ll.h

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#pragma once
 
#include <deque>
#include <format>
#include <iomanip>
#include <optional>
#include <ostream>
#include <ranges>
#include <string>
 
#include <absl/container/btree_set.h>
 
#include <mim/plug/clos/clos.h>
#include <mim/plug/math/math.h>
#include <mim/plug/mem/mem.h>
#include <mim/plug/vec/vec.h>
 
#include "mim/be/emitter.h"
#include "mim/util/print.h"
 
#include "mim/plug/core/core.h"
#include "mim/plug/math/autogen.h"
 
// Lessons learned:
// * **Always** follow all ops - even if you actually want to ignore one.
//   Otherwise, you might end up with an incorrect schedule.
//   This was the case for an Extract of type Mem.
//   While we want to ignore the value obtained from that, since there is no Mem value in LLVM,
//   we still want to **first** recursively emit code for its operands and **then** ignore the Extract itself.
// * i1 has a different meaning in LLVM then in Mim:
//      * Mim: {0,  1} = i1
//      * LLVM:   {0, -1} = i1
//   This is a problem when, e.g., using an index of type i1 as LLVM thinks like this:
//   getelementptr ..., i1 1 == getelementptr .., i1 -1
namespace mim {
 
class World;
 
namespace ll {
 
namespace clos = mim::plug::clos;
namespace core = mim::plug::core;
namespace math = mim::plug::math;
namespace mem  = mim::plug::mem;
namespace vec  = mim::plug::vec;
 
namespace {
inline const char* math_suffix(const Def* type) {
    if (auto w = math::isa_f(type)) {
        switch (*w) {
            case 32: return "f";
            case 64: return "";
        }
    }
    error("unsupported floating point type '{}'", type);
}
 
inline const char* llvm_suffix(const Def* type) {
    if (auto w = math::isa_f(type)) {
        switch (*w) {
            case 16: return ".f16";
            case 32: return ".f32";
            case 64: return ".f64";
        }
    }
    error("unsupported floating point type '{}'", type);
}
 
// [%mem.M 0, T] => T
// TODO there may be more instances where we have to deal with this trickery
inline const Def* isa_mem_sigma_2(const Def* type) {
    if (auto sigma = type->isa<Sigma>())
        if (sigma->num_ops() == 2 && Axm::isa<mem::M>(sigma->op(0))) return sigma->op(1);
    return {};
}
} // namespace
 
void emit(World&, std::ostream&);
 
int compile(World&, std::string name);
int compile(World&, std::string ll, std::string out);
int compile_and_run(World&, std::string name, std::string args = {});
 
struct BB {
    BB()                    = default;
    BB(const BB&)           = delete;
    BB(BB&& other) noexcept = default;
    BB& operator=(BB other) noexcept { return swap(*this, other), *this; }
 
    std::deque<std::ostringstream>& head() { return parts[0]; }
    std::deque<std::ostringstream>& body() { return parts[1]; }
    std::deque<std::ostringstream>& tail() { return parts[2]; }
 
    template<class... Args>
    inline std::string assign(std::string_view name, const char* s, Args&&... args) {
        print(print(body().emplace_back(), "{} = ", name), s, std::forward<Args>(args)...);
        return std::string(name);
    }
 
    template<class... Args>
    inline void tail(const char* s, Args&&... args) {
        print(tail().emplace_back(), s, std::forward<Args>(args)...);
    }
 
    friend inline void swap(BB& a, BB& b) noexcept {
        using std::swap;
        swap(a.phis, b.phis);
        swap(a.parts, b.parts);
    }
 
    DefMap<std::deque<std::pair<std::string, std::string>>> phis;
    std::array<std::deque<std::ostringstream>, 3> parts;
};
 
class Emitter : public mim::Emitter<std::string, std::string, BB, Emitter> {
public:
    using Super = mim::Emitter<std::string, std::string, BB, Emitter>;
 
    Emitter(World& world, std::ostream& ostream)
        : Super(world, "llvm_emitter", ostream) {}
 
    bool is_valid(std::string_view s) { return !s.empty(); }
    void start() override;
    void emit_imported(Lam*);
    virtual void emit_epilogue(Lam*);
    std::string emit_bb(BB&, const Def*);
    virtual std::string prepare();
    void finalize();
 
    virtual inline std::optional<std::string> isa_targetspecific_intrinsic(BB&, const Def*) { return std::nullopt; }
    inline std::string as_targetspecific_intrinsic(BB& bb, const Def* def) {
        if (auto res = isa_targetspecific_intrinsic(bb, def)) return res.value();
        error("target-specific intrinsic detected but not handled in LLVM backend: {} : {}", def, def->type());
    }
 
    template<class... Args>
    void declare(const char* s, Args&&... args) {
        std::ostringstream decl;
        print(decl << "declare ", s, std::forward<Args>(args)...);
        decls_.emplace(decl.str());
    }
 
private:
    std::string id(const Def*, bool force_bb = false) const;
    std::string convert(const Def*, bool simd = true);
    std::string convert_ret_pi(const Pi*);
 
    absl::btree_set<std::string> decls_;
    std::ostringstream type_decls_;
    std::ostringstream vars_decls_;
    std::ostringstream func_decls_;
    std::ostringstream func_impls_;
    LamMap<const Def*> simd_phi_;
};
 
/*
 * convert
 */
 
inline static std::optional<std::pair<nat_t, const Def*>> is_simd(const Def* type) {
    if (auto arr = type->isa<Arr>()) {
        if (auto l = Lit::isa(arr->arity())) {
            if (arr->body()->isa<Nat>() || Idx::isa(arr->body()) || Axm::isa<math::F>(arr->body()))
                return std::pair{*l, arr->body()};
        }
    }
    return {};
}
 
inline static std::optional<std::pair<nat_t, const Def*>> is_simd_aggregate(const std::vector<const Def*> types) {
    if (std::ranges::all_of(types, [&](auto i) { return i == types[0]; })) {
        if (types[0]->isa<Nat>() || Idx::isa(types[0]) || Axm::isa<math::F>(types[0]))
            return std::pair{types.size(), types[0]};
    }
 
    return {};
}
 
inline static const Def* find_common_simd_src(const App* app) {
    const Def* common_src = nullptr;
    for (auto arg : app->args()) {
        if (Axm::isa<mem::M>(arg->type())) continue;
        auto extract = arg->isa<Extract>();
        if (!extract || !is_simd(extract->tuple()->type())) return nullptr;
        if (!common_src)
            common_src = extract->tuple();
        else if (common_src != extract->tuple())
            return nullptr;
    }
    return common_src;
}
 
