<james.jones@firstinvestors.com> schrieb im Newsbeitrag news:A1B722A7A7710742976C7693E2EE8E9E38F0DF@rockfalls...

From: "Matthias Hofmann" <hofmann@anvil-soft.com>

...

Also, I would like to know how the greatest common divisor is defined when one or both of the arguments are zero. In that case, boost::math::gcd() seems to return the nonzero argument, if there is any - but is this mathematically correct?

Yes, it's correct. gcd(a,b) is the greatest integer n such that n|a and n|b. Every integer n has the property that n|0, so gcd(a,0) = a.

I see, thank you for the quick response. I also found out that it does not matter which of the two arguments passed to boost::math::gcd() is the greater one. Some texts require a > b for the euclidean algorithm to work, but this does not seem to be true for boost's implementation: while ( true ) { if ( a == zero ) return b; b %= a; if ( b == zero ) return a; a %= b; } It also plays no role in my own implementation: int gcd( int a, int b ) { while ( b != 0 ) { int r = a % b; a = b; b = r; } return std::abs( a ); } However, it does matter in the following implementation, see the corresponding comment: int gcd( int a, int b ) { // This is crucial! if ( b > a ) std::swap( a, b ); while ( b != 0 ) { int t = b; b = a - b; a = t; if ( b > a ) std::swap( a, b ); } return a; } Just thought that my observations might help someone... -- Matthias Hofmann Anvil-Soft, CEO http://www.anvil-soft.com - The Creators of Toilet Tycoon http://www.anvil-soft.de - Die Macher des Klomanagers