| Copyright | (c) 2019 2021 Composewell Technologies |
|---|---|
| License | BSD-3-Clause |
| Maintainer | streamly@composewell.com |
| Stability | experimental |
| Portability | GHC |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
Streamly.Internal.Data.Unfold.Enumeration
Description
The functions defined in this module should be rarely needed for direct use,
try to use the operations from the Enumerable type class
instances instead.
This module provides an Enumerable type class to enumerate Enum types
into a stream. The operations in this type class correspond to similar
operations in the Enum type class, the only difference is that they produce
a stream instead of a list. These operations cannot be defined generically
based on the Enum type class. We provide instances for commonly used
types. If instances for other types are needed convenience functions defined
in this module can be used to define them. Alternatively, these functions
can be used directly.
Synopsis
- class Enum a => Enumerable a where
- enumerateFrom :: Monad m => Unfold m a a
- enumerateFromTo :: Monad m => Unfold m (a, a) a
- enumerateFromThen :: Monad m => Unfold m (a, a) a
- enumerateFromThenTo :: Monad m => Unfold m (a, a, a) a
- enumerateFromStepNum :: (Monad m, Num a) => Unfold m (a, a) a
- enumerateFromNum :: (Monad m, Num a) => Unfold m a a
- enumerateFromThenNum :: (Monad m, Num a) => Unfold m (a, a) a
- enumerateFromStepIntegral :: (Monad m, Integral a) => Unfold m (a, a) a
- enumerateFromIntegral :: (Monad m, Integral a) => Unfold m a a
- enumerateFromThenIntegral :: (Monad m, Integral a) => Unfold m (a, a) a
- enumerateFromToIntegral :: (Monad m, Integral a) => Unfold m (a, a) a
- enumerateFromThenToIntegral :: (Monad m, Integral a) => Unfold m (a, a, a) a
- enumerateFromIntegralBounded :: (Monad m, Integral a, Bounded a) => Unfold m a a
- enumerateFromThenIntegralBounded :: (Monad m, Integral a, Bounded a) => Unfold m (a, a) a
- enumerateFromToIntegralBounded :: (Monad m, Integral a, Bounded a) => Unfold m (a, a) a
- enumerateFromThenToIntegralBounded :: (Monad m, Integral a, Bounded a) => Unfold m (a, a, a) a
- enumerateFromSmallBounded :: (Monad m, Enum a, Bounded a) => Unfold m a a
- enumerateFromThenSmallBounded :: forall m a. (Monad m, Enum a, Bounded a) => Unfold m (a, a) a
- enumerateFromToSmall :: (Monad m, Enum a) => Unfold m (a, a) a
- enumerateFromThenToSmall :: (Monad m, Enum a) => Unfold m (a, a, a) a
- enumerateFromFractional :: (Monad m, Fractional a) => Unfold m a a
- enumerateFromThenFractional :: (Monad m, Fractional a) => Unfold m (a, a) a
- enumerateFromToFractional :: (Monad m, Fractional a, Ord a) => Unfold m (a, a) a
- enumerateFromThenToFractional :: (Monad m, Fractional a, Ord a) => Unfold m (a, a, a) a
Documentation
class Enum a => Enumerable a where Source #
Types that can be enumerated as a stream. The operations in this type
class are equivalent to those in the Enum type class, except that these
generate a stream instead of a list. Use the functions in
Streamly.Internal.Data.Unfold.Enumeration module to define new instances.
Pre-release
Methods
enumerateFrom :: Monad m => Unfold m a a Source #
Unfolds from generating a stream starting with the element
from, enumerating up to maxBound when the type is Bounded or
generating an infinite stream when the type is not Bounded.
>>>import qualified Streamly.Data.Stream as Stream>>>import qualified Streamly.Internal.Data.Unfold as Unfold
>>> Stream.fold Fold.toList $ Stream.take 4 $ Stream.unfold Unfold.enumerateFrom (0 :: Int) [0,1,2,3]
For Fractional types, enumeration is numerically stable. However, no
overflow or underflow checks are performed.
>>> Stream.fold Fold.toList $ Stream.take 4 $ Stream.unfold Unfold.enumerateFrom 1.1 [1.1,2.1,3.1,4.1]
Pre-release
enumerateFromTo :: Monad m => Unfold m (a, a) a Source #
Unfolds (from, to) generating a finite stream starting with the element
from, enumerating the type up to the value to. If to is smaller than
from then an empty stream is returned.
>>>import qualified Streamly.Data.Stream as Stream>>>import qualified Streamly.Internal.Data.Unfold as Unfold
>>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromTo (0, 4) [0,1,2,3,4]
For Fractional types, the last element is equal to the specified to
value after rounding to the nearest integral value.
>>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromTo (1.1, 4) [1.1,2.1,3.1,4.1] >>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromTo (1.1, 4.6) [1.1,2.1,3.1,4.1,5.1]
Pre-release
enumerateFromThen :: Monad m => Unfold m (a, a) a Source #
Unfolds (from, then) generating a stream whose first element is
from and the successive elements are in increments of then. Enumeration
can occur downwards or upwards depending on whether then comes before or
after from. For Bounded types the stream ends when maxBound is
reached, for unbounded types it keeps enumerating infinitely.
