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Bug in Data.Numbers.CReal inverse sin and cos functions #4

Closed selinger closed 10 years ago

selinger commented 11 years ago

The implementation of asin(x) is not correct for x <= -0.5. The range should be between -pi/2 and pi/2. To reproduce:

Prelude Data.Number.CReal> asin (-0.4) :: CReal -0.4115168460674880193847378976173356048557 Prelude Data.Number.CReal> asin (-0.5) :: CReal -2.6179938779914943653855361527329190701643 Prelude Data.Number.CReal> asin (-0.6) :: CReal -2.4980915447965088516598341545545211284225

Note in particular the discontinuity at x=-0.5. Compare:

Prelude Data.Number.CReal> asin (-0.4) :: Double -0.41151684606748806 Prelude Data.Number.CReal> asin (-0.5) :: Double -0.5235987755982989 Prelude Data.Number.CReal> asin (-0.6) :: Double -0.6435011087932844

To fix: replace the line

        {- x0 <  0 -}   atan (s/x) - pi / 2

by

        {- x0 <  0 -}   - atan (s/x) - pi / 2

Note: this also affects acos(x), but only because it is defined in terms of asin(x). Changing the above line will fix both functions.