inline std::string Emitter::id(const Def* def, bool force_bb /*= false*/) const {
    if (auto global = def->isa<Global>()) return "@" + global->unique_name();
 
    if (auto lam = def->isa_mut<Lam>(); lam && !force_bb) {
        if (lam->type()->ret_pi()) {
            if (lam->is_external() || !lam->is_set())
                return std::string("@") + lam->sym().str(); // TODO or use is_internal or sth like that?
            return std::string("@") + lam->unique_name();
        }
    }
 
    return std::string("%") + def->unique_name();
}
 
inline std::string Emitter::convert(const Def* type, bool simd) {
    if (auto i = types_.find(type); i != types_.end()) return i->second;
 
    assert(!Axm::isa<mem::M>(type));
    std::ostringstream s;
    std::string name;
 
    if (type->isa<Nat>()) {
        return types_[type] = "i64";
    } else if (auto size = Idx::isa(type)) {
        return types_[type] = "i" + std::to_string(*Idx::size2bitwidth(size));
    } else if (auto w = math::isa_f(type)) {
        switch (*w) {
            case 16: return types_[type] = "half";
            case 32: return types_[type] = "float";
            case 64: return types_[type] = "double";
            default: fe::unreachable();
        }
    } else if (auto ptr = Axm::isa<mem::Ptr>(type)) {
        auto [pointee, addr_space] = ptr->args<2>();
        // TODO addr_space
        print(s, "{}*", convert(pointee, false));
    } else if (auto arr = type->isa<Arr>()) {
        if (auto se = is_simd(arr); se && simd) {
            auto [size, elem] = *se;
            print(s, "<{} x {}>", size, convert(elem));
        } else {
            u64 size = 0;
            if (auto arity = Lit::isa(arr->arity())) size = *arity;
            print(s, "[{} x {}]", size, convert(arr->body(), false));
        }
    } else if (auto pi = type->isa<Pi>()) {
        assert(Pi::isa_returning(pi) && "should never have to convert type of BB");
        print(s, "{} (", convert_ret_pi(pi->ret_pi()));
 
        if (auto t = isa_mem_sigma_2(pi->dom()))
            s << convert(t);
        else {
            auto doms = pi->doms();
            for (auto sep = ""; auto dom : doms.view().rsubspan(1)) {
                if (Axm::isa<mem::M>(dom)) continue;
                s << sep << convert(dom);
                sep = ", ";
            }
        }
        s << ")*";
    } else if (auto t = isa_mem_sigma_2(type)) {
        return convert(t);
    } else if (auto sigma = type->isa<Sigma>()) {
        if (sigma->isa_mut()) {
            name          = id(sigma);
            types_[sigma] = name;
            print(s, "{} = type", name);
        }
 
        print(s, "{{");
        for (auto sep = ""; auto t : sigma->ops()) {
            if (Axm::isa<mem::M>(t)) continue;
            s << sep << convert(t);
            sep = ", ";
        }
        print(s, "}}");
    } else {
        fe::unreachable();
    }
 
    if (name.empty()) return types_[type] = s.str();
 
    assert(!s.str().empty());
    type_decls_ << s.str() << '\n';
    return types_[type] = name;
}
 
inline std::string Emitter::convert_ret_pi(const Pi* pi) {
    auto dom = mem::strip_mem_ty(pi->dom());
    if (dom == world().sigma()) return "void";
    return convert(dom);
}
 
/*
 * emit
 */
 
inline void Emitter::start() {
    Super::start();
 
    ostream() << type_decls_.str() << '\n';
    for (auto&& decl : decls_)
        ostream() << decl << '\n';
    ostream() << func_decls_.str() << '\n';
    ostream() << vars_decls_.str() << '\n';
    ostream() << func_impls_.str() << '\n';
}
 
inline void Emitter::emit_imported(Lam* lam) {
    // TODO merge with declare method
    print(func_decls_, "declare {} {}(", convert_ret_pi(lam->type()->ret_pi()), id(lam));
 
    auto doms = lam->doms();
    for (auto sep = ""; auto dom : doms.view().rsubspan(1)) {
        if (Axm::isa<mem::M>(dom)) continue;
        print(func_decls_, "{}{}", sep, convert(dom));
        sep = ", ";
    }
 
    print(func_decls_, ")\n");
}
 
inline std::string Emitter::prepare() {
    auto internal = root()->is_external() ? "" : "internal ";
    auto ret_t    = convert_ret_pi(root()->type()->ret_pi());
    print(func_impls_, "define {} {} {}(", internal, ret_t, id(root()));
 
    auto vars = root()->vars();
    for (auto sep = ""; auto var : vars.view().rsubspan(1)) {
        if (Axm::isa<mem::M>(var->type())) continue;
        if (auto arr = var->type()->isa<Arr>())
            if (is_simd(arr->body())) convert(arr->body()); // pre-add input vector to cache
        auto name    = id(var);
        locals_[var] = name;
        print(func_impls_, "{}{} {}", sep, convert(var->type()), name);
        sep = ", ";
    }
 
    print(func_impls_, ") {{\n");
    return root()->unique_name();
}
 
inline void Emitter::finalize() {
    for (auto& [lam, bb] : lam2bb_) {
        for (const auto& [phi, args] : bb.phis) {
            print(bb.head().emplace_back(), "{} = phi {} ", id(phi), convert(phi->type()));
            for (auto sep = ""; const auto& [arg, pred] : args) {
                print(bb.head().back(), "{}[ {}, {} ]", sep, arg, pred);
                sep = ", ";
            }
        }
    }
 
    for (auto mut : Scheduler::schedule(nest())) {
        if (auto lam = mut->isa_mut<Lam>()) {
            assert(lam2bb_.contains(lam));
            auto& bb = lam2bb_[lam];
            print(func_impls_, "{}:\n", lam->unique_name());
 
            ++tab;
            for (const auto& part : bb.parts)
                for (const auto& line : part)
                    tab.print(func_impls_, "{}\n", line.str());
            --tab;
            func_impls_ << std::endl;
        }
    }
 
    print(func_impls_, "}}\n\n");
}
 
/*
 Block           type              return
BB:
          Cn [M, a, A]         →    2 phi
          Cn «2;A»             →    2 phi
          Cn [M, «2;A»]        →    1 phi
Ret:
          Cn[M,A,A]            →    1 phi
          Cn «2;A»             →    1 phi
          Cn[M, «2;A»]         →    1 phi
 
