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test(tests/playground): rbmap example

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@kha The Lean rbmap is 3x slower than the C++ rb_map.
I tried two different implementations: rbmap2 (Appel's Coq
implementation), and rbmap3 (tries to simulate the C++ version).
I believe rbmap3 is broken since it is too slow.
I have also identified missing reset/reuse opportunities.
The actual implementation misses a case the simple code at reuse.txt gets :(
rbmap3 also exposes the "TODO(Leo): improve this" at library/compiler/reduce_arity.cpp
This commit is contained in:
Leonardo de Moura 2019-02-19 19:01:51 -08:00
parent 6276d1a7f1
commit 5db219aae5
5 changed files with 547 additions and 1 deletions
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tests/playground/.gitignore vendored
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*.out
*.cpp
*.lean.cpp
*.cmi
*.cmx
*.o

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tests/playground/rbmap.cpp Normal file
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#include <cstdlib>
#include <iostream>
#include "util/rb_map.h"
#include "util/nat.h"
using namespace lean;
struct nat_cmp {
int operator()(nat const & n1, nat const & n2) const {
if (n1 < n2) return -1;
if (n2 < n1) return 1;
return 0;
}
};
int main(int argc, char ** argv) {
rb_map<nat, bool, nat_cmp> m;
unsigned n = 0;
if (argc == 2) {
n = std::atoi(argv[1]);
}
for (unsigned i = 0; i < n; i++) {
m.insert(nat(i), i%10 == 0);
}
nat r(0u);
m.for_each([&](nat const & k, bool v) {
if (v) r = r + k;
});
std::cout << r << "\n";
return 0;
}

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tests/playground/rbmap.lean Normal file
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@[reducible] def map : Type := rbmap nat bool (<)
def mk_map_aux : nat → map → map
| 0 m := m
| (n+1) m := mk_map_aux n (m.insert n (n % 10 = 0))
def mk_map (n : nat) :=
mk_map_aux n (mk_rbmap nat bool (<))
def main (xs : list string) : io uint32 :=
let m := mk_map xs.head.to_nat in
let v := rbmap.fold (λ (k : nat) (v : bool) (r : nat), if v then r + k else r) m 0 in
io.println' (to_string v) *>
pure 0

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tests/playground/rbmap2.lean Normal file
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/-
Copyright (c) 2017 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
universes u v w w'
namespace tst
inductive rbcolor
| red | black
inductive rbnode (α : Type u) (β : α → Type v)
| leaf {} : rbnode
| node (c : rbcolor) (lchild : rbnode) (key : α) (val : β key) (rchild : rbnode) : rbnode
namespace rbnode
variables {α : Type u} {β : α → Type v} {σ : Type w}
instance rbcolor.decidable_eq : decidable_eq rbcolor :=
{dec_eq := λ a b, rbcolor.cases_on a
(rbcolor.cases_on b (is_true rfl) (is_false (λ h, rbcolor.no_confusion h)))
(rbcolor.cases_on b (is_false (λ h, rbcolor.no_confusion h)) (is_true rfl))}
open tst.rbcolor
def depth (f : nat → nat → nat) : rbnode α β → nat
| leaf := 0
| (node _ l _ _ r) := (f (depth l) (depth r))+1
protected def min : rbnode α β → option (Σ k : α, β k)
| leaf := none
| (node _ leaf k v _) := some ⟨k, v⟩
| (node _ l _ _ _) := min l
protected def max : rbnode α β → option (Σ k : α, β k)
| leaf := none
| (node _ _ k v leaf) := some ⟨k, v⟩
| (node _ _ _ _ r) := max r
@[specialize] def fold (f : Π (k : α), β k → σ → σ) : rbnode α β → σ → σ
| leaf b := b
