numeric-logarithms (empty) → 0.1.0.0
raw patch · 5 files changed
+541/−0 lines, 5 filesdep +QuickCheckdep +basedep +integer-gmp
Dependencies added: QuickCheck, base, integer-gmp, numeric-logarithms, test-framework, test-framework-quickcheck2
Files
- CHANGELOG.md +4/−0
- LICENSE +202/−0
- numeric-logarithms.cabal +57/−0
- src/Numeric/Logarithms.hs +170/−0
- test/LogarithmsTest.hs +108/−0
+ CHANGELOG.md view
@@ -0,0 +1,4 @@+# 0.1.0.0++Initial version.+
+ LICENSE view
@@ -0,0 +1,202 @@++ Apache License+ Version 2.0, January 2004+ http://www.apache.org/licenses/++ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION++ 1. Definitions.++ "License" shall mean the terms and conditions for use, reproduction,+ and distribution as defined by Sections 1 through 9 of this document.++ "Licensor" shall mean the copyright owner or entity authorized by+ the copyright owner that is granting the License.++ "Legal Entity" shall mean the union of the acting entity and all+ other entities that control, are controlled by, or are under common+ control with that entity. 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+ numeric-logarithms.cabal view
@@ -0,0 +1,57 @@+cabal-version: 1.12++-- This file has been generated from package.yaml by hpack version 0.33.0.+--+-- see: https://github.com/sol/hpack+--+-- hash: 055716fd894ce8e71c2be1db7a3f5a30b6ef588291635e8f57429d608c19eb71++name: numeric-logarithms+version: 0.1.0.0+synopsis: Efficient rounded log2 algorithms on integral and rational types.+description: This provides a user-facing API for the GHC primitive 'integerLog2#', in the+ form of functions computing the floor, ceiling, or other rounded form of the+ base-2 logarithm of 'Integral' or 'Rational' types.+category: Numeric+homepage: https://github.com/google/hs-numeric-logarithms#readme+bug-reports: https://github.com/google/hs-numeric-logarithms/issues+author: Andrew Pritchard <awpr@google.com>+maintainer: Andrew Pritchard <awpr@google.com>+copyright: 2018-2021 Google LLC+license: Apache-2.0+license-file: LICENSE+build-type: Simple+extra-source-files:+ CHANGELOG.md++source-repository head+ type: git+ location: https://github.com/google/hs-numeric-logarithms++library+ exposed-modules:+ Numeric.Logarithms+ other-modules:+ Paths_numeric_logarithms+ hs-source-dirs:+ src+ build-depends:+ base >=4.9 && <4.16+ , integer-gmp >=0.5 && <1.1+ default-language: Haskell2010++test-suite Logarithms-test+ type: exitcode-stdio-1.0+ main-is: LogarithmsTest.hs+ other-modules:+ Paths_numeric_logarithms+ hs-source-dirs:+ test+ build-depends:+ QuickCheck+ , base >=4.9 && <4.16+ , integer-gmp >=0.5 && <1.1+ , numeric-logarithms+ , test-framework+ , test-framework-quickcheck2+ default-language: Haskell2010
+ src/Numeric/Logarithms.hs view
@@ -0,0 +1,170 @@+-- Copyright 2021 Google LLC+--+-- Licensed under the Apache License, Version 2.0 (the "License");+-- you may not use this file except in compliance with the License.+-- You may obtain a copy of the License at+--+-- https://www.apache.org/licenses/LICENSE-2.0+--+-- Unless required by applicable law or agreed to in writing, software+-- distributed under the License is distributed on an "AS IS" BASIS,+-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.