Journal ArticleDOI
Fast evaluation of the elementary functions in single precision
Weng-Fai Wong,E. Goto +1 more
TLDR
A new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method, which can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trig onometric and inverse trigonometric functions, within the latency of two to four floating point multiplies.Abstract:
In this paper we introduce a new method for the fast evaluation of the elementary functions in single precision based on the evaluation of truncated Taylor series using a difference method. We assume the availability of large and fast (at least for read purposes) memory. We call this method the ATA (Add-Table lookup-Add) method. As the name implies, the hardware required for the method are adders (both two/ and multi/operand adders) and fast tables. For IEEE single precision numbers our initial estimates indicate that we can calculate the basic elementary functions, namely reciprocal, square root, logarithm, exponential, trigonometric and inverse trigonometric functions, within the latency of two to four floating point multiplies. >read more
Citations
More filters
Journal ArticleDOI
Multipartite table methods
F. de Dinechin,Arnaud Tisserand +1 more
TL;DR: A unified view of most previous table-lookup-and-addition methods (bipartite tables, SBTM, STAM, and multipartite methods) is presented, allowing a more accurate computation of the error entailed by these methods, leading to tables smaller than the best previously published ones by up to 50 percent.
Journal ArticleDOI
Reciprocation, square root, inverse square root, and some elementary functions using small multipliers
TL;DR: A method is proposed, based on argument reduction and series expansion, that allows fast evaluation of these functions in high precision, and the strength of this method is that the same scheme allows the computation of all these functions.
Proceedings ArticleDOI
Symmetric bipartite tables for accurate function approximation
TL;DR: The method for designing bipartite tables, called the Symmetric Bipartite Table Method, utilizes symmetry in the table entries to reduce the overall memory requirements and requires smaller table lookups to achieve a given accuracy.
Proceedings ArticleDOI
Some improvements on multipartite table methods
F. de Dinechin,Arnaud Tisserand +1 more
TL;DR: This paper presents an unified view of most previous table-lookup-and-addition methods: bipartite tables, SBTM, STAM and multipartite methods, with a new definition that allows a more accurate computation of the error entailed by these methods.
Journal ArticleDOI
Numerical Function Generators Using LUT Cascades
TL;DR: The architecture is based on the lookup table (LUT) cascade, which results in a significant reduction in circuit complexity compared to traditional approaches, suitable for automatic synthesis and a synthesis method that converts a Matlab-like specification into an LUT cascade design is shown.
References
More filters
Proceedings ArticleDOI
Table-lookup algorithms for elementary functions and their error analysis
TL;DR: It is shown that, with careful design, it is feasible to implement table-lookup algorithms in hardware and a uniform approach for carrying out a tight error analysis for such implementations is presented.
Journal ArticleDOI
Fast hardware-based algorithms for elementary function computations using rectangular multipliers
Weng-Fai Wong,E. Gogo +1 more
TL;DR: These algorithms exploit microscopic parallelism using specialized hardware with heavy use of truncation based on detailed accuracy analysis for the computation of the common elementary functions, namely division, logarithm, reciprocal square root, arc tangent, sine and cosine.
Journal ArticleDOI
An accurate elementary mathematical library for the IEEE floating point standard
TL;DR: The algorithms used by the IBM Israel Scientific Center for the elementary mathematical library using the IEEE standard for binary floating point arithmetic are described, based on the “accurate tables method,” which achieves high performance and produces very accurate results.
Journal ArticleDOI
Fast division using accurate quotient approximations to reduce the number of iterations
D.C. Wong,Michael J. Flynn +1 more
TL;DR: A class of iterative integer division algorithms is presented based on look-up table and Taylor-series approximations to the reciprocal, which naturally produce an exact remainder, which is very useful for implementing precise rounding specifications.
Proceedings ArticleDOI
High bandwidth evaluation of elementary functions
TL;DR: This paper elaborate on a technique for computing piecewise quadratric approximations to many elementary functions, which permits the effective use of large RAMs or ROMs and parallel multipliers for rapidly generating single-precision floating-point function values.