Analysis of Finite Word-Length Effects in Fixed-Point Systems

Daniel Ménard (1) , Gabriel Caffarena (2) , Juan Antonio Lopez (3) , David Novo (4) , Olivier Sentieys (5)

1 IETR - Institut d'Électronique et des Technologies du numéRique
2 Department of Ingenierı ́a de Sistemas Electronicos y de Telecomunicacion [San Pablo]
3 Departamento de Ingeniería Electrónica [Madrid]
4 ADAC - ADAptive Computing
5 CAIRN - Energy Efficient Computing ArchItectures with Embedded Reconfigurable Resources

Systems based on fixed-point arithmetic, when carefully designed, seem to behave as their infinite precision analogues. Most often, however, this is only a macroscopic impression: finite word-lengths inevitably approximate the reference behavior introducing quantization errors, and confine the macroscopic correspondence to a restricted range of input values. Understanding these differences is crucial to design optimized fixed-point implementations that will behave “as expected” upon deployment. Thus, in this chapter, we survey the main approaches proposed in literature to model the impact of finite precision in fixed-point systems. In particular, we focus on the rounding errors introduced after reducing the number of least significant bits in signals and coefficients during the so-called quantization process.

Domaines: Systèmes embarqués; Architectures Matérielles [cs.AR]; Arithmétique des ordinateurs; Traitement du signal et de l'image [eess.SP]

Daniel Ménard, Gabriel Caffarena, Juan Antonio Lopez, David Novo, Olivier Sentieys. Analysis of Finite Word-Length Effects in Fixed-Point Systems. Shuvra S. Bhattacharyya. Handbook of Signal Processing Systems, pp.1063-1101, 2019, 978-3-319-91733-7. ⟨10.1007/978-3-319-91734-4_29⟩. ⟨hal-01941888⟩