+-- See the License for the specific language governing permissions and+-- limitations under the License.++-- | Rounded base-2 logarithms of 'Integral' and 'Real' types.++{-# LANGUAGE BangPatterns #-}+{-# LANGUAGE LambdaCase #-}+{-# LANGUAGE MagicHash #-}++module Numeric.Logarithms+ ( -- * Real Logarithms+ log2Floor, log2Ceiling+ -- ** Advanced+ , log2Approx, log2With+ -- * Integer Logarithms+ , ilog2Floor, ilog2Ceiling+ -- ** Advanced+ , ilog2Approx, ilog2With+ ) where++import Data.Bits (bit)+import Data.Ratio (denominator, numerator)+import GHC.Exts (Int(I#))+import GHC.Integer (shiftLInteger)+import GHC.Integer.Logarithms (integerLog2#)+import GHC.Stack (HasCallStack)++integerLog2Floor :: Integer -> Int+integerLog2Floor x = I# (integerLog2# x)++-- Derivation of log2 algorithms for Rational:+--+-- floor(log2(r))+-- = floor(log2(x/y)) with x, y the numerator and denominator of r.+-- = floor(log2((2^n * (1 + k/2^n)) / (2^m * (1 + j/2^m))))+-- with x = 2^n + k, k < 2^n, n an integer+-- y = 2^m + j, j < 2^m, m an integer+-- = floor(log2(2^n/2^m) + log2((1+k/2^n)/(1+j/2^m)))+-- = floor(n - m + log2((1+k/2^n)/(1+j/2^m)))+-- = n - m + floor(log2((1+k/2^n)/(1+j/2^m)))+-- = n - m + if (1+k/2^n) < (1+j/2^m) then -1 else 0+-- because 1+k/2^n and 1+j/2^m are both in [1, 2),+-- so their quotient is in (1/2, 2)+-- so log2 of their quotient is in (-1, 1)+-- so the floor of log2 of their quotient is -1 or 0:+-- -1 if the quotient is less than 1; 0 if the quotient is >= 1+-- = n - m + if k/2^n < j/2^m then -1 else 0+-- = n - m + if k*2^m < j*2^n then -1 else 0+-- = n - m + if (k<<m) < (j<<n) then -1 else 0+--+-- The same derivation holds for ceil(log2(r)) with adjustment values being 0+-- and 1 rather than -1 and 0, and the comparison being <= instead of <.++-- Returns a tuple @(e, num', den')@ s.t. @2^e * num' 'Data.Ratio.%' den' ==+-- num % den@, and @num' % den'@ in /(1\/2, 2)/ (exclusive at both bounds).+{-# INLINE splitLog2Unchecked #-}+splitLog2Unchecked :: Integer -> Integer -> (Int, Integer, Integer)+splitLog2Unchecked num den = (n - m, num', den')+ where+ n = integerLog2Floor num+ m = integerLog2Floor den+ -- Note: the Bits instance for Integer doesn't define unsafeShiftL or shiftL,+ -- so it defaults to testing the sign of the argument and dispatching to left+ -- or right shifts. So, we call what its definition should have been instead.+ shl x (I# s) = shiftLInteger x s+ (num', den') = if m > n+ then (num `shl` (m-n), den)+ else (num, den `shl` (n-m))++{-# INLINE log2Unchecked #-}+log2Unchecked :: Integer -> Integer -> (Int, Ordering)+log2Unchecked num den =+ let (lg, num', den') = splitLog2Unchecked num den+ in (lg, compare num' den')++-- The underscore-suffixed variants here are inlined versions so that GHC will+-- implement the exported functions by big chunks of optimized code, but not+-- try to include that code in the module interface.++{-# INLINE log2Approx_ #-}+log2Approx_ :: (HasCallStack, Real a) => a -> (Int, Ordering)+log2Approx_ x =+ let !xr = toRational x+ !num = numerator xr+ !den = denominator xr+ in if num <= 0+ then error "log2With_: x <= 0"+ else log2Unchecked num den++{-# INLINE log2With_ #-}+log2With_ :: (HasCallStack, Real a) => (Int -> Ordering -> Int) -> a -> Int+log2With_ adj x =+ let !