					12.345678 and max_digit_after_comma is 4
				then the result will be 
					12.3457   (the last digit was rounded)
			if there isn't the comma operator (when the value is too big and we're printing
			it not as scientific) 'max_digit_after_comma' will be ignored

		*	if 'remove_trailing_zeroes' is true that not mattered digits
			in the mantissa will be cut off
			(zero characters at the end -- after the comma operator)

		*	decimal_point - a character which will be used as a decimal point

		output:
			return value:
			0 - ok and 'result' will be an object of type std::string which holds the value
			1 - if there was a carry 
	*/
	uint ToString(	std::string & result,
					uint base                  = 10,
					bool always_scientific     = false,
					sint when_scientific       = 15,
					sint max_digit_after_comma = -1,
					bool remove_trailing_zeroes = true,
					char decimal_point = TTMATH_COMMA_CHARACTER_1 ) const
	{
		static char error_overflow_msg[] = "overflow";
		static char error_nan_msg[]      = "NaN";
		result.erase();

		if( IsNan() )
		{
			result = error_nan_msg;
			return 0;
		}

		if( base<2 || base>16 )
		{
			result = error_overflow_msg;
			return 1;
		}
	
		if( IsZero() )
		{
			result = "0";

		return 0;
		}

		/*
			since 'base' is greater or equal 2 that 'new_exp' of type 'Int<exp>' should
			hold the new value of exponent but we're using 'Int<exp+1>' because
			if the value for example would be 'max()' then we couldn't show it

				max() ->  11111111 * 2 ^ 11111111111  (bin)(the mantissa and exponent have all bits set)
				if we were using 'Int<exp>' we couldn't show it in this format:
				1,1111111 * 2 ^ 11111111111  (bin)
				because we have to add something to the mantissa and because 
				mantissa is full we can't do it and it'll be a carry
				(look at ToString_SetCommaAndExponent(...))

				when the base would be greater than two (for example 10) 
				we could use 'Int<exp>' here
		*/
		Int<exp+1> new_exp;

		if( ToString_CreateNewMantissaAndExponent(result, base, new_exp) )
		{
			result = error_overflow_msg;
			return 1;
		}

		/*
			we're rounding the mantissa only if the base is different from 2,4,8 or 16
			(this formula means that the number of bits in the base is greater than one)
		*/
		if( base!=2 && base!=4 && base!=8 && base!=16 )
			if( ToString_RoundMantissa(result, base, new_exp, decimal_point) )
			{
				result = error_overflow_msg;
				return 1;
			}

		if( ToString_SetCommaAndExponent(	result, base, new_exp, always_scientific,
											when_scientific, max_digit_after_comma,
											remove_trailing_zeroes, decimal_point ) )
		{
			result = error_overflow_msg;
			return 1;
		}

		if( IsSign() )
			result.insert(result.begin(), '-');

	// converted successfully
	return 0;
	}


private:


	/*!
		in the method 'ToString_CreateNewMantissaAndExponent()' we're using 
		type 'Big<exp+1,man>' and we should have the ability to use some
		necessary methods from that class (methods which are private here)
	*/
	friend class Big<exp-1,man>;


	/*!
		an auxiliary method for converting into the string (private)

		input:
			base - the base in range <2,16>

		output:
			return values:
				0 - ok
				1 - if there was a carry
			new_man - the new mantissa for 'base'
			new_exp - the new exponent for 'base'

		mathematic part:

		the value is stored as:
			value = mantissa * 2^exponent
		we want to show 'value' as:
			value = new_man * base^new_exp

		then 'new_man' we'll print using the standard method from UInt<> type for printing
		and 'new_exp' is the offset of the comma operator in a system of a base 'base'

		value = mantissa * 2^exponent
		value = mantissa * 2^exponent * (base^new_exp / base^new_exp)
		value = mantissa * (2^exponent / base^new_exp) * base^new_exp

		look at the part (2^exponent / base^new_exp), there'll be good if we take
		a 'new_exp' equal that value when the (2^exponent / base^new_exp) will be equal one

		on account of the 'base' is not as power of 2 (can be from 2 to 16),
		this formula will not be true for integer 'new_exp' then in our case we take 
		'base^new_exp' _greater_ than '2^exponent' 

		if 'base^new_exp' were smaller than '2^exponent' the new mantissa could be
		greater than the max value of the container UInt<man>

		value = mantissa * (2^exponent / base^new_exp) * base^new_exp
		  let M = mantissa * (2^exponent / base^new_exp) then
		value = M * base^new_exp

		in our calculation we treat M as floating value showing it as:
			M = mm * 2^ee where ee will be <= 0 

		next we'll move all bits of mm into the right when ee is equal zero
		abs(ee) must not to be too big that only few bits from mm we can leave

		then we'll have:
			M = mmm * 2^0
		'mmm' is the new_man which we're looking for


		new_exp we calculate in this way:
			2^exponent <= base^new_exp
			new_exp >= log base (2^exponent)   <- logarithm with the base 'base' from (2^exponent)
			
			but we need 'new'exp' as integer then we take:
			new_exp = [log base (2^exponent)] + 1  <- where [x] means integer value from x
	*/
	uint ToString_CreateNewMantissaAndExponent(	std::string & new_man, uint base,
												Int<exp+1> & new_exp) const
	{
	uint c = 0;

		if(base<2 || base>16)
			return 1;
	
