【编译优化探秘】LLVM Polly：让代码执行如行云流水

import java.util.*;

// 多面体模型中的约束表示
class Constraint {
    List<Integer> coefficients; // 变量系数
    int constant; // 常量项
    boolean isEquality; // 是否为等式约束

    public Constraint(List<Integer> coefficients, int constant, boolean isEquality) {
        this.coefficients = coefficients;
        this.constant = constant;
        this.isEquality = isEquality;
    }

    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < coefficients.size(); i++) {
            int coef = coefficients.get(i);
            if (coef != 0) {
                if (i > 0 && coef > 0) sb.append(" + ");
                else if (coef < 0) sb.append(" - ");
                sb.append(Math.abs(coef)).append("*i").append(i);
            }
        }
        if (isEquality) sb.append(" = ");
        else sb.append(" <= ");
        sb.append(constant);
        return sb.toString();
    }
}

// 多面体表示
class Polyhedron {
    List<Constraint> constraints;

    public Polyhedron() {
        this.constraints = new ArrayList<>();
    }

    public void addConstraint(Constraint constraint) {
        constraints.add(constraint);
    }

    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder("Polyhedron:\n");
        for (Constraint c : constraints) {
            sb.append("  ").append(c).append("\n");
        }
        return sb.toString();
    }
}

// 循环结构表示
class Loop {
    int nestLevel; // 嵌套层级
    int lowerBound; // 下界
    int upperBound; // 上界
    int step; // 步长
    List<Loop> innerLoops; // 内层循环
    List<String> statements; // 循环体语句

    public Loop(int nestLevel, int lowerBound, int upperBound, int step) {
        this.nestLevel = nestLevel;
        this.lowerBound = lowerBound;
        this.upperBound = upperBound;
        this.step = step;
        this.innerLoops = new ArrayList<>();
        this.statements = new ArrayList<>();
    }

    public void addInnerLoop(Loop loop) {
        innerLoops.add(loop);
    }

    public void addStatement(String statement) {
        statements.add(statement);
    }

    @Override
    public String toString() {
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < nestLevel; i++) sb.append("  ");
        sb.append("for (int i").append(nestLevel).append(" = ").append(lowerBound);
        sb.append("; i").append(nestLevel).append(" < ").append(upperBound);
        sb.append("; i").append(nestLevel).append(" += ").append(step).append(") {\n");

        for (Loop innerLoop : innerLoops) {
            sb.append(innerLoop.toString());
        }

        for (String statement : statements) {
            for (int i = 0; i < nestLevel + 1; i++) sb.append("  ");
            sb.append(statement).append("\n");
        }

        for (int i = 0; i < nestLevel; i++) sb.append("  ");
        sb.append("}\n");

        return sb.toString();
    }
}

// 依赖关系分析
class DependenceAnalyzer {
    public static boolean hasDependence(Loop loop, String stmt1, String stmt2) {
        // 简化的依赖分析，实际需要分析数组访问模式
        return stmt1.contains("a[i") && stmt2.contains("a[i");
    }
}

// Polly优化器
class PollyOptimizer {
    // 将循环转换为多面体模型
    public static Polyhedron loopToPolyhedron(Loop loop) {
        Polyhedron polyhedron = new Polyhedron();
        
        // 添加当前循环的约束
        List<Integer> lowerBoundCoef = new ArrayList<>();
        for (int i = 0; i < loop.nestLevel; i++) lowerBoundCoef.add(0);
        lowerBoundCoef.add(-1);
        polyhedron.addConstraint(new Constraint(lowerBoundCoef, -loop.lowerBound, false));
        
        List<Integer> upperBoundCoef = new ArrayList<>();
        for (int i = 0; i < loop.nestLevel; i++) upperBoundCoef.add(0);
        upperBoundCoef.add(1);
        polyhedron.addConstraint(new Constraint(upperBoundCoef, loop.upperBound - 1, false));
        
        // 添加内层循环的约束
        for (Loop innerLoop : loop.innerLoops) {
            Polyhedron innerPoly = loopToPolyhedron(innerLoop);
            polyhedron.constraints.addAll(innerPoly.constraints);
        }
        
        return polyhedron;
    }
    
    // 循环分块优化
    public static Loop applyLoopTiling(Loop loop, int tileSize) {
        if (loop.innerLoops.isEmpty()) {
            // 对最内层循环进行分块
            Loop tiledLoop = new Loop(loop.nestLevel, 0, (loop.upperBound - loop.lowerBound + tileSize - 1) / tileSize, 1);
            Loop innerTileLoop = new Loop(loop.nestLevel + 1, 0, tileSize, 1);
            
            for (String stmt : loop.statements) {
                // 替换循环变量引用
                String newStmt = stmt.replace("i" + loop.nestLevel, 
                                             "i" + loop.nestLevel + " * " + tileSize + " + i" + (loop.nestLevel + 1));
                innerTileLoop.addStatement(newStmt);
            }
            
            tiledLoop.addInnerLoop(innerTileLoop);
            return tiledLoop;
        } else {
            // 对每个内层循环应用分块
            Loop optimizedLoop = new Loop(loop.nestLevel, loop.lowerBound, loop.upperBound, loop.step);
            for (Loop innerLoop : loop.innerLoops) {
                optimizedLoop.addInnerLoop(applyLoopTiling(innerLoop, tileSize));
            }
            for (String stmt : loop.statements) {
                optimizedLoop.addStatement(stmt);
            }
            return optimizedLoop;
        }
    }
    
    // 循环重排序优化
    public static Loop applyLoopPermutation(Loop loop, List<Integer> permutation) {
        // 简化实现，实际需要更复杂的依赖分析和变换
        if (loop.innerLoops.size() < 2) return loop;
        
        List<Loop> newInnerLoops = new ArrayList<>();
        for (int idx : permutation) {
            if (idx < loop.innerLoops.size()) {
                newInnerLoops.add(loop.innerLoops.get(idx));
            }
        }
        
        Loop optimizedLoop = new Loop(loop.nestLevel, loop.lowerBound, loop.upperBound, loop.step);
        for (Loop innerLoop : newInnerLoops) {
            optimizedLoop.addInnerLoop(innerLoop);
        }
        for (String stmt : loop.statements) {
            optimizedLoop.addStatement(stmt);
        }
        
        return optimizedLoop;
    }
}

// 示例使用
public class PollyExample {
    public static void main(String[] args) {
        // 创建一个嵌套循环
        Loop outerLoop = new Loop(0, 0, 100, 1);
        Loop innerLoop = new Loop(1, 0, 100, 1);
        
        innerLoop.addStatement("a[i0][i1] = b[i0][i1] + c[i0][i1];");
        
        outerLoop.addInnerLoop(innerLoop);
        
        System.out.println("原始循环:");
        System.out.println(outerLoop);
        
        // 转换为多面体模型
        Polyhedron polyhedron = PollyOptimizer.loopToPolyhedron(outerLoop);
        System.out.println("多面体模型:");
        System.out.println(polyhedron);
        
        // 应用循环分块优化
        Loop tiledLoop = PollyOptimizer.applyLoopTiling(outerLoop, 8);
        System.out.println("分块优化后的循环:");
        System.out.println(tiledLoop);
        
        // 应用循环重排序优化
        List<Integer> permutation = Arrays.asList(1, 0); // 交换内外循环
        Loop permutedLoop = PollyOptimizer.applyLoopPermutation(outerLoop, permutation);
        System.out.println("重排序优化后的循环:");
        System.out.println(permutedLoop);
    }
}