(lg, cmp) = log2Approx_ x+ in adj lg cmp++-- | Returns an approximate base-2 logarithm of the argument.+--+-- The returned @Int@ is one of the two nearest integers to the exact result,+-- and the returned @Ordering@ tells whether the exact result is greater than,+-- equal to, or less than the @Int@. `LT` means the exact result is less than+-- the rounded result.+--+-- This effectively gives results like "between 7 and 8" and leaves it up to+-- the caller to decide how (or whether) to round the result. See also+-- `log2With` for a version that will always round, but leaves the particular+-- rounding strategy up to the caller.+log2Approx :: (HasCallStack, Real a) => a -> (Int, Ordering)+log2Approx = log2Approx_++-- | Returns the base-2 logarithm with custom rounding.+--+-- The first parameter is a rounding adjustment function: given the approximate+-- result and an 'Ordering' indicating its relation to the exact result, return+-- the rounded result.+--+-- This could be useful if you want something other than floor or ceil, e.g.+-- round-towards-0, round-towards-even, etc.+log2With :: (HasCallStack, Real a) => (Int -> Ordering -> Int) -> a -> Int+log2With = log2With_++-- | Returns the floor of the base-2 logarithm of a 'Real' argument.+log2Floor :: (HasCallStack, Real a) => a -> Int+log2Floor = log2With_ (\x -> \case LT -> x - 1; _ -> x)++-- | Returns the ceiling of the base-2 logarithm of a 'Real' argument.+log2Ceiling :: (HasCallStack, Real a) => a -> Int+log2Ceiling = log2With_ (\x -> \case GT -> x + 1; _ -> x)++{-# INLINE withPositiveInteger #-}+withPositiveInteger :: HasCallStack => (Integer -> r) -> Integer -> r+withPositiveInteger f x = if x <= 0+ then error "withPositiveInteger: x <= 0"+ else f x++-- | Returns the floor of the base-2 logarithm of an 'Integral' argument.+{-# INLINABLE ilog2Floor #-}+ilog2Floor :: (HasCallStack, Integral a) => a -> Int+ilog2Floor x = withPositiveInteger integerLog2Floor (toInteger x)++-- | Returns the ceiling of the base-2 logarithm of an 'Integral' argument.+{-# INLINABLE ilog2Ceiling #-}+ilog2Ceiling :: (HasCallStack, Integral a) => a -> Int+ilog2Ceiling = ilog2With (\x -> \case GT -> x + 1; _ -> x)++-- | Returns the approximate base-2 logarithm of an 'Integral' argument.+{-# INLINABLE ilog2Approx #-}+ilog2Approx :: (HasCallStack, Integral a) => a -> (Int, Ordering)+ilog2Approx x = withPositiveInteger+ (\xi ->+ let lg = integerLog2Floor xi+ in (lg, if xi > bit lg then GT else EQ))+ (toInteger x)++-- | Returns the base-2 logarithm of an 'Integral' with custom rounding.+{-# INLINABLE ilog2With #-}+ilog2With :: (HasCallStack, Integral a) => (Int -> Ordering -> Int) -> a -> Int+ilog2With adj x =+ let !(lg, cmp) = ilog2Approx x+ in adj lg cmp
+ test/LogarithmsTest.hs view
@@ -0,0 +1,108 @@+-- Copyright 2021 Google LLC+--+-- Licensed under the Apache License, Version 2.0 (the "License");+-- you may not use this file except in compliance with the License.+-- You may obtain a copy of the License at+--+-- http://www.apache.org/licenses/LICENSE-2.0+--+-- Unless required by applicable law or agreed to in writing, software+-- distributed under the License is distributed on an "AS IS" BASIS,+-- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.+-- See the License for the specific language governing permissions and+-- limitations under the License.