| (node _ l k v r) b := fold r (f k v (fold l b))
@[specialize] def mfold {m : Type w → Type w'} [monad m] (f : Π (k : α), β k → σ → m σ) : rbnode α β → σ → m σ
| leaf b := pure b
| (node _ l k v r) b := do b₁ ← mfold l b, b₂ ← f k v b₁, mfold r b₂
@[specialize] def rev_fold (f : Π (k : α), β k → σ → σ) : rbnode α β → σ → σ
| leaf b := b
| (node _ l k v r) b := rev_fold l (f k v (rev_fold r b))
@[specialize] def all (p : Π k : α, β k → bool) : rbnode α β → bool
| leaf := tt
| (node _ l k v r) := p k v && all l && all r
@[specialize] def any (p : Π k : α, β k → bool) : rbnode α β → bool
| leaf := ff
| (node _ l k v r) := p k v || any l || any r
set_option pp.implicit true
set_option trace.compiler.llnf true
def balance (rb : rbcolor) (t1 : rbnode α β) (k : α) (vk : β k) (t2 : rbnode α β) :=
match rb with
| red := node red t1 k vk t2
| black :=
match t1 with
| node red (node red a x vx b) y vy c :=
node red (node black a x vx b) y vy (node black c k vk t2)
| node red a x vx (node red b y vy c) :=
node red (node black a x vx b) y vy (node black c k vk t2)
| a := match t2 with
| node red (node red b y vy c) z vz d :=
node red (node black t1 k vk b) y vy (node black c z vz d)
| node red b y vy (node red c z vz d) :=
node red (node black t1 k vk b) y vy (node black c z vz d)
| _ := node black t1 k vk t2
#exit
def make_black (t : rbnode α β) :=
match t with
| leaf := leaf
| node _ a x vx b := node black a x vx b
section insert
variables (lt : α → α → Prop) [decidable_rel lt]
def ins (x : α) (vx : β x) : rbnode α β → rbnode α β
| leaf := node red leaf x vx leaf
| (node c a y vy b) :=
if lt x y then balance c (ins a) y vy b
else if lt y x then balance c a y vy (ins b)
else node c a x vx b
def insert (t : rbnode α β) (k : α) (v : β k) : rbnode α β :=
make_black (ins lt k v t)
end insert
section membership
variable (lt : α → α → Prop)
variable [decidable_rel lt]
def find_core : rbnode α β → Π k : α, option (Σ k : α, β k)
| leaf x := none
| (node _ a ky vy b) x :=
(match cmp_using lt x ky with
| ordering.lt := find_core a x
| ordering.eq := some ⟨ky, vy⟩
| ordering.gt := find_core b x)
def find {β : Type v} : rbnode α (λ _, β) → α → option β
| leaf x := none
| (node _ a ky vy b) x :=
(match cmp_using lt x ky with
| ordering.lt := find a x
| ordering.eq := some vy
| ordering.gt := find b x)
def lower_bound : rbnode α β → α → option (sigma β) → option (sigma β)
| leaf x lb := lb
| (node _ a ky vy b) x lb :=
(match cmp_using lt x ky with
| ordering.lt := lower_bound a x lb
| ordering.eq := some ⟨ky, vy⟩
| ordering.gt := lower_bound b x (some ⟨ky, vy⟩))
end membership
inductive well_formed (lt : α → α → Prop) : rbnode α β → Prop
| leaf_wff : well_formed leaf
| insert_wff {n n' : rbnode α β} {k : α} {v : β k} [decidable_rel lt] : well_formed n → n' = insert lt n k v → well_formed n'
end rbnode
open tst.rbnode
/- TODO(Leo): define d_rbmap -/
def rbmap (α : Type u) (β : Type v) (lt : α → α → Prop) : Type (max u v) :=
{t : rbnode α (λ _, β) // t.well_formed lt }
@[inline] def mk_rbmap (α : Type u) (β : Type v) (lt : α → α → Prop) : rbmap α β lt :=
⟨leaf, well_formed.leaf_wff lt⟩
namespace rbmap
variables {α : Type u} {β : Type v} {σ : Type w} {lt : α → α → Prop}
def depth (f : nat → nat → nat) (t : rbmap α β lt) : nat :=
t.val.depth f
@[inline] def fold (f : α → β → σ → σ) : rbmap α β lt → σ → σ
| ⟨t, _⟩ b := t.fold f b
@[inline] def rev_fold (f : α → β → σ → σ) : rbmap α β lt → σ → σ
| ⟨t, _⟩ b := t.rev_fold f b
