Solving Constraints on the Intermediate Result of Decimal Floating-Point Operations

A symmetric function is called Schur nonnegative if it is a linear combination with nonnegative coefficients of the Schur functions, or, equivalently, if it is the

However, for cost reasons, in this co-processor, as well as in its successors by Intel, Cyrix or AMD, these functions didnot use the hardware algorithm mentioned above, but

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Given a sequential branching algorithm such as that described in Section 3.2, every node defines one partial transfer plan φ t of size t (t being the number of transfers that have

Here we study conditions under which the floor of an exact product (or the Euclidean division, when the divisor can be known in advance) can be implemented using a

We first show that there is no polynomial algorithm that can decide the existence of linear ranking functions for simple floating-point loops as the problem is at least in coNP..

The final step consists in using a variant of the Hahn-Banach theorem which allows us to deduce that the mean curvature is a convex combination of squares of normal derivatives of

7 Such is the case, for instance, of results computed in the long double 80-bit type of the x87 floating-point registers, then rounded to the IEEE double precision type for storage