diff --git a/Cargo.lock b/Cargo.lock
index 18e40cd..5fd33a9 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -279,7 +279,7 @@ checksum = "e8c02a5121d4ea3eb16a80748c74f5549a5665e4c21333c6098f283870fbdea6"
 [[package]]
 name = "fayalite"
 version = "0.2.0"
-source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#d0229fbcfb11666b5abf7ae487ffe335866f9326"
+source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#3939ce2360138c75c53972368069c8f882111571"
 dependencies = [
  "bitvec",
  "blake3",
@@ -300,7 +300,7 @@ dependencies = [
 [[package]]
 name = "fayalite-proc-macros"
 version = "0.2.0"
-source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#d0229fbcfb11666b5abf7ae487ffe335866f9326"
+source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#3939ce2360138c75c53972368069c8f882111571"
 dependencies = [
  "fayalite-proc-macros-impl",
 ]
@@ -308,7 +308,7 @@ dependencies = [
 [[package]]
 name = "fayalite-proc-macros-impl"
 version = "0.2.0"
-source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#d0229fbcfb11666b5abf7ae487ffe335866f9326"
+source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#3939ce2360138c75c53972368069c8f882111571"
 dependencies = [
  "base16ct",
  "num-bigint",
@@ -323,7 +323,7 @@ dependencies = [
 [[package]]
 name = "fayalite-visit-gen"
 version = "0.2.0"
-source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#d0229fbcfb11666b5abf7ae487ffe335866f9326"
+source = "git+https://git.libre-chip.org/libre-chip/fayalite.git?branch=master#3939ce2360138c75c53972368069c8f882111571"
 dependencies = [
  "indexmap",
  "prettyplease",
diff --git a/crates/cpu/src/config.rs b/crates/cpu/src/config.rs
index 2b76d62..e144e32 100644
--- a/crates/cpu/src/config.rs
+++ b/crates/cpu/src/config.rs
@@ -1,18 +1,21 @@
 // SPDX-License-Identifier: LGPL-3.0-or-later
 // See Notices.txt for copyright information
-use crate::instruction::{PRegNum, UnitKind, UnitNum};
+use crate::{
+    instruction::{PRegNum, UnitNum, CONST_ZERO_UNIT_NUM},
+    unit::UnitKind,
+};
 use fayalite::prelude::*;
 
 #[derive(Clone, Eq, PartialEq, Hash, Debug)]
 #[non_exhaustive]
 pub struct CpuConfig {
-    pub units: Vec<UnitKind>,
+    pub unit_kinds: Vec<UnitKind>,
     pub out_reg_num_width: usize,
 }
 
 impl CpuConfig {
     pub fn unit_num_width(&self) -> usize {
-        UInt::range(0..self.units.len()).width()
+        UInt::range((CONST_ZERO_UNIT_NUM + 1)..self.unit_kinds.len()).width()
     }
     pub fn unit_num(&self) -> UnitNum<DynSize> {
         UnitNum[self.unit_num_width()]
diff --git a/crates/cpu/src/instruction.rs b/crates/cpu/src/instruction.rs
index 00617ea..66adb27 100644
--- a/crates/cpu/src/instruction.rs
+++ b/crates/cpu/src/instruction.rs
@@ -1,102 +1,11 @@
 // SPDX-License-Identifier: LGPL-3.0-or-later
 // See Notices.txt for copyright information
-use crate::config::CpuConfig;
+use crate::unit::UnitMOp;
 use fayalite::prelude::*;
 use std::marker::PhantomData;
 
 pub mod power_isa;
 
