# Converting numbers

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Converting between numerical types in haskell must be done explicitly, this is unlike languages like C which automatically cast between numerical types in certain situations.

# 1 Integral types

Integral types are ones which may only contain whole numbers and not fractions such as
Int
and
Integer
in the standard haskell libraries. The workhorse is
fromIntegral
which will convert any integral type into another.

*
toRational
*
fromRational

# 3 Going back and forth

*
toRational

## 3.2 Rational to Integral

this is inherently a lossy transformation since integral types cannot express non-whole numbers. depending on how you wish to convert, you might choose one of several methods.

*
ceiling
*
floor
*
truncate
*
round

# 4 original

hi i am trying to write some funs that convert between two coordinate systems. the first coordinate system, which ill call coord1, starts in the upper left at (0, 0) and ends in the lower right at (500, 500). coords in coord1 have type (Int, Int). the second coord system, which ill call coord2, starts in the lower left at (0.0, 0.0) and ends in the upper right at (1.0, 1.0). coords in coord2 have type (Float, Float). i was hoping someone could help me figure out how i can rewrite the two funs below so that the type checker will accept them.

``` coord1ToCoord2 :: (Int, Int) -> (Float, Float)
coord1ToCoord2 (x, y) = (x/500, (500-y)/500)

coord2ToCoord1 :: (Float, Float) -> (Int, Int)
coord2ToCoord1 (x, y) = (500/(1/x), 500 - 500/(1/y))```

examples of what i want. i think i have the logic right :)

``` coord1ToCoord2 (0, 0) -> (0.0, 1.0)
coord1ToCoord2 (250, 250) -> (0.5, 0.5)
coord1ToCoord2 (350, 350) -> (0.7, 0.3)
coord1ToCoord2 (500, 500) -> (1.0, 0.0)

coord2ToCoord1 (0.0, 0.0) -> (0, 500)
coord2ToCoord1 (0.5, 0.5) -> (250, 250)
coord2ToCoord1 (0.7, 0.7) -> (350, 150)
coord2ToCoord1 (1.0, 1.0) -> (500, 0)```

ah. i realize what is messing me up.

when i saw an expression like

` 500 * 0.2`

i had assumed that 500 :: Integer because it didnt end in a .0. but it actually has type Double. so my problem was i would do something like this

` (toInteger (500 :: Int)) * 0.2`

which of course the typechecker wouldnt accept. now that i have rid myself of my incorrect assumptions i see that i should be writing

` (fromRational (toRational (500 :: Int)) * 0.2) :: Float`

now that i have a better understanding i am able to write my funs. thank you for your help :)