A valid scalar type S must have accessible destructor, default constructor, copy constructor and assignment operator, and must support the following operations:

S operator*( S, S );
S operator/( S, S );
S operator+( S, S );
S operator-( S, S );

S & operator*=( S &, S );
S & operator/=( S &, S );
S & operator+=( S &, S );
S & operator-=( S &, S );

bool operator==( S, S );
bool operator!=( S, S );

In addition, the expression S(0) should construct a scalar of value zero, and S(1) should construct a scalar of value one -or- the scalar_traits template must be specialized appropriately.