问题
In the code below I use mpf_add
to add the string representation of two floating values. What I don't understand at this point is why 2.2 + 3.2 = 5.39999999999999999999999999999999999999
. I would have thought that gmp
was smart enough to give 5.4
.
What am I not comprehending about how gmp does floats?
(BTW, when I first wrote this I wasn't sure how to insert a decimal point, thus the plus/minus digit stuff at the end)
BSTR __stdcall FBIGSUM(BSTR p1, BSTR p2 ) {
USES_CONVERSION;
F(n1);
F(n2);
F(res);
LPSTR sNum1 = W2A( p1 );
LPSTR sNum2 = W2A( p2 );
mpf_set_str( n1, sNum1, 10 );
mpf_set_str( n2, sNum2, 10 );
mpf_add( res, n1, n2 );
char * buff = (char *) _alloca( 1024 );
char expBuffer[ 20 ];
mp_exp_t exp;
mpf_get_str(buff, &exp, 10, 0, res);
char * temp = ltoa( (long) exp, expBuffer, 10 );
if (exp >= 0) {
strcat(buff, "+" );
}
strcat(buff, expBuffer );
BSTR bResult = _com_util::ConvertStringToBSTR( buff );
return bResult;
}
回答1:
This is because of the inherent error of using floating-point arithmetic in a binary environment.
See the IEEE 754 standard for more information.
回答2:
What warren said.
You might have better results if you use binary coded decimal instead of floating point numbers, although I can't really direct you to any libraries for that.
回答3:
I eventually ended up answering this myself. The solution for me was to do in code what I used to do in school. The method works like this:
- Take each number and make sure that the number of digits to the right of the decimal point are the same. So if adding
2.1
and3.457
, 'normalise' the first one to2.100
. Keep a record of the number of digits that are to the right of the decimal, in this case, three. - Now remove the decimal point and use
mpz_add
to add the two numbers, which have now become2100
and3457
. The result is5557
. - Finally, reinsert the decimal point three characters (in this case) from the right, giving the correct answer of
5.557
.
I prototyped the solution in VBScript (below)
function fadd( n1, n2 )
dim s1, s2, max, mul, res
normalise3 n1, n2, s1, s2, max
s1 = replace( s1, ".", "" )
s2 = replace( s2, ".", "" )
mul = clng(s1) + clng(s2)
res = left( mul, len(mul) - max ) & "." & mid( mul, len( mul ) - max + 1 )
fadd = res
end function
sub normalise3( byval n1, byval n2, byref s1, byref s2, byref numOfDigits )
dim a1, a2
dim max
if instr( n1, "." ) = 0 then n1 = n1 & "."
if instr( n2, "." ) = 0 then n2 = n2 & "."
a1 = split( n1, "." )
a2 = split( n2, "." )
max = len( a1(1) )
if len( a2(1) ) > max then max = len( a2( 1 ) )
s1 = a1(0) & "." & a1(1) & string( max - len( a1( 1 )), "0" )
s2 = a2(0) & "." & a2(1) & string( max - len( a2( 1 )), "0" )
numOfDigits = max
end sub
and finally in Visual C++ (below).
#define Z(x) mpz_t x; mpz_init( x );
BSTR __stdcall FADD( BSTR p1, BSTR p2 ) {
USES_CONVERSION;
LPSTR sP1 = W2A( p1 );
LPSTR sP2 = W2A( p2 );
char LeftOf1[ 1024 ];
char RightOf1[ 1024 ];
char LeftOf2[ 1024 ];
char RightOf2[ 1024 ];
char * dotPos;
long numOfDigits;
int i;
int amtOfZeroes;
dotPos = strstr( sP1, "." );
if ( dotPos == NULL ) {
strcpy( LeftOf1, sP1 );
*RightOf1 = '\0';
} else {
*dotPos = '\0';
strcpy( LeftOf1, sP1 );
strcpy( RightOf1, (dotPos + 1) );
}
dotPos = strstr( sP2, "." );
if ( dotPos == NULL ) {
strcpy( LeftOf2, sP2 );
*RightOf2 = '\0';
} else {
*dotPos = '\0';
strcpy( LeftOf2, sP2 );
strcpy( RightOf2, (dotPos + 1) );
}
numOfDigits = strlen( RightOf1 ) > strlen( RightOf2 ) ? strlen( RightOf1 ) : strlen( RightOf2 );
strcpy( sP1, LeftOf1 );
strcat( sP1, RightOf1 );
amtOfZeroes = numOfDigits - strlen( RightOf1 );
for ( i = 0; i < amtOfZeroes; i++ ) {
strcat( sP1, "0" );
}
strcpy( sP2, LeftOf2 );
strcat( sP2, RightOf2 );
amtOfZeroes = numOfDigits - strlen( RightOf2 );
for ( i = 0; i < amtOfZeroes; i++ ) {
strcat( sP2, "0" );
}
Z(n1);
Z(n2);
Z(res);
mpz_set_str( n1, sP1, 10 );
mpz_set_str( n2, sP2, 10 );
mpz_add( res, n1, n2 );
char * buff = (char *) _alloca( mpz_sizeinbase( res, 10 ) + 2 + 1 );
mpz_get_str(buff, 10, res);
char * here = buff + strlen(buff) - numOfDigits;
memmove( here + 1, here, strlen(buff)); // plus trailing null
*(here) = '.';
BSTR bResult = _com_util::ConvertStringToBSTR( buff );
return bResult;
}
I accept that the C is a bit ... well ... dodgy, so please feel free to critique it. All helpful comments gratefully received.
I went on from here to implement FSUB and FMUL as well. FDIV was not nearly so satisfying, ending up in three versions and using rational numbers.
来源:https://stackoverflow.com/questions/178952/adding-floats-with-gmp-gives-correct-results-sort-of