Fun:
          Cn[A, A, Cn R]       →    2 args + ret
          Cn[«2; A», Cn R]     →    1 args + ret
          Cn[M, A, A, Cn R]    →    2 args + ret
          Cn[M, «2; A», Cn R]  →    1 args + ret
*/
inline void Emitter::emit_epilogue(Lam* lam) {
    auto app = lam->body()->as<App>();
    auto& bb = lam2bb_[lam];
    if (app->callee() == root()->ret_var()) { // return
        std::vector<std::string> values;
        std::vector<const Def*> types;
        for (auto arg : app->args()) {
            if (auto val = emit_unsafe(arg); !val.empty()) {
                values.emplace_back(val);
                types.emplace_back(arg->type());
            }
        }
 
        switch (values.size()) {
            case 0: return bb.tail("ret void");
            case 1: return bb.tail("ret {} {}", convert(types[0]), values[0]);
            default: {
                std::string type;
                std::string prev;
 
                if (auto se = is_simd_aggregate(types)) {
                    auto common_src = find_common_simd_src(app);
                    if (common_src) {
                        auto v_src = emit(common_src);
                        auto t     = convert(common_src->type());
                        return bb.tail("ret {} {}", t, v_src);
                    }
                    auto [size, elem] = *se;
                    auto val_t        = convert(elem);
 
                    type = std::format("<{} x {}>", size, val_t);
                    for (auto val : values) {
                        if (prev.empty())
                            prev = "<";
                        else
                            prev += ", ";
                        prev += std::format("{} {}", val_t, val);
                    }
                    prev += ">";
                } else {
                    prev = "undef";
                    type = convert(world().sigma(types));
                    for (size_t i = 0, n = values.size(); i != n; ++i) {
                        auto v_elem = values[i];
                        auto t_elem = convert(types[i]);
                        auto namei  = "%ret_val." + std::to_string(i);
                        bb.tail("{} = insertvalue {} {}, {} {}, {}", namei, type, prev, t_elem, v_elem, i);
                        prev = namei;
                    }
                }
                bb.tail("ret {} {}", type, prev);
            }
        }
 
    } else if (auto dispatch = Dispatch(app)) {
        for (auto callee : dispatch.tuple()->projs([](const Def* def) { return def->isa_mut<Lam>(); })) {
            size_t n = callee->num_tvars();
            if (n == 1 && is_simd(callee->var(0)->type())) {
                auto phi = callee->var(0);
                auto arg = emit(app->arg(n, 0));
                lam2bb_[callee].phis[phi].emplace_back(arg, id(lam, true));
                locals_[phi] = id(phi);
            } else {
                for (size_t i = 0; i != n; ++i) {
                    if (auto arg = emit_unsafe(app->arg(n, i)); !arg.empty()) {
                        auto phi = callee->var(n, i);
                        assert(!Axm::isa<mem::M>(phi->type()));
                        lam2bb_[callee].phis[phi].emplace_back(arg, id(lam, true));
                        locals_[phi] = id(phi);
                    }
                }
            }
        }
 
        auto v_index = emit(dispatch.index());
        size_t n     = dispatch.num_targets();
        auto bbs     = absl::FixedArray<std::string>(n);
        for (size_t i = 0; i != n; ++i)
            bbs[i] = emit(dispatch.target(i));
 
        if (auto branch = Branch(app)) return bb.tail("br i1 {}, label {}, label {}", v_index, bbs[1], bbs[0]);
 
        auto t_index = convert(dispatch.index()->type());
        bb.tail("switch {} {}, label {} [ ", t_index, v_index, bbs[0]);
        for (size_t i = 1; i != n; ++i)
            print(bb.tail().back(), "{} {}, label {} ", t_index, std::to_string(i), bbs[i]);
        print(bb.tail().back(), "]");
    } else if (app->callee()->isa<Bot>()) {
        return bb.tail("ret ; bottom: unreachable");
    } else if (auto callee = Lam::isa_mut_basicblock(app->callee())) { // ordinary jump
 
        auto common_src = find_common_simd_src(app);
        if (common_src) {
            auto v_src      = emit(common_src);
            auto callee_var = callee->var();
            if (simd_phi_.find(callee) == simd_phi_.end()) simd_phi_[callee] = callee_var;
            auto key = simd_phi_[callee];
            lam2bb_[callee].phis[key].emplace_back(v_src, id(lam, true));
            locals_[key] = id(key);
            for (auto var : callee->vars())
                locals_[var] = id(key);
            locals_[callee_var] = id(key);
        } else {
            size_t n = callee->num_tvars();
            for (size_t i = 0; i != n; ++i) {
                if (auto arg = emit_unsafe(app->arg(n, i)); !arg.empty()) {
                    auto phi = callee->var(n, i);
                    assert(!Axm::isa<mem::M>(phi->type()));
                    lam2bb_[callee].phis[phi].emplace_back(arg, id(lam, true));
                    locals_[phi] = id(phi);
                }
            }
        }
        return bb.tail("br label {}", id(callee));
 
    } else if (auto longjmp = Axm::isa<clos::longjmp>(app)) {
        declare("void @longjmp(i8*, i32) noreturn");
 
        auto [mem, jbuf, tag] = app->args<3>();
        emit_unsafe(mem);
        auto v_jb  = emit(jbuf);
        auto v_tag = emit(tag);
        bb.tail("call void @longjmp(i8* {}, i32 {})", v_jb, v_tag);
        return bb.tail("unreachable");
    } else if (Pi::isa_returning(app->callee_type())) { // function call
        auto v_callee = emit(app->callee());
 
        std::vector<std::string> args;
        auto app_args = app->args();
        for (auto arg : app_args.view().rsubspan(1))
            if (auto v_arg = emit_unsafe(arg); !v_arg.empty()) args.emplace_back(convert(arg->type()) + " " + v_arg);
 
        if (app->args().back()->isa<Bot>()) {
            // TODO: Perhaps it'd be better to simply η-wrap this prior to the BE...
            assert(convert_ret_pi(app->callee_type()->ret_pi()) == "void");
            bb.tail("call void {}({, })", v_callee, args);
            return bb.tail("unreachable");
        }
 
        auto ret_lam    = app->args().back()->as_mut<Lam>();
        size_t num_vars = ret_lam->num_vars();
        size_t n        = 0;
        DefVec values(num_vars);
        DefVec types(num_vars);
        for (auto var : ret_lam->vars()) {
            if (Axm::isa<mem::M>(var->type())) continue;
            values[n] = var;
            types[n]  = var->type();
            ++n;
        }
 
        if (n == 0) {
            bb.tail("call void {}({, })", v_callee, args);
        } else {
            auto name  = "%" + app->unique_name() + "ret";
            auto t_ret = convert_ret_pi(ret_lam->type());
            bb.tail("{} = call {} {}({, })", name, t_ret, v_callee, args);
            auto phi = ret_lam->var();
            lam2bb_[ret_lam].phis[phi].emplace_back(name, id(lam, true));
            locals_[phi] = id(phi);
        }
 