		// the speciality for base equal 2
		if( base == 2 )
			return ToString_CreateNewMantissaAndExponent_Base2(new_man, new_exp);

		// this = mantissa * 2^exponent

		// temp = +1 * 2^exponent  
		// we're using a bigger type than 'big<exp,man>' (look below)
		Big<exp+1,man> temp;
		temp.info = 0;
		temp.exponent = exponent;
		temp.mantissa.SetOne();
		c += temp.Standardizing();

		// new_exp_ = [log base (2^exponent)] + 1
		Big<exp+1,man> new_exp_;
		c += new_exp_.ToString_Log(temp, base); // this logarithm isn't very complicated
		new_exp_.SkipFraction();
		temp.SetOne();
		c += new_exp_.Add( temp );

		// because 'base^new_exp' is >= '2^exponent' then 
		// because base is >= 2 then we've got:
		// 'new_exp_' must be smaller or equal 'new_exp'
		// and we can pass it into the Int<exp> type
		// (in fact we're using a greater type then it'll be ok)
		c += new_exp_.ToInt(new_exp);

		// base_ = base
		Big<exp+1,man> base_(base);

		// base_ = base_ ^ new_exp_
		c += base_.Pow( new_exp_ );
		// if we hadn't used a bigger type than 'Big<exp,man>' then the result
		// of this formula 'Pow(...)' would have been with an overflow

		// temp = mantissa * 2^exponent / base_^new_exp_
		// the sign don't interest us here
		temp.mantissa = mantissa;
		temp.exponent = exponent;
		c += temp.Div( base_ );

		// moving all bits of the mantissa into the right 
		// (how many times to move depend on the exponent)
		c += temp.ToString_MoveMantissaIntoRight();

		// because we took 'new_exp' as small as it was
		// possible ([log base (2^exponent)] + 1) that after the division 
		// (temp.Div( base_ )) the value of exponent should be equal zero or 
		// minimum smaller than zero then we've got the mantissa which has 
		// maximum valid bits
		temp.mantissa.ToString(new_man, base);

		// because we had used a bigger type for calculating I think we 
		// shouldn't have had a carry
		// (in the future this can be changed)

	return (c==0)? 0 : 1;
	}


	/*!
		this method calculates the logarithm
		it is used by ToString_CreateNewMantissaAndExponent() method

		it's not too complicated
		because x=+1*2^exponent (mantissa is one) then during the calculation
		the Ln(x) will not be making the long formula from LnSurrounding1()
		and only we have to calculate 'Ln(base)' but it'll be calculated
		only once, the next time we will get it from the 'history'

        x is greater than 0
		base is in <2,16> range
	*/
	uint ToString_Log(const Big<exp,man> & x, uint base)
	{
		TTMATH_REFERENCE_ASSERT( x )
		TTMATH_ASSERT( base>=2 && base<=16 )

		Big<exp,man> temp;
		temp.SetOne();

		if( x == temp )
		{
			// log(1) is 0
			SetZero();

		return 0;
		}

		// there can be only a carry
		// because the 'x' is in '1+2*exponent' form then 
		// the long formula from LnSurrounding1() will not be calculated
		// (LnSurrounding1() will return one immediately)
		uint c = Ln(x);

		// warning! this 'static' is not thread safe
		static Big<exp,man> log_history[15] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0};
		uint index = base - 2;

		if( log_history[index].IsZero() )
		{	
			// we don't have 'base' in 'log_history' then we calculate it now

			if( base==10 && man<=TTMATH_BUILTIN_VARIABLES_SIZE )
			{
				// for the base equal 10 we're using SelLn10() instead of calculating it
				// (only if we have the constant sufficient big)
				temp.SetLn10();
			}
			else
			{
				Big<exp,man> base_(base);
				c += temp.Ln(base_);
			}

