1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
|
-- | Helpers for testing
module Tests.Helpers (
-- * helpers
T(..)
, typeName
, eq
, eqC
, (=~)
-- * Generic QC tests
, monotonicallyIncreases
, monotonicallyIncreasesIEEE
-- * HUnit helpers
, testAssertion
, testEquality
) where
import Data.Complex
import Data.Typeable
import qualified Numeric.IEEE as IEEE
import qualified Test.HUnit as HU
import Test.Framework
import Test.Framework.Providers.HUnit
import Numeric.MathFunctions.Constants
----------------------------------------------------------------
-- Helpers
----------------------------------------------------------------
-- | Phantom typed value used to select right instance in QC tests
data T a = T
-- | String representation of type name
typeName :: Typeable a => T a -> String
typeName = show . typeOf . typeParam
where
typeParam :: T a -> a
typeParam _ = undefined
-- | Approximate equality for 'Double'. Doesn't work well for numbers
-- which are almost zero.
eq :: Double -- ^ Relative error
-> Double -> Double -> Bool
eq eps a b
| a == 0 && b == 0 = True
| otherwise = abs (a - b) <= eps * max (abs a) (abs b)
-- | Approximate equality for 'Complex Double'
eqC :: Double -- ^ Relative error
-> Complex Double
-> Complex Double
-> Bool
eqC eps a@(ar :+ ai) b@(br :+ bi)
| a == 0 && b == 0 = True
| otherwise = abs (ar - br) <= eps * d
&& abs (ai - bi) <= eps * d
where
d = max (realPart $ abs a) (realPart $ abs b)
-- | Approximately equal up to 1 ulp
(=~) :: Double -> Double -> Bool
(=~) = eq m_epsilon
----------------------------------------------------------------
-- Generic QC
----------------------------------------------------------------
-- Check that function is nondecreasing
monotonicallyIncreases :: (Ord a, Ord b) => (a -> b) -> a -> a -> Bool
monotonicallyIncreases f x1 x2 = f (min x1 x2) <= f (max x1 x2)
-- Check that function is nondecreasing taking rounding errors into
-- account.
--
-- In fact funstion is allowed to decrease less than one ulp in order
-- to guard againist problems with excess precision. On x86 FPU works
-- with 80-bit numbers but doubles are 64-bit so rounding happens
-- whenever values are moved from registers to memory
monotonicallyIncreasesIEEE :: (Ord a, IEEE.IEEE b) => (a -> b) -> a -> a -> Bool
monotonicallyIncreasesIEEE f x1 x2 =
y1 <= y2 || (y1 - y2) < y2 * IEEE.epsilon
where
y1 = f (min x1 x2)
y2 = f (max x1 x2)
----------------------------------------------------------------
-- HUnit helpers
----------------------------------------------------------------
testAssertion :: String -> Bool -> Test
testAssertion str cont = testCase str $ HU.assertBool str cont
testEquality :: (Show a, Eq a) => String -> a -> a -> Test
testEquality msg a b = testCase msg $ HU.assertEqual msg a b
|
