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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
214 Chapter 6 Implementation of floating-point arithmetic on a computer
6.7 Rounding
After normalization the mantissa, which in general has a length of 2r C 1 dig its, is
to be rounded to r digits. All roundings of the set
2f
5
, 4,
, D 0.1/bg
are monotone functions. Rounding a number either truncates the number or enlarges
its absolute value. The latter case requires another add operation. So rounding is a
relatively complicated process. The add operation may cause a carry which propagates
from the least significant bit across all digits of the number. Thus a rounding can alter
the mantissa so that jmzjD1 which causes another normalization. See Figur ...
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Publisher Resources

ISBN: 9783110301731