git.iko.soy/rowtype-yoga/purescript-fixed-precision
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commit3b7fd8dfd3ee3e653f0bc6bd40df552ef15de12c authorPhil Freeman <paf31@cantab.net> dateFri 16 Feb 2018, 13:46 (9 years ago)
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.gitignore+9 LICENSE+201 README.md+14 bower.json+17 package.json+14 src/Data/Fixed.purs+273
.gitignorenew file+9
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1+/bower_components/
2+/node_modules/
3+/.pulp-cache/
4+/output/
5+/generated-docs/
6+/.psc-package/
7+/.psc*
8+/.purs*
9+/.psa*
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README.mdnew file+14
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1+# purescript-fixed-precision
2+
3+This package implements a data type for fixed precision arithmetic,
4+where precision is tracked in the types.
5+
6+- [Module Documentation](generated-docs/Data/Fixed.md)
7+
8+## Getting Started
9+
10+You can install this package using Bower:
11+
12+```
13+bower install git@github.com:lumihq/purescript-fixed-precision.git
14+```
bower.jsonnew file+17
@@ -0,0 +1,17 @@
1+{
2+ "name": "purescript-fixed-precision",
3+ "ignore": [
4+ "**/.*",
5+ "node_modules",
6+ "bower_components",
7+ "output"
8+ ],
9+ "dependencies": {
10+ "purescript-integers": "^3.2.0",
11+ "purescript-maybe": "^3.0.0",
12+ "purescript-bigints": "^3.4.0"
13+ },
14+ "devDependencies": {
15+ "purescript-psci-support": "^3.0.0"
16+ }
17+}
package.jsonnew file+14
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1+{
2+ "name": "purescript-fixed-precision",
3+ "version": "1.0.0",
4+ "description": "",
5+ "dependencies": {
6+ "big-integer": "^1.6.26"
7+ },
8+ "devDependencies": {},
9+ "repository": {
10+ "type": "git",
11+ "url": "git+https://github.com/lumihq/purescript-fixed-precision.git"
12+ },
13+ "license": "Apache-2.0"
14+}
src/Data/Fixed.pursnew file+273
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1+-- | This module defines a numeric type `Fixed` for working with
2+-- | fixed point numbers in base 10. The precision is tracked in
3+-- | the types.
4+
5+module Data.Fixed
6+ ( Fixed
7+ , fromInt
8+ , fromNumber
9+ , toNumber
10+ , numerator
11+ , floor
12+ , ceil
13+ , round
14+ , kind Precision
15+ , One
16+ , TenTimes
17+ , P1
18+ , P10
19+ , P100
20+ , P1000
21+ , P10000
22+ , P100000
23+ , P1000000
24+ , PProxy(..)
25+ , class KnownPrecision
26+ , reflectPrecision
27+ , reifyPrecision
28+ ) where
29+
30+import Prelude
31+import Data.BigInt as BigInt
32+import Data.Int as Int
33+import Data.Maybe (Maybe(..))
34+
35+-- | A kind for type-level precision information
36+foreign import kind Precision
37+
38+-- | No decimal places
39+foreign import data One :: Precision
40+
41+-- | One more decimal place
42+foreign import data TenTimes :: Precision -> Precision
43+
44+type P1 = One
45+
46+-- | One decimal place
47+type P10 = TenTimes P1
48+
49+-- | Two decimal places
50+type P100 = TenTimes P10
51+
52+-- | Three decimal places
53+type P1000 = TenTimes P100
54+
55+-- | Four decimal places
56+type P10000 = TenTimes P1000
57+
58+-- | Five decimal places
59+type P100000 = TenTimes P10000
60+
61+-- | Six decimal places
62+type P1000000 = TenTimes P100000
63+
64+-- | A value-level proxy for a type-level precision.
65+data PProxy (precision :: Precision) = PProxy
66+
67+-- | Precision which is known, i.e. it can be reflected to a
68+-- | value at runtime, given a `PProxy`.
69+-- |
70+-- | `reflectPrecision` returns a multiple of ten, corresponding
71+-- | to the maximum number of decimal places which can be stored.
