#include "Simplify_Internal.h"

#include "Simplify.h"

#ifdef _MSC_VER
#include <intrin.h>
#endif

#include <functional>
#include <unordered_map>

namespace Halide {
namespace Internal {

using std::string;
using std::vector;

namespace {

// Rewrite name(broadcast(args)) to broadcast(name(args)).
// Assumes that scalars are implicitly broadcast.
Expr lift_elementwise_broadcasts(Type type, const std::string &name, std::vector<Expr> args, Call::CallType call_type) {
    if (type.lanes() == 1) {
        return Expr();
    }
    int lanes = 0;
    for (Expr &i : args) {
        if (const Broadcast *b = i.as<Broadcast>()) {
            i = b->value;
            if (lanes == 0) {
                lanes = i.type().lanes();
            } else if (lanes != i.type().lanes()) {
                // This is a broadcast of another vector, and does not match another vector argument.
                return Expr();
            }
        } else if (!i.type().is_scalar()) {
            // This is not a scalar or broadcast scalar, we can't lift broadcasts.
            return Expr();
        }
    }
    if (lanes != type.lanes()) {
        return Broadcast::make(Call::make(type.with_lanes(lanes), name, args, call_type), type.lanes() / lanes);
    } else {
        return Expr();
    }
}

}  // namespace

Expr Simplify::visit(const Call *op, ExprInfo *bounds) {
    // Calls implicitly depend on host, dev, mins, and strides of the buffer referenced
    if (op->call_type == Call::Image || op->call_type == Call::Halide) {
        found_buffer_reference(op->name, op->args.size());
    }

    if (op->is_intrinsic(Call::unreachable)) {
        in_unreachable = true;
        return op;
    } else if (op->is_intrinsic(Call::strict_float)) {
        if (Call::as_intrinsic(op->args[0], {Call::strict_float})) {
            // Always simplify strict_float(strict_float(x)) -> strict_float(x).
            Expr arg = mutate(op->args[0], nullptr);
            return arg.same_as(op->args[0]) ? op->args[0] : arg;
        } else {
            ScopedValue<bool> save_no_float_simplify(no_float_simplify, true);
            Expr arg = mutate(op->args[0], nullptr);
            if (arg.same_as(op->args[0])) {
                return op;
            } else {
                return strict_float(arg);
            }
        }
    } else if (op->is_intrinsic(Call::popcount) ||
               op->is_intrinsic(Call::count_leading_zeros) ||
               op->is_intrinsic(Call::count_trailing_zeros)) {
        Expr a = mutate(op->args[0], nullptr);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        uint64_t ua = 0;
        if (const_int(a, (int64_t *)(&ua)) || const_uint(a, &ua)) {
            const int bits = op->type.bits();
            const uint64_t mask = std::numeric_limits<uint64_t>::max() >> (64 - bits);
            ua &= mask;
            static_assert(sizeof(unsigned long long) >= sizeof(uint64_t), "");
            int r = 0;
            if (op->is_intrinsic(Call::popcount)) {
                // popcount *is* well-defined for ua = 0
                r = popcount64(ua);
            } else if (op->is_intrinsic(Call::count_leading_zeros)) {
                // clz64() is undefined for 0, but Halide's count_leading_zeros defines clz(0) = bits
                r = ua == 0 ? bits : (clz64(ua) - (64 - bits));
            } else /* if (op->is_intrinsic(Call::count_trailing_zeros)) */ {
                // ctz64() is undefined for 0, but Halide's count_trailing_zeros defines clz(0) = bits
                r = ua == 0 ? bits : (ctz64(ua));
            }
            return make_const(op->type, r);
        }

        if (a.same_as(op->args[0])) {
            return op;
        } else {
            return Call::make(op->type, op->name, {std::move(a)}, Internal::Call::PureIntrinsic);
        }

    } else if (op->is_intrinsic(Call::shift_left) ||
               op->is_intrinsic(Call::shift_right)) {
        Expr a = mutate(op->args[0], nullptr);
        // TODO: When simplifying b, it would be nice to specify the min/max useful bounds, so
        // stronger simplifications could occur. For example, x >> min(-i8, 0) should be simplified
        // to x >> -max(i8, 0) and then x << max(i8, 0). This isn't safe because -i8 can overflow.
        ExprInfo b_info;
        Expr b = mutate(op->args[1], &b_info);

        if (is_const_zero(b)) {
            return a;
        }

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a, b}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        const Type t = op->type;