        return bb.tail("br label {}", id(ret_lam));
    }
}
 
inline std::string Emitter::emit_bb(BB& bb, const Def* def) {
    if (auto lam = def->isa<Lam>()) return id(lam);
 
    auto name = id(def);
    std::string op;
 
    auto emit_tuple = [&](const Def* tuple) {
        if (isa_mem_sigma_2(tuple->type())) {
            emit_unsafe(tuple->proj(2, 0));
            return emit(tuple->proj(2, 1));
        }
 
        if (tuple->is_closed()) {
            bool is_array   = tuple->type()->isa<Arr>();
            auto simd_array = convert(tuple->type()).front() == '<'; // needed to respect pointer context
            std::string s;
            s += simd_array ? "<" : is_array ? "[" : "{";
            auto sep = "";
            for (size_t i = 0, n = tuple->num_projs(); i != n; ++i) {
                auto e = tuple->proj(n, i);
                if (auto v_elem = emit_unsafe(e); !v_elem.empty()) {
                    auto t_elem = convert(e->type());
                    s += sep + t_elem + " " + v_elem;
                    sep = ", ";
                }
            }
 
            return s += simd_array ? ">" : is_array ? "]" : "}";
        }
 
        std::string prev = "undef";
        auto t           = convert(tuple->type());
        for (size_t src = 0, dst = 0, n = tuple->num_projs(); src != n; ++src) {
            auto e = tuple->proj(n, src);
            if (auto elem = emit_unsafe(e); !elem.empty()) {
                auto elem_t = convert(e->type());
                // TODO: check dst vs src
                auto namei = name + "." + std::to_string(dst);
                if (t.front() == '<') // not using is_simd to respect the pointer context (Pointer Pointee case)
                    prev = bb.assign(namei, "insertelement {} {}, {} {}, {} {}", t, prev, elem_t, elem, elem_t, dst);
                else
                    prev = bb.assign(namei, "insertvalue {} {}, {} {}, {}", t, prev, elem_t, elem, dst);
                dst++;
            }
        }
        return prev;
    };
 
    if (def->isa<Var>()) {
        if (is_simd(def->type())) return id(def);
        auto ts = def->type()->projs();
        if (std::ranges::any_of(ts, [](auto t) { return Axm::isa<mem::M>(t); })) return {};
        return emit_tuple(def);
    }
 
    auto emit_gep_index = [&](const Def* index) {
        auto v_i = emit(index);
        auto t_i = convert(index->type());
 
        if (auto size = Idx::isa(index->type())) {
            if (auto w = Idx::size2bitwidth(size); w && *w < 64) {
                v_i = bb.assign(name + ".zext",
                                "zext {} {} to i{} ; add one more bit for gep index as it is treated as signed value",
                                t_i, v_i, *w + 1);
                t_i = "i" + std::to_string(*w + 1);
            }
        }
 
        return std::pair(v_i, t_i);
    };
 
    if (auto lit = def->isa<Lit>()) {
        if (lit->type()->isa<Nat>() || Idx::isa(lit->type())) {
            return std::to_string(lit->get());
        } else if (auto w = math::isa_f(lit->type())) {
            std::stringstream s;
            u64 hex;
 
            switch (*w) {
                case 16:
                    s << "0xH" << std::setfill('0') << std::setw(4) << std::right << std::hex << lit->get<u16>();
                    return s.str();
                case 32: {
                    hex = std::bit_cast<u64>(f64(lit->get<f32>()));
                    break;
                }
                case 64: hex = lit->get<u64>(); break;
                default: fe::unreachable();
            }
 
            s << "0x" << std::setfill('0') << std::setw(16) << std::right << std::hex << hex;
            return s.str();
        }
        fe::unreachable();
    } else if (def->isa<Bot>()) {
        return "undef";
    } else if (auto top = def->isa<Top>()) {
        if (Axm::isa<mem::M>(top->type())) return {};
        // bail out to error below
    } else if (auto tuple = def->isa<Tuple>()) {
        return emit_tuple(tuple);
    } else if (auto pack = def->isa<Pack>()) {
        if (auto lit = Lit::isa(pack->body()); lit && *lit == 0) return "zeroinitializer";
        return emit_tuple(pack);
    } else if (auto sel = Select(def)) {
        auto t                = convert(sel.extract()->type());
        auto [elem_a, elem_b] = sel.pair()->projs<2>([&](auto e) { return emit_unsafe(e); });
        auto cond_t           = convert(sel.cond()->type());
        auto cond             = emit(sel.cond());
        return bb.assign(name, "select {} {}, {} {}, {} {}", cond_t, cond, t, elem_b, t, elem_a);
    } else if (auto extract = def->isa<Extract>()) {
        auto tuple = extract->tuple();
        auto index = extract->index();
        auto v_tup = emit_unsafe(tuple);
        if (is_simd(tuple->type()) && !Axm::isa<mem::M>(tuple->type())) return v_tup;
 
        // this exact location is important: after emitting the tuple -> ordering of mem ops
        // before emitting the index, as it might be a weird value for mem vars.
        if (Axm::isa<mem::M>(extract->type())) return {};
 
        auto t_tup = convert(tuple->type());
        if (auto li = Lit::isa(index)) {
            if (isa_mem_sigma_2(tuple->type())) return v_tup;
            // Adjust index, if mem is present.
            auto v_i = Axm::isa<mem::M>(tuple->proj(0)->type()) ? std::to_string(*li - 1) : std::to_string(*li);
 
            return bb.assign(name, "extractvalue {} {}, {}", t_tup, v_tup, v_i);
        }
 
        auto t_elem     = convert(extract->type());
        auto [v_i, t_i] = emit_gep_index(index);
 
        print(lam2bb_[root()].body().emplace_front(),
              "{}.alloca = alloca {} ; copy to alloca to emulate extract with store + gep + load", name, t_tup);
        print(bb.body().emplace_back(), "store {} {}, {}* {}.alloca", t_tup, v_tup, t_tup, name);
        print(bb.body().emplace_back(), "{}.gep = getelementptr inbounds {}, {}* {}.alloca, i64 0, {} {}", name, t_tup,
              t_tup, name, t_i, v_i);
        return bb.assign(name, "load {}, {}* {}.gep", t_elem, t_elem, name);
    } else if (auto insert = def->isa<Insert>()) {
        assert(!Axm::isa<mem::M>(insert->tuple()->proj(0)->type()));
        auto t_tup = convert(insert->tuple()->type());
        auto t_val = convert(insert->value()->type());
        auto v_tup = emit(insert->tuple());
        auto v_val = emit(insert->value());
        if (auto idx = Lit::isa(insert->index())) {
            auto v_idx = emit(insert->index());
            if (is_simd(insert->tuple()->type()))
 