>>>import qualified Streamly.Data.Stream as Stream>>>import qualified Streamly.Internal.Data.Unfold as Unfold
>>> Stream.fold Fold.toList $ Stream.take 4 $ Stream.unfold Unfold.enumerateFromThen (0, 2) [0,2,4,6] >>> Stream.fold Fold.toList $ Stream.take 4 $ Stream.unfold Unfold.enumerateFromThen (0,(-2)) [0,-2,-4,-6]
Pre-release
enumerateFromThenTo :: Monad m => Unfold m (a, a, a) a Source #
Unfolds (from, then, to) generating a finite stream whose first element
is from and the successive elements are in increments of then up to
to. Enumeration can occur downwards or upwards depending on whether then
comes before or after from.
>>>import qualified Streamly.Data.Stream as Stream>>>import qualified Streamly.Internal.Data.Unfold as Unfold
>>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromThenTo (0, 2, 6) [0,2,4,6] >>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromThenTo (0, (-2), (-6)) [0,-2,-4,-6]
Pre-release
Instances
Enumerating Num Types
enumerateFromStepNum :: (Monad m, Num a) => Unfold m (a, a) a Source #
Unfolds (from, stride) generating an infinite stream starting from
from and incrementing every time by stride. For Bounded types, after
the value overflows it keeps enumerating in a cycle:
>>> Stream.fold Fold.toList $ Stream.take 10 $ Stream.unfold Unfold.enumerateFromStepNum (255::Word8,1) [255,0,1,2,3,4,5,6,7,8]
The implementation is numerically stable for floating point values.
Note enumerateFromStepIntegral is faster for integrals.
Internal
enumerateFromNum :: (Monad m, Num a) => Unfold m a a Source #
Same as enumerateFromStepNum using a stride of 1:
>>> enumerateFromNum = lmap (from -> (from, 1)) Unfold.enumerateFromStepNum >>> Stream.fold Fold.toList $ Stream.take 6 $ Stream.unfold enumerateFromNum (0.9) [0.9,1.9,2.9,3.9,4.9,5.9]
Also, same as enumerateFromThenNum using a stride of 1 but see the note in
enumerateFromThenNum about the loss of precision:
>>> enumerateFromNum = lmap (from -> (from, from + 1)) Unfold.enumerateFromThenNum >>> Stream.fold Fold.toList $ Stream.take 6 $ Stream.unfold enumerateFromNum (0.9) [0.9,1.9,2.9,3.8999999999999995,4.8999999999999995,5.8999999999999995]
Internal
enumerateFromThenNum :: (Monad m, Num a) => Unfold m (a, a) a Source #
Same as 'enumerateFromStepNum (from, next)' using a stride of next - from:
>>> enumerateFromThenNum = lmap ((from, next) -> (from, next - from)) Unfold.enumerateFromStepNum
Example: @ >>> Stream.fold Fold.toList $ Stream.take 10 $ Stream.unfold enumerateFromThenNum (255::Word8,0) [255,0,1,2,3,4,5,6,7,8]
The implementation is numerically stable for floating point values.
Note that enumerateFromThenIntegral is faster for integrals.
Note that in the strange world of floating point numbers, using
enumerateFromThenNum (from, from + 1) is almost exactly the same as
enumerateFromStepNum (from, 1) but not precisely the same. Because (from +
1) - from is not exactly 1, it may lose some precision, the loss may also
be aggregated in each step, if you want that precision then use
enumerateFromStepNum instead.
Internal
Enumerating unbounded Integral Types
enumerateFromStepIntegral :: (Monad m, Integral a) => Unfold m (a, a) a Source #
Can be used to enumerate unbounded integrals. This does not check for overflow or underflow for bounded integrals.
Internal
Enumerating Bounded Integral Types
enumerateFromThenToIntegralBounded :: (Monad m, Integral a, Bounded a) => Unfold m (a, a, a) a Source #
Enumerating small Integral Types
Small types are always bounded.
enumerateFromSmallBounded :: (Monad m, Enum a, Bounded a) => Unfold m a a Source #
Enumerate from given starting Enum value from with stride of 1 till
maxBound
Internal
enumerateFromThenSmallBounded :: forall m a. (Monad m, Enum a, Bounded a) => Unfold m (a, a) a Source #
Enumerate from given starting Enum value from and next Enum value next
with stride of (fromEnum next - fromEnum from) till maxBound.
Internal
enumerateFromToSmall :: (Monad m, Enum a) => Unfold m (a, a) a Source #
Enumerate from given starting Enum value from and to Enum value to
with stride of 1 till to value.
Internal
enumerateFromThenToSmall :: (Monad m, Enum a) => Unfold m (a, a, a) a Source #
Enumerate from given starting Enum value from and then Enum value next
and to Enum value to with stride of (fromEnum next - fromEnum from)
till to value.
Internal
Enumerating Fractional Types
Enumeration of Num specialized to Fractional types.
enumerateFromFractional :: (Monad m, Fractional a) => Unfold m a a Source #
enumerateFromThenFractional :: (Monad m, Fractional a) => Unfold m (a, a) a Source #
enumerateFromToFractional :: (Monad m, Fractional a, Ord a) => Unfold m (a, a) a Source #
Same as enumerateFromStepNum with a step of 1 and enumerating up to the
specified upper limit rounded to the nearest integral value:
>>> Stream.fold Fold.toList $ Stream.unfold Unfold.enumerateFromToFractional (0.1, 6.3) [0.1,1.1,2.1,3.1,4.1,5.1,6.1]
Internal
enumerateFromThenToFractional :: (Monad m, Fractional a, Ord a) => Unfold m (a, a, a) a Source #