"Joel Eidsath" <jeidsath@gmail.com> wrote in message news:431E2D2F.7090501@gmail.com...
Thats true but irrelevant, because you cant tell, given only the resulting floating point representation, whether your floating-point value is representing an approximation to some value which may be rational or itrrational or alternatively is an exact representation of a rational value.
And so...? I fail to see your point.
My point is that floating point representation of a number is in no way a peer concept of rational number. IOW your assertion : "Examples of basic rational number types in C++: float, double, etc." is equivalent trying to compare two C++ types that dont have a comparison operator. The proper use for a rational number is as a dimensionless constant in an equation. In this case its numerator or denominator values are rarely anything other than small integers. floating-point values on the other hand are useful to represent measured analogue quantities (physical measurement by nature being inexact) , for example the distance between two points, the height of the tide at an analogue instant of time. Physical quantities are never rational numbers but rather analogue values given meaning by the convention of units. The following is an example of how I would consistenly use floating-point types and rationals to give a theoretically better precision then if using floating-point types only. (Of course, due to the lossiness of floats, any multiplication/division of a float by a rational and vice versa must result in a float (rather than a rational) ) // get distance travelled from u,v,a,t double u = U, v = V, t = T, a = A; // analogue velocities expressed in some units of measure double s = u * t + my::rational(1,2) * a * pow(t,2); // find volume of sphere double radius =R; double volume= my::rational(4,3) * pow(r,3); note: Having said that boost::rational can't be used in this way because there is no multiplication or division between boost::rational and floating point types. This in now way invalidates the examples. regards Andy Little