72+class KnownPrecision (precision :: Precision) where
73+ reflectPrecision :: PProxy precision -> Int
74+
75+instance knownPrecisionOne :: KnownPrecision One where
76+ reflectPrecision _ = 1
77+
78+instance knownPrecisionTenTimes :: KnownPrecision p => KnownPrecision (TenTimes p) where
79+ reflectPrecision _ = 10 * reflectPrecision (PProxy :: PProxy p)
80+
81+-- | Reify an non-negative integer (a power of ten) as a `Precision`.
82+-- |
83+-- | For example
84+-- |
85+-- | ```
86+-- | > reifyPrecision 0 reflectPrecision
87+-- | Just 1
88+-- | > reifyPrecision 1 reflectPrecision
89+-- | Just 10
90+-- | > reifyPrecision 2 reflectPrecision
91+-- | Just 100
92+-- | > reifyPrecision (-1) reflectPrecision
93+-- | Nothing
94+-- | ```
95+reifyPrecision :: forall r. Int -> (forall precision. KnownPrecision precision => PProxy precision -> r) -> Maybe r
96+reifyPrecision n _ | n < 0 = Nothing
97+reifyPrecision 0 f = Just (f (PProxy :: PProxy One))
98+reifyPrecision n f = reifyPrecision (n - 1) (f <<< liftTenTimes) where
99+ liftTenTimes :: forall precision. PProxy precision -> PProxy (TenTimes precision)
100+ liftTenTimes _ = PProxy
101+
102+-- | A fixed point representation of a real number, with the specified precision.
103+-- |
104+-- | A value is multiplied by the precision, truncated and stored as a big
105+-- | integer. That is, we approximate the number by numerator/10^precision, storing
106+-- | only the numerator, and carrying the precision around as type information.
107+-- |
108+-- | The `Semiring` and associated instances allow us to perform basic arithmetic
109+-- | operations.
110+newtype Fixed (precision :: Precision) = Fixed BigInt.BigInt
111+
112+-- | Extract the numerator from the representation of the number as a fraction.
113+-- |
114+-- | ```
115+-- | > numerator (fromNumber 0.1234 :: Fixed P1000)
116+-- | fromString "123"
117+-- |
118+-- | > numerator (fromNumber 0.1239 :: Fixed P1000)
119+-- | fromString "123"
120+-- | ```
121+numerator :: forall precision. Fixed precision -> BigInt.BigInt
122+numerator (Fixed n) = n
123+
124+denominator :: forall precision. KnownPrecision precision => Fixed precision -> Int
125+denominator _ = reflectPrecision (PProxy :: PProxy precision)
126+
127+-- | Create a `Fixed` representation of an `Int`.
128+fromInt
129+ :: forall precision
130+ . KnownPrecision precision
131+ => Int
132+ -> Fixed precision
133+fromInt i = Fixed (BigInt.fromInt i * BigInt.fromInt (reflectPrecision (PProxy :: PProxy precision)))
134+
135+-- | Approximate a `Number` as a `Fixed` value with the specified precision.
136+-- |
137+-- | ```
138+-- | > fromNumber 0.1234 :: Fixed P10000
139+-- | fromNumber 0.1234 :: P100
140+-- |
141+-- | > fromNumber 0.1234 :: Fixed P100
142+-- | fromNumber 0.12 :: P100
143+-- | ```
144+fromNumber
145+ :: forall precision
146+ . KnownPrecision precision
147+ => Number
148+ -> Fixed precision
149+fromNumber n = Fixed (BigInt.fromNumber (n * Int.toNumber (reflectPrecision (PProxy :: PProxy precision))))
150+
151+-- | Convert a `Fixed` value to a `Number`.
152+-- |
153+-- | _Note_: Overflow is possible here if the numerator is sufficiently large.
154+toNumber
155+ :: forall precision
156+ . KnownPrecision precision
157+ => Fixed precision
158+ -> Number
159+toNumber f = BigInt.toNumber (numerator f) / Int.toNumber (denominator f)
160+
161+-- | Calculate the largest whole number smaller than or equal to the provided
162+-- | value.