			// the next time we'll get the 'Ln(base)' from the history,
			// this 'log_history' can have (16-2+1) items max
			log_history[index] = temp;

			c += Div(temp);
		}
		else
		{
			// we've calculated the 'Ln(base)' beforehand and we're getting it now
			c += Div( log_history[index] );
		}

	return (c==0)? 0 : 1;
	}



	/*!
		an auxiliary method for converting into the string (private)

		this method moving all bits from mantissa into the right side
		the exponent tell us how many times moving (the exponent is <=0)
	*/
	uint ToString_MoveMantissaIntoRight()
	{
		if( exponent.IsZero() )
			return 0;
		
		// exponent can't be greater than zero
		// because we would cat the highest bits of the mantissa
		if( !exponent.IsSign() )
			return 1;


		if( exponent <= -sint(man*TTMATH_BITS_PER_UINT) )
			// if 'exponent' is <= than '-sint(man*TTMATH_BITS_PER_UINT)'
			// it means that we must cut the whole mantissa
			// (there'll not be any of the valid bits)
			return 1;

		// e will be from (-man*TTMATH_BITS_PER_UINT, 0>
		sint e = -( exponent.ToInt() );
		mantissa.Rcr(e,0);

	return 0;
	}


	/*!
		a special method similar to the 'ToString_CreateNewMantissaAndExponent'
		when the 'base' is equal 2

		we use it because if base is equal 2 we don't have to make those
		complicated calculations and the output is directly from the source
		(there will not be any small distortions)

		(we can make that speciality when the base is 4,8 or 16 as well 
		but maybe in further time)
	*/
	uint ToString_CreateNewMantissaAndExponent_Base2(	std::string & new_man,
														Int<exp+1> & new_exp     ) const
	{
		for( sint i=man-1 ; i>=0 ; --i )
		{
			uint value = mantissa.table[i]; 

			for( uint bit=0 ; bit<TTMATH_BITS_PER_UINT ; ++bit )
			{
				if( (value & TTMATH_UINT_HIGHEST_BIT) != 0 )
					new_man += '1';
				else
					new_man += '0';

				value <<= 1;
			}
		}

		new_exp = exponent;

	return 0;
	}


	/*!
		an auxiliary method for converting into the string

		this method roundes the last character from the new mantissa
		(it's used in systems where the base is different from 2)
	*/
	uint ToString_RoundMantissa(std::string & new_man, uint base, Int<exp+1> & new_exp, char decimal_point) const
	{
		// we must have minimum two characters
		if( new_man.length() < 2 )
			return 0;

		std::string::size_type i = new_man.length() - 1;

		// we're erasing the last character
		uint digit = UInt<man>::CharToDigit( new_man[i] );
		new_man.erase( i, 1 );
		uint carry = new_exp.AddOne();

		// if the last character is greater or equal 'base/2'
		// we'll add one into the new mantissa
		if( digit >= base / 2 )
			ToString_RoundMantissa_AddOneIntoMantissa(new_man, base, decimal_point);

	return carry;
	}
	

	/*!
		an auxiliary method for converting into the string

		this method addes one into the new mantissa
	*/
	void ToString_RoundMantissa_AddOneIntoMantissa(std::string & new_man, uint base, char decimal_point) const
	{
		if( new_man.empty() )
			return;

		sint i = sint( new_man.length() ) - 1;
		bool was_carry = true;

		for( ; i>=0 && was_carry ; --i )
		{
			// we can have the comma as well because
			// we're using this method later in ToString_CorrectDigitsAfterComma_Round()
			// (we're only ignoring it)
			if( new_man[i] == decimal_point )
				continue;

			// we're adding one
			uint digit = UInt<man>::CharToDigit( new_man[i] ) + 1;

			if( digit == base )
				digit = 0;
			else
				was_carry = false;

			new_man[i] = UInt<man>::DigitToChar( digit );
		}

		if( i<0 && was_carry )
			new_man.insert( new_man.begin() , '1' );
	}


	/*!
		an auxiliary method for converting into the string

		this method sets the comma operator and/or puts the exponent
		into the string
	*/
	uint ToString_SetCommaAndExponent(	std::string & new_man, uint base,
										Int<exp+1> & new_exp,
										bool always_scientific,
										sint when_scientific,
										sint max_digit_after_comma,
										bool remove_trailing_zeroes,
										char decimal_point) const
	{
	uint carry = 0;

		if( new_man.empty() )
			return carry;

		Int<exp+1> scientific_exp( new_exp );

		// 'new_exp' depends on the 'new_man' which is stored like this e.g:
		//  32342343234 (the comma is at the end)
		// we'd like to show it in this way:
		//  3.2342343234 (the 'scientific_exp' is connected with this example)

		sint offset = sint( new_man.length() ) - 1;
		carry += scientific_exp.Add( offset );
		// there shouldn't have been a carry because we're using
		// a greater type -- 'Int<exp+1>' instead of 'Int<exp>'

		if( !always_scientific )
		{
			if( scientific_exp > when_scientific || scientific_exp < -sint(when_scientific) )
				always_scientific = true;
		}