        // We might swap from a right to left shift or the reverse.
        std::string result_op = op->name;

        // If we know the sign of this shift, change it to an unsigned shift.
        if (b_info.min_defined && b_info.min >= 0) {
            b = mutate(cast(b.type().with_code(halide_type_uint), b), nullptr);
        } else if (b_info.max_defined && b_info.max <= 0) {
            result_op = Call::get_intrinsic_name(op->is_intrinsic(Call::shift_right) ? Call::shift_left : Call::shift_right);
            b = mutate(cast(b.type().with_code(halide_type_uint), -b), nullptr);
        }

        // If the shift is by a constant, it should now be unsigned.
        uint64_t ub = 0;
        if (const_uint(b, &ub)) {
            // LLVM shl and shr instructions produce poison for
            // shifts >= typesize, so we will follow suit in our simplifier.
            if (ub >= (uint64_t)(t.bits())) {
                clear_bounds_info(bounds);
                return make_signed_integer_overflow(t);
            }
            if (a.type().is_uint() || ub < ((uint64_t)t.bits() - 1)) {
                b = make_const(t, ((int64_t)1LL) << ub);
                if (result_op == Call::get_intrinsic_name(Call::shift_left)) {
                    return mutate(Mul::make(a, b), bounds);
                } else {
                    return mutate(Div::make(a, b), bounds);
                }
            } else {
                // For signed types, (1 << (t.bits() - 1)) will overflow into the sign bit while
                // (-32768 >> (t.bits() - 1)) propagates the sign bit, making decomposition
                // into mul or div problematic, so just special-case them here.
                if (result_op == Call::get_intrinsic_name(Call::shift_left)) {
                    return mutate(select((a & 1) != 0, make_const(t, ((int64_t)1LL) << ub), make_zero(t)), bounds);
                } else {
                    return mutate(select(a < 0, make_const(t, -1), make_zero(t)), bounds);
                }
            }
        }

        // Rewrite shifts with negated RHSes as shifts of the other direction.
        if (const Sub *sub = b.as<Sub>()) {
            if (is_const_zero(sub->a)) {
                result_op = Call::get_intrinsic_name(op->is_intrinsic(Call::shift_right) ? Call::shift_left : Call::shift_right);
                b = sub->b;
                return mutate(Call::make(op->type, result_op, {a, b}, Call::PureIntrinsic), bounds);
            }
        }

        if (a.same_as(op->args[0]) && b.same_as(op->args[1])) {
            internal_assert(result_op == op->name);
            return op;
        } else {
            return Call::make(op->type, result_op, {a, b}, Call::PureIntrinsic);
        }
    } else if (op->is_intrinsic(Call::bitwise_and)) {
        Expr a = mutate(op->args[0], nullptr);
        Expr b = mutate(op->args[1], nullptr);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a, b}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        int64_t ia, ib = 0;
        uint64_t ua, ub = 0;
        int bits;