-macro_rules! all_units {
-    (
-        #[hdl_unit_kind = $HdlUnitKind:ident]
-        #[unit_kind = $UnitKind:ident]
-        #[hdl]
-        $(#[$enum_meta:meta])*
-        $vis:vis enum $UnitMOpEnum:ident<$RegWidth:ident: Size> {
-            $(
-                $(#[$variant_meta:meta])*
-                $Unit:ident($Op:ty),
-            )*
-        }
-    ) => {
-        $(#[$enum_meta])*
-        #[derive(Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug)]
-        $vis enum $UnitKind {
-            $(
-                $(#[$variant_meta])*
-                $Unit,
-            )*
-        }
-
-        impl ToExpr for $UnitKind {
-            type Type = $HdlUnitKind;
-
-            fn to_expr(&self) -> Expr<Self::Type> {
-                match self {
-                    $($UnitKind::$Unit => $HdlUnitKind.$Unit(),)*
-                }
-            }
-        }
-
-        #[hdl]
-        $(#[$enum_meta])*
-        $vis enum $HdlUnitKind {
-            $(
-                $(#[$variant_meta])*
-                $Unit,
-            )*
-        }
-
-        #[hdl]
-        $(#[$enum_meta])*
-        $vis enum $UnitMOpEnum<$RegWidth: Size> {
-            $(
-                $(#[$variant_meta])*
-                $Unit($Op),
-            )*
-        }
-
-        impl<$RegWidth: Size> $UnitMOpEnum<$RegWidth> {
-            #[hdl]
-            $vis fn kind(expr: impl ToExpr<Type = Self>) -> Expr<$HdlUnitKind> {
-                #[hdl]
-                let unit_kind = wire();
-                #[hdl]
-                match expr {
-                    $($UnitMOpEnum::<$RegWidth>::$Unit(_) => connect(unit_kind, $HdlUnitKind.$Unit()),)*
-                }
-                unit_kind
-            }
-        }
-
-        impl CpuConfig {
-            #[hdl]
-            pub fn available_units_for_kind(&self, unit_kind: impl ToExpr<Type = $HdlUnitKind>) -> Expr<Array<Bool>> {
-                #[hdl]
-                let available_units_for_kind = wire(Array[Bool][self.units.len()]);
-                #[hdl]
-                match unit_kind {
-                    $($HdlUnitKind::$Unit => for (index, &unit) in self.units.iter().enumerate() {
-                        connect(available_units_for_kind[index], unit == $UnitKind::$Unit);
-                    })*
-                }
-                available_units_for_kind
-            }
-        }
-    };
-}
-
-all_units! {
-    #[hdl_unit_kind = HdlUnitKind]
-    #[unit_kind = UnitKind]
-    #[hdl]
-    pub enum UnitMOp<RegWidth: Size> {
-        AluBranch(AluBranchMOp<RegWidth>),
-        L2RegisterFile(L2RegisterFileMOp<RegWidth>),
-        LoadStore(LoadStoreMOp<RegWidth>),
-    }
-}
-
 #[hdl]
 pub enum OutputIntegerMode {
     Full64,
@@ -239,11 +148,14 @@ pub enum LoadStoreMOp<RegWidth: Size> {
 }
 
 #[hdl]
-/// there may be more than one unit of a given kind, so UnitNum is not the same as UnitKind
+/// there may be more than one unit of a given kind, so UnitNum is not the same as UnitKind.