		// 'always_scientific' could be changed
		if( !always_scientific )
			ToString_SetCommaAndExponent_Normal(new_man, base, new_exp, max_digit_after_comma, remove_trailing_zeroes, decimal_point);
		else
			// we're passing the 'scientific_exp' instead of 'new_exp' here
			ToString_SetCommaAndExponent_Scientific(new_man, base, scientific_exp, max_digit_after_comma, remove_trailing_zeroes, decimal_point);

	return (carry==0)? 0 : 1;
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_SetCommaAndExponent_Normal(
											std::string & new_man,
											uint base, 
											Int<exp+1> & new_exp,
											sint max_digit_after_comma,
											bool remove_trailing_zeroes,
											char decimal_point) const
	{
		if( !new_exp.IsSign() ) //if( new_exp >= 0 )
			return ToString_SetCommaAndExponent_Normal_AddingZero(new_man, new_exp);
		else
			return ToString_SetCommaAndExponent_Normal_SetCommaInside(new_man, base, new_exp, max_digit_after_comma, remove_trailing_zeroes, decimal_point);
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_SetCommaAndExponent_Normal_AddingZero(std::string & new_man,
																Int<exp+1> & new_exp) const
	{
		// we're adding zero characters at the end
		// 'i' will be smaller than 'when_scientific' (or equal)
		uint i = new_exp.ToInt();
		
		if( new_man.length() + i > new_man.capacity() )
			// about 6 characters more (we'll need it for the comma or something)
			new_man.reserve( new_man.length() + i + 6 );
		
		for( ; i>0 ; --i)
			new_man += '0';
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_SetCommaAndExponent_Normal_SetCommaInside(
														std::string & new_man,
														uint base,
														Int<exp+1> & new_exp,
														sint max_digit_after_comma,
														bool remove_trailing_zeroes,
														char decimal_point) const
	{
		// new_exp is < 0 

		sint new_man_len = sint(new_man.length()); // 'new_man_len' with a sign
		sint e = -( new_exp.ToInt() ); // 'e' will be positive

		if( new_exp > -new_man_len )
		{
			// we're setting the comma within the mantissa
			
			sint index = new_man_len - e;
			new_man.insert( new_man.begin() + index, decimal_point);
		}
		else
		{
			// we're adding zero characters before the mantissa

			uint how_many = e - new_man_len;
			std::string man_temp(how_many+1, '0');

			man_temp.insert( man_temp.begin()+1, decimal_point);
			new_man.insert(0, man_temp);
		}

		ToString_CorrectDigitsAfterComma(new_man, base, max_digit_after_comma, remove_trailing_zeroes, decimal_point);
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_SetCommaAndExponent_Scientific(	std::string & new_man,
													uint base,
													Int<exp+1> & scientific_exp,
													sint max_digit_after_comma,
													bool remove_trailing_zeroes,
													char decimal_point) const
	{
		if( new_man.empty() )
			return;
		
		new_man.insert( new_man.begin()+1, decimal_point );

		ToString_CorrectDigitsAfterComma(new_man, base, max_digit_after_comma, remove_trailing_zeroes, decimal_point);
	
		if( base == 10 )
		{
			new_man += 'e';

			if( !scientific_exp.IsSign() )
				new_man += "+";
		}
		else
		{
			// the 10 here is meant as the base 'base'
			// (no matter which 'base' we're using there'll always be 10 here)
			new_man += "*10^";
		}

		std::string temp_exp;
		scientific_exp.ToString( temp_exp, base );

		new_man += temp_exp;
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_CorrectDigitsAfterComma(	std::string & new_man,
											uint base,
											sint max_digit_after_comma,
											bool remove_trailing_zeroes,
											char decimal_point) const
	{
		if( max_digit_after_comma >= 0 )
			ToString_CorrectDigitsAfterComma_Round(new_man, base, max_digit_after_comma, decimal_point);

		if( remove_trailing_zeroes )
			ToString_CorrectDigitsAfterComma_CutOffZeroCharacters(new_man, decimal_point);
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_CorrectDigitsAfterComma_CutOffZeroCharacters(
												std::string & new_man,
												char decimal_point) const
	{
		// minimum two characters
		if( new_man.length() < 2 )
			return;

		// we're looking for the index of the last character which is not zero
		uint i = uint( new_man.length() ) - 1;
		for( ; i>0 && new_man[i]=='0' ; --i );

		// if there is another character than zero at the end
		// we're finishing
		if( i == new_man.length() - 1 )
			return;

		// we must have a comma 
		// (the comma can be removed by ToString_CorrectDigitsAfterComma_Round
		// which is called before)
		if( new_man.find_last_of(decimal_point, i) == std::string::npos )
			return;

