46090bd · rowtype-yoga/purescript-fixed-precision

git.iko.soy/rowtype-yoga/purescript-fixed-precision

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Remove the EuclideanRing instance, add approxDiv instead

46090bdPhil Freeman9 years ago

generated-docs/Data/Fixed.md+21−1

compare with main

unifiedsplit

@@ -26,7 +26,6 @@ Eq (Fixed precision)

26Ord (Fixed precision)

27(KnownPrecision precision) => Semiring (Fixed precision)

28(KnownPrecision precision) => Ring (Fixed precision)

29−(KnownPrecision precision) => EuclideanRing (Fixed precision)

30(KnownPrecision precision) => CommutativeRing (Fixed precision)

29(KnownPrecision precision) => CommutativeRing (Fixed precision)

31```

30```

@@ -142,6 +141,27 @@ fromNumber 1.0 :: P10

142fromNumber 0.0 :: P10

141fromNumber 0.0 :: P10

143```

142```

144

143

144+#### `approxDiv`

145+

146+``` purescript

147+approxDiv :: forall precision. KnownPrecision precision => Fixed precision -> Fixed precision -> Fixed precision

148+```

149+

150+Approximate division of fixed-precision numbers.

151+

152+```

153+> fromNumber 22.0 `approxDiv` fromNumber 7.0 :: Fixed P100

154+fromNumber 3.14 :: P100

155+```

156+

157+_Note_: `Fixed` is not a `EuclideanRing` in general - it is not even

158+an integral domain, since it has non-zero zero-divisors:

159+

160+```

161+> fromNumber 0.1 * fromNumber 0.1 :: Fixed P10

162+fromNumber 0.0 :: P10

163+```

164+

145#### `Precision`

165#### `Precision`

146

166

147``` purescript

167``` purescript

src/Data/Fixed.purs+27−13

@@ -11,6 +11,7 @@ module Data.Fixed

11 , floor

12 , ceil

13 , round

14+ , approxDiv

14 , kind Precision

15 , kind Precision

15 , One

16 , One

16 , TenTimes

17 , TenTimes

@@ -234,6 +235,32 @@ round n = Fixed (numerator n + x) where

234 | m * BigInt.fromInt 2 >= d = d - m

235 | m * BigInt.fromInt 2 >= d = d - m

235 | otherwise = -m

236 | otherwise = -m

236

237

238+-- | Approximate division of fixed-precision numbers.

239+-- |

240+-- | ```

241+-- | > fromNumber 22.0 `approxDiv` fromNumber 7.0 :: Fixed P100

242+-- | fromNumber 3.14 :: P100

243+-- | ```

244+-- |

245+-- | _Note_: `Fixed` is not a `EuclideanRing` in general - it is not even

246+-- | an integral domain, since it has non-zero zero-divisors:

247+-- |

248+-- | ```

249+-- | > fromNumber 0.1 * fromNumber 0.1 :: Fixed P10

250+-- | fromNumber 0.0 :: P10

251+-- | ```

252+approxDiv

253+ :: forall precision

254+ . KnownPrecision precision

255+ => Fixed precision

256+ -> Fixed precision

257+ -> Fixed precision

258+approxDiv a b = Fixed (x * n / y)

259+ where

260+ x = numerator a

261+ y = numerator b

262+ n = BigInt.fromInt (denominator a)

263+

237instance showFixed :: KnownPrecision precision => Show (Fixed precision) where

264instance showFixed :: KnownPrecision precision => Show (Fixed precision) where

238 show n =

265 show n =

239 "(fromNumber "

266 "(fromNumber "

@@ -257,17 +284,4 @@ instance semiringFixed :: KnownPrecision precision => Semiring (Fixed precision)

257instance ringFixed :: KnownPrecision precision => Ring (Fixed precision) where

284instance ringFixed :: KnownPrecision precision => Ring (Fixed precision) where

258 sub (Fixed n) (Fixed m) = Fixed (n - m)

285 sub (Fixed n) (Fixed m) = Fixed (n - m)

259

286

260−instance euclideanRingFixed :: KnownPrecision precision => EuclideanRing (Fixed precision) where

261− div a b = Fixed (x * n / y)

262− where

263− x = numerator a

264− y = numerator b

265− n = BigInt.fromInt (denominator a)

266− mod a b = Fixed (((x * n) `mod` y) / n)

267− where

268− x = numerator a

269− y = numerator b

270− n = BigInt.fromInt (denominator a)

271− degree = degree <<< numerator

272−

273instance commutativeRingFixed :: KnownPrecision precision => CommutativeRing (Fixed precision)

287instance commutativeRingFixed :: KnownPrecision precision => CommutativeRing (Fixed precision)