Abstract: A method and arrangements for increased precision in the computation of a reciprocal square root is disclosed. In accordance with the present invention, it is possible to achieve fifty three (53) bits of precision in less processing time than previously possible.

Abstract: A method, apparatus, and computer instructions for processing instructions. A data dependency graph is built. The data dependency graph is analyzed for recurrences, and unpipelined instructions that lie outside of the recurrences are expanded.

Abstract: The present invention provides a system and method for systematic random testing of single/double-precision, one/two-variable or scalar/vector mathematical functions against a known higher precision reference mathematical library or to the result of an arbitrary precision mathematical package. The systematic random testing of mathematical functions is performed across the entire floating-point range or a test interval defined therein, including denormalized numbers with random test arguments appropriately distributed over the test interval. By ensuring the density of coverage of random test arguments across the test interval by comparison against a statistical model and identifying the exception behavior of the mathematical function, an accurate picture of the performance and accuracy of the mathematical function can be assessed.

Abstract: A method and arrangements for increased precision in the computation of a reciprocal square root is disclosed. In accordance with the present invention, it is possible to achieve fifty three (53) bits of precision in less processing time than previously possible.