		// if directly before the first zero is the comma operator
		// we're cutting it as well
		if( i>0 && new_man[i]==decimal_point )
			--i;

		new_man.erase(i+1, new_man.length()-i-1);
	}


	/*!
		an auxiliary method for converting into the string
	*/
	void ToString_CorrectDigitsAfterComma_Round(
											std::string & new_man,
											uint base,
											sint max_digit_after_comma,
											char decimal_point) const
	{
		// first we're looking for the comma operator
		std::string::size_type index = new_man.find(decimal_point, 0);

		if( index == std::string::npos )
			// nothing was found (actually there can't be this situation)
			return;

		// we're calculating how many digits there are at the end (after the comma)
		// 'after_comma' will be greater than zero because at the end
		// we have at least one digit
		std::string::size_type after_comma = new_man.length() - index - 1;

		// if 'max_digit_after_comma' is greater than 'after_comma' (or equal)
		// we don't have anything for cutting
		if( std::string::size_type(max_digit_after_comma) >= after_comma )
			return;

		uint last_digit = UInt<man>::CharToDigit( new_man[ index + max_digit_after_comma + 1 ], base );

		// we're cutting the rest of the string
		new_man.erase(index + max_digit_after_comma + 1, after_comma - max_digit_after_comma);

		if( max_digit_after_comma == 0 )
		{
			// we're cutting the comma operator as well
			// (it's not needed now because we've cut the whole rest after the comma)
			new_man.erase(index, 1);
		}

		if( last_digit >= base / 2 )
			// we must round here
			ToString_RoundMantissa_AddOneIntoMantissa(new_man, base, decimal_point);
	}




public:


	/*!
		a method for converting a string into its value

		it returns 1 if the value will be too big -- we cannot pass it into the range
		of our class Big<exp,man> (or if the base is incorrect)

		that means only digits before the comma operator can make this value too big, 
		all digits after the comma we can ignore

		'source' - pointer to the string for parsing

		if 'after_source' is set that when this method finishes
		it sets the pointer to the new first character after parsed value

		'value_read' - if the pointer is provided that means the value_read will be true
		only when a value has been actually read, there can be situation where only such
		a string '-' or '+' will be parsed -- 'after_source' will be different from 'source' but
		no value has been read (there are no digits)
		on other words if 'value_read' is true -- there is at least one digit in the string
	*/
	uint FromString(const char * source, uint base = 10, const char ** after_source = 0, bool * value_read = 0)
	{
	bool is_sign;
	bool value_read_temp = false;

		if( base<2 || base>16 )
		{
			SetNan();

			if( after_source )
				*after_source = source;

			if( value_read )
				*value_read = value_read_temp;

			return 1;
		}

		SetZero();
		FromString_TestSign( source, is_sign );

		uint c = FromString_ReadPartBeforeComma( source, base, value_read_temp );

		if( FromString_TestCommaOperator(source) )
			c += FromString_ReadPartAfterComma( source, base, value_read_temp );

		if( value_read_temp && base == 10 )
			c += FromString_ReadScientificIfExists( source );

		if( is_sign && !IsZero() )
			ChangeSign();

		if( after_source )
			*after_source = source;

		if( value_read )
			*value_read = value_read_temp;

	return CheckCarry(c);
	}



private:


	/*!
		we're testing whether the value is with the sign

		(this method is used from 'FromString_ReadPartScientific' too)
	*/
	void FromString_TestSign( const char * & source, bool & is_sign )
	{
		UInt<man>::SkipWhiteCharacters(source);

		is_sign = false;

		if( *source == '-' )
		{
			is_sign = true;
			++source;
		}
		else
		if( *source == '+' )
		{
			++source;
		}
	}


	/*!
		we're testing whether there's a comma operator
	*/
	bool FromString_TestCommaOperator(const char * & source)
	{
		if( (*source == TTMATH_COMMA_CHARACTER_1) || 
			(*source == TTMATH_COMMA_CHARACTER_2 && TTMATH_COMMA_CHARACTER_2 != 0 ) )
		{
			++source;

		return true;
		}

	return false;
	}


	/*!
		this method reads the first part of a string
		(before the comma operator)
	*/
	uint FromString_ReadPartBeforeComma( const char * & source, uint base, bool & value_read )
	{
		sint character;
		Big<exp, man> temp;
		Big<exp, man> base_( base );
		
