Data.Number.Flint.Arb.FpWrap

Warning: This module is experimental (as of Arb 2.21). It has not been extensively tested, and interfaces may change in the future.

This module provides wrappers of Arb functions intended users who want accurate floating-point mathematical functions without necessarily caring about ball arithmetic. The wrappers take floating-point input, give floating-point output, and automatically increase the internal working precision to ensure that the output is accurate (in the rare case of failure, they output NaN along with an error code).

Outputs are passed by reference so that we can return status flags and so that the interface is uniform for functions with multiple outputs.

The Haskell version of the c-functions require Ptr for the complex values. The functions can be wrapped to a regular Haskell function

Example

import System.IO.Unsafe
import Foreign.Ptr
import Foreign.C.Types

import Data.Number.Flint.Arb.FpWrap

main = do
  print $ airy_ai  1
  print $ airy_ai' 1

airy_ai  = liftD arb_fpwrap_double_airy_ai
airy_ai' = liftD arb_fpwrap_double_airy_ai_prime

liftD :: (Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn)
       -> (Double -> Double)
liftD f x = unsafePerformIO $ do
  r <- malloc :: IO (Ptr CDouble)
  flag <- f r (realToFrac x) 0
  res <- peek r
  free r
  return $ realToFrac res

Running main yields:

>>> main

produces the output

0.13529241631288141
-0.1591474412967932

Floating-point wrappers of Arb mathematical functions

Option and return flags

newtype FpWrapReturn

Return type for fpwrap functions

Constructors

FpWrapReturn

Fields

• _FpWrapReturn :: CInt

Instances

Show FpWrapReturn

Defined in Data.Number.Flint.Arb.FpWrap.FFI

Methods

showsPrec :: Int -> FpWrapReturn -> ShowS

show :: FpWrapReturn -> String

showList :: [FpWrapReturn] -> ShowS

Eq FpWrapReturn

Defined in Data.Number.Flint.Arb.FpWrap.FFI

Methods

(==) :: FpWrapReturn -> FpWrapReturn -> Bool

(/=) :: FpWrapReturn -> FpWrapReturn -> Bool

fpwrap_success :: FpWrapReturn

Indicates an accurate result. (Up to inevitable underflow or overflow in the final conversion to a floating-point result; see above.)

This flag has the numerical value 0.

fpwrap_unable :: FpWrapReturn

Indicates failure (unable to achieve to target accuracy, possibly because of a singularity). The output is set to NaN.

This flag has the numerical value 1. Functions take a flags parameter specifying optional rounding and termination behavior. This can be set to 0 to use defaults.

fpwrap_accurate_parts :: FpWrapReturn

For complex output, compute both real and imaginary parts to full relative accuracy. By default (if this flag is not set), complex results are computed to at least 53-bit accuracy as a whole, but if either the real or imaginary part is much smaller than the other, that part can have a large relative error. Setting this flag can result in slower evaluation or failure to converge in some cases.

This flag has the numerical value 1.

fpwrap_correct_rounding :: FpWrapReturn

Guarantees correct rounding. By default (if this flag is not set), real results are accurate up to the rounding of the last bit, but the last bit is not guaranteed to be rounded optimally. Setting this flag can result in slower evaluation or failure to converge in some cases. Correct rounding automatically applies to both real and imaginary parts of complex numbers, so it is unnecessary to set both this flag and FPWRAP_ACCURATE_PARTS.

This flag has the numerical value 2.

fpwrap_work_limit :: FpWrapReturn

Multiplied by an integer, specifies the maximum working precision to use before giving up. With n * FPWRAP_WORK_LIMIT added to flags, levels of precision will be used. The default is equivalent to , which for double means trying with a working precision of 64, 128, 256, 512, 1024, 2048, 4096, 8192 bits. With flags = 2 * FPWRAP_WORK_LIMIT, we only try 64 and 128 bits, and with flags = 16 * FPWRAP_WORK_LIMIT we go up to 2097152 bits.

This flag has the numerical value 65536.

