Apparatus for computing transcendental functions quickly

Electrical computers: arithmetic processing and calculating – Electrical digital calculating computer – Particular function performed

Reexamination Certificate

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Details

C708S501000

Reexamination Certificate

active

06317764

ABSTRACT:

BACKGROUND OF THE INVENTION
1. Field of the Invention
This invention relates to apparatus for computing transcendental functions quickly.
2. Description of Related Art
Computing transcendental functions by Taylor series generally requires one “add” instruction (which might take, for example, three clock times) and one “multiply” instruction (which might also take, for example, three more clock times) for each term. For processors computing transcendental functions to significant accuracy, it requires a number of terms to achieve a residual error less than the least significant bit of the answer. In a processor providing a floating point result having a 64-bit fraction, the number of terms is about ten for achieving 64-bit accuracy for the full range of an ordinary Taylor series; if multiply and add operations each take about three clock times, this would take about sixty clock times, which can be a significant amount of time when computation resources are at a premium. To obtain greater accuracy, even more terms and thus even more time would be required.
Accordingly, it would be advantageous to provide a technique for computing transcendental functions quickly. This advantage is achieved by apparatus according to the present invention in which terms of a Taylor series are computed in parallel and combined after parallel computation, so as to take only about one sixth of the “natural” amount of time per term.
SUMMARY OF THE INVENTION
The invention provides a method and system for computing transcendental functions quickly. In a preferred embodiment, (1) the multiply ALU is enhanced to include the operation of adding a term to the product, (2) rounding operations for intermediate multiply and add operations are skipped, (3) the Taylor series for the transcendental function is separated into two partial series which are performed in parallel, and (4) subtraction and reciprocals, if any, are reserved for the end of the computation. Where appropriate, an alternative Taylor series is used for faster convergence for part of the range of the transcendental function. Thereby, transcendental functions computed using a series with multiple terms (for example, SIN, COS, TAN, ARCTAN, EXP, or LOG), are thus performed in about one sixth of the “natural” amount of time per term, or about one clock time per term in processors in which multiply and add operations each take about three clock times each.


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patent: 5703801 (1997-12-01), Pan et al.
patent: 5963460 (1999-10-01), Rarick
patent: 5991863 (1999-11-01), Dao et al.

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