From 6b17fd584e9135b2c1eed1d3ff5b2c42322c2b73 Mon Sep 17 00:00:00 2001 From: Daniel Fischer Date: Sat, 1 Oct 2011 21:15:22 +0200 Subject: [PATCH] Add rules for powers with small exponents (fixes #5237) --- GHC/Real.lhs | 38 ++++++++++++++++++++++++++++++++++++++ 1 files changed, 38 insertions(+), 0 deletions(-) diff --git a/GHC/Real.lhs b/GHC/Real.lhs index 8597c45..125713d 100644 --- a/GHC/Real.lhs +++ b/GHC/Real.lhs @@ -469,6 +469,44 @@ x ^^ n = if n >= 0 then x^n else recip (x^(negate n)) \d1 d2 x y -> blah after the gentle round of simplification. -} +{- Rules for powers with known small exponent + see #5237 + For small exponents, (^) is inefficient compared to manually + expanding the multiplication tree. + Here, rules for the most common exponent types are given. + The range of exponents for which rules are given is quite + arbitrary and kept small to not unduly increase the number of rules. + 0 and 1 are excluded based on the assumption that nobody would + write x^0 or x^1 in code and the cases where an exponent could + be statically resolved to 0 or 1 are rare. +-} + +{-# RULES +"^2/Int" forall x. x ^ (2 :: Int) = let u = x in u*u +"^3/Int" forall x. x ^ (3 :: Int) = let u = x in (u*u)*u +"^4/Int" forall x. x ^ (4 :: Int) = let u = x; y = u*u in y*y +"^2/Integer" forall x. x ^ (2 :: Integer) = let u = x in u*u +"^3/Integer" forall x. x ^ (3 :: Integer) = let u = x in (u*u)*u +"^4/Integer" forall x. x ^ (4 :: Integer) = let u = x; y = u*u in y*y + #-} + +{- With the above, (x :: Type1) ^ (2 :: Type2) isn't rewritten if + there is a specialisation for (^) :: Type1 -> Type2 -> Type1, + hence special rules for those cases. +-} + +{-# RULES +"^2/Int2" forall (x :: Int). x ^ (2 :: Int) = let u = x in u*u +"^3/Int2" forall (x :: Int). x ^ (3 :: Int) = let u = x in (u*u)*u +"^4/Int2" forall (x :: Int). x ^ (4 :: Int) = let u = x; y = u*u in y*y +"^2/Integer2" forall (x :: Integer). x ^ (2 :: Integer) = let u = x in u*u +"^3/Integer2" forall (x :: Integer). x ^ (3 :: Integer) = let u = x in (u*u)*u +"^4/Integer2" forall (x :: Integer). x ^ (4 :: Integer) = let u = x; y = u*u in y*y +"^2/Integer3" forall (x :: Integer). x ^ (2 :: Int) = let u = x in u*u +"^3/Integer3" forall (x :: Integer). x ^ (3 :: Int) = let u = x in (u*u)*u +"^4/Integer3" forall (x :: Integer). x ^ (4 :: Int) = let u = x; y = u*u in y*y + #-} + ------------------------------------------------------- -- Special power functions for Rational -- -- 1.7.3.4