Properties of two's complement floating point notations

Sylvie Boldo (1) , Marc Daumas (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme

Few designs, mostly those of Texas Instruments, continue to use tworsquos complement floating point units. Such units are simpler to build and to validate, but they do not comply to the dominant IEEE standard for floating point arithmetic. We compare some properties of the two systems in this text. Some features are lost, but others remain unchanged. One strong example is the case of Sterbenzrsquos theorem and our recent extension. We show in the paper that the theorem and its extension hold for the tworsquos complement architecture. Still, users should ensure that results are large enough on circuits that do not implement gradual underflow. Theorems have been proven and validated using the Coq automatic proof checker.

Mots clés: Digital signal processing; Avionics; Formal proof

Domaines: Arithmétique des ordinateurs

Sylvie Boldo, Marc Daumas. Properties of two's complement floating point notations. International Journal on Software Tools for Technology Transfer, 2003, 5 (2-3), pp.237-246. ⟨10.1007/s10009-003-0120-y⟩. ⟨hal-00157268⟩