1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
|
{-# OPTIONS -fno-implicit-prelude #-}
-----------------------------------------------------------------------------
-- |
-- Module : Numeric
-- Copyright : (c) The University of Glasgow 2002
-- License : BSD-style (see the file libraries/base/LICENSE)
--
-- Maintainer : libraries@haskell.org
-- Stability : provisional
-- Portability : portable
--
-- Odds and ends, mostly functions for reading and showing
-- 'RealFloat'-like kind of values.
--
-----------------------------------------------------------------------------
module Numeric (
-- * Showing
showSigned, -- :: (Real a) => (a -> ShowS) -> Int -> a -> ShowS
showIntAtBase, -- :: Integral a => a -> (a -> Char) -> a -> ShowS
showInt, -- :: Integral a => a -> ShowS
showHex, -- :: Integral a => a -> ShowS
showOct, -- :: Integral a => a -> ShowS
showEFloat, -- :: (RealFloat a) => Maybe Int -> a -> ShowS
showFFloat, -- :: (RealFloat a) => Maybe Int -> a -> ShowS
showGFloat, -- :: (RealFloat a) => Maybe Int -> a -> ShowS
showFloat, -- :: (RealFloat a) => a -> ShowS
floatToDigits, -- :: (RealFloat a) => Integer -> a -> ([Int], Int)
-- * Reading
-- | /NB:/ 'readInt' is the \'dual\' of 'showIntAtBase',
-- and 'readDec' is the \`dual\' of 'showInt'.
-- The inconsistent naming is a historical accident.
readSigned, -- :: (Real a) => ReadS a -> ReadS a
readInt, -- :: (Integral a) => a -> (Char -> Bool)
-- -> (Char -> Int) -> ReadS a
readDec, -- :: (Integral a) => ReadS a
readOct, -- :: (Integral a) => ReadS a
readHex, -- :: (Integral a) => ReadS a
readFloat, -- :: (RealFloat a) => ReadS a
lexDigits, -- :: ReadS String
-- * Miscellaneous
fromRat, -- :: (RealFloat a) => Rational -> a
) where
#ifdef __GLASGOW_HASKELL__
import GHC.Base
import GHC.Read
import GHC.Real
import GHC.Float
import GHC.Num
import GHC.Show
import Data.Maybe
import Text.ParserCombinators.ReadP( ReadP, readP_to_S, pfail )
import qualified Text.Read.Lex as L
#else
import Data.Char
#endif
#ifdef __HUGS__
import Hugs.Prelude
import Hugs.Numeric
#endif
#ifdef __GLASGOW_HASKELL__
-- -----------------------------------------------------------------------------
-- Reading
-- | Reads an /unsigned/ 'Integral' value in an arbitrary base.
readInt :: Num a
=> a -- ^ the base
-> (Char -> Bool) -- ^ a predicate distinguishing valid digits in this base
-> (Char -> Int) -- ^ a function converting a valid digit character to an 'Int'
-> ReadS a
readInt base isDigit valDigit = readP_to_S (L.readIntP base isDigit valDigit)
-- | Read an unsigned number in octal notation.
readOct :: Num a => ReadS a
readOct = readP_to_S L.readOctP
-- | Read an unsigned number in decimal notation.
readDec :: Num a => ReadS a
readDec = readP_to_S L.readDecP
-- | Read an unsigned number in hexadecimal notation.
-- Both upper or lower case letters are allowed.
readHex :: Num a => ReadS a
readHex = readP_to_S L.readHexP
-- | Reads an /unsigned/ 'RealFrac' value,
-- expressed in decimal scientific notation.
readFloat :: RealFrac a => ReadS a
readFloat = readP_to_S readFloatP
readFloatP :: RealFrac a => ReadP a
readFloatP =
do tok <- L.lex
case tok of
L.Rat y -> return (fromRational y)
L.Int i -> return (fromInteger i)
other -> pfail
-- It's turgid to have readSigned work using list comprehensions,
-- but it's specified as a ReadS to ReadS transformer
-- With a bit of luck no one will use it.
