import Data.Maybe

cao_20_7_4 = (*1.15)
kg_to_lb = (*2.2)
ft_to_metre = (*0.3048)
litre_to_kg_avgas = (*0.72)
taxi_fuel_kg = 5
modrem x d = fromInteger (x `mod` d) / fromInteger d

-- Calculate pressure altitude

isatemp = 15
isapressure = 1013.25
pressure_altitude ele qnh = max 0 (fromIntegral ele + (isapressure - fromIntegral qnh) * 30)
declared_temp da = isatemp - da / 500

-- Find the 4 numbers to interpolate
--     nw     ne
--     sw     se
-- Calculate the proportion of the temperature to interpolate (0 >= temp_prop <= 1)
-- Calculate the proportion of the pressure altutide to interpolate (0 >= pa_prop <= 1)

data DistanceRequired =
  DistanceRequired {
    distance_required_ft
      :: Double
  , distance_required_ft_cao20_7_4
      :: Double
  , distance_required_metre
      :: Double
  , distance_required_metre_cao20_7_4
      :: Double
 } deriving (Eq, Show)

f <<$>> DistanceRequired nw sw ne se =
  DistanceRequired (f nw) (f sw) (f ne) (f se)

eachDistanceRequired f (DistanceRequired nw1 sw1 ne1 se1) (DistanceRequired nw2 sw2 ne2 se2) =
  DistanceRequired (f nw1 nw2) (f sw1 sw2) (f ne1 ne2) (f se1 se2)

distanceRequired1 x =
  DistanceRequired x (cao_20_7_4 x) (ft_to_metre x) (cao_20_7_4 (ft_to_metre x))

grass gr clear50ft =
  let gr' = (*1.45) <<$>> gr
      t = eachDistanceRequired (+) (eachDistanceRequired (-) clear50ft gr) gr'
  in  (gr', t)

interpolate ::
  Double
  -> Double
  -> Double
  -> Double
  -> Double
  -> Double
  -> DistanceRequired
interpolate nw sw ne se da temp =
  let temp_prop = modrem (round temp) 10
      interpolate' a b prop = (a-b)*prop+b
      interpolate_temp a b = interpolate' a b temp_prop
      result = interpolate' (interpolate_temp se sw) (interpolate_temp ne nw) (modrem (round da) 1000)
  in distanceRequired1 result

data Check a =
  Check a a
  deriving (Eq, Ord, Show)

(===) ::
  a
  -> a
  -> Check a
(===) =
  Check

infixl 4 ===

v ::
  Check a
  -> a
v (Check a _) =
  a

check ::
  (Show a, Eq a) =>
  Check a
  -> Maybe String
check (Check a1 a2) =
  if a1 == a2
    then Nothing
    else Just (concat [show a1, " /= ", show a2])

----

---- YBAF

ybaf_declared_density = 1450 -- ft (winter)
ybaf_ele = 65 -- ft
ybaf_declared_density_height = ybaf_declared_density + ybaf_ele === 1515
ybaf_declared_temp = declared_temp (v ybaf_declared_density_height) === 11.97
ybaf_interpolate nw sw ne se = interpolate nw sw ne se (v ybaf_declared_density_height) (v ybaf_declared_temp)

---- YSPE

yspe_declared_density = 1450 -- ft (winter)
yspe_ele = 2934 -- ft
yspe_declared_density_height = yspe_declared_density + yspe_ele === 4384
yspe_declared_temp = declared_temp (v yspe_declared_density_height) === 6.231999999999999
yspe_interpolate nw sw ne se = interpolate nw sw ne se (v yspe_declared_density_height) (v yspe_declared_temp)

----

-- TODR YBAF
-- *2550lb*

todr_ybaf_groundroll = ybaf_interpolate 1010 1110 1090 1195 ===
  DistanceRequired {
    distance_required_ft = 1078.015
  , distance_required_ft_cao20_7_4 = 1239.71725
  , distance_required_metre = 328.578972
  , distance_required_metre_cao20_7_4 = 377.8658178
  }

todr_ybaf_50ft = ybaf_interpolate 1720 1890 1850 2035 ===
  DistanceRequired {
    distance_required_ft = 1835.095
  , distance_required_ft_cao20_7_4 = 2110.35925
  , distance_required_metre = 559.336956
  , distance_required_metre_cao20_7_4 = 643.2374993999999
  }

-- LDR YSPE
-- *2550lb*

ldr_yspe_groundroll = yspe_interpolate 630 655 655 680 ===
  DistanceRequired {
    distance_required_ft = 654.6
  , distance_required_ft_cao20_7_4 = 752.79
  , distance_required_metre = 199.52208000000002
  , distance_required_metre_cao20_7_4 = 229.450392
  }

ldr_yspe_50ft = yspe_interpolate 1425 1460 1460 1500 ===
  DistanceRequired {
    distance_required_ft = 1460.592
  , distance_required_ft_cao20_7_4 = 1679.6808
  , distance_required_metre = 445.18844160000003
  , distance_required_metre_cao20_7_4 = 511.96670784
  }

-- TODR YSPE
-- *2550lb*

todr_yspe_groundroll = yspe_interpolate 1235 1355 1215 1335 ===
  DistanceRequired {
    distance_required_ft = 1269.08
  , distance_required_ft_cao20_7_4 = 1459.4419999999998
  , distance_required_metre = 386.815584
  , distance_required_metre_cao20_7_4 = 444.83792159999996
  }

todr_yspe_50ft = yspe_interpolate 2120 2345 2295 2545 ===
  DistanceRequired {
    distance_required_ft = 2317.16
  , distance_required_ft_cao20_7_4 = 2664.7339999999995
  , distance_required_metre = 706.270368
  , distance_required_metre_cao20_7_4 = 812.2109231999999
  }

-- LDR YBAF
-- *2550lb*

ldr_ybaf_groundroll = ybaf_interpolate 585 610 605 630 ===
  DistanceRequired {
    distance_required_ft = 601.875
  , distance_required_ft_cao20_7_4 = 692.15625
  , distance_required_metre = 183.4515
  , distance_required_metre_cao20_7_4 = 210.969225
  }

ldr_ybaf_50ft = ybaf_interpolate 1350 1385 1385 1420 ===
  DistanceRequired {
    distance_required_ft = 1375.025
  , distance_required_ft_cao20_7_4 = 1581.27875
  , distance_required_metre = 419.10762000000005
  , distance_required_metre_cao20_7_4 = 481.973763
  }


----

ybaf_checks =
  [
    ybaf_declared_density_height
  , ybaf_declared_temp
  ]

yspe_checks =
  [
    yspe_declared_density_height
  , yspe_declared_temp
  ]

todr_ybaf_checks =
  [
    todr_ybaf_groundroll
  , todr_ybaf_50ft
  ]

ldr_yspe_checks =
  [
    ldr_yspe_groundroll
  , ldr_yspe_50ft
  ]

todr_yspe_checks =
  [
    todr_yspe_groundroll
  , todr_yspe_50ft
  ]

ldr_ybaf_checks =
  [
    ldr_ybaf_groundroll
  , ldr_ybaf_50ft
  ]

checks =
  concat
    [
      ybaf_checks
    , yspe_checks
    ]

todr_checks =
  concat
    [
      todr_ybaf_checks
    , todr_yspe_checks
    ]

ldr_checks =
  concat
    [
      ldr_ybaf_checks
    , ldr_yspe_checks
    ]

all_checks =
  map check checks ++
  map check todr_checks ++
  map check ldr_checks

failed_checks =
  catMaybes all_checks