                return bb.assign(name, "insertelement {} {}, {} {}, i32 {}", t_tup, v_tup, t_val, v_val, v_idx);
            else
 
                return bb.assign(name, " insertvalue {} {}, {} {}, {}", t_tup, v_tup, t_val, v_val, v_idx);
        } else {
            if (is_simd(insert->tuple()->type())) {
                auto v_i = emit(insert->index());
                auto t_i = convert(insert->index()->type());
                if (t_i != "i32") {
                    auto w_src = *Idx::size2bitwidth(Idx::isa(insert->index()->type()));
                    v_i        = bb.assign(name + ".idx", "{} {} {} to i32", w_src < 32 ? "zext" : "trunc", t_i, v_i);
                }
                return bb.assign(name, "insertelement {} {}, {} {}, i32 {}", t_tup, v_tup, t_val, v_val, v_i);
            }
            auto t_elem     = convert(insert->value()->type());
            auto [v_i, t_i] = emit_gep_index(insert->index());
            print(lam2bb_[root()].body().emplace_front(),
                  "{}.alloca = alloca {} ; copy to alloca to emulate insert with store + gep + load", name, t_tup);
            print(bb.body().emplace_back(), "store {} {}, {}* {}.alloca", t_tup, v_tup, t_tup, name);
            print(bb.body().emplace_back(), "{}.gep = getelementptr inbounds {}, {}* {}.alloca, i64 0, {} {}", name,
                  t_tup, t_tup, name, t_i, v_i);
            print(bb.body().emplace_back(), "store {} {}, {}* {}.gep", t_val, v_val, t_val, name);
            return bb.assign(name, "load {}, {}* {}.alloca", t_tup, t_tup, name);
        }
    } else if (auto global = def->isa<Global>()) {
        auto v_init                = emit(global->init());
        auto [pointee, addr_space] = Axm::as<mem::Ptr>(global->type())->args<2>();
        print(vars_decls_, "{} = global {} {}\n", name, convert(pointee), v_init);
        return globals_[global] = name;
    } else if (auto nat = Axm::isa<core::nat>(def)) {
        auto [a, b] = nat->args<2>([this](auto def) { return emit(def); });
 
        switch (nat.id()) {
            case core::nat::add: op = "add"; break;
            case core::nat::sub: op = "sub"; break;
            case core::nat::mul: op = "mul"; break;
        }
 
        return bb.assign(name, "{} nsw nuw i64 {}, {}", op, a, b);
    } else if (auto ncmp = Axm::isa<core::ncmp>(def)) {
        auto [a, b] = ncmp->args<2>([this](auto def) { return emit(def); });
        op          = "icmp ";
 
        switch (ncmp.id()) {
                // clang-format off
            case core::ncmp::e:  op += "eq" ; break;
            case core::ncmp::ne: op += "ne" ; break;
            case core::ncmp::g:  op += "ugt"; break;
            case core::ncmp::ge: op += "uge"; break;
            case core::ncmp::l:  op += "ult"; break;
            case core::ncmp::le: op += "ule"; break;
            // clang-format on
            default: fe::unreachable();
        }
 
        return bb.assign(name, "{} i64 {}, {}", op, a, b);
    } else if (auto idx = Axm::isa<core::idx>(def)) {
        auto x = emit(idx->arg());
        auto s = *Idx::size2bitwidth(Idx::isa(idx->type()));
        auto t = convert(idx->type());
        if (s < 64) return bb.assign(name, "trunc i64 {} to {}", x, t);
        return x;
    } else if (auto bit1 = Axm::isa<core::bit1>(def)) {
        assert(bit1.id() == core::bit1::neg);
        auto x = emit(bit1->arg());
        auto t = convert(bit1->type());
        return bb.assign(name, "xor {} -1, {}", t, x);
    } else if (auto bit2 = Axm::isa<core::bit2>(def)) {
        auto [a, b] = bit2->args<2>([this](auto def) { return emit(def); });
        auto t      = convert(bit2->type());
 
        auto neg = [&](std::string_view x) { return bb.assign(name + ".neg", "xor {} -1, {}", t, x); };
 
        switch (bit2.id()) {
                // clang-format off
            case core::bit2::and_: return bb.assign(name, "and {} {}, {}", t, a, b);
            case core::bit2:: or_: return bb.assign(name, "or  {} {}, {}", t, a, b);
            case core::bit2::xor_: return bb.assign(name, "xor {} {}, {}", t, a, b);
            case core::bit2::nand: return neg(bb.assign(name, "and {} {}, {}", t, a, b));
            case core::bit2:: nor: return neg(bb.assign(name, "or  {} {}, {}", t, a, b));
            case core::bit2::nxor: return neg(bb.assign(name, "xor {} {}, {}", t, a, b));
            case core::bit2:: iff: return bb.assign(name, "and {} {}, {}", neg(a), b);
            case core::bit2::niff: return bb.assign(name, "or  {} {}, {}", neg(a), b);
            // clang-format on
            default: fe::unreachable();
        }
    } else if (auto shr = Axm::isa<core::shr>(def)) {
        auto [a, b] = shr->args<2>([this](auto def) { return emit(def); });
        auto t      = convert(shr->type());
 
        switch (shr.id()) {
            case core::shr::a: op = "ashr"; break;
            case core::shr::l: op = "lshr"; break;
        }
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto wrap = Axm::isa<core::wrap>(def)) {
        auto [mode, ab] = wrap->uncurry_args<2>();
        auto [a, b]     = ab->projs<2>([this](auto def) { return emit(def); });
        auto t          = convert(wrap->type());
        auto lmode      = Lit::as(mode);
 
        switch (wrap.id()) {
            case core::wrap::add: op = "add"; break;
            case core::wrap::sub: op = "sub"; break;
            case core::wrap::mul: op = "mul"; break;
            case core::wrap::shl: op = "shl"; break;
        }
 
        if (lmode & core::Mode::nuw) op += " nuw";
        if (lmode & core::Mode::nsw) op += " nsw";
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto div = Axm::isa<core::div>(def)) {
        auto [m, xy] = div->args<2>();
        auto [x, y]  = xy->projs<2>();
        auto t       = convert(x->type());
        emit_unsafe(m);
        auto a = emit(x);
        auto b = emit(y);
 
        switch (div.id()) {
            case core::div::sdiv: op = "sdiv"; break;
            case core::div::udiv: op = "udiv"; break;
            case core::div::srem: op = "srem"; break;
            case core::div::urem: op = "urem"; break;
        }
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto icmp = Axm::isa<core::icmp>(def)) {
        auto [a, b] = icmp->args<2>([this](auto def) { return emit(def); });
        auto t      = convert(icmp->arg(0)->type());
        op          = "icmp ";
 
