2 - Copyright (C) 2009-2010 Nick Bowler.
4 - License BSD2: 2-clause BSD license. See LICENSE for full terms.
5 - This is free software: you are free to change and redistribute it.
6 - There is NO WARRANTY, to the extent permitted by law.
9 -- | Generic classes for floating point types. The interface is loosely based
10 -- off of the C math library.
11 module Data
.Floating
.Classes
where
13 import Prelude
hiding (Floating
(..), RealFloat
(..), RealFrac
(..), Ord
(..))
17 -- | Classification of floating point values.
18 data FPClassification
= FPInfinite | FPNaN | FPNormal | FPSubNormal | FPZero
19 deriving (Show, Read, Eq
, Enum
, Bounded
)
21 -- | Class for types which can be rounded to integers. The rounding functions
22 -- in the Prelude are inadequate for floating point because they shoehorn their
23 -- results into an integral type.
25 -- Minimal complete definition: 'toIntegral' and 'round'.
26 class (Fractional a
, Poset a
) => Roundable a
where
27 -- | Discards the fractional component from a value. Results in 'Nothing'
28 -- if the result cannot be represented as an integer, such as if the input
29 -- is infinite or NaN.
30 toIntegral
:: Integral b
=> a
-> Maybe b
38 |
otherwise = round $ x
- fromRational (1%2
)
41 |
otherwise = round $ x
+ fromRational (1%2
)
47 -- | Class for floating point types (real or complex-valued).
49 -- Minimal complete definition: everything.
50 class Fractional a
=> Floating a
where
68 -- | Class for real-valued floating point types.
70 -- Minimal complete definition: all except 'pi', 'infinity', 'epsilon' and
72 class Floating a
=> RealFloat a
where
73 -- | Fused multiply-add.
74 fma
:: a
-> a
-> a
-> a
75 -- | @copysign x y@ computes a value with the magnitude of @x@ but the sign
77 copysign
:: a
-> a
-> a
78 -- | @nextafter x y@ computes the next representable value after @x@ in the
80 nextafter
:: a
-> a
-> a
81 -- | @atan2 y x@ computes the principal value of the arctangent of @y/x@.
82 -- The signs of the input determine the quadrant of the result.
84 -- | @fmod x y@ computes @x - n*y@, where @n@ is the integral quotient of
85 -- @x/y@, rounded towards zero.
87 -- | @frem x y@ computes @x - n*y@, where @n@ is the integral quotient of
88 -- @x/y@, rounded to the nearest integer, with halfway values rounded to
91 -- | Euclidean distance function without undue overflow.
95 -- | Base-2 exponential function.
97 -- | Computes @exp x - 1@ without undue cancellation.
99 -- | Base-10 logarithm function.
101 -- | Computes @log (x + 1)@ without undue cancellation.
103 -- | Base-2 logarithm function.
107 -- | Complementary error function.
111 -- | Log gamma function.
113 -- | Round to the nearest integer according to the current rounding
114 -- direction. The default rounding direction is towards the nearest
115 -- integer with halfway values rounded to even. If the resulting value
116 -- differs from the input, the 'Inexact' exception is raised.
118 -- | Same as 'rint', except that the 'Inexact' exception is not raised.
127 epsilon
= nextafter
1 infinity
- 1
130 -- | Class for the basic floating point types.
131 class (Roundable a
, RealFloat a
) => PrimFloat a
where
132 -- | Radix of significand digits.
133 floatRadix :: Num b
=> a
-> b
134 -- | Number of digits in the significand.
135 floatPrecision
:: Num b
=> a
-> b
136 -- | Minimum and maximum integers, respectively, such that the radix raised
137 -- to one less than that power is representable as a normalized, finite
138 -- floating point number.
139 floatRange :: Num b
=> a
-> (b
, b
)
140 classify
:: a
-> FPClassification
141 -- | Extracts the exponent of a floating point value. If the value is
142 -- subnormal, the result is as if the value were normalized.
144 -- | Scales a floating point value by an integral power of the radix.
145 scalb
:: Integral b
=> a
-> b
-> a