@[inline] def mfold {m : Type w → Type w'} [monad m] (f : α → β → σ → m σ) : rbmap α β lt → σ → m σ
| ⟨t, _⟩ b := t.mfold f b
@[inline] def mfor {m : Type w → Type w'} [monad m] (f : α → β → m σ) (t : rbmap α β lt) : m punit :=
t.mfold (λ k v _, f k v *> pure ⟨⟩) ⟨⟩
@[inline] def empty : rbmap α β lt → bool
| ⟨leaf, _⟩ := tt
| _ := ff
@[specialize] def to_list : rbmap α β lt → list (α × β)
| ⟨t, _⟩ := t.rev_fold (λ k v ps, (k, v)::ps) []
@[inline] protected def min : rbmap α β lt → option (α × β)
| ⟨t, _⟩ :=
match t.min with
| some ⟨k, v⟩ := some (k, v)
| none := none
@[inline] protected def max : rbmap α β lt → option (α × β)
| ⟨t, _⟩ :=
match t.max with
| some ⟨k, v⟩ := some (k, v)
| none := none
instance [has_repr α] [has_repr β] : has_repr (rbmap α β lt) :=
⟨λ t, "rbmap_of " ++ repr t.to_list⟩
variables [decidable_rel lt]
def insert : rbmap α β lt → α → β → rbmap α β lt
| ⟨t, w⟩ k v := ⟨t.insert lt k v, well_formed.insert_wff w rfl⟩
@[specialize] def of_list : list (α × β) → rbmap α β lt
| [] := mk_rbmap _ _ _
| (⟨k,v⟩::xs) := (of_list xs).insert k v
def find_core : rbmap α β lt → α → option (Σ k : α, β)
| ⟨t, _⟩ x := t.find_core lt x
def find : rbmap α β lt → α → option β
| ⟨t, _⟩ x := t.find lt x
/-- (lower_bound k) retrieves the kv pair of the largest key smaller than or equal to `k`,
if it exists. -/
def lower_bound : rbmap α β lt → α → option (Σ k : α, β)
| ⟨t, _⟩ x := t.lower_bound lt x none
@[inline] def contains (t : rbmap α β lt) (a : α) : bool :=
(t.find a).is_some
def from_list (l : list (α × β)) (lt : α → α → Prop) [decidable_rel lt] : rbmap α β lt :=
l.foldl (λ r p, r.insert p.1 p.2) (mk_rbmap α β lt)
@[inline] def all : rbmap α β lt → (α → β → bool) → bool
| ⟨t, _⟩ p := t.all p
@[inline] def any : rbmap α β lt → (α → β → bool) → bool
| ⟨t, _⟩ p := t.any p
end rbmap
def rbmap_of {α : Type u} {β : Type v} (l : list (α × β)) (lt : α → α → Prop) [decidable_rel lt] : rbmap α β lt :=
rbmap.from_list l lt
end tst
@[reducible] def map : Type := tst.rbmap nat bool (<)
def mk_map_aux : nat → nat → map → map
| 0 i m := m
| (n+1) i m := mk_map_aux n (i+1) (tst.rbmap.insert m i (i % 10 = 0))
def mk_map (n : nat) :=
mk_map_aux n 0 (tst.mk_rbmap nat bool (<))
def main (xs : list string) : io uint32 :=
let m := mk_map xs.head.to_nat in
let v := tst.rbmap.fold (λ (k : nat) (v : bool) (r : nat), if v then r + k else r) m 0 in
io.println' (to_string v) *>
pure 0

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prelude
import init.core init.io init.data.ordering
universes u v w
inductive rbcolor
| red | black
inductive rbnode (α : Type u) (β : α → Type v)
| leaf {} : rbnode
| node (c : rbcolor) (lchild : rbnode) (key : α) (val : β key) (rchild : rbnode) : rbnode
instance rbcolor.decidable_eq : decidable_eq rbcolor :=
{dec_eq := λ a b, rbcolor.cases_on a
(rbcolor.cases_on b (is_true rfl) (is_false (λ h, rbcolor.no_confusion h)))
(rbcolor.cases_on b (is_false (λ h, rbcolor.no_confusion h)) (is_true rfl))}
namespace rbnode
variables {α : Type u} {β : α → Type v} {σ : Type w}
open rbcolor
def depth (f : nat → nat → nat) : rbnode α β → nat
| leaf := 0
| (node _ l _ _ r) := (f (depth l) (depth r)) + 1
protected def min : rbnode α β → option (Σ k : α, β k)
| leaf := none
| (node _ leaf k v _) := some ⟨k, v⟩
| (node _ l k v _) := min l
protected def max : rbnode α β → option (Σ k : α, β k)
| leaf := none
| (node _ _ k v leaf) := some ⟨k, v⟩
| (node _ _ k v r) := max r