        switch (icmp.id()) {
                // clang-format off
            case core::icmp::e:   op += "eq" ; break;
            case core::icmp::ne:  op += "ne" ; break;
            case core::icmp::sg:  op += "sgt"; break;
            case core::icmp::sge: op += "sge"; break;
            case core::icmp::sl:  op += "slt"; break;
            case core::icmp::sle: op += "sle"; break;
            case core::icmp::ug:  op += "ugt"; break;
            case core::icmp::uge: op += "uge"; break;
            case core::icmp::ul:  op += "ult"; break;
            case core::icmp::ule: op += "ule"; break;
            // clang-format on
            default: fe::unreachable();
        }
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto extr = Axm::isa<core::extrema>(def)) {
        auto [x, y]   = extr->args<2>();
        auto t        = convert(x->type());
        auto a        = emit(x);
        auto b        = emit(y);
        std::string f = "llvm.";
        switch (extr.id()) {
            case core::extrema::Sm: f += "smin."; break;
            case core::extrema::SM: f += "smax."; break;
            case core::extrema::sm: f += "umin."; break;
            case core::extrema::sM: f += "umax."; break;
        }
        f += t;
        declare("{} @{}({}, {})", t, f, t, t);
        return bb.assign(name, "tail call {} @{}({} {}, {} {})", t, f, t, a, t, b);
    } else if (auto abs = Axm::isa<core::abs>(def)) {
        auto [m, x]   = abs->args<2>();
        auto t        = convert(x->type());
        auto a        = emit(x);
        std::string f = "llvm.abs." + t;
        declare("{} @{}({}, {})", t, f, t, "i1");
        return bb.assign(name, "tail call {} @{}({} {}, {} {})", t, f, t, a, "i1", "1");
    } else if (auto conv = Axm::isa<core::conv>(def)) {
        auto v_src = emit(conv->arg());
        auto t_src = convert(conv->arg()->type());
        auto t_dst = convert(conv->type());
 
        nat_t w_src = *Idx::size2bitwidth(Idx::isa(conv->arg()->type()));
        nat_t w_dst = *Idx::size2bitwidth(Idx::isa(conv->type()));
 
        if (w_src == w_dst) return v_src;
 
        switch (conv.id()) {
            case core::conv::s: op = w_src < w_dst ? "sext" : "trunc"; break;
            case core::conv::u: op = w_src < w_dst ? "zext" : "trunc"; break;
        }
 
        return bb.assign(name, "{} {} {} to {}", op, t_src, v_src, t_dst);
    } else if (auto bitcast = Axm::isa<core::bitcast>(def)) {
        auto dst_type_ptr = Axm::isa<mem::Ptr>(bitcast->type());
        auto src_type_ptr = Axm::isa<mem::Ptr>(bitcast->arg()->type());
        auto v_src        = emit(bitcast->arg());
        auto t_src        = convert(bitcast->arg()->type());
        auto t_dst        = convert(bitcast->type());
 
        if (auto lit = Lit::isa(bitcast->arg()); lit && *lit == 0) return "zeroinitializer";
        // clang-format off
        if (src_type_ptr && dst_type_ptr) return bb.assign(name,  "bitcast {} {} to {}", t_src, v_src, t_dst);
        if (src_type_ptr)                 return bb.assign(name, "ptrtoint {} {} to {}", t_src, v_src, t_dst);
        if (dst_type_ptr)                 return bb.assign(name, "inttoptr {} {} to {}", t_src, v_src, t_dst);
        // clang-format on
 
        auto size2width = [&](const Def* type) {
            if (type->isa<Nat>()) return 64_n;
            if (auto size = Idx::isa(type)) return *Idx::size2bitwidth(size);
            return 0_n;
        };
 
        auto src_size = size2width(bitcast->arg()->type());
        auto dst_size = size2width(bitcast->type());
 
        op = "bitcast";
        if (src_size && dst_size) {
            if (src_size == dst_size) return v_src;
            op = (src_size < dst_size) ? "zext" : "trunc";
        }
        return bb.assign(name, "{} {} {} to {}", op, t_src, v_src, t_dst);
    } else if (auto lea = Axm::isa<mem::lea>(def)) {
        auto [ptr, i]  = lea->args<2>();
        auto pointee   = Axm::as<mem::Ptr>(ptr->type())->arg(0);
        auto v_ptr     = emit(ptr);
        auto t_pointee = convert(pointee);
        auto t_ptr     = convert(ptr->type());
        if (pointee->isa<Sigma>())
            return bb.assign(name, "getelementptr inbounds {}, {} {}, i64 0, i32 {}", t_pointee, t_ptr, v_ptr,
                             Lit::as(i));
 
        assert(pointee->isa<Arr>());
        auto [v_i, t_i] = emit_gep_index(i);
 
        return bb.assign(name, "getelementptr inbounds {}, {} {}, i64 0, {} {}", t_pointee, t_ptr, v_ptr, t_i, v_i);
    } else if (auto malloc = Axm::isa<mem::malloc>(def)) {
        declare("i8* @malloc(i64)");
 
        emit_unsafe(malloc->arg(0));
        auto size  = emit(malloc->arg(1));
        auto ptr_t = convert(Axm::as<mem::Ptr>(def->proj(1)->type()));
        bb.assign(name + "i8", "call i8* @malloc(i64 {})", size);
        return bb.assign(name, "bitcast i8* {} to {}", name + "i8", ptr_t);
    } else if (auto free = Axm::isa<mem::free>(def)) {
        declare("void @free(i8*)");
        emit_unsafe(free->arg(0));
        auto ptr   = emit(free->arg(1));
        auto ptr_t = convert(Axm::as<mem::Ptr>(free->arg(1)->type()));
 
