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Precision Control for Floating Point Arithmetic

IP.com Disclosure Number: IPCOM000091086D
Original Publication Date: 1969-Oct-01
Included in the Prior Art Database: 2005-Mar-05
Document File: 1 page(s) / 12K

Publishing Venue

IBM

Related People

Senzig, DN: AUTHOR

Abstract

This method enables floating point calculations to be done accurately with an expected error of zero. The method provides for programming of range or interval arithmetic. In range arithmetic, a number x is known to be in the range a

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Precision Control for Floating Point Arithmetic

This method enables floating point calculations to be done accurately with an expected error of zero. The method provides for programming of range or interval arithmetic. In range arithmetic, a number x is known to be in the range a</-x</-b. This can be represented by >a,b|. The addition of two range arithmetic numbers is defined as >a,b|+>c,d| = >a+c,b+d|. Similar definitions are possible for -,*,/ except that >a,b|/>c,d| is not defined if c</-0</-d. Sign and magnitude floating point arithmetic is assumed. Methods for radix complement or reduced radix complement arithmetic proceed similarly.

Range arithmetic error control can be implemented by Or'ing together the discarded bits of a floating point operation and using the result to set a flip-flop, called the Precision Control PC bit. That is, if the discarded bits are all zero, the PC bit is set to zero. If any of the discarded bits is a one, the PC bit is set to one. The discarded bits are the right-shifted bits in addition and subtraction, the least- significant n or n-1 bits in multiplication where n is the fraction length, and the remainder in division.

To Round-up in addition, i.e., obtain the upper bound on the range b+d, if the sign is positive, the content of the PC bit is added to the least-significant bit of that portion of the number remained. If the sign of the number is negative, no operation is performed. To Round-down, or obtain the lower bound on the range, the process is reversed. For positive numbers, no operation is performed. For negative numbers, the content of the PC bit is added to the least-significant bit of the n...