@[specialize] def fold (f : Π (k : α), β k → σ → σ) : rbnode α β → σ → σ
| leaf b := b
| (node _ l k v r) b := fold r (f k v (fold l b))
@[specialize] def rev_fold (f : Π (k : α), β k → σ → σ) : rbnode α β → σ → σ
| leaf b := b
| (node _ l k v r) b := rev_fold l (f k v (rev_fold r b))
@[specialize] def all (p : Π k : α, β k → bool) : rbnode α β → bool
| leaf := tt
| (node _ l k v r) := p k v && all l && all r
@[specialize] def any (p : Π k : α, β k → bool) : rbnode α β → bool
| leaf := ff
| (node _ l k v r) := p k v || any l || any r
def is_red : rbnode α β → bool
| (node red _ _ _ _) := tt
| _ := ff
def rotate_left : Π (n : rbnode α β), n ≠ leaf → rbnode α β
| n@(node hc hl hk hv (node red xl xk xv xr)) _ :=
if not (is_red hl)
then (node hc (node red hl hk hv xl) xk xv xr)
else n
| leaf h := absurd rfl h
| e _ := e
theorem if_node_node_ne_leaf {c : Prop} [decidable c] {l1 l2 : rbnode α β} {c1 k1 v1 r1 c2 k2 v2 r2} : (if c then node c1 l1 k1 v1 r1 else node c2 l2 k2 v2 r2) ≠ leaf :=
λ h, if hc : c
then have h1 : (if c then node c1 l1 k1 v1 r1 else node c2 l2 k2 v2 r2) = node c1 l1 k1 v1 r1, from if_pos hc,
rbnode.no_confusion (eq.trans h1.symm h)
else have h1 : (if c then node c1 l1 k1 v1 r1 else node c2 l2 k2 v2 r2) = node c2 l2 k2 v2 r2, from if_neg hc,
rbnode.no_confusion (eq.trans h1.symm h)
theorem rotate_left_ne_leaf : ∀ (n : rbnode α β) (h : n ≠ leaf), rotate_left n h ≠ leaf
| (node _ hl _ _ (node red _ _ _ _)) _ h := if_node_node_ne_leaf h
| leaf h _ := absurd rfl h
| (node _ _ _ _ (node black _ _ _ _)) _ h := rbnode.no_confusion h
def rotate_right : Π (n : rbnode α β), n ≠ leaf → rbnode α β
| n@(node hc (node red xl xk xv xr) hk hv hr) _ :=
if is_red xl
then (node hc xl xk xv (node red xr hk hv hr))
else n
| leaf h := absurd rfl h
| e _ := e
theorem rotate_right_ne_leaf : ∀ (n : rbnode α β) (h : n ≠ leaf), rotate_right n h ≠ leaf
| (node _ (node red _ _ _ _) _ _ _) _ h := if_node_node_ne_leaf h
| leaf h _ := absurd rfl h
| (node _ (node black _ _ _ _) _ _ _) _ h := rbnode.no_confusion h
def flip : rbcolor → rbcolor
| red := black
| black := red
def flip_color : rbnode α β → rbnode α β
| (node c l k v r) := node (flip c) l k v r
| leaf := leaf
def flip_colors : Π (n : rbnode α β), n ≠ leaf → rbnode α β
| n@(node c l k v r) _ :=
if is_red l ∧ is_red r
then node black (flip_color l) k v (flip_color r)
else n
| leaf h := absurd rfl h
def fixup (n : rbnode α β) (h : n ≠ leaf) : rbnode α β :=
let n₁ := rotate_left n h in
let h₁ := (rotate_left_ne_leaf n h) in
let n₂ := rotate_right n₁ h₁ in
let h₂ := (rotate_right_ne_leaf n₁ h₁) in
flip_colors n₂ h₂
def set_black : rbnode α β → rbnode α β
| (node red l k v r) := node black l k v r
| n := n
section insert
variables (lt : α → α → Prop) [decidable_rel lt]
def ins (x : α) (vx : β x) : rbnode α β → rbnode α β
| leaf := node red leaf x vx leaf
| (node c l k v r) :=
if lt x k then fixup (node c (ins l) k v r) (λ h, rbnode.no_confusion h)
else if lt k x then fixup (node c l k v (ins r)) (λ h, rbnode.no_confusion h)
else node c l x vx r
def insert (t : rbnode α β) (k : α) (v : β k) : rbnode α β :=
set_black (ins lt k v t)
end insert
section membership
variable (lt : α → α → Prop)
variable [decidable_rel lt]
def find_core : rbnode α β → Π k : α, option (Σ k : α, β k)
| leaf x := none
| (node _ a ky vy b) x :=
(match cmp_using lt x ky with
| ordering.lt := find_core a x
| ordering.eq := some ⟨ky, vy⟩
| ordering.gt := find_core b x)