        if (const_int(a, &ia) &&
            const_int(b, &ib)) {
            return make_const(op->type, ia & ib);
        } else if (const_uint(a, &ua) &&
                   const_uint(b, &ub)) {
            return make_const(op->type, ua & ub);
        } else if (const_int(b, &ib) &&
                   !b.type().is_max(ib) &&
                   is_const_power_of_two_integer(make_const(a.type(), ib + 1), &bits)) {
            return Mod::make(a, make_const(a.type(), ib + 1));
        } else if (const_uint(b, &ub) &&
                   b.type().is_max(ub)) {
            return a;
        } else if (const_int(b, &ib) &&
                   ib == -1) {
            return a;
        } else if (const_uint(b, &ub) &&
                   is_const_power_of_two_integer(make_const(a.type(), ub + 1), &bits)) {
            return Mod::make(a, make_const(a.type(), ub + 1));
        } else if (a.same_as(op->args[0]) && b.same_as(op->args[1])) {
            return op;
        } else {
            return a & b;
        }
    } else if (op->is_intrinsic(Call::bitwise_or)) {
        Expr a = mutate(op->args[0], nullptr);
        Expr b = mutate(op->args[1], nullptr);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a, b}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        int64_t ia, ib;
        uint64_t ua, ub;
        if (const_int(a, &ia) &&
            const_int(b, &ib)) {
            return make_const(op->type, ia | ib);
        } else if (const_uint(a, &ua) &&
                   const_uint(b, &ub)) {
            return make_const(op->type, ua | ub);
        } else if (a.same_as(op->args[0]) && b.same_as(op->args[1])) {
            return op;
        } else {
            return a | b;
        }
    } else if (op->is_intrinsic(Call::bitwise_not)) {
        Expr a = mutate(op->args[0], nullptr);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        int64_t ia;
        uint64_t ua;
        if (const_int(a, &ia)) {
            return make_const(op->type, ~ia);
        } else if (const_uint(a, &ua)) {
            return make_const(op->type, ~ua);
        } else if (a.same_as(op->args[0])) {
            return op;
        } else {
            return ~a;
        }
    } else if (op->is_intrinsic(Call::bitwise_xor)) {
        Expr a = mutate(op->args[0], nullptr);
        Expr b = mutate(op->args[1], nullptr);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a, b}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        int64_t ia, ib;
        uint64_t ua, ub;
        if (const_int(a, &ia) &&
            const_int(b, &ib)) {
            return make_const(op->type, ia ^ ib);
        } else if (const_uint(a, &ua) &&
                   const_uint(b, &ub)) {
            return make_const(op->type, ua ^ ub);
        } else if (a.same_as(op->args[0]) && b.same_as(op->args[1])) {
            return op;
        } else {
            return a ^ b;
        }
    } else if (op->is_intrinsic(Call::reinterpret)) {
        Expr a = mutate(op->args[0], nullptr);

        int64_t ia;
        uint64_t ua;
        bool vector = op->type.is_vector() || a.type().is_vector();
        if (op->type == a.type()) {
            return a;
        } else if (const_int(a, &ia) && op->type.is_uint() && !vector) {
            // int -> uint
            return make_const(op->type, (uint64_t)ia);
        } else if (const_uint(a, &ua) && op->type.is_int() && !vector) {
            // uint -> int
            return make_const(op->type, (int64_t)ua);
        } else if (a.same_as(op->args[0])) {
            return op;
        } else {
            return reinterpret(op->type, a);
        }
    } else if (op->is_intrinsic(Call::abs)) {
        // Constant evaluate abs(x).
        ExprInfo a_bounds;
        Expr a = mutate(op->args[0], &a_bounds);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        Type ta = a.type();
        int64_t ia = 0;
        double fa = 0;
        if (ta.is_int() && const_int(a, &ia)) {
            if (ia < 0 && !(Int(64).is_min(ia))) {
                ia = -ia;
            }
            return make_const(op->type, ia);
        } else if (ta.is_uint()) {
            // abs(uint) is a no-op.
            return a;
        } else if (const_float(a, &fa)) {
            if (fa < 0) {
                fa = -fa;
            }
            return make_const(a.type(), fa);
        } else if (a.type().is_int() && a_bounds.min_defined && a_bounds.min >= 0) {
            return cast(op->type, a);
        } else if (a.type().is_int() && a_bounds.max_defined && a_bounds.max <= 0) {
            return cast(op->type, -a);
        } else if (a.same_as(op->args[0])) {
            return op;
        } else {
            return abs(a);
        }
    } else if (op->is_intrinsic(Call::absd)) {
        // Constant evaluate absd(a, b).
        ExprInfo a_bounds, b_bounds;
        Expr a = mutate(op->args[0], &a_bounds);
        Expr b = mutate(op->args[1], &b_bounds);

        Expr unbroadcast = lift_elementwise_broadcasts(op->type, op->name, {a, b}, op->call_type);
        if (unbroadcast.defined()) {
            return mutate(unbroadcast, bounds);
        }

