Improved normalization results for digit on-line arithmetic

In digit on-line arithmetic, operands are introduced a digit at a time. After the first few operand digits have been introduced, the result begins to appear a digit at a time. This feature of digit on-line arithmetic allows a significant amount of overlapping of arithmetic operations. Digit on-line arithmetic can sometimes produce unnormalized results. This can present a problem for the divide and square root algorithms. If the divisor and radicand are highly unnormalized, these algorithms will not produce the correct results. Two advances in overcoming this problem are presented. First, several techniques for producing results that are closer to being normalized are developed. Second, it is shown that normalized results are not necessary for divide and square root to work properly. Combining these results yields algorithms that will always give the correct results.

[1]  Robert L. Ashenhurst,et al.  Unnormalized Floating Point Arithmetic , 1959, JACM.

[2]  Pat H. Sterbenz,et al.  Floating-point computation , 1973 .

[3]  Milos D. Ercegovac,et al.  An on-line square rooting algorithm , 1978, 1978 IEEE 4th Symposium onomputer Arithmetic (ARITH).

[4]  Robert Michael Owens Compound algorithms for digit online arithmetic , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[5]  Milos D. Ercegovac Radix-16 Evaluation of Certain Elementary Functions , 1973, IEEE Transactions on Computers.

[6]  Robert Michael Owens Digit on-line algorithms for pipeline architectures , 1980 .

[7]  Kishor S. Trivedi,et al.  Higher radix on-line division , 1978, 1978 IEEE 4th Symposium onomputer Arithmetic (ARITH).

[8]  Milos D. Ercegovac,et al.  Floating-point on-line arithmetic: Error analysis , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[9]  Bruce Gene De Lugish,et al.  A class of algorithms for automatic evaluation of certain elementary functions in a binary computer , 1970 .

[10]  Milos D. Ercegovac,et al.  Floating-point on-line arithmetic: Algorithms , 1981, 1981 IEEE 5th Symposium on Computer Arithmetic (ARITH).

[11]  Daniel E. Atkins,et al.  Introduction to the Role of Redundancy in Computer Arithmetic , 1975, Computer.