changed: version of the library: 0.9.1 now

git-svn-id: svn://ttmath.org/publicrep/ttmath/trunk@286 e52654a7-88a9-db11-a3e9-0013d4bc506e

CHANGELOG

@@ -1,3 +1,30 @@
+Version 0.9.1 (2010.02.07):
+    * fixed:   the parser didn't use characters for changing the base (# and &)
+               those characters were skipped
+               (this bug was introduced in 0.9.0)
+    * fixed:   added in the parser: operator's associativity
+               operator ^ (powering) is right-associative:
+               sample: 2^3^4 is equal 2^(3^4) and it is: 2.41e+24
+               previously was: 2^3^4 = (2^3)^4 = 4096
+    * fixed:   in Big::ToString_CreateNewMantissaAndExponent() changed the formula:
+               new_exp_ = [log base (2^exponent)] + 1
+               now the part '+ 1' is only made when the logarithm is positive and with fraction
+               if the value is negative we can only skip the fraction, previously
+               we lost some last digits from the new mantissa
+               Consider this binary value (32 bit mantissa):
+               (bin)1.0000000000000000000000000000011
+               previously ToString() gave 1, now we have: 1.000000001
+    * changed: in Big::ToString() the base rounding is made only if the result value
+               would not be an integer, e.g. if the value is 1.999999999999 then
+               the base rounding will not be done - because as the result would be 2
+    * added:   IEEE 754 half-to-even rounding (bankers' rounding) to the following
+               floating point algorithms: Big::Add, Big::Sub, Big::Mul, Big::Div
+    * added:   static sint UInt<value_size>::FindLowestBitInWord(uint x)
+               this method is looking for the lowest set bit in a word
+    * added:   UInt::FindLowestBit(uint & table_id, uint & index)
+               this method is looking for the lowest set bit
+
+               
 Version 0.9.0 (2009.11.25):
     * added:   support for wide characters (wchar_t, std::wstring)
     * added:   Big::IsInteger()

COPYRIGHT

@@ -1,4 +1,4 @@
-Copyright (c) 2006-2009, Tomasz Sowa
+Copyright (c) 2006-2010, Tomasz Sowa
 All rights reserved.
 
 Redistribution and use in source and binary forms, with or without

samples/Makefile

@@ -8,7 +8,7 @@ CFLAGS = -Wall -pedantic -s -O2 -I..
 	$(CC) -c $(CFLAGS) $<
 
 
-all: uint int big parser
+all: uint int big big2 parser
 
 
 uint: uint.o
@@ -20,6 +20,9 @@ int: int.o
 big: big.o
 	$(CC) -o big $(CFLAGS) big.o
 
+big2: big2.o
+	$(CC) -o big2 $(CFLAGS) big2.o
+
 parser: parser.o
 	$(CC) -o parser $(CFLAGS) parser.o
 
@@ -27,6 +30,7 @@ parser: parser.o
 uint.o:		uint.cpp
 int.o:		int.cpp
 big.o:		big.cpp
+big2.o:		big2.cpp
 parser.o:	parser.cpp
 
 
@@ -36,6 +40,7 @@ clean:
 	rm -f uint
 	rm -f int
 	rm -f big
+	rm -f big2
 	rm -f parser
 # on MS Windows can automatically be added suffixes .exe to the names of output programs
 	rm -f *.exe

samples/big.cpp

@@ -5,6 +5,8 @@
 // this type has 2 words for its mantissa and 1 word for its exponent
 // (on a 32bit platform one word means a word of 32 bits,
 // and on a 64bit platform one word means a word of 64 bits)
+
+// Big<exponent, mantissa>
 typedef ttmath::Big<1,2> MyBig;
 
        
@@ -56,6 +58,7 @@ MyBig atemp;
 	
 }
 
+
 int main()
 {
 MyBig a,b;
@@ -86,12 +89,12 @@ b = 98767878.124322
 a + b = 98891334.667778
 a - b = -98644421.580866
 a * b = 12193540837712.2708
-a / b = 0.0012499665458095765
+a / b = 0.00124996654580957646
 Calculating with a carry
-a = 1.624801256070839555e+646457012
-b = 456.31999999999999
-a + b = 1.624801256070839555e+646457012
-a - b = 1.624801256070839555e+646457012
+a = 1.624801256066640878e+646457012
+b = 456.319999999999993
+a + b = 1.624801256066640878e+646457012
+a - b = 1.624801256066640878e+646457012
 a * b = (carry)
-a / b = 3.56066193914542334e+646457009
+a / b = 3.560661939136222174e+646457009
 */

