Modeling System C Fixed-Point Arithmetic in HOL
نویسندگان
چکیده
SystemC is a new C-based system level design language whose ultimate objective is to enable System-on-a-Chip (SoC) design and verification. Fixed-point design based on the SystemC data types is rapidly becoming the standard for optimizing DSP systems. In this paper, we propose to create a formalization of SystemC fixed-point arithmetic in the HOL theorem proving environment. The SystemC fixedpoint number representation which contains a new generalized format and different rounding and overflow modes is described, and then it is formalized in higher-order logic. This formalization is then compared with the formalization of IEEE standard based floating-point arithmetic in HOL. A set of theorems are proved to bound the error in fixed-point rounding and to verify the fixed-point arithmetic operations against their abstract mathematical counterparts. Finally, we show by an example how this formalization can be used in verification of the translation from floating-point and fixed-point algorithmic, down to register transfer and netlist gate levels in the design flow of SoC systems.
منابع مشابه
Formalization of Fixed-Point Arithmetic in HOL
This paper addresses the formalization in higher-order logic of fixed-point arithmetic. We encoded the fixed-point number system and specified the different quantization modes in fixed-point arithmetic such as the directed and even quantization modes. We also considered the formalization of exceptions detection and their handling like overflow and invalid operation. An error analysis is then pe...
متن کاملA Parameterized Floating-Point Formalizaton in HOL Light
We present a new, open-source formalization of fixed and floating-point numbers for arbitrary radix and precision that is now part of the HOL Light distribution [10]. We prove correctness and error bounds for the four different rounding modes, and formalize a subset of the IEEE 754 [1] standard by gluing together a set of fixed-point and floating-point numbers to represent the subnormals and no...
متن کاملError analysis of digital filters using HOL theorem proving
When a digital filter is realized with floating-point or fixed-point arithmetics, errors and constraints due to finite word length are unavoidable. In this paper, we show how these errors can be mechanically analysed using the HOL theorem prover. We first model the ideal real filter specification and the corresponding floating-point and fixedpoint implementations as predicates in higher-order l...
متن کاملAIOSC: Analytical Integer Word-length Optimization based on System Characteristics for Recursive Fixed-point LTI Systems
The integer word-length optimization known as range analysis (RA) of the fixed-point designs is a challenging problem in high level synthesis and optimization of linear-time-invariant (LTI) systems. The analysis has significant effects on the resource usage, accuracy and efficiency of the final implementation, as well as the optimization time. Conventional methods in recursive LTI systems suffe...
متن کامل