decimal-literals (empty) → 0.1.0.0
raw patch · 6 files changed
+990/−0 lines, 6 filesdep +basedep +decimal-literalsdep +tastysetup-changed
Dependencies added: base, decimal-literals, tasty, tasty-hunit
Files
- ChangeLog.md +5/−0
- LICENSE +674/−0
- Numeric/Literals/Decimal.hs +176/−0
- Setup.hs +2/−0
- decimal-literals.cabal +41/−0
- test/tasty/test.hs +92/−0
+ ChangeLog.md view
@@ -0,0 +1,5 @@+# Revision history for decimal-literals++## 0.1.0.0 -- YYYY-mm-dd++* First version. Released on an unsuspecting world.
+ LICENSE view
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+ Numeric/Literals/Decimal.hs view
@@ -0,0 +1,176 @@+-- |+-- Module : Numeric.Literals.Decimal+-- Copyright : (c) Justus Sagemüller 2017+-- License : GPL v3+-- +-- Maintainer : (@) jsagemue $ uni-koeln.de+-- Stability : experimental+-- Portability : portable+-- +{-# LANGUAGE PatternSynonyms, ViewPatterns #-}++module Numeric.Literals.Decimal+ ( FractionalLit+ , pattern (:%)+ , pattern Scientific+ -- * Auxiliary+ , B₁₀Digit+ ) where++import Data.Ratio+++-- | A type whose 'Fractional' instance gives a somewhat reliable indication whether+-- a value was actually defined as an integer or a ratio, or as a decimal-fraction+-- literal. This is useful to know for a type that supports both exact fraction+-- values and more floating-point-like / physical values; it allows avoiding+-- issues like @0.524@ showing up as @589971551185535/1125899906842624@, or conversely+-- @7/23@ as @0.30434782608695654@. Both of these scenarios are quite awkward.+data FractionalLit = ExactRatio Rational+ | DecimalFraction {+ decimalMantissa :: Integer+ , decimalExponent :: Int }++asFraction :: FractionalLit -> Maybe (Integer, Integer)+asFraction (ExactRatio r) = Just (numerator r, denominator r)+asFraction (DecimalFraction _ _) = Nothing++-- | Construct an exact fraction. The values behave like 'Rational', until combined+-- – e.g. added – with a 'Scientific' value (which has an implicit+-- measurement-uncertainty, and that carries over to the result).+pattern (:%) :: Integer -> Integer -> FractionalLit+pattern n:%d <- (asFraction -> Just (n,d))+ where n:%d = ExactRatio $ fromInteger n % fromInteger d++asScientific :: FractionalLit -> Maybe ((Int, [B₁₀Digit]), Int)+asScientific (ExactRatio _) = Nothing+asScientific n = case break (=='e') $ show n of+ (m, 'e':e) -> Just (splitMantissa m, read e)+ (m, []) -> Just (splitMantissa m, 0)+ where splitMantissa m = case break (=='.') m of+ (pm,'.':am) -> (read pm, parseB₁₀<$>am)+ (pm,[]) -> (read pm, [])+ parseB₁₀ c = case fromEnum c - fromEnum '0' of+ i | i>=0 && i<10 -> toEnum i+ | otherwise -> error $+ "Impossible digit "++[c]++" in number "++show n++-- | Construct a scientific number of the form @m.n * 10^e@, where @m@ and @e@ are+-- integers and @n@ is a list of digits after the decimal point. The result+-- is considered to be only exact up to the precision indicated by the number+-- of digits. I.e. @Scientific 2 [4,8,3]\ (-4)@ basically means @2.483×10⁻⁴ ± 10⁻⁷@,+-- +-- The 'Fractional' instance allows these values to be written in the standard+-- @2.483e-4@ notation. Note that this cannot completely reconstruct the written+-- form, e.g. @12.483e-4@ will actually show up as @Scientific 1 [2,4,8,3]\ (-3)@.