samples/big2.cpp

@@ -0,0 +1,113 @@
+#include <ttmath/ttmath.h>
+#include <iostream>
+
+
+// this is a similar example to big.cpp
+// but now we're using TTMATH_BITS() macro
+// this macro returns how many words we need to store
+// the given number of bits
+
+// TTMATH_BITS(64) 
+//   on a 32bit platform the macro returns 2 (2*32=64)
+//   on a 64bit platform the macro returns 1
+
+// TTMATH_BITS(128)
+//   on a 32bit platform the macro returns 4 (4*32=128)
+//   on a 64bit platform the macro returns 2 (2*64=128)
+
+// Big<exponent, mantissa>
+typedef ttmath::Big<TTMATH_BITS(64), TTMATH_BITS(128)> MyBig;
+
+// consequently on a 32bit platform we define: Big<2, 4>
+// and on a 64bit platform: Big<1, 2>
+// and the calculations will be the same on both platforms       
+       
+       
+void SimpleCalculating(const MyBig & a, const MyBig & b)
+{
+	std::cout << "Simple calculating" << std::endl;
+	std::cout << "a = " << a << std::endl;
+	std::cout << "b = " << b << std::endl;
+	std::cout << "a + b = " << a+b << std::endl;
+	std::cout << "a - b = " << a-b << std::endl;
+	std::cout << "a * b = " << a*b << std::endl;
+	std::cout << "a / b = " << a/b << std::endl;
+}
+
+
+void CalculatingWithCarry(const MyBig & a, const MyBig & b)
+{
+MyBig atemp;
+
+	std::cout << "Calculating with a carry" << std::endl;
+	std::cout << "a = " << a << std::endl;
+	std::cout << "b = " << b << std::endl;
+
+	atemp = a;
+	if( !atemp.Add(b) )
+		std::cout << "a + b = " << atemp << std::endl;
+	else
+		std::cout << "a + b = (carry)" << std::endl;
+		// it have no sense to print 'atemp' (it's undefined)
+
+	atemp = a;
+	if( !atemp.Sub(b) )
+		std::cout << "a - b = " << atemp << std::endl;
+	else
+		std::cout << "a - b = (carry)" << std::endl;
+		
+	atemp = a;
+	if( !atemp.Mul(b) )
+		std::cout << "a * b = " << atemp << std::endl;
+	else
+		std::cout << "a * b = (carry)" << std::endl;
+		
+		
+	atemp = a;
+	if( !atemp.Div(b) )
+		std::cout << "a / b = " << atemp << std::endl;
+	else
+		std::cout << "a / b = (carry or division by zero) " << std::endl;
+	
+}
+
+
+int main()
+{
+MyBig a,b;
+	
+	// conversion from 'const char *'
+	a = "123456.543456";
+	b = "98767878.124322";
+	
+	SimpleCalculating(a,b);
+	
+	// 'a' will have the max value which can be held in this type
+	a.SetMax();
+	
+	// conversion from double
+	b = 456.32;
+	
+	// Look at the value 'a' and the product from a+b and a-b
+	// Don't worry this is the nature of floating point numbers
+	CalculatingWithCarry(a,b);
+}
+
+/*
+the result (the same on a 32 or 64bit platform):
+
+Simple calculating
+a = 123456.543456
+b = 98767878.124322
+a + b = 98891334.667778
+a - b = -98644421.580866
+a * b = 12193540837712.270763536832
+a / b = 0.001249966545809576460596448526166860913
+Calculating with a carry
+a = 2.3495345545711177736883282090959505003e+2776511644261678604
+b = 456.3199999999999931787897367030382156
+a + b = 2.3495345545711177736883282090959505003e+2776511644261678604
+a - b = 2.3495345545711177736883282090959505003e+2776511644261678604
+a * b = (carry)
+a / b = 5.1488748127873374141170361292780486452e+2776511644261678601
+*/

samples/parser.cpp

@@ -29,6 +29,11 @@ const char equation[] = " (34 + 24) * 123 - 34.32 ^ 6 * sin(2.56) - atan(10)";
 
 /*
 the result (on 32 bit platform):
-
 -897705014.52573107
 */
+
+
+/*
+the result (on 64 bit platform):
+-897705014.5257310676097719585259773124
+*/

ttmath/ttmath.h

@@ -2807,7 +2807,7 @@ namespace ttmath
 		}
 
 		// the simplest way to initialize is to call the Gamma function with (TTMATH_GAMMA_BOUNDARY + 1)
-		// when x is larger then less coefficients we need
+		// when x is larger then fewer coefficients we need
 		Gamma(x, *this);
 	}
 

ttmath/ttmathbig.h

@@ -5,7 +5,7 @@
  */
 
 /* 
- * Copyright (c) 2006-2009, Tomasz Sowa
+ * Copyright (c) 2006-2010, Tomasz Sowa
  * All rights reserved.
  * 
  * Redistribution and use in source and binary forms, with or without
@@ -714,6 +714,51 @@ public:
 
 
 
