25-04-2012, 04:56 PM
High-Radix Dividers
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Difficulty of High-Radix Division
Guessing the correct quotient digit is more
difficult.
Division is naturally a sequential process:
• Guess a quotient digit
Carry-Save Remainders
More important for speed than high-radix.
Lead to large performance increases by replacing
carry-propagate adder with carry-save adder.
Key to keeping remainder in carry-save form is:
Redundancy in the representation of q.
• Allows less precise guessing of quotient digit based
on approximate magnitude of partial remainder.
• More redundancy → less precision required.
Intel’s Pentium Division Bug
Intel used the Radix-4 SRT division algorithm.
Quotient selection was implemented as a PLA.
The p-d plot was numerically generated.
Script to download entries into the PLA
inadvertently removed a few table entries from
the table.
When hit, these missing entries resulted in digit 0,
instead of the intended digits ±2.
These entries are consulted very rarely, and thus
the bug was very subtle and difficult to detect.