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
and 3.457
, 'normalise' the first one to 2.100
. 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 become 2100
and 3457
. The result is 5557
.
- 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.