++{-# LANGUAGE AllowAmbiguousTypes #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE TypeApplications #-}++module Main(main) where++import Test.Framework.Providers.QuickCheck2 (testProperty)+import Test.QuickCheck+ ( (===), (.&&.), Arbitrary(..), Property+ , forAll, suchThat, withMaxSuccess+ )++import Test.Framework(defaultMain)++import Numeric.Logarithms+ ( log2Floor, log2Ceiling, log2Approx+ , ilog2Floor, ilog2Ceiling+ )++exp2 :: Int -> Rational+exp2 x | x < 0 = recip (exp2 (-x))+exp2 x = 2 ^ x++prop_log2FloorCorrect :: forall a. (Arbitrary a, Real a, Show a) => Property+prop_log2FloorCorrect =+ withMaxSuccess 10000 $+ forAll (arbitrary @a `suchThat` (>0)) $ \x ->+ let xr = toRational x+ lg = log2Floor x+ lo = exp2 lg+ hi = exp2 (lg+1)+ in (lo <= xr) === True .&&. (xr < hi) === True++prop_log2CeilingCorrect :: forall a. (Arbitrary a, Real a, Show a) => Property+prop_log2CeilingCorrect =+ withMaxSuccess 10000 $+ forAll (arbitrary @a `suchThat` (>0)) $ \x ->+ let xr = toRational x+ lg = log2Ceiling x+ lo = exp2 (lg-1)+ hi = exp2 lg+ in (lo < xr) === True .&&. (xr <= hi) === True++prop_log2ApproxCorrect :: forall a. (Arbitrary a, Real a, Show a) => Property+prop_log2ApproxCorrect =+ withMaxSuccess 10000 $+ forAll (arbitrary @a `suchThat` (>0)) $ \x ->+ let xr = toRational x+ (lg, o) = log2Approx x+ lt = exp2 (lg-1)+ eq = exp2 lg+ gt = exp2 (lg+1)+ in case o of+ LT -> (lt < xr) === True .&&. (xr < eq) === True+ EQ -> xr === eq+ GT -> (eq < xr) === True .&&. (xr < gt) === True++prop_ilog2FloorAgrees :: forall a. (Arbitrary a, Integral a, Show a) => Property+prop_ilog2FloorAgrees =+ withMaxSuccess 10000 $+ forAll (arbitrary @a `suchThat` (>0)) $ \x ->+ ilog2Floor x === log2Floor x++prop_ilog2CeilingAgrees :: forall a. (Arbitrary a, Integral a, Show a) => Property+prop_ilog2CeilingAgrees =+ withMaxSuccess 10000 $+ forAll (arbitrary @a `suchThat` (>0)) $ \x ->+ ilog2Ceiling x === log2Ceiling x++main :: IO ()+main = defaultMain+ [ testProperty "log2Floor @Int" (prop_log2FloorCorrect @Int)+ , testProperty "log2Floor @Integer" (prop_log2FloorCorrect @Integer)+ , testProperty "log2Floor @Double" (prop_log2FloorCorrect @Double)+ , testProperty "log2Floor @Rational" (prop_log2FloorCorrect @Rational)++ , testProperty "log2Ceiling @Int" (prop_log2CeilingCorrect @Int)+ , testProperty "log2Ceiling @Integer" (prop_log2CeilingCorrect @Integer)+ , testProperty "log2Ceiling @Double" (prop_log2CeilingCorrect @Double)+ , testProperty "log2Ceiling @Rational" (prop_log2CeilingCorrect @Rational)++ , testProperty "log2Approx @Int" (prop_log2ApproxCorrect @Int)+ , testProperty "log2Approx @Integer" (prop_log2ApproxCorrect @Integer)+ , testProperty "log2Approx @Double" (prop_log2ApproxCorrect @Double)+ , testProperty "log2Approx @Rational" (prop_log2ApproxCorrect @Rational)++ , testProperty "ilog2Floor @Int" (prop_ilog2FloorAgrees @Int)+ , testProperty "ilog2Floor @Integer" (prop_ilog2FloorAgrees @Integer)+ , testProperty "ilog2Floor @Word" (prop_ilog2FloorAgrees @Word)++ , testProperty "ilog2Ceiling @Int" (prop_ilog2CeilingAgrees @Int)+ , testProperty "ilog2Ceiling @Integer" (prop_ilog2CeilingAgrees @Integer)+ , testProperty "ilog2Ceiling @Word" (prop_ilog2CeilingAgrees @Word)+ ]