+private:
+
+	/*!
+		this method does the half-to-even rounding (banker's rounding)
+
+		if is_half is:
+		  true  - that means the rest was equal the half (0.5 decimal)
+		  false - that means the rest was greater than a half (greater than 0.5 decimal)
+
+	    if the rest was less than a half then don't call this method
+		(the rounding should does nothing then)
+	*/
+	uint RoundHalfToEven(bool is_half, bool rounding_up = true)
+	{
+	uint c = 0;
+
+		if( !is_half || mantissa.IsTheLowestBitSet() )
+		{
+			if( rounding_up )
+			{
+				if( mantissa.AddOne() )
+				{
+					mantissa.Rcr(1, 1);
+					c = exponent.AddOne();
+				}
+			}
+			else
+			{
+				#ifdef TTMATH_DEBUG
+				uint c_from_zero =
+				#endif
+				mantissa.SubOne();
+
+				// we're using rounding_up=false in Add() when the mantissas have different signs
+				// mantissa can be zero only when previous mantissa was equal to ss2.mantissa
+				// but in such a case 'last_bit_set' will not be set and consequently 'do_rounding' will be false
+				TTMATH_ASSERT( c_from_zero == 0 )
+			}
+		}
+
+	return c;
+	}
+
+
+
 
 
 	/*!
@@ -722,59 +767,76 @@ public:
 	*
 	*/
 
+private:
+
 
 	/*!
-		Addition this = this + ss2
-
-		it returns carry if the sum is too big
+		an auxiliary method for adding
 	*/
-	uint Add(Big<exp, man> ss2)
+	void AddCheckExponents(	Big<exp, man> & ss2,
+							Int<exp> & exp_offset,
+							bool & last_bit_set,
+							bool & rest_zero,
+							bool & do_adding,
+							bool & do_rounding)
 	{
-	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);
-
-		if( ss2.IsZero() )
-			return 0;
-
-		exp_offset.Sub( ss2.exponent );
-		exp_offset.Abs();
-
-		// (1) abs(this) will be >= abs(ss2)
-		if( SmallerWithoutSignThan(ss2) )
+		if( exp_offset == mantissa_size_in_bits )
 		{
-			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;
+			last_bit_set = ss2.mantissa.IsTheHighestBitSet();
+			rest_zero    = ss2.mantissa.AreFirstBitsZero(man*TTMATH_BITS_PER_UINT - 1);
+			do_rounding  = true;	// we'are only rounding
 		}
 		else
 		if( exp_offset < mantissa_size_in_bits )
 		{
+			uint moved = exp_offset.ToInt(); // how many times we must move ss2.mantissa
+			rest_zero  = true;
+
+			if( moved > 0 )
+			{
+				last_bit_set = static_cast<bool>( ss2.mantissa.GetBit(moved-1) );
+
+				if( moved > 1 )
+					rest_zero = ss2.mantissa.AreFirstBitsZero(moved - 1);
+			
 				// (2) moving 'exp_offset' times
-			ss2.mantissa.Rcr( exp_offset.ToInt(), 0 );
+				ss2.mantissa.Rcr(moved, 0);
 			}
 
+			do_adding    = true; 
+			do_rounding  = true;
+		}
+
+		// if exp_offset is greater than mantissa_size_in_bits then we do nothing
+		// ss2 is too small for taking into consideration in the sum
+	}
+
+
+	/*!
+		an auxiliary method for adding
+	*/
+	uint AddMantissas(	Big<exp, man> & ss2,
+						bool & last_bit_set,
+						bool & rest_zero,
+						bool & rounding_up)
+	{
+	uint c = 0;
 
 		if( IsSign() == ss2.IsSign() )
 		{
 			// values have the same signs
 			if( mantissa.Add(ss2.mantissa) )
 			{
-				mantissa.Rcr(1,1);
-				c = exponent.AddOne();
+				// we have one bit more from addition (carry)
+				// now rest_zero means the old rest_zero with the old last_bit_set
+				rest_zero    = (!last_bit_set && rest_zero);
+				last_bit_set = mantissa.Rcr(1,1);
+				c += exponent.AddOne();
 			}
+
+			rounding_up = true;
 		}
 		else
 		{
@@ -784,30 +846,80 @@ public:
 			// is greater than or equal to the mantissa of the ss2
 
 			#ifdef TTMATH_DEBUG
-			// this is to get rid of a warning saying that c_temp is not used
-			uint c_temp = /* mantissa.Sub(ss2.mantissa); */
+			uint c_temp =
 			#endif
 			mantissa.Sub(ss2.mantissa);
 