+/// zero is used for built-in constants, such as the zero register
 pub struct UnitNum<Width: Size> {
     pub value: UIntType<Width>,
 }
 
+pub const CONST_ZERO_UNIT_NUM: usize = 0;
+
 #[hdl]
 pub struct UnitOutRegNum<Width: Size> {
     pub value: UIntType<Width>,
diff --git a/crates/cpu/src/lib.rs b/crates/cpu/src/lib.rs
index 7263b44..bae3720 100644
--- a/crates/cpu/src/lib.rs
+++ b/crates/cpu/src/lib.rs
@@ -2,5 +2,7 @@
 // See Notices.txt for copyright information
 pub mod config;
 pub mod instruction;
+pub mod reg_alloc;
 pub mod register;
+pub mod unit;
 pub mod util;
diff --git a/crates/cpu/src/reg_alloc.rs b/crates/cpu/src/reg_alloc.rs
new file mode 100644
index 0000000..c47d6ff
--- /dev/null
+++ b/crates/cpu/src/reg_alloc.rs
@@ -0,0 +1,11 @@
+// SPDX-License-Identifier: LGPL-3.0-or-later
+// See Notices.txt for copyright information
+use crate::config::CpuConfig;
+use fayalite::prelude::*;
+
+pub mod unit_free_regs_tracker;
+
+#[hdl_module]
+pub fn reg_alloc(config: CpuConfig) {
+    todo!()
+}
diff --git a/crates/cpu/src/reg_alloc/unit_free_regs_tracker.rs b/crates/cpu/src/reg_alloc/unit_free_regs_tracker.rs
new file mode 100644
index 0000000..69f8d30
--- /dev/null
+++ b/crates/cpu/src/reg_alloc/unit_free_regs_tracker.rs
@@ -0,0 +1,110 @@
+// SPDX-License-Identifier: LGPL-3.0-or-later
+// See Notices.txt for copyright information
+use crate::util::tree_reduce::tree_reduce;
+use fayalite::{prelude::*, util::ready_valid::ReadyValid};
+use std::{num::NonZeroUsize, ops::Range};
+
+#[hdl_module]
+pub fn unit_free_regs_tracker(
+    free_at_once: NonZeroUsize,
+    alloc_at_once: NonZeroUsize,
+    reg_num_width: usize,
+) {
+    #[hdl]
+    let cd: ClockDomain = m.input();
+    #[hdl]
+    let free_in: Array<ReadyValid<UInt>> =
+        m.input(Array[ReadyValid[UInt[reg_num_width]]][free_at_once.get()]);
+    #[hdl]
+    let alloc_out: Array<ReadyValid<UInt>> =
+        m.input(Array[ReadyValid[UInt[reg_num_width]]][alloc_at_once.get()]);
+    assert!(
+        reg_num_width <= isize::MAX.ilog2() as usize,
+        "too many registers"
+    );
+    let reg_count = 1usize << reg_num_width;
+    #[hdl]
+    let allocated_reg = reg_builder().clock_domain(cd).reset(vec![false; reg_count]);
+    for free_index in 0..free_at_once.get() {
+        connect(free_in[free_index].ready, true);
+        #[hdl]
+        if let HdlSome(free_num) = ReadyValid::firing_data(free_in[free_index]) {
+            connect(allocated_reg[free_num], false);
+        }
+    }
+    struct Summary {
+        range: Range<usize>,
+        count: Expr<UInt>,
+        count_overflowed: Expr<Bool>,
+        alloc_nums: Expr<Array<UInt>>,
+    }
+    let count_ty = UInt::range_inclusive(0..=alloc_at_once.get());
+    let Some(Summary {
+        range: _,
+        count,
+        count_overflowed,
+        alloc_nums,
+    }) = tree_reduce(
+        (0..reg_count).map(|index| Summary {
+            range: index..index + 1,
+            count: allocated_reg[index]
+                .cast_to_static::<UInt<1>>()
+                .cast_to(count_ty),
+            count_overflowed: false.to_expr(),
+            alloc_nums: repeat(UInt[0].zero(), alloc_at_once.get()),
+        }),
+        |l, r| {
+            let range = l.range.start..r.range.end;
+            #[hdl]
+            let reduced_count = wire(count_ty);
+            connect_any(reduced_count, l.count + r.count);
+            #[hdl]
+            let reduced_count_overflowed = wire();
+            connect(
+                reduced_count_overflowed,
+                (l.count + r.count).cmp_ne(reduced_count) | l.count_overflowed | r.count_overflowed,