+-- Leading and trailing zeroes are always ignored.+pattern Scientific :: Int -- ^ Integral part of the mantissa+ -> [B₁₀Digit] -- ^ Digits after the point of the mantissa+ -> Int -- ^ Base-10 exponent of the number in scientific form+ -> FractionalLit+pattern Scientific pc ac ex <- (asScientific -> Just ((pc,ac),ex))+ where Scientific pc ac ex = DecimalFraction (nqr (fromIntegral pc) ac) $ ex - length ac+ where nqr n [] = n+ nqr n (d:ds) = nqr (n*10 + fromIntegral (fromEnum d)) ds+ ++-- | A number between @0@ and @9@.+data B₁₀Digit = D0 | D1 | D2 | D3 | D4 | D5 | D6 | D7 | D8 | D9 deriving (Enum, Eq, Ord)+instance Show B₁₀Digit where show = show . fromEnum+instance Num B₁₀Digit where+ fromInteger = toEnum . (`mod`10) . fromInteger+ d + e = toEnum $ (fromEnum d + fromEnum e)`mod`10+ d * e = toEnum $ (fromEnum d * fromEnum e)`mod`10+ d - e = toEnum $ (fromEnum d - fromEnum e)`mod`10+ abs = id+ signum D0 = 0+ signum _ = 1++instance Eq FractionalLit where+ ExactRatio r₀ == ExactRatio r₁ = r₀==r₁+ DecimalFraction m₀ e₀ == DecimalFraction m₁ e₁ = m₀==m₁ && e₀==e₁+ ExactRatio r == DecimalFraction m e+ | e>0 = ExactRatio r == DecimalFraction (m*10^e) 0+ | (ers,0) <- (10^(-e)) `divMod` denominator r+ = m == numerator r*ers+ | otherwise = False+ n == m = m == n++instance Show FractionalLit where+ showsPrec p (ExactRatio r)+ | denominator r > 1 = showParen (p>6)+ $ showsPrec 7 (numerator r) . ('/':) . showsPrec 7 (denominator r)+ | otherwise = shows $ numerator r+ showsPrec p (DecimalFraction m e)+ | m < 0 = showParen (p>5) $ ('-':) . shows (DecimalFraction (-m) e)+ | e > 4 || e < -2 = case show m of+ lsh | e<0, length lsh + 1 > -e+ -> case splitAt (-e) $ reverse lsh of+ (acs, []) -> ("0."++) . (replicate (-e-length acs) '0'++)+ . (reverse acs++)+ (acs, pcs) -> (reverse pcs++) . ('.':) . (reverse acs++)+ (hd:[]) -> (hd:) . ("e"++) . shows e+ (hd:lds) -> (hd:) . ('.':) . (lds++) . ("e"++) . shows (e + length lds)+ | e < 0 = case splitAt (-e) . reverse $ show m of+ (acs, []) -> ("0."++) . (replicate (-e-length acs) '0'++) . (reverse acs++)+ (acs, pcs) -> (reverse pcs++) . ('.':) . (reverse acs++)+ | otherwise = shows m . (replicate e '0'++)++infixl 7 `unbiasedDiv`+unbiasedDiv :: Integral a => a -> a -> a+unbiasedDiv x y = (x + y`quot`2)`div`y++instance Num FractionalLit where+ fromInteger = ExactRatio . fromInteger+ ExactRatio r₀ + ExactRatio r₁ = ExactRatio $ r₀ + r₁+ DecimalFraction m e + ExactRatio r+ = DecimalFraction (m + round (r * 10^^(-e))) e+ DecimalFraction m₀ e₀ + DecimalFraction m₁ e₁+ | e₀ <= e₁ = DecimalFraction (m₀`unbiasedDiv`10^(e₁ - e₀) + m₁) e₁+ n + m = m + n+ ExactRatio r₀ * ExactRatio r₁ = ExactRatio $ r₀ * r₁+ DecimalFraction m e * ExactRatio r+ = DecimalFraction ((m * numerator