Elementary functions

arb_fpwrap_double_exp :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_exp res x flags

arb_fpwrap_cdouble_exp :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_exp res x flags

arb_fpwrap_double_expm1 :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_expm1 res x flags

arb_fpwrap_cdouble_expm1 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_expm1 res x flags

arb_fpwrap_double_log :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_log res x flags

arb_fpwrap_cdouble_log :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_log res x flags

arb_fpwrap_double_log1p :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_log1p res x flags

arb_fpwrap_cdouble_log1p :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_log1p res x flags

arb_fpwrap_double_pow :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_pow res x y flags

arb_fpwrap_cdouble_pow :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_pow res x y flags

arb_fpwrap_double_sqrt :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sqrt res x flags

arb_fpwrap_cdouble_sqrt :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sqrt res x flags

arb_fpwrap_double_rsqrt :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_rsqrt res x flags

arb_fpwrap_cdouble_rsqrt :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_rsqrt res x flags

arb_fpwrap_double_cbrt :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cbrt res x flags

arb_fpwrap_cdouble_cbrt :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cbrt res x flags

arb_fpwrap_double_sin :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sin res x flags

arb_fpwrap_cdouble_sin :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sin res x flags

arb_fpwrap_double_cos :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cos res x flags

arb_fpwrap_cdouble_cos :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cos res x flags

arb_fpwrap_double_tan :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_tan res x flags

arb_fpwrap_cdouble_tan :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_tan res x flags

arb_fpwrap_double_cot :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cot res x flags

arb_fpwrap_cdouble_cot :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cot res x flags

arb_fpwrap_double_sec :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sec res x flags

arb_fpwrap_cdouble_sec :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sec res x flags

arb_fpwrap_double_csc :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_csc res x flags

arb_fpwrap_cdouble_csc :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_csc res x flags

arb_fpwrap_double_sinc :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sinc res x flags

arb_fpwrap_cdouble_sinc :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sinc res x flags

arb_fpwrap_double_sin_pi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sin_pi res x flags

arb_fpwrap_cdouble_sin_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sin_pi res x flags

arb_fpwrap_double_cos_pi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cos_pi res x flags

arb_fpwrap_cdouble_cos_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cos_pi res x flags

arb_fpwrap_double_tan_pi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_tan_pi res x flags

arb_fpwrap_cdouble_tan_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_tan_pi res x flags

arb_fpwrap_double_cot_pi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cot_pi res x flags

arb_fpwrap_cdouble_cot_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cot_pi res x flags

arb_fpwrap_double_sinc_pi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sinc_pi res x flags

arb_fpwrap_cdouble_sinc_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sinc_pi res x flags

arb_fpwrap_double_asin :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_asin res x flags

arb_fpwrap_cdouble_asin :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_asin res x flags

arb_fpwrap_double_acos :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_acos res x flags

arb_fpwrap_cdouble_acos :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_acos res x flags

arb_fpwrap_double_atan :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_atan res x flags

arb_fpwrap_cdouble_atan :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_atan res x flags

arb_fpwrap_double_atan2 :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_atan2 res x1 x2 flags

arb_fpwrap_double_asinh :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_asinh res x flags

arb_fpwrap_cdouble_asinh :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_asinh res x flags

arb_fpwrap_double_acosh :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_acosh res x flags

arb_fpwrap_cdouble_acosh :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_acosh res x flags

arb_fpwrap_double_atanh :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_atanh res x flags

arb_fpwrap_cdouble_atanh :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_atanh res x flags

arb_fpwrap_double_lambertw :: Ptr CDouble -> CDouble -> CLong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_lambertw res x branch flags

arb_fpwrap_cdouble_lambertw :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CLong -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_lambertw res x branch flags

Gamma, zeta and related functions

arb_fpwrap_double_rising :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_rising res x n flags

arb_fpwrap_cdouble_rising :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_rising res x n flags

Rising factorial.

arb_fpwrap_double_gamma :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_gamma res x flags

arb_fpwrap_cdouble_gamma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_gamma res x flags

Gamma function.

arb_fpwrap_double_rgamma :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_rgamma res x flags

arb_fpwrap_cdouble_rgamma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_rgamma res x flags

Reciprocal gamma function.

arb_fpwrap_double_lgamma :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_lgamma res x flags

arb_fpwrap_cdouble_lgamma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_lgamma res x flags

Log-gamma function.

arb_fpwrap_double_digamma :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_digamma res x flags

arb_fpwrap_cdouble_digamma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_digamma res x flags

Digamma function.

arb_fpwrap_double_zeta :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_zeta res x flags

arb_fpwrap_cdouble_zeta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_zeta res x flags

Riemann zeta function.

arb_fpwrap_double_hurwitz_zeta :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hurwitz_zeta res s z flags

arb_fpwrap_cdouble_hurwitz_zeta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hurwitz_zeta res s z flags

Hurwitz zeta function.

arb_fpwrap_double_lerch_phi :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_lerch_phi res z s a flags

arb_fpwrap_cdouble_lerch_phi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_lerch_phi res z s a flags

Lerch transcendent.

arb_fpwrap_double_barnes_g :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_barnes_g res x flags

arb_fpwrap_cdouble_barnes_g :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_barnes_g res x flags