 			TTMATH_ASSERT( c_temp == 0 )
 		}
 
+	return c;
+	}
+
+
+public:
+
+
+	/*!
+		Addition this = this + ss2
+
+		it returns carry if the sum is too big
+	*/
+	uint Add(Big<exp, man> ss2, bool round = true)
+	{
+	bool last_bit_set, rest_zero, do_adding, do_rounding, rounding_up;
+	Int<exp> exp_offset( exponent );
+	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) )
+		{
+			// !! use Swap here (not implemented yet)
+			Big<exp, man> temp(ss2);
+
+			ss2   = *this;
+			*this = temp;
+		}
+	
+		if( ss2.IsZero() )
+			return 0;
+
+		last_bit_set = rest_zero = do_adding = do_rounding = rounding_up = false;
+		AddCheckExponents(ss2, exp_offset, last_bit_set, rest_zero, do_adding, do_rounding);
+
+		if( do_adding )
+			c += AddMantissas(ss2, last_bit_set, rest_zero, rounding_up);
+
+		if( !round || !last_bit_set )
+			do_rounding = false;
+
+		if( do_rounding )
+			c += RoundHalfToEven(rest_zero, rounding_up);
+
+		if( do_adding || do_rounding )
 			c += Standardizing();
 
 	return CheckCarry(c);
 	}
 
 
+
 	/*!
 		Subtraction this = this - ss2
 
 		it returns carry if the result is too big
 	*/
-	uint Sub(Big<exp, man> ss2)
+	uint Sub(Big<exp, man> ss2, bool round = true)
 	{
 		ss2.ChangeSign();
 
-	return Add(ss2);
+	return Add(ss2, round);
 	}
 		
 
@@ -1078,16 +1190,52 @@ public:
 	}
 
 
+private:
+
+
+	/*!
+		this method checks whether a table pointed by 'tab' and 'len'
+		has the value 0.5 decimal
+		(it is treated as the comma operator would be before the highest bit)
+		call this method only if the highest bit is set - you have to test it beforehand
+
+		return:
+		  true  - tab was equal the half (0.5 decimal)
+		  false - tab was greater than a half (greater than 0.5 decimal)
+
+	*/
+	bool CheckGreaterOrEqualHalf(uint * tab, uint len)
+	{
+	uint i;
+
+		TTMATH_ASSERT( len>0 && (tab[len-1] & TTMATH_UINT_HIGHEST_BIT)!=0 )
+
+		for(i=0 ; i<len-1 ; ++i)
+			if( tab[i] != 0 )
+				return false;
+
+		if( tab[i] != TTMATH_UINT_HIGHEST_BIT )
+			return false;
+
+	return true;
+	}
+
+
+
+public:
+
+
 	/*!
 		multiplication this = this * ss2
 		this method returns a carry
 	*/
-	uint Mul(const Big<exp, man> & ss2)
+	uint Mul(const Big<exp, man> & ss2, bool round = true)
 	{
 	TTMATH_REFERENCE_ASSERT( ss2 )
 
 	UInt<man*2> man_result;
-	uint i,c;
+	uint c = 0;
+	uint i;
 
 		if( IsNan() || ss2.IsNan() )
 			return CheckCarry(1);
@@ -1110,13 +1258,22 @@ public:
 		// 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();
+		uint exp_add = man * TTMATH_BITS_PER_UINT - i;
+
+		if( exp_add )
+			c += exponent.Add( exp_add );
 
-		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( round && (man_result.table[man-1] & TTMATH_UINT_HIGHEST_BIT) != 0 )
+		{
+			bool is_half = CheckGreaterOrEqualHalf(man_result.table, man);
+			c += RoundHalfToEven(is_half);		
+		}
+
 		if( IsSign() == ss2.IsSign() )
 		{
 			// the signs are the same, the result is positive
@@ -1143,7 +1300,7 @@ public:
 		1 - carry (in a division carry can be as well)
 		2 - improper argument (ss2 is zero)
 	*/
-	uint Div(const Big<exp, man> & ss2)
+	uint Div(const Big<exp, man> & ss2, bool round = true)
 	{
 	TTMATH_REFERENCE_ASSERT( ss2 )
 
@@ -1187,6 +1344,12 @@ public:
 		for(i=0 ; i<man ; ++i)
 			mantissa.table[i] = man1.table[i+man];
 
+		if( round && (man1.table[man-1] & TTMATH_UINT_HIGHEST_BIT) != 0 )
+		{
+			bool is_half = CheckGreaterOrEqualHalf(man1.table, man);
+			c += RoundHalfToEven(is_half);
+		}
+
 		if( IsSign() == ss2.IsSign() )
 			Abs();
 		else
@@ -1408,7 +1571,7 @@ public:
 			if( pow.Mod2() )
 				c += result.Mul(start);
 
-			c += pow.exponent.Sub( e_one );
+			c += pow.exponent.Sub( e_one ); // !! may use SubOne() here?
 
 			if( pow < one )
 				break;
@@ -3058,22 +3221,12 @@ private:
 		*/
 		Int<exp+1> new_exp;
 
