Browsing by Author "Briggs, Preston"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Multiplication by Integer Constants
    (2003-10-21) Briggs, Preston; Harvey, Timothy J.
    Some modern machines have no integer multiple instruction and must rely on expensive software methods to compute integer products. In other cases, the multiply instruction is significantly slower than simple integer addition. When faced with computing n*c, where n is some unknown integer value and c is a known integer constant, we can avoid the need for a general-purpose multiply by rewriting the expression in terms of shifts, adds, and subtracts—typically all one-cycle instructions. Bernstein gives a detailed discussion of the problem and presents a solution, including Ada code for its implementation. Unfortunately, the code is flawed, at least in part due to typesetting errors. It's also quite difficult to understand. This document represents an attempt to explain the elements of Bernstein's approach. At the same time, we will develop a complete, working, and hopefully understandable implementation of his approach.
  • Thumbnail Image
    Item
    Register allocation via graph coloring
    (1992) Briggs, Preston; Cooper, Keith D.
    Chaitin and his colleagues at IBM in Yorktown Heights built the first global register allocator based on graph coloring. This thesis describes a series of improvements and extensions to the Yorktown allocator. There are four primary results: (1) Optimistic coloring. Chaitin's coloring heuristic pessimistically assumes any node of high degree will not be colored and must therefore be spilled. By optimistically assuming that nodes of high degree will receive colors, I often achieve lower spill costs and faster code; my results are never worse. (2) Coloring pairs. The pessimism of Chaitin's coloring heuristic is emphasized when trying to color register pairs. My heuristic handles pairs as a natural consequence of its optimism. (3) Rematerialization. Chaitin et al. introduced the idea of rematerialization to avoid the expense of spilling and reloading certain simple values. By propagating rematerialization information around the SSA graph using a simple variation of Wegman and Zadeck's constant propagation techniques, I discover and isolate a larger class of such simple values. (4) Live range splitting. Chow and Hennessy's technique, priority-based coloring, includes a form of live range splitting. By aggressively splitting live ranges at selected points before coloring, I am able to incorporate live range splitting into the framework of Chaitin's allocator. Additionally, I report the results of experimental studies measuring the effectiveness of each of my improvements. I also report the results of an experiment suggesting that priority-based coloring requires O($n\sp2$) time and that the Yorktown allocator requires only O(n log n) time. Finally, I include a chapter describing many implementation details and including further measurements designed to provide an accurate intuition about the time and space requirements of coloring allocators.
  • Thumbnail Image
    Item
    Register Allocation via Graph Coloring
    (1992-04) Briggs, Preston
    Chaitin and his colleagues at IBM in Yorktown Heights built the first global register allocator based on graph coloring. This thesis describes a series of improvements and extensions to the Yorktown allocator. There are four primary results: Optimistic coloring—Chaitin's coloring heuristic pessimistically assumes any node of high degree will not be colored and must therefore be spilled. By optimistically assuming that nodes of high degree will receive colors, I often achieve lower spill costs and faster code; my results are never worse. Coloring pairs—The pessimism of Chaitin's coloring heuristic is emphasized when trying to color register pairs. My heuristic handles pairs as a natural consequence of its optimism. Rematerialization—Chaitin et al. introduced the idea of rematerialization to avoid the expense of spilling and reloading certain simple values. By propagating rematerialization information around the SSA graph using a simple variation of Wegman and Zadeck's constant propagation techniques, I discover and isolate a larger class of such simple values. Live range splitting—Chow and Hennessy's technique, priority-based coloring, includes a form of live range splitting. By aggressively splitting live ranges at selected points before coloring, I am able to incorporate live range splitting into the framework of Chaitin's allocator. Additionally, I report the results of experimental studies measuring the effectiveness of each of my improvements. I also report the results of an experiment suggesting that priority-based coloring requires O(n2) time and that the Yorktown allocator requires only O(n log n) time. Finally, I include a chapter describing many implementation details and including further measurements designed to provide an accurate intuition about the time and space requirements of coloring allocators.