        Type ta = a.type();
        // absd() should enforce identical types for a and b when the node is created
        internal_assert(ta == b.type());

        int64_t ia = 0, ib = 0;
        uint64_t ua = 0, ub = 0;
        double fa = 0, fb = 0;
        if (ta.is_int() && const_int(a, &ia) && const_int(b, &ib)) {
            // Note that absd(int, int) always produces a uint result
            internal_assert(op->type.is_uint());
            const uint64_t d = ia > ib ? (uint64_t)(ia - ib) : (uint64_t)(ib - ia);
            return make_const(op->type, d);
        } else if (ta.is_uint() && const_uint(a, &ua) && const_uint(b, &ub)) {
            const uint64_t d = ua > ub ? ua - ub : ub - ua;
            return make_const(op->type, d);
        } else if (const_float(a, &fa) && const_float(b, &fb)) {
            const double d = fa > fb ? fa - fb : fb - fa;
            return make_const(op->type, d);
        } else if (a.same_as(op->args[0]) && b.same_as(op->args[1])) {
            return op;
        } else {
            return absd(a, b);
        }
    } else if (op->is_intrinsic(Call::stringify)) {
        // Eagerly concat constant arguments to a stringify.
        bool changed = false;
        vector<Expr> new_args;
        const StringImm *last = nullptr;
        for (const auto &a : op->args) {
            Expr arg = mutate(a, nullptr);
            if (!arg.same_as(a)) {
                changed = true;
            }
            const StringImm *string_imm = arg.as<StringImm>();
            const IntImm *int_imm = arg.as<IntImm>();
            const FloatImm *float_imm = arg.as<FloatImm>();
            // We use snprintf here rather than stringstreams,
            // because the runtime's float printing is guaranteed
            // to match snprintf.
            char buf[64];  // Large enough to hold the biggest float literal.
            if (last && string_imm) {
                new_args.back() = last->value + string_imm->value;
                changed = true;
            } else if (int_imm) {
                snprintf(buf, sizeof(buf), "%lld", (long long)int_imm->value);
                if (last) {
                    new_args.back() = last->value + buf;
                } else {
                    new_args.emplace_back(string(buf));
                }
                changed = true;
            } else if (last && float_imm) {
                snprintf(buf, sizeof(buf), "%f", float_imm->value);
                if (last) {
                    new_args.back() = last->value + buf;
                } else {
                    new_args.emplace_back(string(buf));
                }
                changed = true;
            } else {
                new_args.push_back(arg);
            }
            last = new_args.back().as<StringImm>();
        }

        if (new_args.size() == 1 && new_args[0].as<StringImm>()) {
            // stringify of a string constant is just the string constant
            return new_args[0];
        } else if (changed) {
            return Call::make(op->type, op->name, new_args, op->call_type);
        } else {
            return op;
        }
    } else if (op->is_intrinsic(Call::prefetch)) {
        // Collapse the prefetched region into lower dimension whenever is possible.
        // TODO(psuriana): Deal with negative strides and overlaps.

        internal_assert(op->args.size() % 2 == 0);  // Prefetch: {base, offset, extent0, stride0, ...}

        auto [args, changed] = mutate_with_changes(op->args, nullptr);

        // The {extent, stride} args in the prefetch call are sorted
        // based on the storage dimension in ascending order (i.e. innermost
        // first and outermost last), so, it is enough to check for the upper
        // triangular pairs to see if any contiguous addresses exist.
        for (size_t i = 2; i < args.size(); i += 2) {
            Expr extent_0 = args[i];
            Expr stride_0 = args[i + 1];
            for (size_t j = i + 2; j < args.size(); j += 2) {
                Expr extent_1 = args[j];
                Expr stride_1 = args[j + 1];

                if (is_const_one(mutate(extent_0 * stride_0 == stride_1, nullptr))) {
                    Expr new_extent = mutate(extent_0 * extent_1, nullptr);
                    args.erase(args.begin() + j, args.begin() + j + 2);
                    args[i] = new_extent;
                    args[i + 1] = stride_0;
                    i -= 2;
                    break;
                }
            }
        }
        internal_assert(args.size() <= op->args.size());

