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Calculating a 'Guess' Factor for a Two-It Square Root Algorithm

IP.com Disclosure Number: IPCOM000100127D
Original Publication Date: 1990-Mar-01
Included in the Prior Art Database: 2005-Mar-15
Document File: 6 page(s) / 137K

IBM

Related People

Fleischer, H: AUTHOR

Abstract

A technique is described whereby the 'guess' factor r1, required for two-bit square root algorithms (see the preceding article), is calculated based on input values. The procedure shown is designed so that the factor can be calculated independently from the square root computation. Different 'guess' factor ranges are suitable, depending on the interpretation of the square root scheme. The technique described herein outlines the logic for the square root and 'guess' table utilizing a factor in the range of -3 to +3. The concept achieves a higher computational speed but also needs more hardware to implement than a slower similar logic which uses a factor range of -2 to +2.

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Calculating a 'Guess' Factor for a

Two-It Square

Root Algorithm

A technique is described whereby the 'guess' factor r1,
required for two-bit square root algorithms (see the preceding
article), is calculated based on input values. The procedure shown is
designed so that the factor can be calculated independently from the
square root computation. Different 'guess' factor ranges are
suitable, depending on the interpretation of the square root scheme.
The technique described herein outlines the logic for the square root
and 'guess' table utilizing a factor in the range of -3 to +3.  The
concept achieves a higher computational speed but also needs more
hardware to implement than a slower similar logic which uses a factor
range of -2 to +2.

'Guess'-logic is based on the requirement of keeping the
deviation of every intermediate step result value (the remainder) to
a minimum, as related to the 'true' square root value.  A
'guess'-table is generated by taking eleven bits (identical to the
key) as a base and then extending it by 2 or 4 bits.  Using the
predefined input values, the 'guess'-factor r1 can be calculated by
applying the logic of the square root scheme.

Figs. 1A, 1B and 1C comprise a flow diagram illustrating the
steps encountered in determining the 'guess'-factor r1.  For
reference purposes, the first logic flow diagrams describe the square
root algorithm as disclosed in the preceding article.

Obtaining the 'guess'-factor r1: The 'guess'-fa...