From 73df946d56c74384511a194dd01dbe099584fd1a Mon Sep 17 00:00:00 2001 From: Daniel Baumann Date: Sun, 28 Apr 2024 15:14:23 +0200 Subject: Adding upstream version 1.16.10. Signed-off-by: Daniel Baumann --- src/cmd/compile/internal/ssa/lca.go | 123 ++++++++++++++++++++++++++++++++++++ 1 file changed, 123 insertions(+) create mode 100644 src/cmd/compile/internal/ssa/lca.go (limited to 'src/cmd/compile/internal/ssa/lca.go') diff --git a/src/cmd/compile/internal/ssa/lca.go b/src/cmd/compile/internal/ssa/lca.go new file mode 100644 index 0000000..5cb7391 --- /dev/null +++ b/src/cmd/compile/internal/ssa/lca.go @@ -0,0 +1,123 @@ +// Copyright 2016 The Go Authors. All rights reserved. +// Use of this source code is governed by a BSD-style +// license that can be found in the LICENSE file. + +package ssa + +// Code to compute lowest common ancestors in the dominator tree. +// https://en.wikipedia.org/wiki/Lowest_common_ancestor +// https://en.wikipedia.org/wiki/Range_minimum_query#Solution_using_constant_time_and_linearithmic_space + +// lcaRange is a data structure that can compute lowest common ancestor queries +// in O(n lg n) precomputed space and O(1) time per query. +type lcaRange struct { + // Additional information about each block (indexed by block ID). + blocks []lcaRangeBlock + + // Data structure for range minimum queries. + // rangeMin[k][i] contains the ID of the minimum depth block + // in the Euler tour from positions i to i+1< 0 { + n := len(q) - 1 + bid := q[n].bid + cid := q[n].cid + q = q[:n] + + // Add block to tour. + blocks[bid].pos = int32(len(tour)) + tour = append(tour, bid) + + // Proceed down next child edge (if any). + if cid == 0 { + // This is our first visit to b. Set its depth. + blocks[bid].depth = blocks[blocks[bid].parent].depth + 1 + // Then explore its first child. + cid = blocks[bid].firstChild + } else { + // We've seen b before. Explore the next child. + cid = blocks[cid].sibling + } + if cid != 0 { + q = append(q, queueEntry{bid, cid}, queueEntry{cid, 0}) + } + } + + // Compute fast range-minimum query data structure + var rangeMin [][]ID + rangeMin = append(rangeMin, tour) // 1-size windows are just the tour itself. + for logS, s := 1, 2; s < len(tour); logS, s = logS+1, s*2 { + r := make([]ID, len(tour)-s+1) + for i := 0; i < len(tour)-s+1; i++ { + bid := rangeMin[logS-1][i] + bid2 := rangeMin[logS-1][i+s/2] + if blocks[bid2].depth < blocks[bid].depth { + bid = bid2 + } + r[i] = bid + } + rangeMin = append(rangeMin, r) + } + + return &lcaRange{blocks: blocks, rangeMin: rangeMin} +} + +// find returns the lowest common ancestor of a and b. +func (lca *lcaRange) find(a, b *Block) *Block { + if a == b { + return a + } + // Find the positions of a and bin the Euler tour. + p1 := lca.blocks[a.ID].pos + p2 := lca.blocks[b.ID].pos + if p1 > p2 { + p1, p2 = p2, p1 + } + + // The lowest common ancestor is the minimum depth block + // on the tour from p1 to p2. We've precomputed minimum + // depth blocks for powers-of-two subsequences of the tour. + // Combine the right two precomputed values to get the answer. + logS := uint(log64(int64(p2 - p1))) + bid1 := lca.rangeMin[logS][p1] + bid2 := lca.rangeMin[logS][p2-1<