        if (changed || (args.size() != op->args.size())) {
            return Call::make(op->type, Call::prefetch, args, Call::Intrinsic);
        } else {
            return op;
        }
    } else if (op->is_intrinsic(Call::require)) {
        Expr cond = mutate(op->args[0], nullptr);
        // likely(const-bool) is deliberately not reduced
        // by the simplify(), but for our purposes here, we want
        // to ignore the likely() wrapper. (Note that this is
        // equivalent to calling can_prove() without needing to
        // create a new Simplifier instance.)
        if (const Call *c = cond.as<Call>()) {
            if (c->is_intrinsic(Call::likely)) {
                cond = c->args[0];
            }
        }

        if (is_const_zero(cond)) {
            // (We could simplify this to avoid evaluating the provably-false
            // expression, but since this is a degenerate condition, don't bother.)
            user_warning << "This pipeline is guaranteed to fail a require() expression at runtime: \n"
                         << Expr(op) << "\n";
        }

        Expr result;
        {
            // Can assume the condition is true when evaluating the value.
            auto t = scoped_truth(cond);
            result = mutate(op->args[1], bounds);
        }

        if (is_const_one(cond)) {
            return result;
        }

        Expr message = mutate(op->args[2], nullptr);

        if (cond.same_as(op->args[0]) &&
            result.same_as(op->args[1]) &&
            message.same_as(op->args[2])) {
            return op;
        } else {
            return Internal::Call::make(op->type,
                                        Internal::Call::require,
                                        {std::move(cond), std::move(result), std::move(message)},
                                        Internal::Call::PureIntrinsic);
        }
    } else if (op->is_intrinsic(Call::promise_clamped) ||
               op->is_intrinsic(Call::unsafe_promise_clamped)) {
        // If the simplifier can infer that the clamp is unnecessary,
        // we should be good to discard the promise.
        internal_assert(op->args.size() == 3);
        ExprInfo arg_info, lower_info, upper_info;
        Expr arg = mutate(op->args[0], &arg_info);
        Expr lower = mutate(op->args[1], &lower_info);
        Expr upper = mutate(op->args[2], &upper_info);

        const Broadcast *b_arg = arg.as<Broadcast>();
        const Broadcast *b_lower = lower.as<Broadcast>();
        const Broadcast *b_upper = upper.as<Broadcast>();

        if (arg_info.min_defined &&
            arg_info.max_defined &&
            lower_info.max_defined &&
            upper_info.min_defined &&
            arg_info.min >= lower_info.max &&
            arg_info.max <= upper_info.min) {
            return arg;
        } else if (b_arg && b_lower && b_upper) {
            // Move broadcasts outwards
            return Broadcast::make(Call::make(b_arg->value.type(), op->name,
                                              {b_arg->value, b_lower->value, b_upper->value},
                                              Call::Intrinsic),
                                   b_arg->lanes);
        } else if (arg.same_as(op->args[0]) &&
                   lower.same_as(op->args[1]) &&
                   upper.same_as(op->args[2])) {
            return op;

        } else {
            return Call::make(op->type, op->name,
                              {arg, lower, upper},
                              Call::Intrinsic);
        }
    } else if (Call::as_tag(op)) {
        // The bounds of the result are the bounds of the arg
        internal_assert(op->args.size() == 1);
        Expr arg = mutate(op->args[0], bounds);
        if (arg.same_as(op->args[0])) {
            return op;
        } else {
            return Call::make(op->type, op->name, {arg}, op->call_type);
        }
    } else if (op->is_intrinsic(Call::if_then_else)) {
        // Note that this call promises to evaluate exactly one of the conditions,
        // so this optimization should be safe.

        internal_assert(op->args.size() == 2 || op->args.size() == 3);
        Expr cond_value = mutate(op->args[0], nullptr);