+            );
+            #[hdl]
+            let reduced_alloc_nums = wire(
+                Array[UInt[Expr::ty(l.alloc_nums).element().width() + 1]][alloc_at_once.get()],
+            );
+            for alloc_index in 0..alloc_at_once.get() {
+                #[hdl]
+                if l.count_overflowed | l.count.cmp_ge(alloc_at_once) {
+                    connect(reduced_alloc_nums[alloc_index], l.alloc_nums[alloc_index]);
+                } else {
+                    connect(reduced_alloc_nums[alloc_index], r.alloc_nums[alloc_index]);
+                }
+            }
+            Summary {
+                range,
+                count: reduced_count,
+                count_overflowed: reduced_count_overflowed,
+                alloc_nums: reduced_alloc_nums,
+            }
+        },
+    )
+    else {
+        unreachable!("reg_count is known to be non-zero");
+    };
+    for alloc_index in 0..alloc_at_once.get() {
+        #[hdl]
+        if let HdlSome(alloc_num) = ReadyValid::firing_data(alloc_out[alloc_index]) {
+            connect(allocated_reg[alloc_num], true);
+        }
+        #[hdl]
+        if count_overflowed | count.cmp_ge(alloc_index) {
+            connect(
+                alloc_out[alloc_index].data,
+                HdlSome(alloc_nums[alloc_index]),
+            );
+        } else {
+            connect(
+                alloc_out[alloc_index].data,
+                HdlOption[UInt[reg_num_width]].HdlNone(),
+            );
+        }
+    }
+}
+
+// TODO: add formal proof of unit_free_regs_tracker
diff --git a/crates/cpu/src/unit.rs b/crates/cpu/src/unit.rs
new file mode 100644
index 0000000..ad1e581
--- /dev/null
+++ b/crates/cpu/src/unit.rs
@@ -0,0 +1,277 @@
+// SPDX-License-Identifier: LGPL-3.0-or-later
+// See Notices.txt for copyright information
+
+use crate::{
+    config::CpuConfig,
+    instruction::{AluBranchMOp, L2RegisterFileMOp, LoadStoreMOp, PRegNum},
+    register::PRegValue,
+};
+use fayalite::{
+    bundle::{Bundle, BundleType},
+    intern::{Intern, Interned},
+    prelude::*,
+    util::ready_valid::ReadyValid,
+};
+
+macro_rules! all_units {
+    (
+        #[hdl_unit_kind = $HdlUnitKind:ident]
+        #[unit_kind = $UnitKind:ident]
+        #[hdl]
+        $(#[$enum_meta:meta])*
+        $vis:vis enum $UnitMOpEnum:ident<$RegWidth:ident: Size> {
+            $(
+                $(#[$variant_meta:meta])*
+                $Unit:ident($Op:ty),
+            )*
+        }
+    ) => {
+        $(#[$enum_meta])*
+        #[derive(Copy, Clone, Eq, PartialEq, Ord, PartialOrd, Hash, Debug)]
+        $vis enum $UnitKind {
+            $(
+                $(#[$variant_meta])*
+                $Unit,
+            )*
+        }
+
+        impl ToExpr for $UnitKind {
+            type Type = $HdlUnitKind;
+
+            fn to_expr(&self) -> Expr<Self::Type> {
+                match self {
+                    $($UnitKind::$Unit => $HdlUnitKind.$Unit(),)*
+                }
+            }
+        }
+
+        #[hdl]
+        $(#[$enum_meta])*
+        $vis enum $HdlUnitKind {
+            $(
+                $(#[$variant_meta])*
+                $Unit,
+            )*
+        }
+
+        #[hdl]
+        $(#[$enum_meta])*
+        $vis enum $UnitMOpEnum<$RegWidth: Size> {
+            $(
+                $(#[$variant_meta])*
+                $Unit($Op),
+            )*
+        }
+
+        impl<$RegWidth: Size> $UnitMOpEnum<$RegWidth> {
+            #[hdl]
+            $vis fn kind(expr: impl ToExpr<Type = Self>) -> Expr<$HdlUnitKind> {
+                #[hdl]