def find {β : Type v} : rbnode α (λ _, β) → α → option β
| leaf x := none
| (node _ a ky vy b) x :=
(match cmp_using lt x ky with
| ordering.lt := find a x
| ordering.eq := some vy
| ordering.gt := find b x)
def lower_bound : rbnode α β → α → option (sigma β) → option (sigma β)
| leaf x lb := lb
| (node _ a ky vy b) x lb :=
(match cmp_using lt x ky with
| ordering.lt := lower_bound a x lb
| ordering.eq := some ⟨ky, vy⟩
| ordering.gt := lower_bound b x (some ⟨ky, vy⟩))
end membership
inductive well_formed (lt : α → α → Prop) : rbnode α β → Prop
| leaf_wff : well_formed leaf
| insert_wff {n n' : rbnode α β} {k : α} {v : β k} [decidable_rel lt] : well_formed n → n' = insert lt n k v → well_formed n'
end rbnode
open rbnode
/- TODO(Leo): define d_rbmap -/
def rbmap (α : Type u) (β : Type v) (lt : α → α → Prop) : Type (max u v) :=
{t : rbnode α (λ _, β) // t.well_formed lt }
@[inline] def mk_rbmap (α : Type u) (β : Type v) (lt : α → α → Prop) : rbmap α β lt :=
⟨leaf, well_formed.leaf_wff lt⟩
namespace rbmap
variables {α : Type u} {β : Type v} {σ : Type w} {lt : α → α → Prop}
def depth (f : nat → nat → nat) (t : rbmap α β lt) : nat :=
t.val.depth f
@[inline] def fold (f : α → β → σ → σ) : rbmap α β lt → σ → σ
| ⟨t, _⟩ b := t.fold f b
@[inline] def rev_fold (f : α → β → σ → σ) : rbmap α β lt → σ → σ
| ⟨t, _⟩ b := t.rev_fold f b
@[inline] def empty : rbmap α β lt → bool
| ⟨leaf, _⟩ := tt
| _ := ff
@[specialize] def to_list : rbmap α β lt → list (α × β)
| ⟨t, _⟩ := t.rev_fold (λ k v ps, (k, v)::ps) []
@[inline] protected def min : rbmap α β lt → option (α × β)
| ⟨t, _⟩ :=
match t.min with
| some ⟨k, v⟩ := some (k, v)
| none := none
@[inline] protected def max : rbmap α β lt → option (α × β)
| ⟨t, _⟩ :=
match t.max with
| some ⟨k, v⟩ := some (k, v)
| none := none
instance [has_repr α] [has_repr β] : has_repr (rbmap α β lt) :=
⟨λ t, "rbmap_of " ++ repr t.to_list⟩
variables [decidable_rel lt]
def insert : rbmap α β lt → α → β → rbmap α β lt
| ⟨t, w⟩ k v := ⟨t.insert lt k v, well_formed.insert_wff w rfl⟩
@[specialize] def of_list : list (α × β) → rbmap α β lt
| [] := mk_rbmap _ _ _
| (⟨k,v⟩::xs) := (of_list xs).insert k v
def find_core : rbmap α β lt → α → option (Σ k : α, β)
| ⟨t, _⟩ x := t.find_core lt x
def find : rbmap α β lt → α → option β
| ⟨t, _⟩ x := t.find lt x
/-- (lower_bound k) retrieves the kv pair of the largest key smaller than or equal to `k`,
if it exists. -/
def lower_bound : rbmap α β lt → α → option (Σ k : α, β)
| ⟨t, _⟩ x := t.lower_bound lt x none
@[inline] def contains (t : rbmap α β lt) (a : α) : bool :=
(t.find a).is_some
def from_list (l : list (α × β)) (lt : α → α → Prop) [decidable_rel lt] : rbmap α β lt :=
l.foldl (λ r p, r.insert p.1 p.2) (mk_rbmap α β lt)
@[inline] def all : rbmap α β lt → (α → β → bool) → bool
| ⟨t, _⟩ p := t.all p
@[inline] def any : rbmap α β lt → (α → β → bool) → bool
| ⟨t, _⟩ p := t.any p
end rbmap
def rbmap_of {α : Type u} {β : Type v} (l : list (α × β)) (lt : α → α → Prop) [decidable_rel lt] : rbmap α β lt :=
rbmap.from_list l lt
/- Test -/
@[reducible] def map : Type := rbmap nat bool (<)
def mk_map_aux : nat → map → map
| 0 m := m
| (n+1) m := mk_map_aux n (m.insert n (n % 10 = 0))
def mk_map (n : nat) :=
mk_map_aux n (mk_rbmap nat bool (<))
def main (xs : list string) : io uint32 :=
let m := mk_map xs.head.to_nat in
let v := rbmap.fold (λ (k : nat) (v : bool) (r : nat), if v then r + k else r) m 0 in
io.println' (to_string v) *>
pure 0