163+-- |
164+-- | ```
165+-- | > floor $ fromNumber 0.1 :: Fixed P10
166+-- | fromNumber 0.0 :: P10
167+-- |
168+-- | > floor $ fromNumber 1.0 :: Fixed P10
169+-- | fromNumber 1.0 :: P10
170+-- |
171+-- | > floor $ fromNumber (-0.1) :: Fixed P10
172+-- | fromNumber (-1.0) :: P10
173+-- | ```
174+floor
175+ :: forall precision
176+ . KnownPrecision precision
177+ => Fixed precision
178+ -> Fixed precision
179+floor n = Fixed (numerator n - x) where
180+ d = BigInt.fromInt (denominator n)
181+ m = numerator n `mod` d
182+ x | m < zero = m + d
183+ | otherwise = m
184+
185+-- | Calculate the smallest whole number greater than or equal to the provided
186+-- | value.
187+-- |
188+-- | ```
189+-- | > ceil $ fromNumber 0.1 :: Fixed P10
190+-- | fromNumber 1.0 :: P10
191+-- |
192+-- | > ceil $ fromNumber 1.0 :: Fixed P10
193+-- | fromNumber 1.0 :: P10
194+-- |
195+-- | > ceil $ fromNumber (-0.1) :: Fixed P10
196+-- | fromNumber 0.0 :: P10
197+-- | ```
198+ceil
199+ :: forall precision
200+ . KnownPrecision precision
201+ => Fixed precision
202+ -> Fixed precision
203+ceil n = Fixed (numerator n + x) where
204+ d = BigInt.fromInt (denominator n)
205+ m = numerator n `mod` d
206+ x | m == zero = zero
207+ | m < zero = -m
208+ | otherwise = d - m
209+
210+-- | Round the specified value to the nearest whole number.
211+-- |
212+-- | ```
213+-- | > round $ fromNumber 0.1 :: Fixed P10
214+-- | fromNumber 0.0 :: P10
215+-- |
216+-- | > round $ fromNumber 0.9 :: Fixed P10
217+-- | fromNumber 1.0 :: P10
218+-- |
219+-- | > round $ fromNumber 0.5 :: Fixed P10
220+-- | fromNumber 1.0 :: P10
221+-- |
222+-- | > round $ fromNumber (-0.1) :: Fixed P10
223+-- | fromNumber 0.0 :: P10
224+-- | ```
225+round
226+ :: forall precision
227+ . KnownPrecision precision
228+ => Fixed precision
229+ -> Fixed precision
230+round n = Fixed (numerator n + x) where
231+ d = BigInt.fromInt (denominator n)
232+ m = numerator n `mod` d
233+ x | m < zero && (m + d) * BigInt.fromInt 2 >= d = -m
234+ | m * BigInt.fromInt 2 >= d = d - m
235+ | otherwise = -m
236+
237+instance showFixed :: KnownPrecision precision => Show (Fixed precision) where
238+ show n =
239+ "(fromNumber "
240+ <> show (toNumber n)
241+ <> " :: P"
242+ <> show (reflectPrecision (PProxy :: PProxy precision))
243+ <> ")"
244+
245+instance eqFixed :: Eq (Fixed precision) where
246+ eq (Fixed n) (Fixed m) = eq n m
247+
248+instance ordFixed :: Ord (Fixed precision) where
249+ compare (Fixed n) (Fixed m) = compare n m
250+
251+instance semiringFixed :: KnownPrecision precision => Semiring (Fixed precision) where
252+ zero = Fixed zero
253+ add (Fixed n) (Fixed m) = Fixed (n + m)
254+ one = Fixed (BigInt.fromInt (reflectPrecision (PProxy :: PProxy precision)))
255+ mul a b = Fixed (numerator a * numerator b / BigInt.fromInt (denominator a))
256+
257+instance ringFixed :: KnownPrecision precision => Ring (Fixed precision) where
258+ sub (Fixed n) (Fixed m) = Fixed (n - m)
259+
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+
273+instance commutativeRingFixed :: KnownPrecision precision => CommutativeRing (Fixed precision)