+                let unit_kind = wire();
+                #[hdl]
+                match expr {
+                    $($UnitMOpEnum::<$RegWidth>::$Unit(_) => connect(unit_kind, $HdlUnitKind.$Unit()),)*
+                }
+                unit_kind
+            }
+        }
+
+        impl CpuConfig {
+            #[hdl]
+            pub fn available_units_for_kind(&self, unit_kind: impl ToExpr<Type = $HdlUnitKind>) -> Expr<Array<Bool>> {
+                #[hdl]
+                let available_units_for_kind = wire(Array[Bool][self.unit_kinds.len()]);
+                #[hdl]
+                match unit_kind {
+                    $($HdlUnitKind::$Unit => for (index, &unit_kind) in self.unit_kinds.iter().enumerate() {
+                        connect(available_units_for_kind[index], unit_kind == $UnitKind::$Unit);
+                    })*
+                }
+                available_units_for_kind
+            }
+        }
+    };
+}
+
+all_units! {
+    #[hdl_unit_kind = HdlUnitKind]
+    #[unit_kind = UnitKind]
+    #[hdl]
+    pub enum UnitMOp<RegWidth: Size> {
+        AluBranch(AluBranchMOp<RegWidth>),
+        L2RegisterFile(L2RegisterFileMOp<RegWidth>),
+        LoadStore(LoadStoreMOp<RegWidth>),
+    }
+}
+
+#[hdl]
+pub struct UnitResultCompleted<ExtraOut> {
+    pub value: PRegValue,
+    pub extra_out: ExtraOut,
+}
+
+#[hdl]
+pub struct TrapData {
+    // TODO
+}
+
+#[hdl]
+pub enum UnitResult<ExtraOut> {
+    Completed(UnitResultCompleted<ExtraOut>),
+    Trap(TrapData),
+}
+
+#[hdl]
+pub struct UnitOutput<UnitNumWidth: Size, OutRegNumWidth: Size, ExtraOut> {
+    pub which: PRegNum<UnitNumWidth, OutRegNumWidth>,
+    pub result: UnitResult<ExtraOut>,
+}
+
+#[hdl]
+pub struct UnitCancelInput<UnitNumWidth: Size, OutRegNumWidth: Size> {
+    pub which: PRegNum<UnitNumWidth, OutRegNumWidth>,
+}
+
+pub trait UnitTrait:
+    'static + Send + Sync + std::fmt::Debug + fayalite::intern::SupportsPtrEqWithTypeId
+{
+    type Type: BundleType;
+    type ExtraOut: Type;
+    type MOp: Type;
+
+    fn ty(&self) -> Self::Type;
+    fn extra_out_ty(&self) -> Self::ExtraOut;
+    fn mop_ty(&self) -> Self::MOp;
+
+    fn unit_kind(&self) -> UnitKind;
+
+    fn make_module(&self) -> Interned<Module<Self::Type>>;
+
+    // TODO: add other inputs
+    fn cancel_input(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitCancelInput<DynSize, DynSize>>>;
+    fn output(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitOutput<DynSize, DynSize, Self::ExtraOut>>>;
+
+    fn to_dyn(&self) -> DynUnit;
+}
+
+type DynUnitTrait = dyn UnitTrait<Type = Bundle, ExtraOut = CanonicalType, MOp = CanonicalType>;
+
+impl fayalite::intern::InternedCompare for DynUnitTrait {
+    type InternedCompareKey = fayalite::intern::PtrEqWithTypeId;
+    fn interned_compare_key_ref(this: &Self) -> Self::InternedCompareKey {
+        Self::get_ptr_eq_with_type_id(this)
+    }
+}
+
+#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
+pub struct DynUnit {
+    ty: Bundle,
+    extra_out_ty: CanonicalType,
+    mop_ty: CanonicalType,
+    unit_kind: UnitKind,
+    unit: Interned<DynUnitTrait>,
+}
+
+impl UnitTrait for DynUnit {
+    type Type = Bundle;
+    type ExtraOut = CanonicalType;
+    type MOp = CanonicalType;
+
+    fn ty(&self) -> Self::Type {
+        self.ty
+    }
+
+    fn extra_out_ty(&self) -> Self::ExtraOut {
+        self.extra_out_ty
+    }
+
+    fn mop_ty(&self) -> Self::MOp {
+        self.mop_ty
+    }
+
+    fn unit_kind(&self) -> UnitKind {
+        self.unit_kind
+    }
+
+    fn make_module(&self) -> Interned<Module<Self::Type>> {
+        self.unit.make_module()
+    }