-- | Reads a /signed/ 'Real' value, given a reader for an unsigned value.
readSigned :: (Real a) => ReadS a -> ReadS a
readSigned readPos = readParen False read'
where read' r = read'' r ++
(do
("-",s) <- lex r
(x,t) <- read'' s
return (-x,t))
read'' r = do
(str,s) <- lex r
(n,"") <- readPos str
return (n,s)
-- -----------------------------------------------------------------------------
-- Showing
-- | Show /non-negative/ 'Integral' numbers in base 10.
showInt :: Integral a => a -> ShowS
showInt n cs
| n < 0 = error "Numeric.showInt: can't show negative numbers"
| otherwise = go n cs
where
go n cs
| n < 10 = case unsafeChr (ord '0' + fromIntegral n) of
c@(C# _) -> c:cs
| otherwise = case unsafeChr (ord '0' + fromIntegral r) of
c@(C# _) -> go q (c:cs)
where
(q,r) = n `quotRem` 10
-- Controlling the format and precision of floats. The code that
-- implements the formatting itself is in @PrelNum@ to avoid
-- mutual module deps.
{-# SPECIALIZE showEFloat ::
Maybe Int -> Float -> ShowS,
Maybe Int -> Double -> ShowS #-}
{-# SPECIALIZE showFFloat ::
Maybe Int -> Float -> ShowS,
Maybe Int -> Double -> ShowS #-}
{-# SPECIALIZE showGFloat ::
Maybe Int -> Float -> ShowS,
Maybe Int -> Double -> ShowS #-}
-- | Show a signed 'RealFloat' value
-- using scientific (exponential) notation (e.g. @2.45e2@, @1.5e-3@).
--
-- In the call @'showEFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
showEFloat :: (RealFloat a) => Maybe Int -> a -> ShowS
-- | Show a signed 'RealFloat' value
-- using standard decimal notation (e.g. @245000@, @0.0015@).
--
-- In the call @'showFFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
showFFloat :: (RealFloat a) => Maybe Int -> a -> ShowS
-- | Show a signed 'RealFloat' value
-- using standard decimal notation for arguments whose absolute value lies
-- between @0.1@ and @9,999,999@, and scientific notation otherwise.
--
-- In the call @'showGFloat' digs val@, if @digs@ is 'Nothing',
-- the value is shown to full precision; if @digs@ is @'Just' d@,
-- then at most @d@ digits after the decimal point are shown.
showGFloat :: (RealFloat a) => Maybe Int -> a -> ShowS
showEFloat d x = showString (formatRealFloat FFExponent d x)
showFFloat d x = showString (formatRealFloat FFFixed d x)
showGFloat d x = showString (formatRealFloat FFGeneric d x)
#endif /* __GLASGOW_HASKELL__ */
-- ---------------------------------------------------------------------------
-- Integer printing functions
-- | Shows a /non-negative/ 'Integral' number using the base specified by the
-- first argument, and the character representation specified by the second.
showIntAtBase :: Integral a => a -> (Int -> Char) -> a -> ShowS
showIntAtBase base toChr n r
| base <= 1 = error ("Numeric.showIntAtBase: applied to unsupported base " ++ show base)
| n < 0 = error ("Numeric.showIntAtBase: applied to negative number " ++ show n)
| otherwise = showIt (quotRem n base) r
where
showIt (n,d) r = seq c $ -- stricter than necessary
case n of
0 -> r'
_ -> showIt (quotRem n base) r'
where
c = toChr (fromIntegral d)
r' = c : r
-- | Show /non-negative/ 'Integral' numbers in base 16.
showHex :: Integral a => a -> ShowS
showHex = showIntAtBase 16 intToDigit
-- | Show /non-negative/ 'Integral' numbers in base 8.
showOct :: Integral a => a -> ShowS
showOct = showIntAtBase 8 intToDigit
|