-		if( ToString_CreateNewMantissaAndExponent(result, conv, new_exp) )
+		if( ToString_CreateNewMantissaAndExponent<string_type, char_type>(result, conv, new_exp) )
 		{
 			Misc::AssignString(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( conv.base_round && conv.base!=2 && conv.base!=4 && conv.base!=8 && conv.base!=16 )
-			if( ToString_RoundMantissa<string_type, char_type>(result, conv, new_exp) )
-			{
-				Misc::AssignString(result, error_overflow_msg);
-				return 1;
-			}
 			
 		if( ToString_SetCommaAndExponent<string_type, char_type>(result, conv, new_exp) )
 		{
@@ -3084,6 +3237,7 @@ private:
 		if( IsSign() )
 			result.insert(result.begin(), '-');
 
+
 	// converted successfully
 	return 0;
 	}
@@ -3143,7 +3297,7 @@ private:
 			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
+		abs(ee) must not be too big that only few bits from mm we can leave
 
 		then we'll have:
 			M = mmm * 2^0
@@ -3154,10 +3308,13 @@ private:
 			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
+			but we need new_exp as integer then we test:
+			if new_exp is greater than zero and with fraction we add one to new_exp
+			  new_exp = new_exp + 1    (if new_exp>0 and with fraction)
+			and at the end we take the integer part:
+			  new_exp = int(new_exp)
 	*/
-	template<class string_type>
+	template<class string_type, class char_type>
 	uint ToString_CreateNewMantissaAndExponent(	string_type & new_man, const Conv & conv,
 												Int<exp+1> & new_exp) const
 	{
@@ -3193,12 +3350,26 @@ private:
 		temp.mantissa.SetOne();
 		c += temp.Standardizing();
 
-		// new_exp_ = [log base (2^exponent)] + 1
+		// new_exp_ = log base (2^exponent)   
+		// if new_exp_ is positive and with fraction then we add one 
 		Big<exp+1,man> new_exp_;
 		c += new_exp_.ToString_Log(temp, conv.base); // this logarithm isn't very complicated
-		new_exp_.SkipFraction();
+
+		// adding some epsilon value (to get rid of some floating point errors)
+		temp.Set05();
+		temp.exponent.SubOne(); // temp = 0.5/2 = 0.25
+		c += new_exp_.Add(temp);
+
+		if( !new_exp_.IsSign() && !new_exp_.IsInteger() )
+		{
+			// new_exp_ > 0 and with fraction
 			temp.SetOne();
 			c += new_exp_.Add( temp );
+		}
+
+		// new_exp_ = int(new_exp_)
+		new_exp_.SkipFraction();
+
 
 		// because 'base^new_exp' is >= '2^exponent' then 
 		// because base is >= 2 then we've got:
@@ -3219,7 +3390,7 @@ private:
 		// the sign don't interest us here
 		temp.mantissa = mantissa;
 		temp.exponent = exponent;
-		c += temp.Div( base_ );
+		c += temp.Div(base_, false); // dividing without rounding
 
 		// moving all bits of the mantissa into the right 
 		// (how many times to move depend on the exponent)
@@ -3232,9 +3403,9 @@ private:
 		// maximum valid bits
 		temp.mantissa.ToString(new_man, conv.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)
+		// base rounding
+		if( conv.base_round )
+			c += ToString_BaseRound<string_type, char_type>(new_man, conv, new_exp);
 
 	return (c==0)? 0 : 1;
 	}
@@ -3569,21 +3740,68 @@ private:
 
 	/*!
 		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)
 	*/
 	template<class string_type, class char_type>
-	uint ToString_RoundMantissa(string_type & new_man, const Conv & conv, Int<exp+1> & new_exp) const
+	bool ToString_RoundMantissaWouldBeInteger(string_type & new_man, const Conv & conv, Int<exp+1> & new_exp) const
+	{
+		// if new_exp is greater or equal to zero then we have an integer value,
+		// if new_exp is equal -1 then we have only one digit after the comma
+		// and after rounding it would be an integer value
+		if( !new_exp.IsSign() || new_exp == -1 )
+			return true;
+
+		if( new_man.size() >= TTMATH_UINT_HIGHEST_BIT || new_man.size() < 2 )
+			return true; // oops, the mantissa is too large for calculating (or too small) - we are not doing the base rounding
+		
+		uint i = 0;
+		char_type digit;
+
+		if( new_exp >= -sint(new_man.size()) )
+		{
+			uint new_exp_abs = -new_exp.ToInt();
+			i = new_man.size() - new_exp_abs; // start from the first digit after the comma operator
+		}
+		
+		if( Misc::CharToDigit(new_man[new_man.size()-1]) >= conv.base/2 )
+		{
+			if( new_exp < -sint(new_man.size()) )
+			{
+				// there are some zeroes after the comma operator
+				// (between the comma and the first digit from the mantissa)
+				// and the result value will never be an integer
+				return false;
+			}
+
+			digit = static_cast<char_type>( Misc::DigitToChar(conv.base-1) );
+		}
+		else
+		{
+			digit = '0';
+		}
+
+		for( ; i < new_man.size()-1 ; ++i)
+			if( new_man[i] != digit )
+				return false; // it will not be an integer
+
+	return true; // it will be integer after rounding
+	}
+
+
+	/*!
+		an auxiliary method for converting into the string
+
+		this method is used for base!=2, base!=4, base!=8 and base!=16
+		we do the rounding when the value has fraction (is not an integer)
+	*/
+	template<class string_type, class char_type>
+	uint ToString_BaseRound(string_type & new_man, const Conv & conv, Int<exp+1> & new_exp) const
 	{
 		// we must have minimum two characters
-		if( new_man.length() < 2 )
+		if( new_man.size() < 2 )
 			return 0;
 