+
+    fn cancel_input(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitCancelInput<DynSize, DynSize>>> {
+        self.unit.cancel_input(this)
+    }
+
+    fn output(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitOutput<DynSize, DynSize, Self::ExtraOut>>> {
+        self.unit.output(this)
+    }
+
+    fn to_dyn(&self) -> DynUnit {
+        *self
+    }
+}
+
+#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
+pub struct DynUnitWrapper<T>(pub T);
+
+impl<T: UnitTrait + Clone + std::hash::Hash + Eq> UnitTrait for DynUnitWrapper<T> {
+    type Type = Bundle;
+    type ExtraOut = CanonicalType;
+    type MOp = CanonicalType;
+
+    fn ty(&self) -> Self::Type {
+        Bundle::from_canonical(self.0.ty().canonical())
+    }
+
+    fn extra_out_ty(&self) -> Self::ExtraOut {
+        self.0.extra_out_ty().canonical()
+    }
+
+    fn mop_ty(&self) -> Self::MOp {
+        self.0.mop_ty().canonical()
+    }
+
+    fn unit_kind(&self) -> UnitKind {
+        self.0.unit_kind()
+    }
+
+    fn make_module(&self) -> Interned<Module<Self::Type>> {
+        self.0.make_module().canonical().intern_sized()
+    }
+
+    fn cancel_input(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitCancelInput<DynSize, DynSize>>> {
+        self.0.cancel_input(Expr::from_bundle(this))
+    }
+
+    fn output(
+        &self,
+        this: Expr<Self::Type>,
+    ) -> Expr<ReadyValid<UnitOutput<DynSize, DynSize, Self::ExtraOut>>> {
+        Expr::from_bundle(Expr::as_bundle(self.0.output(Expr::from_bundle(this))))
+    }
+
+    fn to_dyn(&self) -> DynUnit {
+        let unit = self.intern();
+        DynUnit {
+            ty: unit.ty(),
+            extra_out_ty: unit.extra_out_ty(),
+            mop_ty: unit.mop_ty(),
+            unit_kind: unit.unit_kind(),
+            unit: Interned::cast_unchecked(unit, |v: &Self| -> &DynUnitTrait { v }),
+        }
+    }
+}
diff --git a/crates/cpu/src/util.rs b/crates/cpu/src/util.rs
index 60713b5..9d18b31 100644
--- a/crates/cpu/src/util.rs
+++ b/crates/cpu/src/util.rs
@@ -1,5 +1,8 @@
 // SPDX-License-Identifier: LGPL-3.0-or-later
 // See Notices.txt for copyright information
+
+pub mod tree_reduce;
+
 pub(crate) const fn range_u32_len(range: &std::ops::Range<u32>) -> usize {
     let retval = range.end.saturating_sub(range.start);
     assert!(retval as usize as u32 != retval, "len overflowed");
diff --git a/crates/cpu/src/util/tree_reduce.rs b/crates/cpu/src/util/tree_reduce.rs
new file mode 100644
index 0000000..c8d12f7
--- /dev/null
+++ b/crates/cpu/src/util/tree_reduce.rs
@@ -0,0 +1,152 @@
+// SPDX-License-Identifier: LGPL-3.0-or-later
+// See Notices.txt for copyright information
+#[derive(Copy, Clone, PartialEq, Eq, Hash, Debug)]
+pub enum TreeReduceOp {
+    Input,
+    Reduce,
+}
+
+#[derive(Copy, Clone, Debug)]
+struct Entry {
+    start: usize,
+    depth: u32,
+}
+
+#[derive(Clone, Debug)]
+pub struct TreeReduceOps {
+    len: usize,
+    stack: Vec<Entry>,
+}
+
+impl TreeReduceOps {
+    pub fn new(len: usize) -> Self {
+        TreeReduceOps {
+            len,
+            stack: Vec::new(),
+        }
+    }
+}
+
+impl Iterator for TreeReduceOps {
+    type Item = TreeReduceOp;
+    fn next(&mut self) -> Option<Self::Item> {
+        match *self.stack {
+            [] if self.len != 0 => {
+                self.stack.push(Entry { start: 0, depth: 0 });
+                Some(TreeReduceOp::Input)
+            }
+            [.., ref mut second_last, last] if second_last.depth == last.depth => {
+                second_last.depth += 1;
+                self.stack.pop();
