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Fast and Perfectly Rounding Decimal/Hexadecimal Conversions

IP.com Disclosure Number: IPCOM000121342D
Original Publication Date: 1991-Aug-01
Included in the Prior Art Database: 2005-Apr-03
Document File: 1 page(s) / 27K

Publishing Venue

IBM

Related People

Slishman, GR: AUTHOR

Abstract

Disclosed is a method for fast and perfectly rounding conversions between decimal and hexadecimal floating-point representations of real data. Perfect rounding means symmetric and consistent rounding, with no exceptions. This method applies as well to conversions between decimal and any radix-2**N floating-point representation, IEEE in particular.

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Fast and Perfectly Rounding Decimal/Hexadecimal Conversions

      Disclosed is a method for fast and perfectly rounding
conversions between decimal and hexadecimal floating-point
representations of real data.  Perfect rounding means symmetric and
consistent rounding, with no exceptions.  This method applies as well
to conversions between decimal and any radix-2**N floating-point
representation, IEEE in particular.

      The method uses a table of powers of ten for speed. The
precision of computation is such that only one conversion in 65,536
requires execution of a special path to round highly ambiguous cases.
Therefore, the method is very fast on average.

      The ambiguous cases execute a special path that determines the
correct rounding by evaluating an inequality, both comparands of
which are computable to infinite precision.  Therefore, the method
never fails to round correctly.  Details appear in (*).

      Reference
(*)  G. Slishman, "Fast and Perfectly Rounding Decimal/Hexadecimal
Conversions," IBM Research Report RC 15683, IBM T. J. Watson Research
Center, Yorktown Heights, New York 10598 (April 1990).