r)`unbiasedDiv`denominator r) e+ DecimalFraction m₀ e₀ * DecimalFraction m₁ e₁+ = DecimalFraction (m₀*m₁) (e₀+e₁)+ n * m = m * n+ negate (ExactRatio r) = ExactRatio $ -r+ negate (DecimalFraction m e) = DecimalFraction (-m) e+ abs (ExactRatio r) = ExactRatio $ abs r+ abs (DecimalFraction m e) = DecimalFraction (abs m) e+ signum (ExactRatio r) = ExactRatio $ signum r+ signum (DecimalFraction m e) = ExactRatio . fromIntegral $ signum m++-- | Despite the name, 'fromRational' should /not/ be used to promote a 'Rational'+-- value to 'FractionalLit', because that method contains the heuristic which interprets+-- decimal\/scientific literals (which in Haskell are, perhaps unfortunately, always+-- desugared through 'fromRational'). Use '/' or ':%' instead, to define exact-ratio+-- values.+instance Fractional FractionalLit where+ fromRational r+ | r < 0 = negate $ fromRational (-r)+ | denominator r == 1 = goI 0 0 $ numerator r+ | otherwise = goF 0 0 $ denominator r+ where goI n2 n5 u+ | (u', 0) <- u`divMod`2 = goI (n2+1) n5 u'+ | (u', 0) <- u`divMod`5 = goI n2 (n5+1) u'+ | n2 > 3 && n5 > n2 = DecimalFraction (u*5^(n5-n2)) n2+ | n5 > 3 && n2 >= n5 = DecimalFraction (u*2^(n2-n5)) n5+ | otherwise = ExactRatio r+ goF 0 0 1 = ExactRatio r+ goF n2 n5 1+ | n2>n5 = DecimalFraction (numerator r*5^(n2-n5)) (-n2)+ | otherwise = DecimalFraction (numerator r*2^(n5-n2)) (-n5)+ goF n2 n5 d+ | (d', 0) <- d`divMod`2 = goF (n2+1) n5 d'+ | (d', 0) <- d`divMod`5 = goF n2 (n5+1) d'+ | otherwise = ExactRatio r+ ExactRatio r₀ / ExactRatio r₁ = ExactRatio $ r₀ / r₁+ DecimalFraction m e / ExactRatio r+ = DecimalFraction ((m * denominator r)`unbiasedDiv`numerator r) e+ ExactRatio r / DecimalFraction m e+ = DecimalFraction (round $ r * 10^dp / fromIntegral m) (-dp-e)+ where dp = ceiling . logBase 10 $ fromIntegral m+ DecimalFraction m₀ e₀ / DecimalFraction m₁ e₁+ = DecimalFraction ((m₀*10^dp)`unbiasedDiv`m₁) (e₀-e₁-dp)+ where dp = ceiling . logBase 10 $ fromIntegral m₁
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ decimal-literals.cabal view
@@ -0,0 +1,41 @@+-- Initial decimal-literals.cabal generated by cabal init. For further +-- documentation, see http://haskell.org/cabal/users-guide/++name: decimal-literals+version: 0.1.0.0+synopsis: Preprocessing decimal literals more or less as they are (instead of via fractions)+-- description: +license: GPL-3+license-file: LICENSE+author: Justus Sagemüller+maintainer: (@) jsagemue $ uni-koeln.de+homepage: https://github.com/leftaroundabout/decimal-literals+-- copyright: +category: Math+build-type: Simple+extra-source-files: ChangeLog.md+cabal-version: >=1.10++library+ exposed-modules: Numeric.Literals.Decimal+ -- other-modules: + -- other-extensions: + build-depends: base >=4.10 && <4.11+ -- hs-source-dirs: + default-language: Haskell2010++test-suite test+ default-language:+ Haskell2010+ type:+ exitcode-stdio-1.0+ hs-source-dirs:+ test/tasty+ main-is:+ test.hs+ build-depends:+ base >= 4 && < 5+ , tasty >= 0.7+ , tasty-hunit+ , decimal-literals+
