Parallel Prefix Computations
Tom Kelliher, CS 315
Mar. 3, 1999
Carry lookahead addition.
- Computing the prefixes.
Carry save addition.
- General form of a prefix computation:
where is a function of an input bit.
- Consider carry lookahead addition. Let be the s, p, or g for
bit position i. Then:
Note that this is written ``backwards.''
Why the initial s?
- Multiplication table for carry lookahead addition:
This operation must be associative for the carry computation to work. Why?
What's going on here?
- Using a four-leaf tree, label each leaf with it's and
- Can the class derive the calculation for the tree? Hint: each vertex
in the tree stores the product of its sub-tree leaves.
- General idea:
- Rising phase: each vertex computes the product of inputs from its
children. Action of a leaf, internal vertex.
- Computed values are passed from left child to right child.
- Falling phase: each internal vertex takes received value and
transmits it to children. Leaves concatenate received values on left.
- Show an example on a nine-leaf tree.
Thomas P. Kelliher
Wed Mar 3 11:16:47 EST 1999