		UInt<man>::SkipWhiteCharacters( source );

		for( ; (character=UInt<man>::CharToDigit(*source, base)) != -1 ; ++source )
		{
			value_read = true;

			temp = character;

			if( Mul(base_) )
				return 1;

			if( Add(temp) )
				return 1;
		}

	return 0;
	}


	/*!
		this method reads the second part of a string
		(after the comma operator)
	*/
	uint FromString_ReadPartAfterComma( const char * & source, uint base, bool & value_read )
	{
	sint character;
	uint c = 0, index = 1;
	Big<exp, man> part, power, old_value, base_( base );

		// we don't remove any white characters here

		// this is only to avoid getting a warning about an uninitialized object 'old_value' which GCC reports
		// (in fact we will initialize it later when the condition 'testing' is fulfilled)
		old_value.SetZero();

		power.SetOne();

		for( ; (character=UInt<man>::CharToDigit(*source, base)) != -1 ; ++source, ++index )
		{
			value_read = true;

			part = character;

			if( power.Mul( base_ ) )
				// there's no sens to add the next parts, but we can't report this
				// as an error (this is only inaccuracy)
				break;

			if( part.Div( power ) )
				break;

			// every 5 iteration we make a test whether the value will be changed or not
			// (character must be different from zero to this test)
			bool testing = (character != 0 && (index % 5) == 0);

			if( testing )
				old_value = *this;

			// there actually shouldn't be a carry here
			c += Add( part );

			if( testing && old_value == *this )
				// after adding 'part' the value has not been changed
				// there's no sense to add any next parts
				break;
		}

		// we could break the parsing somewhere in the middle of the string,
		// but the result (value) still can be good
		// we should set a correct value of 'source' now
		for( ; UInt<man>::CharToDigit(*source, base) != -1 ; ++source );

	return (c==0)? 0 : 1;
	}


	/*!
		this method checks whether there is a scientific part: [e|E][-|+]value

		it is called when the base is 10 and some digits were read before
	*/
	uint FromString_ReadScientificIfExists(const char * & source)
	{
	uint c = 0;

		bool scientific_read = false;
		const char * before_scientific = source;

		if( FromString_TestScientific(source) )
			c += FromString_ReadPartScientific( source, scientific_read );

		if( !scientific_read )
			source = before_scientific;

	return (c==0)? 0 : 1;
	}



	/*!
		we're testing whether is there the character 'e'

		this character is only allowed when we're using the base equals 10
	*/
	bool FromString_TestScientific(const char * & source)
	{
		UInt<man>::SkipWhiteCharacters(source);

		if( *source=='e' || *source=='E' )
		{
			++source;

		return true;
		}

	return false;
	}


	/*!
		this method reads the exponent (after 'e' character) when there's a scientific
		format of value and only when we're using the base equals 10
	*/
	uint FromString_ReadPartScientific( const char * & source, bool & scientific_read )
	{
	uint c = 0;
	Big<exp, man> new_exponent, temp;
	bool was_sign = false;

		FromString_TestSign( source, was_sign );
		c += FromString_ReadPartScientific_ReadExponent( source, new_exponent, scientific_read );

		if( scientific_read )
		{
			if( was_sign )
				new_exponent.ChangeSign();

			temp = 10;
			c += temp.Pow( new_exponent );
			c += Mul(temp);
		}

	return (c==0)? 0 : 1;
	}


	/*!
		this method reads the value of the extra exponent when scientific format is used
		(only when base == 10)
	*/
	uint FromString_ReadPartScientific_ReadExponent( const char * & source, Big<exp, man> & new_exponent, bool & scientific_read )
	{
	sint character;
	Big<exp, man> base, temp;

		UInt<man>::SkipWhiteCharacters(source);

		new_exponent.SetZero();
		base = 10;

		for( ; (character=UInt<man>::CharToDigit(*source, 10)) != -1 ; ++source )
		{
			scientific_read = true;

			temp = character;

			if( new_exponent.Mul(base) )
				return 1;

			if( new_exponent.Add(temp) )
				return 1;
		}

	return 0;
	}


public:


	/*!
		a method for converting a string into its value		
	*/
	uint FromString(const std::string & string, uint base = 10)
	{
		return FromString( string.c_str(), base );
	}


	/*!
		a constructor for converting a string into this class
	*/
	Big(const char * string)
	{
		FromString( string );
	}


	/*!
		a constructor for converting a string into this class
	*/
	Big(const std::string & string)
	{
		FromString( string.c_str() );
	}


	/*!
		an operator= for converting a string into its value
	*/
	Big<exp, man> & operator=(const char * string)
	{
		FromString( string );

	return *this;
	}


	/*!
		an operator= for converting a string into its value
	*/
	Big<exp, man> & operator=(const std::string & string)
	{
		FromString( string.c_str() );

	return *this;
	}



	/*!
	*
	*	methods for comparing
	*
	*/


	/*!
		this method performs the formula 'abs(this) < abs(ss2)'
		and returns the result

