Sometimes 64 bits just aren't enough.

Written 2010-12-05

Tags:Fixed-point Universe Jupiter 64 bit Math 

Often times in programming, fixed point numbers are used. For example, a 32 bit representation of angle(0:1) using fixed point provides much greater accuracy than the same 32 bits used for a floating point representation. The resolution of the circumference of the earth in 32 bit fixed point is about a centimeter, but 10 feet or so in 32 bit floating point.

But what if we expand this same idea? The approximate diameter of the known universe is about 156 billion light years. There are 18446744073709551616 unique 64 bit integers. Thus, the resolution of a 64 bit scaled representation would be about 80,000 kilometers, or the radius of Jupiter. That is to say that the known universe is about 2^63 Jupiters wide.