Generating integers

[effectfully]

Previously we only needed to generate integers in comparisons, but now we have plenty of places where it would be useful to generate integers. I'm now getting test failures only with the F17 field, because the Arbitrary instance of Rational is just extremely unlikely to produce an integer at all:

arbitrarySizedFractional :: Fractional a => Gen a
arbitrarySizedFractional =
  sized $ \n ->
    let n' = toInteger n in
      do b <- choose (1, precision)
         a <- choose ((-n') * b, n' * b)
         return (fromRational (a % b))
 where
  precision = 9999999999999 :: Integer

instance Integral a => Arbitrary (Ratio a) where
  arbitrary = arbitrarySizedFractional

This begs to be resolved.

[effectfully]

Changed the field elements generator in 967a8b0 to

Field  -> frequency
    [ (2, fromIntegral <$> arbitrarySizedBoundedIntegral @Int)
    , (1, arbitrary)
    ]

Now we produce integer-valued field elements pretty often. Not sure why we didn't do this earlier.

[effectfully]

Made it

Field  -> frequency
    [ (1, fromIntegral <$> arbitrary @Int)
    , (1, fromIntegral <$> arbitrarySizedBoundedIntegral @Int)
    , (1, arbitrary)
    ]

in b02791e so that fairly small integers also get generated.

[effectfully]

Whenever we generate assert x < i we should also generate values for x less than i most of the time.