Er, what? Floating point numbers do "round correctly" (in binary) -- that's pretty much the whole point of the IEEE standard. In particular, to compute a produ

Er, what? Floating point numbers do "round correctly" (in binary) -- that's pretty much the whole point of the IEEE standard. In particular, to compute a product of two 53-bit floating-point numbers with correct rounding (as the standard mandates), it is certainly not sufficient in general to compute just a 54-bit approximation and round that.