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# Randomization of Otherwise Systematic Truncation Errors in Computers

IP.com Disclosure Number: IPCOM000078022D
Original Publication Date: 1972-Oct-01
Included in the Prior Art Database: 2005-Feb-25
Document File: 1 page(s) / 11K

IBM

## Related People

Davis, JB: AUTHOR [+3]

## Abstract

The scheme consists of connecting the last bit, which is the bit which is one more than necessary for the precision required in a calculation, to any shot noise source of sufficient frequency such as a diode. The truncation error being systematic and data dependent cannot be controlled, and increases the number of necessary bits carried for predetermined accuracy. The random process will cut down the necessary bits. As an example consider the generation of a sin table. sin (n+1) theta = 200 cos theta sin n theta - sin (n-1) theta.

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Randomization of Otherwise Systematic Truncation Errors in Computers

The scheme consists of connecting the last bit, which is the bit which is one more than necessary for the precision required in a calculation, to any shot noise source of sufficient frequency such as a diode. The truncation error being systematic and data dependent cannot be controlled, and increases the number of necessary bits carried for predetermined accuracy. The random process will cut down the necessary bits. As an example consider the generation of a sin table. sin (n+1) theta = 200 cos theta sin n theta - sin (n-1) theta.

On generation of 1000 coefficients, 1000 bits may be dropped. With a random generator it becomes 1/12 of a bit since on 1000 degrees, standard deviation in a uniform distribution is a/2//12, "a" being equal to 1 bit.

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