High-precision division and square root

Authors:
Alan H. Karp;Peter Markstein
Affiliations:
Hewlett-Packard Labs;Hewlett-Packard Labs
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1997

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Abstract

We present division and square root algorithm for calculations with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.