New Algorithms for the Approximate Evaluation in Hardware of Binary Logarithms and Elementary Functions
- 1 December 1972
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Computers
- Vol. C-21 (12) , 1416-1421
- https://doi.org/10.1109/t-c.1972.223516
Abstract
After an analysis of the errors introduced in the approximate computation of the x2function (O ≤ x ≤ 1) and its distributions, we find that a parabolic rather than linear fit to log2 (1 + x), (O ≤ x ≤ 1) can be performed in hardware without increasing the number of necessary sums. An improvement, by a factor of about 2.5, in the absolute maximum error can be expected. Full simulation on a digital computer confirms the theoretical analysis. We used partitioning of the range in only two subranges; the resulting hardware is not harder than in piecewise linear approximation. Examples are also included to show the effectiveness of the method for approximation of different functions.Keywords
This publication has 3 references indexed in Scilit:
- Generation of Products and Quotients Using Approximate Binary Logarithms for Digital Filtering ApplicationsIEEE Transactions on Computers, 1970
- Computation of the Base Two Logarithm of Binary NumbersIEEE Transactions on Electronic Computers, 1965
- Computer Multiplication and Division Using Binary LogarithmsIEEE Transactions on Electronic Computers, 1962