{-# LINE 1 "src/Data/Number/Flint/Support/D/Extras/FFI.hsc" #-} {-| module : Data.Number.Flint.Support.D.Extras.FFI copyright : (c) 2022 Hartmut Monien license : GNU GPL, version 2 or above (see LICENSE) maintainer : hmonien@uni-bonn.de -} module Data.Number.Flint.Support.D.Extras.FFI ( -- * Support functions for double arithmetic -- * Random functions d_randtest , d_randtest_signed , d_randtest_special -- * Arithmetic , d_polyval -- * Special functions , d_lambertw , d_is_nan , d_log2 ) where -- Support functions for double arithmetic ------------------------------------- import Foreign.Ptr import Foreign.C.Types import Data.Number.Flint.Flint -- Random functions ------------------------------------------------------------ -- | /d_randtest/ /state/ -- -- Returns a random number in the interval \([0.5, 1)\). foreign import ccall "double_extras.h d_randtest" d_randtest :: Ptr CFRandState -> IO CDouble -- | /d_randtest_signed/ /state/ /minexp/ /maxexp/ -- -- Returns a random signed number with exponent between @minexp@ and -- @maxexp@ or zero. foreign import ccall "double_extras.h d_randtest_signed" d_randtest_signed :: Ptr CFRandState -> CLong -> CLong -> IO CDouble -- | /d_randtest_special/ /state/ /minexp/ /maxexp/ -- -- Returns a random signed number with exponent between @minexp@ and -- @maxexp@, zero, @D_NAN@ or \(\pm\)@D_INF@. foreign import ccall "double_extras.h d_randtest_special" d_randtest_special :: Ptr CFRandState -> CLong -> CLong -> IO CDouble -- Arithmetic ------------------------------------------------------------------ -- | /d_polyval/ /poly/ /len/ /x/ -- -- Uses Horner\'s rule to evaluate the polynomial defined by the given -- @len@ coefficients. Requires that @len@ is nonzero. foreign import ccall "double_extras.h d_polyval" d_polyval :: Ptr CDouble -> CInt -> CDouble -> IO CDouble -- Special functions ----------------------------------------------------------- -- | /d_lambertw/ /x/ -- -- Computes the principal branch of the Lambert W function, solving the -- equation \(x = W(x) \exp(W(x))\). If \(x < -1/e\), the solution is -- complex, and NaN is returned. -- -- Depending on the magnitude of \(x\), we start from a piecewise rational -- approximation or a zeroth-order truncation of the asymptotic expansion -- at infinity, and perform 0, 1 or 2 iterations with Halley\'s method to -- obtain full accuracy. -- -- A test of \(10^7\) random inputs showed a maximum relative error smaller -- than 0.95 times @DBL_EPSILON@ (2^{-52}) for positive \(x\). Accuracy for -- negative \(x\) is slightly worse, and can grow to about 10 times -- @DBL_EPSILON@ close to \(-1/e\). However, accuracy may be worse -- depending on compiler flags and the accuracy of the system libm -- functions. foreign import ccall "double_extras.h d_lambertw" d_lambertw :: CDouble -> IO CDouble -- | /d_is_nan/ /x/ -- -- Returns a nonzero integral value if @x@ is @D_NAN@, and otherwise -- returns 0. foreign import ccall "double_extras.h d_is_nan" d_is_nan :: CDouble -> IO CInt -- | /d_log2/ /x/ -- -- Returns the base 2 logarithm of @x@ provided @x@ is positive. If a -- domain or pole error occurs, the appropriate error value is returned. foreign import ccall "double_extras.h d_log2" d_log2 :: CDouble -> IO CDouble