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Verifying the error bound of numerical computation implemented in computer systems

A verification tool receives a finite precision definition for an approximation of an infinite precision numerical function implemented in a processor in the form of a polynomial of bounded functions. The verification tool receives a domain for verifying outputs of segments associated with the infinite precision numerical function. The verification tool splits the domain into at least two segments, wherein each segment is non-overlapping with any other segment and converts, for each segment, a polynomial of bounded functions for the segment to a simplified formula comprising a polynomial, an inequality, and a constant for a selected segment. The verification tool calculates upper bounds of the polynomial for the at least two segments, beginning with the selected segment and reports the segments that violate a bounding condition.

97 MATHEMATICS AND COMPUTING↗

System for detecting operating errors in a variable valve timing engine using pressure sensors

A method and control module includes a pressure sensor data comparison module that compares measured pressure volume signal segments to ideal pressure volume segments. A valve actuation hardware remedy module performs a hardware remedy in response to comparing the measured pressure volume signal segments to the ideal pressure volume segments when a valve actuation hardware failure is detected.

47 OTHER INSTRUMENTATION↗