+ test/tasty/test.hs view
@@ -0,0 +1,92 @@+-- |+-- Module : Main+-- Copyright : (c) Justus Sagemüller 2017+-- License : GPL v3+-- +-- Maintainer : (@) sagemueller $ geo.uni-koeln.de+-- Stability : experimental+-- Portability : portable+-- ++module Main where++import Numeric.Literals.Decimal++import Test.Tasty+import Test.Tasty.HUnit++++main = defaultMain tests+++reshowTest :: FractionalLit -> String -> TestTree+reshowTest n str = reshowTestCase str n str++reshowTestCase :: String -> FractionalLit -> String -> TestTree+reshowTestCase info n str = testCase info $ show n @?= str++scientificTest :: FractionalLit -> ((Int, String), Int) -> TestTree+scientificTest l ((pc,ac),e) = testCase (show pc++'.':ac++"×10^"++show e) $ case l of+ Scientific pc' ac' e' | pc'==pc && ac==(show=<<ac') && e'==e+ -> return ()+ | otherwise+ -> assertFailure $ "Got "++show pc'++'.':(show=<<ac')+ ++ "×10^"++show e'+ _ -> assertFailure "Got exact fraction"+ ++tests :: TestTree+tests = testGroup "Tests"+ [ testGroup "Re-showing literals"+ [ reshowTest 4 "4"+ , reshowTest 142125 "142125"+ , reshowTest 125.278 "125.278"+ , reshowTest 0.2 "0.2"+ , reshowTest 0.04 "0.04"+ , reshowTest 0.008 "8e-3"+ , reshowTest 1e-52 "1e-52"+ , reshowTest 3.11e9 "3.11e9"+ , reshowTest 1.167925373e-12 "1.167925373e-12"+ , reshowTest 0.254 "0.254"+ , reshowTest (-1.167925373e-12) "-1.167925373e-12"+ , reshowTest (-142125) "-142125"+ ]+ , testGroup "Simple arithmetic"+ [ reshowTestCase "37 + 15" (37 + 15) "52"+ , reshowTestCase "37 + 15.8" (37 + 15.8) "52.8"+ , reshowTestCase "37.1 + 15.8" (37.1 + 15.8) "52.9"+ , reshowTestCase "3.11e-13 + 15" (3.11e-13 + 15) "15.000000000000311"+ , reshowTestCase "3.11e9 + 15" -- the 15 is insignificant here!+ (3.11e9 + 15) "3.11e9"+ , reshowTestCase "3.11e6 + 15" -- it's insignificant here too, but we'd still rather+ -- not discard it when showing the zeroes anyway.+ (3.11e6 + 15)--3110015+ "3110000"+ , reshowTestCase "37 * 15" (37 * 15) "555"+ , reshowTestCase "37 * 15.8" (37 * 15.8) "584.6"+ , reshowTestCase "37.1 * 15.8" (37.1 * 15.8) "586.18"+ , reshowTestCase "3.11e-13 * 15" (3.11e-13 * 15) "4.665e-12"+ , reshowTestCase "3.11e9 * 15" (3.11e9 * 15) "4.665e10"+ , reshowTestCase "abs $ -1.167925373e-12" (abs $ -1.167925373e-12) "1.167925373e-12"+ , reshowTestCase "abs $ -142125" (abs $ -142125) "142125"+ , reshowTestCase "37 / 15" (37 / 15) "37/15"+ , reshowTestCase "37 / 15.8" (37 / 15.8) "2.34"+ , reshowTestCase "37.1 / 15.8" (37.1 / 15.8) "2.348"+ , reshowTestCase "3.11e-13 / 15" (3.11e-13 / 15) "2.1e-14"+ , reshowTestCase "3.11e9 / 15" (3.11e9 / 15) "2.1e8"+ ]+ , testGroup "Scientific deconstruction"+ [ scientificTest 0.2537 ((0,"2537"),0)+ , scientificTest 1.12e-17 ((1,"12"),-17)+ , scientificTest 1.12e17 ((1,"12"),17)+ , scientificTest 12.412 ((12,"412"),0)+ , scientificTest (-12.4) ((-12,"4"),0)+ , scientificTest 2.483e-4 ((2,"483"),-4)+ , scientificTest 12.483e-4 ((1,"2483"),-3)+ , scientificTest 257.35e7 ((2,"5735"),9)+ ]+ ]+++