4 The complete unum format

4.1 Overcoming the tyranny of fixed storage size

Ivan Sutherland talks about “the tyranny of the clock,” referring to the way traditional computer design requires operations to fit into clock cycles instead of letting operations go as fast as possible. There is a similar tyranny in the way we are currently forced to use a fixed storage size for numbers, instead of letting them fit in as small a space as they can. The two concepts go hand-in-hand; smaller numbers should be allowed to do arithmetic as quickly as possible, and larger numbers should be allowed more time to complete their calculations.

In doing arithmetic using pencil-and-paper, it is natural to increase and decrease the number of digits as needed. Computer ...

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