-		// the rounding is only made when new_exp is less than zero
-		// if new_exp is greater or equal zero then the value is integer and 
-		// don't have to be rounded
-		if( !new_exp.IsSign() )
+		// assert that there will not be an integer after rounding
+		if( ToString_RoundMantissaWouldBeInteger<string_type, char_type>(new_man, conv, new_exp) )
 			return 0;
 
 		typename string_type::size_type i = new_man.length() - 1;
@@ -3591,14 +3809,14 @@ private:
 		// we're erasing the last character
 		uint digit = Misc::CharToDigit( new_man[i] );
 		new_man.erase(i, 1);
-		uint carry = new_exp.AddOne();
+		uint c = new_exp.AddOne();
 
 		// if the last character is greater or equal 'base/2'
-		// we'll add one into the new mantissa
+		// we are adding one into the new mantissa
 		if( digit >= conv.base / 2 )
 			ToString_RoundMantissa_AddOneIntoMantissa<string_type, char_type>(new_man, conv);
 
-	return carry;
+	return c;
 	}
 	
 
@@ -3640,6 +3858,7 @@ private:
 	}
 
 
+
 	/*!
 		an auxiliary method for converting into the string
 
@@ -3767,9 +3986,12 @@ private:
 		if( new_man.empty() )
 			return;
 		
+		if( new_man.size() > 1 )
+		{
 			new_man.insert( new_man.begin()+1, static_cast<char_type>(conv.comma) );
-
 			ToString_CorrectDigitsAfterComma<string_type, char_type>(new_man, conv);
+		}
+
 		ToString_Group_man<string_type, char_type>(new_man, conv);
 
 		if( conv.base == 10 )
@@ -4194,7 +4416,7 @@ private:
 	{
 	sint character;
 	uint c = 0, index = 1;
-	Big<exp, man> part, power, old_value, base_( conv.base );
+	Big<exp, man> sum, part, power, old_value, base_( conv.base );
 
 		// we don't remove any white characters here
 
@@ -4203,6 +4425,7 @@ private:
 		old_value.SetZero();
 
 		power.SetOne();
+		sum.SetZero();
 
 		for( ; true ; ++source, ++index )
 		{
@@ -4231,12 +4454,12 @@ private:
 			bool testing = (character != 0 && (index % 5) == 0);
 
 			if( testing )
-				old_value = *this;
+				old_value = sum;
 
 			// there actually shouldn't be a carry here
-			c += Add( part );
+			c += sum.Add( part );
 
-			if( testing && old_value == *this )
+			if( testing && old_value == sum )
 				// after adding 'part' the value has not been changed
 				// there's no sense to add any next parts
 				break;
@@ -4247,6 +4470,8 @@ private:
 		// we should set a correct value of 'source' now
 		for( ; Misc::CharToDigit(*source, conv.base) != -1 ; ++source );
 
+		c += Add(sum);
+
 	return (c==0)? 0 : 1;
 	}
 
@@ -4866,8 +5091,6 @@ public:
 
 	
 
-
-
 	/*!
 	*
 	*	input/output operators for standard streams

ttmath/ttmathparser.h

@@ -5,7 +5,7 @@
  */
 
 /* 
- * Copyright (c) 2006-2009, Tomasz Sowa
+ * Copyright (c) 2006-2010, Tomasz Sowa
  * All rights reserved.
  * 
  * Redistribution and use in source and binary forms, with or without
@@ -159,14 +159,20 @@ private:
 			none,add,sub,mul,div,pow,lt,gt,let,get,eq,neq,lor,land,shortmul
 		};
 
+		enum Assoc
+		{
+			right,		// right-associative
+			non_right	// associative or left-associative
+		};
 
