Formal verification of iterative algorithms in microprocessors
Proceedings of the 37th Annual Design Automation Conference
Modular proof: the fundamental theorem of calculus
Computer-Aided reasoning
The Correctness of the Fast Fourier Transform: A Structured Proof in ACL2
Formal Methods in System Design
Journal of Automated Reasoning
A Mechanically Checked Proof of Correctness of the AMD K5 Floating Point Square Root Microcode
Formal Methods in System Design
Formal Verification of Floating Point Trigonometric Functions
FMCAD '00 Proceedings of the Third International Conference on Formal Methods in Computer-Aided Design
Verifying the Accuracy of Polynomial Approximations in HOL
TPHOLs '97 Proceedings of the 10th International Conference on Theorem Proving in Higher Order Logics
Series Approximation Methods for Divide and Square Root in the Power3(TM) Processor
ARITH '99 Proceedings of the 14th IEEE Symposium on Computer Arithmetic
Mechanically verifying real-valued algorithms in acl2
Mechanically verifying real-valued algorithms in acl2
Formal Verification of Square Root Algorithms
Formal Methods in System Design
Formalization of fixed-point arithmetic in HOL
Formal Methods in System Design
Combining ACL2 and an automated verification tool to verify a multiplier
ACL2 '06 Proceedings of the sixth international workshop on the ACL2 theorem prover and its applications
Journal of Automated Reasoning
Formal Verification of Exact Computations Using Newton's Method
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Automatic verification of estimate functions with polynomials of bounded functions
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
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The IBM Power4驴 processor uses Chebyshev polynomials to calculate square root. We formally verified the correctness of this algorithm using the ACL2(r) theorem prover. The proof requires the analysis on the approximation error of Chebyshev polynomials. This is done by proving Taylor's theorem, and then analyzing the Chebyshev polynomial using Taylor polynomials. Taylor's theorem is proven by way ofnon-standard analysis, as implemented in ACL2(r). Since a Taylor polynomial has less accuracy than the Chebyshev polynomial ofthe same degree, we used hundreds of Taylor polynomial generated by ACL2(r) to evaluate the error ofa Chebyshev polynomial.