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# Hardware-centric method to calculate accurate and fast Poisson CDF

IP.com Disclosure Number: IPCOM000243804D
Publication Date: 2015-Oct-17
Document File: 3 page(s) / 61K

## Publishing Venue

The IP.com Prior Art Database

## Abstract

Hardware-friendly fast and accurate method to compute Poisson Cumulative Distribution Function for large values

This text was extracted from a PDF file.
This is the abbreviated version, containing approximately 92% of the total text.

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Hardware-centric method to calculate accurate and fast Poisson CDF

Poisson distribution is important in theoretical and applied probability and statistics. It expresses the probability of a given number of events occurring in fixed interval of time if these events occur with known average rate.

Poisson Cumulative Distribution Function is defined as below:

where 'mu' is average rate.

As we can see, for 'mu' or 'i' greater than 30, individual probability terms will start overflowing/underflowing.

This is the problem this disclosed system is going to address.

Disclosed is a system which computes Poisson Cumulative Distribution Function even for large values of "mean (lambda)" and "trials (n)" e.g. 1e6.

This system is hardware friendly and uses primitive double-precision floating point addition, multiplication and division.

All data and operations use novel data representation to manage large intermediate numbers. Described as "DataRep" format in Fig 1.

Figure 1

Addition function of two numbers in "DataRep" format is described in Fig 2.

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Figure 2

Multiplication function of two numbers in "DataRep" format is described in Fig 3. It is used to calculate "lambda-power-of-n" and "factorial-of-n" recursively.

Figure 3.

Poisson Cumulative Distribution Function is defined as below:

Expression "exp(-mu)" is calculated separately as in Fig 4 below:

Figure 4

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"i-th" term is calculated as in Fig 5 below:

Figure 5 (Ee from Fig 4)

Final calculation is...