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Convert between a signed integral and the corresponding ZigZag encoded unsigned integral (e.g. between Int8 and Word8 or Integral and Natural).

Allow conversion only between compatible types, invalid conversions produce a type error:

zigZag (-1::Int64) :: Word32
...
... Couldn't match type ...
...

>>> zigZag (0::Int8)
0

>>> zigZag (-1::Int16)
1

>>> zigZag (1::Int32)
2

>>> zigZag (-2::Int16)
3

>>> zigZag (-50::Integer)
99

>>> zigZag (50::Integer)
100

>>> zigZag (64::Integer)
128

>>> zigZag (-256::Integer)
511

>>> zigZag (256::Integer)
512

>>> map zigZag [-3..3::Integer]
[5,3,1,0,2,4,6]

>>> map zagZig [0..6::Word8]
[0,-1,1,-2,2,-3,3]

\(f::Integer) -> zagZig (zigZag f) == f

+++ OK, passed 100 tests.

\(f::Natural) -> zigZag (zagZig f) == f

+++ OK, passed 100 tests.

\(f::Int8) -> zagZig (zigZag f) == f

+++ OK, passed 100 tests.

\(f::Word8) -> zigZag (zagZig f) == f

+++ OK, passed 100 tests.

\(s::Int8) -> zigZag s == fromIntegral (zigZag (fromIntegral s :: Integer))

+++ OK, passed 100 tests.

\(u::Word8) -> zagZig u == fromIntegral (zagZig (fromIntegral u :: Natural))

+++ OK, passed 100 tests.

\(f::Int64) -> zagZig (zigZag f) == f

+++ OK, passed 100 tests.

\(f::Word64) -> zigZag (zagZig f) == f

+++ OK, passed 100 tests.

\(s::Int64) -> zigZag s == fromIntegral (zigZag (fromIntegral s :: Integer))

+++ OK, passed 100 tests.

\(u::Word64) -> zagZig u == fromIntegral (zagZig (fromIntegral u :: Natural))

+++ OK, passed 100 tests.