summaryrefslogtreecommitdiff
path: root/backend/SelectDiv.vp
diff options
context:
space:
mode:
Diffstat (limited to 'backend/SelectDiv.vp')
-rw-r--r--backend/SelectDiv.vp156
1 files changed, 156 insertions, 0 deletions
diff --git a/backend/SelectDiv.vp b/backend/SelectDiv.vp
new file mode 100644
index 0000000..e60a97d
--- /dev/null
+++ b/backend/SelectDiv.vp
@@ -0,0 +1,156 @@
+(* *********************************************************************)
+(* *)
+(* The Compcert verified compiler *)
+(* *)
+(* Xavier Leroy, INRIA Paris-Rocquencourt *)
+(* *)
+(* Copyright Institut National de Recherche en Informatique et en *)
+(* Automatique. All rights reserved. This file is distributed *)
+(* under the terms of the INRIA Non-Commercial License Agreement. *)
+(* *)
+(* *********************************************************************)
+
+(** Instruction selection for integer division and modulus *)
+
+Require Import Coqlib.
+Require Import AST.
+Require Import Integers.
+Require Import Floats.
+Require Import Op.
+Require Import CminorSel.
+Require Import SelectOp.
+
+Open Local Scope cminorsel_scope.
+
+(** We try to turn divisions by a constant into a multiplication by
+ a pseudo-inverse of the divisor. The approach is described in
+- Torbjörn Granlund, Peter L. Montgomery: "Division by Invariant
+ Integers using Multiplication". PLDI 1994.
+- Henry S. Warren, Jr: "Hacker's Delight". Addison-Wesley. Chapter 10.
+*)
+
+Fixpoint find_div_mul_params (fuel: nat) (nc: Z) (d: Z) (p: Z) : option (Z * Z) :=
+ match fuel with
+ | O => None
+ | S fuel' =>
+ let twp := two_p p in
+ if zlt (nc * (d - twp mod d)) twp
+ then Some(p - 32, (twp + d - twp mod d) / d)
+ else find_div_mul_params fuel' nc d (p + 1)
+ end.
+
+Definition divs_mul_params (d: Z) : option (Z * Z) :=
+ match find_div_mul_params
+ Int.wordsize
+ (Int.half_modulus - Int.half_modulus mod d - 1)
+ d 32 with
+ | None => None
+ | Some(p, m) =>
+ if zlt 0 d
+ && zlt (two_p (32 + p)) (m * d)
+ && zle (m * d) (two_p (32 + p) + two_p (p + 1))
+ && zle 0 m && zlt m Int.modulus
+ && zle 0 p && zlt p 32
+ then Some(p, m) else None
+ end.
+
+Definition divu_mul_params (d: Z) : option (Z * Z) :=
+ match find_div_mul_params
+ Int.wordsize
+ (Int.modulus - Int.modulus mod d - 1)
+ d 32 with
+ | None => None
+ | Some(p, m) =>
+ if zlt 0 d
+ && zle (two_p (32 + p)) (m * d)
+ && zle (m * d) (two_p (32 + p) + two_p p)
+ && zle 0 m && zlt m Int.modulus
+ && zle 0 p && zlt p 32
+ then Some(p, m) else None
+ end.
+
+Definition divu_mul (p: Z) (m: Z) :=
+ shruimm (Eop Omulhu (Eletvar O ::: Eop (Ointconst (Int.repr m)) Enil ::: Enil))
+ (Int.repr p).
+
+Definition divuimm (e1: expr) (n2: int) :=
+ match Int.is_power2 n2 with
+ | Some l => shruimm e1 l
+ | None =>
+ match divu_mul_params (Int.unsigned n2) with
+ | None => divu_base e1 (Eop (Ointconst n2) Enil)
+ | Some(p, m) => Elet e1 (divu_mul p m)
+ end
+ end.
+
+Nondetfunction divu (e1: expr) (e2: expr) :=
+ match e2 with
+ | Eop (Ointconst n2) Enil => divuimm e1 n2
+ | _ => divu_base e1 e2
+ end.
+
+Definition mod_from_div (equo: expr) (n: int) :=
+ Eop Osub (Eletvar O ::: mulimm n equo ::: Enil).
+
+Definition moduimm (e1: expr) (n2: int) :=
+ match Int.is_power2 n2 with
+ | Some l => andimm (Int.sub n2 Int.one) e1
+ | None =>
+ match divu_mul_params (Int.unsigned n2) with
+ | None => modu_base e1 (Eop (Ointconst n2) Enil)
+ | Some(p, m) => Elet e1 (mod_from_div (divu_mul p m) n2)
+ end
+ end.
+
+Nondetfunction modu (e1: expr) (e2: expr) :=
+ match e2 with
+ | Eop (Ointconst n2) Enil => moduimm e1 n2
+ | _ => modu_base e1 e2
+ end.
+
+Definition divs_mul (p: Z) (m: Z) :=
+ let e2 :=
+ Eop Omulhs (Eletvar O ::: Eop (Ointconst (Int.repr m)) Enil ::: Enil) in
+ let e3 :=
+ if zlt m Int.half_modulus then e2 else add e2 (Eletvar O) in
+ add (shrimm e3 (Int.repr p))
+ (shruimm (Eletvar O) (Int.repr (Int.zwordsize - 1))).
+
+Definition divsimm (e1: expr) (n2: int) :=
+ match Int.is_power2 n2 with
+ | Some l =>
+ if Int.ltu l (Int.repr 31)
+ then shrximm e1 l
+ else divs_base e1 (Eop (Ointconst n2) Enil)
+ | None =>
+ match divs_mul_params (Int.signed n2) with
+ | None => divs_base e1 (Eop (Ointconst n2) Enil)
+ | Some(p, m) => Elet e1 (divs_mul p m)
+ end
+ end.
+
+Nondetfunction divs (e1: expr) (e2: expr) :=
+ match e2 with
+ | Eop (Ointconst n2) Enil => divsimm e1 n2
+ | _ => divs_base e1 e2
+ end.
+
+Definition modsimm (e1: expr) (n2: int) :=
+ match Int.is_power2 n2 with
+ | Some l =>
+ if Int.ltu l (Int.repr 31)
+ then Elet e1 (mod_from_div (shrximm (Eletvar O) l) n2)
+ else mods_base e1 (Eop (Ointconst n2) Enil)
+ | None =>
+ match divs_mul_params (Int.signed n2) with
+ | None => mods_base e1 (Eop (Ointconst n2) Enil)
+ | Some(p, m) => Elet e1 (mod_from_div (divs_mul p m) n2)
+ end
+ end.
+
+Nondetfunction mods (e1: expr) (e2: expr) :=
+ match e2 with
+ | Eop (Ointconst n2) Enil => modsimm e1 n2
+ | _ => mods_base e1 e2
+ end.
+