Instruction Selection

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开始将规范树转化为汇编代码了

Instruction Selection：apping IR into abstract assembly code

Register Allocation：Deciding which values will reside in registers，Replace abstract registers with real register

Instruction Selection: Why and What

The intermediate representation (Tree) language expresses only one operation in each tree node.

Areal machine instruction can often perform several of primitive operations.

The instruction selection phase: Finding the appropriate machine instructions to implement a given intermediate representation tree

Tree Patterns

Each machine instruction can be expressed a fragment of an IR tree, called a tree pattern.

Instruction selection: tiling the tree with a minimal set of tree patterns.

Tiling: cover the tree with nonoverlapping tree patterns

The tiles are the set of tree patterns corresponding to legal machine instructions

To illustrate instruction selection, we use the Jouette architecture invented in the textbook

The Jouette architecture

Specification about Jouette Architecture

Register r0 always contains zero

Some instructions correspond to more than one tree pattern

Tree Patterns- Example

It is always possible to tile the tree with tiny tiles, each covering only one node

Optimal and Optimum Tilings

Best tiling: an instruction sequence of least cost
- the shortest sequence of instructions
- Orthe least-cost sequence has the lowest total time if the instructions take different amount of time to execute.
Optimum tiling: the one whose tiles sum to the lowest possible value
- 全局最优，cost 最小的覆盖

Optimal tiling: the one where no two adjacent tiles can be combined into a single tile of lower cost
- 局部最优，如果选择任意两个瓦片进行合并，代价没有变得更低，那么当前的就是最佳（Optimal）覆盖

Every optimum tiling is also optimal, but not vice versa

Algorithms for Instruction Selection

Maximal Munch

always finds an optimal tiling, but not necessarily an optimum

Assume larger tiles = better
Main idea: Greedy algorithm
- 自顶向下遍历 IR tree，用尽可能大的瓦片进行覆盖当前的结点，再递归检查剩下的
- 能保证任意两个瓦片都不能合并

Largest tile: the one with the most nodes

具体流程
1. Starting at the root of the tree, find the largest tile that fits.
2. Cover the root node– and perhaps several other nodes near the root– with this tile, leaving several subtrees.
3. Repeat the same algorithm for each subtree.

The instructions are generated in reverse order

If twotiles of equal size match at the root, then the choice between them is arbitrary