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Enabling Floating-Point Arithmetic in the Coq Proof Assistant
Floating-point arithmetic is a well-known and extremely efficient way of performing approximate computations over the real numbers. Although it...
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Hammering Floating-Point Arithmetic
Sledgehammer, a component of the interactive proof assistant Isabelle/HOL, aims to increase proof automation by automatically discharging proof goals...
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Hierarchical search algorithm for error detection in floating-point arithmetic expressions
Scientific and engineering applications rely on floating-point arithmetic to approximate real numbers. Due to the inherent rounding errors in...
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Floating-Point Operations
In this chapter, the RISC-V floating-point extensions will be studied. The floating-point extensions provide useful instructions for working with...
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Formal Verification of Emulated Floating-Point Arithmetic in Falcon
We show that there is a discrepancy between the emulated floating-point multiplication in the submission package of the digital signature Falcon and...
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A Real-Blasting Extension of cvc5 for Reasoning About Floating-Point Arithmetic
We present a new floating-point arithmetic (FPA) theory solver implemented in the cvc5 SMT solver. Differently from the major bit-blasting method, we...
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Floating-Point Arithmetic
Working with large numbers can be seen as abstract art, as covered in Chapter 4 . If the encryption schemes...
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Accurate Low-Bit Length Floating-Point Arithmetic with Sorting Numbers
A 32-bit floating-point format is often used for the development and training of deep neural networks. Training and inference in deep...
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ACL2 Support for Floating-Point Computations
Formal methods tools vary widely but generally have logical foundations. For ACL2, a general purpose theorem prover under continuous development...
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Correct approximation of IEEE 754 floating-point arithmetic for program verification
Verification of programs using floating-point arithmetic is challenging on several accounts. One of the difficulties of reasoning about such programs...
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TrueFloat: A Templatized Arithmetic Library for HLS Floating-Point Operators
Hardware designers working on FPGA accelerators are free to explore ad-hoc value representations that differ from the IEEE 754 floating-point...
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AVX Programming – Scalar Floating-Point
In the previous three chapters, you studied core x86-64 assembly language topics including integer arithmetic, bitwise logical operations, memory...
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AVX Programming – Packed Floating-Point
The source code examples of the previous chapter elucidated the fundamentals of AVX programming using packed integer operands. In this chapter,...
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Next Generation Arithmetic 5th International Conference, CoNGA 2024, Sydney, NSW, Australia, February 20–21, 2024, Proceedings
This book constitutes the refereed post-conference proceedings of the 5th International Conference for Next Generation Arithmetic, CoNGA 2024, held...
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PESA: error sensitivity analysis tool for floating-point computational programs
Floating-point programs are currently extensively applied across various domains of scientific computing. Within such computational programs, there...
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Symbolic Calculation Behind Floating-Point Arithmetic: Didactic Examples and Experiment Using CAS
Floating-point arithmetic (FP) is taught at universities in the framework of different academic courses, for example: Numerical Analysis, Computer...
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Combining rule- and SMT-based reasoning for verifying floating-point Java programs in KeY
Deductive verification has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for...
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Rigorous Floating-Point Round-Off Error Analysis in PRECiSA 4.0
Small round-off errors in safety-critical systems can lead to catastrophic consequences. In this context, determining if the result computed by a...
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AVX2 Programming – Packed Floating-Point – Part 1
In Chapter 9 , you learned how to carry out elementary arithmetic using packed floating-point operands and AVX...
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