        bb.assign(name + "i8", "bitcast {} {} to i8*", ptr_t, ptr);
        bb.tail("call void @free(i8* {})", name + "i8");
        return {};
    } else if (auto mslot = Axm::isa<mem::mslot>(def)) {
        auto [Ta, msi]             = mslot->uncurry_args<2>();
        auto [pointee, addr_space] = Ta->projs<2>();
        auto [mem, _, __]          = msi->projs<3>();
        emit_unsafe(mslot->arg(0));
        // TODO array with size
        // auto v_size = emit(mslot->arg(1));
        print(bb.body().emplace_back(), "{} = alloca {}", name, convert(pointee, false));
        return name;
    } else if (auto load = Axm::isa<mem::load>(def)) {
        emit_unsafe(load->arg(0));
        auto v_ptr     = emit(load->arg(1));
        auto t_ptr     = convert(load->arg(1)->type());
        auto t_pointee = convert(Axm::as<mem::Ptr>(load->arg(1)->type())->arg(0), false);
        return bb.assign(name, "load {}, {} {}", t_pointee, t_ptr, v_ptr);
    } else if (auto store = Axm::isa<mem::store>(def)) {
        emit_unsafe(store->arg(0));
        auto v_ptr = emit(store->arg(1));
        auto v_val = emit(store->arg(2));
        auto t_ptr = convert(store->arg(1)->type());
        auto t_val = convert(store->arg(2)->type(), false);
        print(bb.body().emplace_back(), "store {} {}, {} {}", t_val, v_val, t_ptr, v_ptr);
        return {};
    } else if (auto q = Axm::isa<clos::alloc_jmpbuf>(def)) {
        declare("i64 @jmpbuf_size()");
 
        emit_unsafe(q->arg());
        auto size = name + ".size";
        bb.assign(size, "call i64 @jmpbuf_size()");
        return bb.assign(name, "alloca i8, i64 {}", size);
    } else if (auto setjmp = Axm::isa<clos::setjmp>(def)) {
        declare("i32 @_setjmp(i8*) returns_twice");
 
        auto [mem, jmpbuf] = setjmp->arg()->projs<2>();
        emit_unsafe(mem);
        auto v_jb = emit(jmpbuf);
        return bb.assign(name, "call i32 @_setjmp(i8* {})", v_jb);
    } else if (auto arith = Axm::isa<math::arith>(def)) {
        auto [mode, ab] = arith->uncurry_args<2>();
        auto [a, b]     = ab->projs<2>([this](auto def) { return emit(def); });
        auto t          = convert(arith->type());
        auto lmode      = Lit::as(mode);
 
        switch (arith.id()) {
            case math::arith::add: op = "fadd"; break;
            case math::arith::sub: op = "fsub"; break;
            case math::arith::mul: op = "fmul"; break;
            case math::arith::div: op = "fdiv"; break;
            case math::arith::rem: op = "frem"; break;
        }
 
        if (lmode == math::Mode::fast)
            op += " fast";
        else {
            // clang-format off
            if (lmode & math::Mode::nnan    ) op += " nnan";
            if (lmode & math::Mode::ninf    ) op += " ninf";
            if (lmode & math::Mode::nsz     ) op += " nsz";
            if (lmode & math::Mode::arcp    ) op += " arcp";
            if (lmode & math::Mode::contract) op += " contract";
            if (lmode & math::Mode::afn     ) op += " afn";
            if (lmode & math::Mode::reassoc ) op += " reassoc";
            // clang-format on
        }
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto tri = Axm::isa<math::tri>(def)) {
        auto a = emit(tri->arg());
        auto t = convert(tri->type());
 
        std::string f;
 
        if (tri.id() == math::tri::sin) {
            f = std::string("llvm.sin") + llvm_suffix(tri->type());
        } else if (tri.id() == math::tri::cos) {
            f = std::string("llvm.cos") + llvm_suffix(tri->type());
        } else {
            if (tri.sub() & sub_t(math::tri::a)) f += "a";
 
            switch (math::tri((tri.id() & 0x3) | Annex::base<math::tri>())) {
                case math::tri::sin: f += "sin"; break;
                case math::tri::cos: f += "cos"; break;
                case math::tri::tan: f += "tan"; break;
                case math::tri::ahFF: error("this axm is supposed to be unused");
                default: fe::unreachable();
            }
 
            if (tri.sub() & sub_t(math::tri::h)) f += "h";
            f += math_suffix(tri->type());
        }
 
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto extrema = Axm::isa<math::extrema>(def)) {
        auto [a, b]   = extrema->args<2>([this](auto def) { return emit(def); });
        auto t        = convert(extrema->type());
        std::string f = "llvm.";
        switch (extrema.id()) {
            case math::extrema::fmin: f += "minnum"; break;
            case math::extrema::fmax: f += "maxnum"; break;
            case math::extrema::ieee754min: f += "minimum"; break;
            case math::extrema::ieee754max: f += "maximum"; break;
        }
        f += llvm_suffix(extrema->type());
 
        declare("{} @{}({}, {})", t, f, t, t);
        return bb.assign(name, "tail call {} @{}({} {}, {} {})", t, f, t, a, t, b);
    } else if (auto pow = Axm::isa<math::pow>(def)) {
        auto [a, b]   = pow->args<2>([this](auto def) { return emit(def); });
        auto t        = convert(pow->type());
        std::string f = "llvm.pow";
        f += llvm_suffix(pow->type());
        declare("{} @{}({}, {})", t, f, t, t);
        return bb.assign(name, "tail call {} @{}({} {}, {} {})", t, f, t, a, t, b);
    } else if (auto rt = Axm::isa<math::rt>(def)) {
        auto a = emit(rt->arg());
        auto t = convert(rt->type());
        std::string f;
        if (rt.id() == math::rt::sq)
            f = std::string("llvm.sqrt") + llvm_suffix(rt->type());
        else
            f = std::string("cbrt") += math_suffix(rt->type());
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto exp = Axm::isa<math::exp>(def)) {
        auto a        = emit(exp->arg());
        auto t        = convert(exp->type());
        std::string f = "llvm.";
        f += (exp.sub() & sub_t(math::exp::log)) ? "log" : "exp";
        f += (exp.sub() & sub_t(math::exp::bin)) ? "2" : (exp.sub() & sub_t(math::exp::dec)) ? "10" : "";
        f += llvm_suffix(exp->type());
        // TODO doesn't work for exp10"
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto er = Axm::isa<math::er>(def)) {
        auto a = emit(er->arg());
        auto t = convert(er->type());
        auto f = er.id() == math::er::f ? std::string("erf") : std::string("erfc");
        f += math_suffix(er->type());
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto gamma = Axm::isa<math::gamma>(def)) {
        auto a        = emit(gamma->arg());
        auto t        = convert(gamma->type());
        std::string f = gamma.id() == math::gamma::t ? "tgamma" : "lgamma";
        f += math_suffix(gamma->type());
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto cmp = Axm::isa<math::cmp>(def)) {
        auto [a, b] = cmp->args<2>([this](auto def) { return emit(def); });
        auto t      = convert(cmp->arg(0)->type());
        op          = "fcmp ";
 