        // Ignore tags for our purposes here
        Expr cond = unwrap_tags(cond_value);
        if (in_unreachable) {
            return op;
        }

        if (is_const_one(cond)) {
            return mutate(op->args[1], bounds);
        } else if (is_const_zero(cond)) {
            if (op->args.size() == 3) {
                return mutate(op->args[2], bounds);
            } else {
                return mutate(make_zero(op->type), bounds);
            }
        } else {
            Expr true_value = mutate(op->args[1], nullptr);
            bool true_unreachable = in_unreachable;
            in_unreachable = false;
            Expr false_value = op->args.size() == 3 ? mutate(op->args[2], nullptr) : Expr();
            bool false_unreachable = in_unreachable;

            if (true_unreachable && false_unreachable) {
                return true_value;
            }
            in_unreachable = false;
            if (true_unreachable) {
                return false_value;
            } else if (false_unreachable) {
                return true_value;
            }

            if (cond_value.same_as(op->args[0]) &&
                true_value.same_as(op->args[1]) &&
                (op->args.size() == 2 || false_value.same_as(op->args[2]))) {
                return op;
            } else {
                vector<Expr> args = {std::move(cond_value), std::move(true_value)};
                if (op->args.size() == 3) {
                    args.push_back(std::move(false_value));
                }
                return Internal::Call::make(op->type, Call::if_then_else, args, op->call_type);
            }
        }
    } else if (op->is_intrinsic(Call::mux)) {
        internal_assert(op->args.size() >= 2);
        int num_values = (int)op->args.size() - 1;
        if (num_values == 1) {
            // Mux of a single value
            return mutate(op->args[1], bounds);
        }
        ExprInfo index_info;
        Expr index = mutate(op->args[0], &index_info);

        // Check if the mux has statically resolved
        if (index_info.min_defined &&
            index_info.max_defined &&
            index_info.min == index_info.max) {
            if (index_info.min >= 0 && index_info.min < num_values) {
                // In-range, return the (simplified) corresponding value.
                return mutate(op->args[index_info.min + 1], bounds);
            } else {
                // It's out-of-range, so return the last value.
                return mutate(op->args.back(), bounds);
            }
        }

        // The logic above could be extended to also truncate the
        // range of values in the case where the mux index has a
        // constant bound. This seems unlikely to ever come up though.

        bool unchanged = index.same_as(op->args[0]);
        vector<Expr> mutated_args(op->args.size());
        mutated_args[0] = index;
        for (size_t i = 1; i < op->args.size(); ++i) {
            mutated_args[i] = mutate(op->args[i], nullptr);
            unchanged &= mutated_args[i].same_as(op->args[i]);
        }

        if (unchanged) {
            return op;
        } else {
            return Call::make(op->type, Call::mux, mutated_args, Call::PureIntrinsic);
        }
    } else if (op->call_type == Call::PureExtern) {
        // TODO: This could probably be simplified into a single map-lookup
        // with a bit more cleverness; not sure if the reduced lookup time
        // would pay for itself (in comparison with the possible lost code clarity).

        // Handle all the PureExtern cases of float -> bool
        {
            using FnType = bool (*)(double);
            // Some GCC versions are unable to resolve std::isnan (etc) directly, so
            // wrap them in lambdas.
            const FnType is_finite = [](double a) -> bool { return std::isfinite(a); };
            const FnType is_inf = [](double a) -> bool { return std::isinf(a); };
            const FnType is_nan = [](double a) -> bool { return std::isnan(a); };
            static const std::unordered_map<std::string, FnType>
                pure_externs_f1b = {
                    {"is_finite_f16", is_finite},
                    {"is_finite_f32", is_finite},
                    {"is_finite_f64", is_finite},
                    {"is_inf_f16", is_inf},
                    {"is_inf_f32", is_inf},
                    {"is_inf_f64", is_inf},
                    {"is_nan_f16", is_nan},
                    {"is_nan_f32", is_nan},
                    {"is_nan_f64", is_nan},
                };
            auto it = pure_externs_f1b.find(op->name);
            if (it != pure_externs_f1b.end()) {
                Expr arg = mutate(op->args[0], nullptr);
                double f = 0.0;
                if (const_float(arg, &f)) {
                    auto fn = it->second;
                    return make_bool(fn(f));
                } else if (arg.same_as(op->args[0])) {
                    return op;
                } else {
                    return Call::make(op->type, op->name, {arg}, op->call_type);
                }
            }
            // else fall thru
        }