		(in other words it treats 'this' and 'ss2' as values without a sign)
		we don't check the NaN flag
	*/
	bool SmallerWithoutSignThan(const Big<exp,man> & ss2) const
	{
		// we should check the mantissas beforehand because sometimes we can have
		// a mantissa set to zero but in the exponent something another value
		// (maybe we've forgotten about calling CorrectZero() ?)
		if( mantissa.IsZero() )
		{
			if( ss2.mantissa.IsZero() )
				// we've got two zeroes
				return false;
			else
				// this==0 and ss2!=0
				return true;
		}

		if( ss2.mantissa.IsZero() )
			// this!=0 and ss2==0
			return false;

		// we're using the fact that all bits in mantissa are pushed
		// into the left side -- Standardizing()
		if( exponent == ss2.exponent )
			return mantissa < ss2.mantissa;

	return exponent < ss2.exponent;
	}


	/*!
		this method performs the formula 'abs(this) > abs(ss2)'
		and returns the result

		(in other words it treats 'this' and 'ss2' as values without a sign)
		we don't check the NaN flag
	*/
	bool GreaterWithoutSignThan(const Big<exp,man> & ss2) const
	{
		// we should check the mantissas beforehand because sometimes we can have
		// a mantissa set to zero but in the exponent something another value
		// (maybe we've forgotten about calling CorrectZero() ?)
		if( mantissa.IsZero() )
		{
			if( ss2.mantissa.IsZero() )
				// we've got two zeroes
				return false;
			else
				// this==0 and ss2!=0
				return false;
		}

		if( ss2.mantissa.IsZero() )
			// this!=0 and ss2==0
			return true;

		// we're using the fact that all bits in mantissa are pushed
		// into the left side -- Standardizing()
		if( exponent == ss2.exponent )
			return mantissa > ss2.mantissa;

	return exponent > ss2.exponent;
	}


	/*!
		this method performs the formula 'abs(this) == abs(ss2)'
		and returns the result

		(in other words it treats 'this' and 'ss2' as values without a sign)
		we don't check the NaN flag
	*/
	bool EqualWithoutSign(const Big<exp,man> & ss2) const
	{
		// we should check the mantissas beforehand because sometimes we can have
		// a mantissa set to zero but in the exponent something another value
		// (maybe we've forgotten about calling CorrectZero() ?)
		if( mantissa.IsZero() )
		{
			if( ss2.mantissa.IsZero() )
				// we've got two zeroes
				return true;
			else
				// this==0 and ss2!=0
				return false;
		}

		if( ss2.mantissa.IsZero() )
			// this!=0 and ss2==0
			return false;

		if( exponent==ss2.exponent && mantissa==ss2.mantissa )
			return true;

	return false;
	}


	bool operator<(const Big<exp,man> & ss2) const
	{
		if( IsSign() && !ss2.IsSign() )
			// this<0 and ss2>=0
			return true;

		if( !IsSign() && ss2.IsSign() )
			// this>=0 and ss2<0
			return false;

		// both signs are the same

		if( IsSign() )
			return ss2.SmallerWithoutSignThan( *this );

	return SmallerWithoutSignThan( ss2 );
	}




	bool operator==(const Big<exp,man> & ss2) const
	{
		if( IsSign() != ss2.IsSign() )
			return false;

	return EqualWithoutSign( ss2 );
	}




	bool operator>(const Big<exp,man> & ss2) const
	{
		if( IsSign() && !ss2.IsSign() )
			// this<0 and ss2>=0
			return false;

		if( !IsSign() && ss2.IsSign() )
			// this>=0 and ss2<0
			return true;

		// both signs are the same

		if( IsSign() )
			return ss2.GreaterWithoutSignThan( *this );

	return GreaterWithoutSignThan( ss2 );
	}



	bool operator>=(const Big<exp,man> & ss2) const
	{
		return !operator<( ss2 );
	}


	bool operator<=(const Big<exp,man> & ss2) const
	{
		return !operator>( ss2 );
	}


	bool operator!=(const Big<exp,man> & ss2) const
	{
		return !operator==(ss2);
	}





	/*!
	*
	*	standard mathematical operators 
	*
	*/


	/*!
		an operator for changing the sign

		it's not changing 'this' but the changed value will be returned
	*/
	Big<exp,man> operator-() const
	{
		Big<exp,man> temp(*this);

		temp.ChangeSign();

	return temp;
	}


	Big<exp,man> operator-(const Big<exp,man> & ss2) const
	{
	Big<exp,man> temp(*this);

		temp.Sub(ss2);

	return temp;
	}

	Big<exp,man> & operator-=(const Big<exp,man> & ss2)
	{
		Sub(ss2);