        switch (cmp.id()) {
                // clang-format off
            case math::cmp::  e: op += "oeq"; break;
            case math::cmp::  l: op += "olt"; break;
            case math::cmp:: le: op += "ole"; break;
            case math::cmp::  g: op += "ogt"; break;
            case math::cmp:: ge: op += "oge"; break;
            case math::cmp:: ne: op += "one"; break;
            case math::cmp::  o: op += "ord"; break;
            case math::cmp::  u: op += "uno"; break;
            case math::cmp:: ue: op += "ueq"; break;
            case math::cmp:: ul: op += "ult"; break;
            case math::cmp::ule: op += "ule"; break;
            case math::cmp:: ug: op += "ugt"; break;
            case math::cmp::uge: op += "uge"; break;
            case math::cmp::une: op += "une"; break;
            // clang-format on
            default: fe::unreachable();
        }
 
        return bb.assign(name, "{} {} {}, {}", op, t, a, b);
    } else if (auto conv = Axm::isa<math::conv>(def)) {
        auto v_src = emit(conv->arg());
        auto t_src = convert(conv->arg()->type());
        auto t_dst = convert(conv->type());
 
        auto s_src = math::isa_f(conv->arg()->type());
        auto s_dst = math::isa_f(conv->type());
 
        switch (conv.id()) {
            case math::conv::f2f: op = s_src < s_dst ? "fpext" : "fptrunc"; break;
            case math::conv::s2f: op = "sitofp"; break;
            case math::conv::u2f: op = "uitofp"; break;
            case math::conv::f2s: op = "fptosi"; break;
            case math::conv::f2u: op = "fptoui"; break;
        }
 
        return bb.assign(name, "{} {} {} to {}", op, t_src, v_src, t_dst);
    } else if (auto abs = Axm::isa<math::abs>(def)) {
        auto a        = emit(abs->arg());
        auto t        = convert(abs->type());
        std::string f = "llvm.fabs";
        f += llvm_suffix(abs->type());
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto round = Axm::isa<math::round>(def)) {
        auto a        = emit(round->arg());
        auto t        = convert(round->type());
        std::string f = "llvm.";
        switch (round.id()) {
            case math::round::f: f += "floor"; break;
            case math::round::c: f += "ceil"; break;
            case math::round::r: f += "round"; break;
            case math::round::t: f += "trunc"; break;
        }
        f += llvm_suffix(round->type());
        declare("{} @{}({})", t, f, t);
        return bb.assign(name, "tail call {} @{}({} {})", t, f, t, a);
    } else if (auto zip = Axm::isa<vec::zip>(def)) {
        auto ni_n   = zip->decurry()->decurry()->decurry()->arg();
        auto nat_ni = *Lit::isa(ni_n->proj(2, 0));
        auto f      = zip->decurry()->arg();
        auto inputs = zip->arg();
        auto t_in   = convert(inputs->proj(nat_ni, 0)->type());
        auto t_out  = convert(def->type()); // <n x T>
 
        std::string op;
        std::string prev;
 
        if (auto nat_op = Axm::isa<core::nat, 1>(f)) {
            switch (nat_op.id()) {
                case core::nat::add: op = "add nuw nsw"; break;
                case core::nat::sub: op = "sub nuw nsw"; break;
                case core::nat::mul: op = "mul nuw nsw"; break;
            }
        } else if (auto arith_op = Axm::isa<math::arith, 1>(f)) {
            auto lmode = Lit::as(f->as<App>()->arg());
            switch (arith_op.id()) {
                case math::arith::add: op = "fadd"; break;
                case math::arith::sub: op = "fsub"; break;
                case math::arith::mul: op = "fmul"; break;
                case math::arith::div: op = "fdiv"; break;
                case math::arith::rem: op = "frem"; break;
            }
 
            if (lmode == math::Mode::fast)
                op += " fast";
            else {
                if (lmode & math::Mode::nnan) op += " nnan";
                if (lmode & math::Mode::ninf) op += " ninf";
                if (lmode & math::Mode::nsz) op += " nsz";
                if (lmode & math::Mode::arcp) op += " arcp";
                if (lmode & math::Mode::contract) op += " contract";
                if (lmode & math::Mode::afn) op += " afn";
                if (lmode & math::Mode::reassoc) op += " reassoc";
            }
        } else if (auto ncmp_op = Axm::isa<core::ncmp, 1>(f)) {
            op = "icmp ";
            switch (ncmp_op.id()) {
                case core::ncmp::e: op += "eq"; break;
                case core::ncmp::ne: op += "ne"; break;
                case core::ncmp::g: op += "ugt"; break;
                case core::ncmp::ge: op += "uge"; break;
                case core::ncmp::l: op += "ult"; break;
                case core::ncmp::le: op += "ule"; break;
                default: fe::unreachable();
            }
        } else if (auto icmp_op = Axm::isa<core::icmp, 1>(f)) {
            op = "icmp ";
            switch (icmp_op.id()) {
                case core::icmp::e: op += "eq"; break;
                case core::icmp::ne: op += "ne"; break;
                case core::icmp::sg: op += "sgt"; break;
                case core::icmp::sge: op += "sge"; break;
                case core::icmp::sl: op += "slt"; break;
                case core::icmp::sle: op += "sle"; break;
                case core::icmp::ug: op += "ugt"; break;
                case core::icmp::uge: op += "uge"; break;
                case core::icmp::ul: op += "ult"; break;
                case core::icmp::ule: op += "ule"; break;
                default: fe::unreachable();
            }
        } else if (auto mcmp_op = Axm::isa<math::cmp, 1>(f)) {
            op = "fcmp ";
            switch (mcmp_op.id()) {
                case math::cmp::e: op += "oeq"; break;
                case math::cmp::l: op += "olt"; break;
                case math::cmp::le: op += "ole"; break;
                case math::cmp::g: op += "ogt"; break;
                case math::cmp::ge: op += "oge"; break;
                case math::cmp::ne: op += "one"; break;
                case math::cmp::o: op += "ord"; break;
                case math::cmp::u: op += "uno"; break;
                case math::cmp::ue: op += "ueq"; break;
                case math::cmp::ul: op += "ult"; break;
                case math::cmp::ule: op += "ule"; break;
                case math::cmp::ug: op += "ugt"; break;
                case math::cmp::uge: op += "uge"; break;
                case math::cmp::une: op += "une"; break;
                default: fe::unreachable();
            }
        } else {
            error("unhandled vec.zip operation: {}", f);
        }
 
        auto v1 = emit(inputs->proj(nat_ni, 0));
        auto v2 = emit(inputs->proj(nat_ni, 1));
        prev    = bb.assign(name, "{} {} {}, {}", op, t_in, v1, v2);
        return prev;
    } else if (auto res = isa_targetspecific_intrinsic(bb, def)) {
        return res.value();
    }
    error("unhandled def in LLVM backend: {} : {}", def, def->type());
}
 
} // namespace ll
} // namespace mim