 		Type  GetType()     const { return type; }
 		int   GetPriority() const { return priority; }
-
+		Assoc GetAssoc()    const { return assoc; }
 
 		void SetType(Type t)
 		{
 			type  = t;
+			assoc = non_right;
 
 			switch( type )
 			{		
@@ -200,6 +206,7 @@ private:
 
 			case pow:
 				priority = 14;
+				assoc    = right;
 				break;
 
 			default:
@@ -208,7 +215,7 @@ private:
 			}
 		}
 
-		MatOperator(): type(none), priority(0)
+		MatOperator(): type(none), priority(0), assoc(non_right)
 		{
 		}
 
@@ -216,7 +223,7 @@ private:
 
 		Type  type;
 		int   priority;
-
+		Assoc assoc;
 	}; // end of MatOperator class
 
 
@@ -464,6 +471,8 @@ int param_sep;
 */
 bool calculated;
 
+
+
 /*!
 	we're using this method for reporting an error
 */
@@ -1737,6 +1746,8 @@ return is_it_name_of_function;
 }
 
 
+
+
 /*!
 	we're reading a numerical value directly from the string
 */
@@ -1746,7 +1757,7 @@ const char * new_stack_pointer;
 bool value_read;
 Conv conv;
 
-	conv.base   = base;
+	conv.base   = reading_base;
 	conv.comma  = comma;
 	conv.comma2 = comma2;
 	conv.group  = group;
@@ -2152,7 +2163,17 @@ void TryRollingUpStackWithOperatorPriority()
 			stack[stack_index-3].type == Item::mat_operator    &&
 			stack[stack_index-2].type == Item::numerical_value &&
 			stack[stack_index-1].type == Item::mat_operator    &&
-			stack[stack_index-3].moperator.GetPriority() >= stack[stack_index-1].moperator.GetPriority()
+			(
+				(
+					// the first operator has greater priority
+					stack[stack_index-3].moperator.GetPriority() > stack[stack_index-1].moperator.GetPriority()
+				) ||
+				(
+					// or both operators have the same priority and the first operator is not right associative
+					stack[stack_index-3].moperator.GetPriority() == stack[stack_index-1].moperator.GetPriority() &&
+					stack[stack_index-3].moperator.GetAssoc()    == MatOperator::non_right
+				)
+			)
 		 )
 	{
 		MakeStandardMathematicOperation(stack[stack_index-4].value,
@@ -2710,7 +2731,7 @@ ErrorCode Parse(const std::wstring & str)
 /*!
 	this method returns true is something was calculated
 	(at least one mathematical operator was used or a function or variable)
-	e.g. the string to Parse() looked like this:
+	e.g. true if the string to Parse() looked like this:
 	"1+1"
 	"2*3"
 	"sin(5)"
@@ -2722,6 +2743,7 @@ bool Calculated()
 	return calculated;
 }
 
+
 };
 
 

ttmath/ttmathtypes.h

@@ -5,7 +5,7 @@
  */
 
 /* 
- * Copyright (c) 2006-2009, Tomasz Sowa
+ * Copyright (c) 2006-2010, Tomasz Sowa
  * All rights reserved.
  * 
  * Redistribution and use in source and binary forms, with or without
@@ -64,7 +64,7 @@
 */
 #define TTMATH_MAJOR_VER		0
 #define TTMATH_MINOR_VER		9
-#define TTMATH_REVISION_VER		0
+#define TTMATH_REVISION_VER		1
 #define TTMATH_PRERELEASE_VER	0
 
 

ttmath/ttmathuint.h

@@ -627,7 +627,7 @@ public:
 			if 'this' is not zero:
 				return value - true
 				'table_id'   - the index of a word <0..value_size-1>
-				'index'      - the index of this set bit in the word <0..31>
+				'index'      - the index of this set bit in the word <0..TTMATH_BITS_PER_UINT)
 
 			if 'this' is zero: 
 				return value - false
@@ -645,7 +645,7 @@ public:
 		return false;
 		}
 		
-		// table[table_id] != 0
+		// table[table_id] is different from 0
 		index = FindLeadingBitInWord( table[table_id] );
 
 	return true;
@@ -653,7 +653,40 @@ public:
 
 
 	/*!
-		setting the 'bit_index' bit
+		this method looks for the smallest set bit
+		
+		result:
+			if 'this' is not zero:
+				return value - true
+				'table_id'   - the index of a word <0..value_size-1>
+				'index'      - the index of this set bit in the word <0..TTMATH_BITS_PER_UINT)
+
+			if 'this' is zero: 
+				return value - false
+				both 'table_id' and 'index' are zero
+	*/
+	bool FindLowestBit(uint & table_id, uint & index) const
+	{
+		for(table_id=0 ; table_id<value_size && table[table_id]==0 ; ++table_id);
+
+		if( table_id >= value_size )
+		{
+			// is zero
+			index    = 0;
+			table_id = 0;
+
+		return false;
+		}
+		
+		// table[table_id] is different from 0
+		index = FindLowestBitInWord( table[table_id] );
+
+	return true;
+	}
+
+
+	/*!
+		getting the 'bit_index' bit
 
 		bit_index bigger or equal zero
 	*/
@@ -2370,7 +2403,28 @@ public:
 	}
 
 
+	/*!
+		returning true if first 'bits' bits are equal zero
+	*/
+	bool AreFirstBitsZero(uint bits) const
+	{
+		TTMATH_ASSERT( bits <= value_size * TTMATH_BITS_PER_UINT )
 