	return *this;
	}


	Big<exp,man> operator+(const Big<exp,man> & ss2) const
	{
	Big<exp,man> temp(*this);

		temp.Add(ss2);

	return temp;
	}


	Big<exp,man> & operator+=(const Big<exp,man> & ss2)
	{
		Add(ss2);

	return *this;
	}


	Big<exp,man> operator*(const Big<exp,man> & ss2) const
	{
	Big<exp,man> temp(*this);

		temp.Mul(ss2);

	return temp;
	}


	Big<exp,man> & operator*=(const Big<exp,man> & ss2)
	{
		Mul(ss2);

	return *this;
	}


	Big<exp,man> operator/(const Big<exp,man> & ss2) const
	{
	Big<exp,man> temp(*this);

		temp.Div(ss2);

	return temp;
	}


	Big<exp,man> & operator/=(const Big<exp,man> & ss2)
	{
		Div(ss2);

	return *this;
	}


	/*!
		this method makes an integer value by skipping any fractions

		for example:
			10.7 will be 10
			12.1  -- 12
			-20.2 -- 20
			-20.9 -- 20
			-0.7  -- 0
			0.8   -- 0
	*/
	void SkipFraction()
	{
		if( IsNan() || IsZero() )
			return;

		if( !exponent.IsSign() )
			// exponent >=0 -- the value don't have any fractions
			return;

		if( exponent <= -sint(man*TTMATH_BITS_PER_UINT) )
		{
			// the value is from (-1,1), we return zero
			SetZero();
			return;
		}

		// exponent is in range (-man*TTMATH_BITS_PER_UINT, 0)
		sint e = exponent.ToInt();
	
		mantissa.ClearFirstBits( -e );
		
		// we don't have to standardize 'Standardizing()' the value because
		// there's at least one bit in the mantissa
		// (the highest bit which we didn't touch)
	}


	/*!
		this method remains only a fraction from the value

		for example:
			30.56 will be 0.56
			-12.67 -- -0.67
	*/
	void RemainFraction()
	{
		if( IsNan() || IsZero() )
			return;

		if( !exponent.IsSign() )
		{
			// exponent >= 0 -- the value doesn't have any fractions
			// we return zero
			SetZero();
			return;
		}

		if( exponent <= -sint(man*TTMATH_BITS_PER_UINT) )
		{
			// the value is from (-1,1)
			// we don't make anything with the value
			return;
		}

		// e will be from (-man*TTMATH_BITS_PER_UINT, 0)
		sint e = exponent.ToInt();

		sint how_many_bits_leave = sint(man*TTMATH_BITS_PER_UINT) + e; // there'll be a subtraction -- e is negative
		mantissa.Rcl( how_many_bits_leave, 0);

		// there'll not be a carry because the exponent is too small
		exponent.Sub( how_many_bits_leave );

		// we must call Standardizing() here
		Standardizing();
	}




	/*!
		this method rounds to the nearest integer value
		(it returns a carry if it was)

		for example:
			2.3 = 2
			2.8 = 3

			-2.3 = -2
			-2.8 = 3
	*/
	uint Round()
	{
	Big<exp,man> half;
	uint c;

		if( IsNan() )
			return 1;

		half.Set05();

		if( IsSign() )
		{
			// 'this' is < 0
			c = Sub( half );
		}
		else
		{
			// 'this' is >= 0
			c = Add( half );
		}

		SkipFraction();

	return CheckCarry(c);
	}





	/*!
	*
	*	input/output operators for standard streams
	*
	*/

	friend std::ostream & operator<<(std::ostream & s, const Big<exp,man> & l)
	{
	std::string ss;

		l.ToString(ss);
		s << ss;

	return s;
	}


	friend std::istream & operator>>(std::istream & s, Big<exp,man> & l)
	{
	std::string ss;
	
	// 'char' for operator>>
	unsigned char z;
	bool was_comma = false;

		// operator>> omits white characters if they're set for ommiting
		s >> z;

		if( z=='-' || z=='+' )
		{
			ss += z;
			s >> z; // we're reading a next character (white characters can be ommited)
		}

		// we're reading only digits (base=10) and only one comma operator
		for( ; s.good() ; z=s.get() )
		{
			if( z == TTMATH_COMMA_CHARACTER_1 ||
			  ( z == TTMATH_COMMA_CHARACTER_2 && TTMATH_COMMA_CHARACTER_2 != 0 ) )
			{
				if( was_comma )
					// second comma operator
					break;

				was_comma = true;
			}
			else
			if( UInt<man>::CharToDigit(z, 10) < 0 )
				break;


			ss += z;
		}

		// we're leaving the last read character
		// (it's not belonging to the value)
		s.unget();

		l.FromString( ss );

	return s;
	}

};


} // namespace

#endif