add regression tests for extra floating point functions

tests/Regression.hs

@@ -3,6 +3,7 @@
 
 module Main (main) where
 
+import Numeric
 import qualified Numeric.AD.Mode.Forward as F
 import qualified Numeric.AD.Mode.Forward.Double as FD
 import qualified Numeric.AD.Mode.Reverse as R
@@ -30,7 +31,11 @@ tests = testGroup "tests" [
   mode "reverse-double" (\ f -> RD.diff' f) (\ f -> RD.grad f) (\ f -> RD.jacobian f) (\ f -> RD.hessian f)]
 
 mode :: String -> Diff' -> Grad -> Jacobian -> Hessian -> TestTree
-mode name diff grad jacobian hessian = testGroup name [basic diff grad jacobian hessian, issue97 diff, issue104 diff grad]
+mode name diff grad jacobian hessian = testGroup name [
+  basic diff grad jacobian hessian,
+  issue97 diff,
+  issue104 diff grad,
+  issue108 diff]
 
 basic :: Diff' -> Grad -> Jacobian -> Hessian -> TestTree
 basic diff grad jacobian hessian = testGroup "basic" [tdiff, tgrad, tjacobian, thessian] where
@@ -92,6 +97,42 @@ issue104 diff grad = testGroup "issue-104" [inside, outside] where
     f x y = sqrt x * sqrt y -- grad f [x, y] = [sqrt y / 2 sqrt x, sqrt x / 2 sqrt y]
   binary f [x, y] = f x y
 
+issue108 :: Diff' -> TestTree
+issue108 diff = testGroup "issue-108" [tlog1p, texpm1, tlog1pexp, tlog1mexp] where
+  tlog1p = testCase "log1p" $ do
+    equal (-inf, inf) $ diff log1p (-1)
+    equal (-1.0000000000000007e-15, 1.000000000000001) $ diff log1p (-1e-15)
+    equal (-1e-20, 1) $ diff log1p (-1e-20)
+    equal (0, 1) $ diff log1p 0
+    equal (1e-20, 1) $ diff log1p 1e-20
+    equal (9.999999999999995e-16, 0.9999999999999989) $ diff log1p 1e-15
+    equal (0.6931471805599453, 0.5) $ diff log1p 1
+  texpm1 = testCase "expm1" $ do
+    equal (-0.6321205588285577, 0.36787944117144233) $ diff expm1 (-1)
+    equal (-9.999999999999995e-16, 0.999999999999999) $ diff expm1 (-1e-15)
+    equal (-1e-20, 1) $ diff expm1 (-1e-20)
+    equal (0, 1) $ diff expm1 0
+    equal (1e-20, 1) $ diff expm1 1e-20
+    equal (1.0000000000000007e-15, 1.000000000000001) $ diff expm1 1e-15
+    equal (1.718281828459045, 2.718281828459045) $ diff expm1 1
+  tlog1pexp = testCase "log1pexp" $ do
+    equal (0, 0) $ diff log1pexp (-1000)
+    equal (3.720075976020836e-44, 3.7200759760208356e-44) $ diff log1pexp (-100)
+    equal (0.31326168751822286, 0.2689414213699951) $ diff log1pexp (-1)
+    equal (0.6931471805599453, 0.5) $ diff log1pexp 0
+    equal (1.3132616875182228, 0.7310585786300049) $ diff log1pexp 1
+    equal (100, 1) $ diff log1pexp 100
+    equal (1000, 1) $ diff log1pexp 1000
+  tlog1mexp = testCase "log1mexp" $ do
+    equal (-0, -0) $ diff log1mexp (-1000)
+    equal (-3.720075976020836e-44, -3.7200759760208356e-44) $ diff log1mexp (-100)
+    equal (-0.45867514538708193, -0.5819767068693265) $ diff log1mexp (-1)
+    equal (-0.9327521295671886, -1.5414940825367982) $ diff log1mexp (-0.5)
+    equal (-2.3521684610440907, -9.50833194477505) $ diff log1mexp (-0.1)
+    equal (-34.538776394910684, -9.999999999999994e14) $ diff log1mexp (-1e-15)
+    equal (-46.051701859880914, -1e20) $ diff log1mexp (-1e-20)
+  equal = expect $ \ (a, b) (c, d) -> eq a c && eq b d
+
 -- TODO: ideally, we would consider `0` and `-0` to be different
 --       however, zero signedness is currently not reliably propagated through some modes
 --       see also https://github.com/ekmett/ad/issues/109 and https://github.com/ekmett/ad/pull/110