+		uint index = bits / TTMATH_BITS_PER_UINT;
+		uint rest  = bits % TTMATH_BITS_PER_UINT;
+		uint i;
+
+		for(i=0 ; i<index ; ++i)
+			if(table[i] != 0 )
+				return false;
+
+		if( rest == 0 )
+			return true;
+
+		uint mask = TTMATH_UINT_MAX_VALUE >> (TTMATH_BITS_PER_UINT - rest);
+
+	return (table[i] & mask) == 0;
+	}
 
 
 
@@ -3431,6 +3485,7 @@ public:
 	uint SubInt(uint value, uint index = 0);
 	static uint SubVector(const uint * ss1, const uint * ss2, uint ss1_size, uint ss2_size, uint * result);
 	static sint FindLeadingBitInWord(uint x);
+	static sint FindLowestBitInWord(uint x);
 	static uint SetBitInWord(uint & value, uint bit);
 	static void MulTwoWords(uint a, uint b, uint * result_high, uint * result_low);
 	static void DivTwoWords(uint a,uint b, uint c, uint * r, uint * rest);

ttmath/ttmathuint_noasm.h

@@ -588,6 +588,27 @@ namespace ttmath
 
 
 
+	/*!
+		this method returns the number of the highest set bit in x
+		if the 'x' is zero this method returns '-1'
+	*/
+	template<uint value_size>
+	sint UInt<value_size>::FindLowestBitInWord(uint x)
+	{
+		if( x == 0 )
+			return -1;
+
+		uint bit = 0;
+		
+		while( (x & 1) == 0 )
+		{
+			x = x >> 1;
+			++bit;
+		}
+
+	return bit;
+	}
+
 
 
 	/*!

ttmath/ttmathuint_x86.h

@@ -1353,6 +1353,50 @@ namespace ttmath
 
 
 
+	/*
+		this method returns the number of the smallest set bit in one 32-bit word
+		if the 'x' is zero this method returns '-1'
+	*/
+	template<uint value_size>
+	sint UInt<value_size>::FindLowestBitInWord(uint x)
+	{
+	sint result;
+
+		#ifndef __GNUC__
+			__asm
+			{
+				push eax
+				push edx
+
+				mov edx,-1
+				bsf eax,[x]
+				cmovz eax,edx
+				mov [result], eax
+
+				pop edx
+				pop eax
+			}
+		#endif
+
+
+		#ifdef __GNUC__
+		uint dummy;
+
+				__asm__ (
+
+				"movl $-1, %1          \n"
+				"bsfl %2, %0           \n"
+				"cmovz %1, %0          \n"
+
+				: "=r" (result), "=&r" (dummy)
+				: "r" (x)
+				: "cc" );
+
+		#endif
+
+	return result;
+	}
+
 
 
 	/*!

ttmath/ttmathuint_x86_64.h

@@ -987,6 +987,55 @@ namespace ttmath
 	}
 
 
+	/*
+		this method returns the number of the highest set bit in one 64-bit word
+		if the 'x' is zero this method returns '-1'
+
+		***this method is created only on a 64bit platform***
+	*/
+	template<uint value_size>
+	sint UInt<value_size>::FindLowestBitInWord(uint x)
+	{
+	sint result;
+
+
+		#if !defined(__GNUC__) && !defined(_MSC_VER)
+			#error "another compiler than GCC or Microsoft VC is currently not supported in 64bit mode, you can compile with TTMATH_NOASM macro"
+		#endif
+
+		
+		#ifdef _MSC_VER
+
+			unsigned long nIndex = 0;
+
+			if( _BitScanForward64(&nIndex,x) == 0 )
+				result = -1;
+			else
+				result = nIndex;
+
+		#endif
+
+
+		#ifdef __GNUC__
+		uint dummy;
+
+				__asm__ (
+
+				"movq $-1, %1          \n"
+				"bsfq %2, %0           \n"
+				"cmovz %1, %0          \n"
+
+				: "=r" (result), "=&r" (dummy)
+				: "r" (x)
+				: "cc" );
+
+		#endif
+
+
+	return result;
+	}
+
+
 	/*!
 		this method sets a special bit in the 'value'
 		and returns the last state of the bit (zero or one)