sym_expr_opt.cpp

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#include "mim/phase/sym_expr_opt.h"
 
#include <absl/container/fixed_array.h>
 
namespace mim {
 
const Def* SymExprOpt::Analysis::propagate(const Def* var, const Def* def) {
    auto [i, ins] = lattice_.emplace(var, def);
    if (ins) {
        invalidate();
        DLOG("propagate: {} → {}", var, def);
        return def;
    }
 
    auto cur = i->second;
    if (!cur || def->isa<Bot>() || cur == def || cur == var || cur->isa<Proxy>()) return cur;
 
    invalidate();
    DLOG("cannot propagate {}, trying GVN", var);
    if (cur->isa<Bot>()) return i->second = def;
    return i->second = nullptr; // we reached top for propagate; nullptr marks this to bundle for GVN
}
 
static nat_t get_index(const Def* def) { return Lit::as(def->as<Extract>()->index()); }
 
const Def* SymExprOpt::Analysis::rewrite_imm_App(const App* app) {
    if (auto lam = app->callee()->isa_mut<Lam>(); isa_optimizable(lam)) {
        auto n          = app->num_targs();
        auto abstr_args = absl::FixedArray<const Def*>(n);
        auto abstr_vars = absl::FixedArray<const Def*>(n);
 
        // propagate
        for (size_t i = 0; i != n; ++i) {
            auto abstr    = rewrite(app->targ(i));
            abstr_vars[i] = propagate(lam->tvar(i), abstr);
            abstr_args[i] = abstr;
        }
 
        // GVN bundle: All things marked as top (nullptr) by propagate are now treated as one entity by bundling them
        // into one proxy
        for (size_t i = 0; i != n; ++i) {
            if (abstr_vars[i]) continue;
 
            auto vars = DefVec();
            auto vi   = lam->tvar(i);
            auto ai   = abstr_args[i];
            vars.emplace_back(vi);
 
            for (size_t j = i + 1; j != n; ++j) {
                auto vj = lam->tvar(j);
                if (!abstr_vars[j] && abstr_args[j] == ai) vars.emplace_back(vj);
            }
 
            if (vars.size() == 1) {
                lattice_[vi] = abstr_vars[i] = vi; // top
            } else {
                auto proxy = world().proxy(vi->type(), vars, 0, 0);
 
                for (auto p : proxy->ops()) {
                    auto j       = get_index(p);
                    auto vj      = lam->tvar(j);
                    lattice_[vj] = abstr_vars[j] = proxy;
                }
 
                DLOG("bundle: {}", proxy);
            }
        }
 
        // GVN split: We have to prove that all incoming args for all vars in a bundle are the same value.
        // Otherwise we have to refine the bundle by splitting off contradictions.
        // E.g.: Say we started with `{a, b, c, d, e}` as a single bundle for all tvars of `lam`.
        // Now, we see `lam (x, y, x, y, z)`. Then we have to build:
        // a -> {a, c}
        // b -> {b, d}
        // c -> {a, c}
        // d -> {b, d}
        // e -> e      (top)
        for (size_t i = 0; i != n; ++i) {
            if (auto proxy = abstr_vars[i]->isa<Proxy>()) {
                auto num  = proxy->num_ops();
                auto vars = DefVec();
                auto ai   = abstr_args[i];
 
                for (auto p : proxy->ops()) {
                    auto j  = get_index(p);
                    auto vj = lam->tvar(j);
                    if (p == vj) {
                        if (ai == abstr_args[j]) vars.emplace_back(vj);
                    }
                }
 
                auto new_num = vars.size();
                if (new_num == 1) {
                    invalidate();
                    auto vi      = lam->tvar(i);
                    lattice_[vi] = abstr_vars[i] = vi;
                    DLOG("single: {}", vi);
                } else if (new_num != num) {
                    invalidate();
                    auto new_proxy = world().proxy(ai->type(), vars, 0, 0);
                    DLOG("split: {}", new_proxy);
 
                    for (auto p : new_proxy->ops()) {
                        auto j  = get_index(p);
                        auto vj = lam->tvar(j);
                        if (p == vj) lattice_[vj] = abstr_vars[j] = new_proxy;
                    }
                }
                // if new_num == num: do nothing
            }
        }
 
        set(lam->var(), world().tuple(abstr_vars)); // set new abstract var
        return world().app(rewrite_deps(lam), abstr_args);
    }
 
    return mim::Analysis::rewrite_imm_App(app);
}
 
static bool keep(const Def* old_var, const Def* abstr) {
    if (old_var == abstr) return true; // top
    auto proxy = abstr->isa<Proxy>();
    return proxy && proxy->op(0) == old_var; // first in GVN bundle?
}
 
const Def* SymExprOpt::rewrite_imm_App(const App* old_app) {
    if (auto old_lam = old_app->callee()->isa_mut<Lam>()) {
        if (auto l = lattice(old_lam->var()); l && l != old_lam->var()) {
            invalidate();
 
            size_t num_old = old_lam->num_tvars();
            Lam* new_lam;
            if (auto i = lam2lam_.find(old_lam); i != lam2lam_.end())
                new_lam = i->second;
            else {
                // build new dom
                auto new_doms = DefVec();
                for (size_t i = 0; i != num_old; ++i) {
                    auto old_var = old_lam->var(num_old, i);
                    auto abstr   = lattice(old_var);
                    if (keep(old_var, abstr)) new_doms.emplace_back(rewrite(old_lam->dom(num_old, i)));
                }
 
                // build new lam
                size_t num_new    = new_doms.size();
                auto new_vars     = absl::FixedArray<const Def*>(num_old);
                new_lam           = new_world().mut_lam(new_doms, rewrite(old_lam->codom()))->set(old_lam->dbg());
                lam2lam_[old_lam] = new_lam;
 
                // build new var
                for (size_t i = 0, j = 0; i != num_old; ++i) {
                    auto old_var = old_lam->var(num_old, i);
                    auto abstr   = lattice(old_var);
 
                    if (keep(old_var, abstr)) {
                        auto v      = new_lam->var(num_new, j++);
                        new_vars[i] = v;
                        if (abstr != old_var) map(abstr, v); // GVN bundle
                    } else {
                        new_vars[i] = rewrite(abstr); // SCCP propagate
                    }
                }
 
                map(old_lam->var(), new_vars);
                auto new_filter = rewrite(old_lam->filter());
                auto new_body   = rewrite(old_lam->body());
                new_lam->set(new_filter, new_body);
            }
 
            // build new app
            size_t num_new = new_lam->num_vars();
            auto new_args  = absl::FixedArray<const Def*>(num_new);
            for (size_t i = 0, j = 0; i != num_old; ++i) {
                auto old_var = old_lam->var(num_old, i);
                auto abstr   = lattice(old_var);
                if (keep(old_var, abstr)) new_args[j++] = rewrite(old_app->targ(i));
            }
 
            return map(old_app, new_world().app(new_lam, new_args));
        }
    }
 
    return RWPhase::rewrite_imm_App(old_app);
}
 
} // namespace mim