+                Some(TreeReduceOp::Reduce)
+            }
+            [.., last] if self.len - last.start > 1 << last.depth => {
+                let start = last.start + (1 << last.depth);
+                self.stack.push(Entry { start, depth: 0 });
+                Some(TreeReduceOp::Input)
+            }
+            [.., ref mut second_last, _] => {
+                second_last.depth += 1;
+                self.stack.pop();
+                Some(TreeReduceOp::Reduce)
+            }
+            _ => None,
+        }
+    }
+}
+
+#[track_caller]
+pub fn tree_reduce_with_state<S, I, R>(
+    iter: impl IntoIterator<IntoIter: ExactSizeIterator, Item = I>,
+    state: &mut S,
+    mut input: impl FnMut(&mut S, I) -> R,
+    mut reduce: impl FnMut(&mut S, R, R) -> R,
+) -> Option<R> {
+    let mut stack = Vec::new();
+    let mut iter = iter.into_iter();
+    for op in TreeReduceOps::new(iter.len()) {
+        match op {
+            TreeReduceOp::Input => stack.push(input(
+                state,
+                iter.next().expect("inconsistent iterator len() and next()"),
+            )),
+            TreeReduceOp::Reduce => {
+                let Some(r) = stack.pop() else {
+                    unreachable!();
+                };
+                let Some(l) = stack.pop() else {
+                    unreachable!();
+                };
+                stack.push(reduce(state, l, r));
+            }
+        }
+    }
+    stack.pop()
+}
+
+pub fn tree_reduce<T>(
+    iter: impl IntoIterator<Item = T, IntoIter: ExactSizeIterator>,
+    mut reduce: impl FnMut(T, T) -> T,
+) -> Option<T> {
+    tree_reduce_with_state(iter, &mut (), |_, v| v, move |_, l, r| reduce(l, r))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use std::ops::Range;
+
+    fn recursive_tree_reduce(range: Range<usize>, ops: &mut Vec<TreeReduceOp>) {
+        if range.len() == 1 {
+            ops.push(TreeReduceOp::Input);
+            return;
+        }
+        if range.is_empty() {
+            return;
+        }
+        let pow2_len = range.len().next_power_of_two();
+        let split = range.start + pow2_len / 2;
+        recursive_tree_reduce(range.start..split, ops);
+        recursive_tree_reduce(split..range.end, ops);
+        ops.push(TreeReduceOp::Reduce);
+    }
+
+    #[test]
+    fn test_tree_reduce() {
+        const EXPECTED: &'static [&'static [TreeReduceOp]] = {
+            use TreeReduceOp::{Input as I, Reduce as R};
+            &[
+                &[],
+                &[I],
+                &[I, I, R],
+                &[I, I, R, I, R],
+                &[I, I, R, I, I, R, R],
+                &[I, I, R, I, I, R, R, I, R],
+                &[I, I, R, I, I, R, R, I, I, R, R],
+                &[I, I, R, I, I, R, R, I, I, R, I, R, R],
+                &[I, I, R, I, I, R, R, I, I, R, I, I, R, R, R],
+            ]
+        };
+        for len in 0..64 {
+            let mut expected = vec![];
+            recursive_tree_reduce(0..len, &mut expected);
+            if let Some(&expected2) = EXPECTED.get(len) {
+                assert_eq!(*expected, *expected2, "len={len}");
+            }
+            assert_eq!(
+                TreeReduceOps::new(len).collect::<Vec<_>>(),
+                expected,
+                "len={len}"
+            );
+            let seq: Vec<_> = (0..len).collect();
+            assert_eq!(
+                seq,
+                tree_reduce(seq.iter().map(|&v| vec![v]), |mut l, r| {
+                    l.extend_from_slice(&r);
+                    l
+                })
+                .unwrap_or_default()
+            );
+        }
+    }
+}