The above equation is used for opaque facades in, and renders intermediate calculation of unnecessary.

Programming languages should allow a user to specify a minimum precision for intermediate calculations of expressions for each radix.

Thus for instance a compiler targeting x87 floating point hardware should have a means of specifying that intermediate calculations must use doubled extended format.

He struggled to imagine the tangle of billions of intermediate calculations, somehow "making sense" of themselves, bridging the gap.

Leonardo described the operation as mental, using his right and left hands to carry the intermediate calculations.

By representing the carry graphically, the user can read off the results of simple multiplication problems directly, with no intermediate mental calculations.

(If no roundoff is used in the intermediate calculations above, the final figure for the NNH is 123.)

Conversely, in extended-precision mode, extended precision may be used for intermediate compiler-generated calculations even when the final results are stored at a lower precision.

Extended precision can help minimise accumulation of round-off error in intermediate calculations.

The basic idea was to introduce a few deliberate faults in the intermediate calculations, making it possible to deduce the last eight round keys.