        // Handle all the PureExtern cases of float -> float
        // TODO: should we handle the f16 and f64 cases here? (We never did before.)
        // TODO: should we handle fast_inverse and/or fast_inverse_sqrt here?
        {
            using FnType = double (*)(double);
            static const std::unordered_map<std::string, FnType>
                pure_externs_f1 = {
                    {"acos_f32", std::acos},
                    {"acosh_f32", std::acosh},
                    {"asin_f32", std::asin},
                    {"asinh_f32", std::asinh},
                    {"atan_f32", std::atan},
                    {"atanh_f32", std::atanh},
                    {"cos_f32", std::cos},
                    {"cosh_f32", std::cosh},
                    {"exp_f32", std::exp},
                    {"log_f32", std::log},
                    {"sin_f32", std::sin},
                    {"sinh_f32", std::sinh},
                    {"sqrt_f32", std::sqrt},
                    {"tan_f32", std::tan},
                    {"tanh_f32", std::tanh},
                };
            auto it = pure_externs_f1.find(op->name);
            if (it != pure_externs_f1.end()) {
                Expr arg = mutate(op->args[0], nullptr);
                if (const double *f = as_const_float(arg)) {
                    auto fn = it->second;
                    return make_const(arg.type(), fn(*f));
                } else if (arg.same_as(op->args[0])) {
                    return op;
                } else {
                    return Call::make(op->type, op->name, {arg}, op->call_type);
                }
            }
            // else fall thru
        }

        // Handle all the PureExtern cases of float -> integerized-float
        {
            using FnType = double (*)(double);
            static const std::unordered_map<std::string, FnType>
                pure_externs_truncation = {
                    {"ceil_f32", std::ceil},
                    {"floor_f32", std::floor},
                    {"round_f32", std::nearbyint},
                    {"trunc_f32", [](double a) -> double { return (a < 0 ? std::ceil(a) : std::floor(a)); }},
                };
            auto it = pure_externs_truncation.find(op->name);
            if (it != pure_externs_truncation.end()) {
                internal_assert(op->args.size() == 1);
                Expr arg = mutate(op->args[0], nullptr);

                const Call *call = arg.as<Call>();
                if (const double *f = as_const_float(arg)) {
                    auto fn = it->second;
                    return make_const(arg.type(), fn(*f));
                } else if (call && call->call_type == Call::PureExtern &&
                           (it = pure_externs_truncation.find(call->name)) != pure_externs_truncation.end()) {
                    // For any combination of these integer-valued functions, we can
                    // discard the outer function. For example, floor(ceil(x)) == ceil(x).
                    return call;
                } else if (!arg.same_as(op->args[0])) {
                    return Call::make(op->type, op->name, {arg}, op->call_type);
                } else {
                    return op;
                }
            }
            // else fall thru
        }

        // Handle all the PureExtern cases of (float, float) -> integerized-float
        {
            using FnType = double (*)(double, double);
            static const std::unordered_map<std::string, FnType>
                pure_externs_f2 = {
                    {"atan2_f32", std::atan2},
                    {"pow_f32", std::pow},
                };
            auto it = pure_externs_f2.find(op->name);
            if (it != pure_externs_f2.end()) {
                Expr arg0 = mutate(op->args[0], nullptr);
                Expr arg1 = mutate(op->args[1], nullptr);

                const double *f0 = as_const_float(arg0);
                const double *f1 = as_const_float(arg1);
                if (f0 && f1) {
                    auto fn = it->second;
                    return make_const(arg0.type(), fn(*f0, *f1));
                } else if (!arg0.same_as(op->args[0]) || !arg1.same_as(op->args[1])) {
                    return Call::make(op->type, op->name, {arg0, arg1}, op->call_type);
                } else {
                    return op;
                }
            }
            // else fall thru
        }

        // There are other PureExterns we don't bother with (e.g. fast_inverse_f32)...
        // just fall thru and take the general case.
        debug(2) << "Simplifier: unhandled PureExtern: " << op->name;
    } else if (op->is_intrinsic(Call::signed_integer_overflow)) {
        clear_bounds_info(bounds);
    }

    // No else: we want to fall thru from the PureExtern clause.
    {
        auto [new_args, changed] = mutate_with_changes(op->args, nullptr);
        if (!changed) {
            return op;
        } else {
            return Call::make(op->type, op->name, new_args, op->call_type,
                              op->func, op->value_index, op->image, op->param);
        }
    }
}

}  // namespace Internal
}  // namespace Halide