Barnes G-function.

arb_fpwrap_double_log_barnes_g :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_log_barnes_g res x flags

arb_fpwrap_cdouble_log_barnes_g :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_log_barnes_g res x flags

Logarithmic Barnes G-function.

arb_fpwrap_double_polygamma :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_polygamma res s z flags

arb_fpwrap_cdouble_polygamma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_polygamma res s z flags

Polygamma function.

arb_fpwrap_double_polylog :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_polylog res s z flags

arb_fpwrap_cdouble_polylog :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_polylog res s z flags

Polylogarithm.

arb_fpwrap_cdouble_dirichlet_eta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_dirichlet_eta res s flags

arb_fpwrap_cdouble_riemann_xi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_riemann_xi res s flags

arb_fpwrap_cdouble_hardy_theta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hardy_theta res z flags

arb_fpwrap_cdouble_hardy_z :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hardy_z res z flags

arb_fpwrap_cdouble_zeta_zero :: Ptr (Complex CDouble) -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_zeta_zero res n flags

Error functions and exponential integrals

arb_fpwrap_double_erf :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_erf res x flags

arb_fpwrap_cdouble_erf :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_erf res x flags

arb_fpwrap_double_erfc :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_erfc res x flags

arb_fpwrap_cdouble_erfc :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_erfc res x flags

arb_fpwrap_double_erfi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_erfi res x flags

arb_fpwrap_cdouble_erfi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_erfi res x flags

arb_fpwrap_double_erfinv :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_erfinv res x flags

arb_fpwrap_double_erfcinv :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_erfcinv res x flags

arb_fpwrap_double_fresnel_s :: Ptr CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_fresnel_s res x normalized flags

arb_fpwrap_cdouble_fresnel_s :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_fresnel_s res x normalized flags

arb_fpwrap_double_fresnel_c :: Ptr CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_fresnel_c res x normalized flags

arb_fpwrap_cdouble_fresnel_c :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_fresnel_c res x normalized flags

arb_fpwrap_double_gamma_upper :: Ptr CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_gamma_upper res s z regularized flags

arb_fpwrap_cdouble_gamma_upper :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_gamma_upper res s z regularized flags

arb_fpwrap_double_gamma_lower :: Ptr CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_gamma_lower res s z regularized flags

arb_fpwrap_cdouble_gamma_lower :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_gamma_lower res s z regularized flags

arb_fpwrap_double_beta_lower :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_beta_lower res a b z regularized flags

arb_fpwrap_cdouble_beta_lower :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_beta_lower res a b z regularized flags

arb_fpwrap_double_exp_integral_e :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_exp_integral_e res s z flags

arb_fpwrap_cdouble_exp_integral_e :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_exp_integral_e res s z flags

arb_fpwrap_double_exp_integral_ei :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_exp_integral_ei res x flags

arb_fpwrap_cdouble_exp_integral_ei :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_exp_integral_ei res x flags

arb_fpwrap_double_sin_integral :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sin_integral res x flags

arb_fpwrap_cdouble_sin_integral :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sin_integral res x flags

arb_fpwrap_double_cos_integral :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cos_integral res x flags

arb_fpwrap_cdouble_cos_integral :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cos_integral res x flags

arb_fpwrap_double_sinh_integral :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_sinh_integral res x flags

arb_fpwrap_cdouble_sinh_integral :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_sinh_integral res x flags

arb_fpwrap_double_cosh_integral :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_cosh_integral res x flags

arb_fpwrap_cdouble_cosh_integral :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_cosh_integral res x flags

arb_fpwrap_double_log_integral :: Ptr CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_log_integral res x offset flags

arb_fpwrap_cdouble_log_integral :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_log_integral res x offset flags

arb_fpwrap_double_dilog :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_dilog res x flags

arb_fpwrap_cdouble_dilog :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_dilog res x flags

Bessel, Airy and Coulomb functions

arb_fpwrap_double_bessel_j :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_bessel_j res nu x flags

arb_fpwrap_cdouble_bessel_j :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_bessel_j res nu x flags

arb_fpwrap_double_bessel_y :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_bessel_y res nu x flags

arb_fpwrap_cdouble_bessel_y :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_bessel_y res nu x flags

arb_fpwrap_double_bessel_i :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_bessel_i res nu x flags

arb_fpwrap_cdouble_bessel_i :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_bessel_i res nu x flags

arb_fpwrap_double_bessel_k :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_bessel_k res nu x flags

arb_fpwrap_cdouble_bessel_k :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_bessel_k res nu x flags

arb_fpwrap_double_bessel_k_scaled :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_bessel_k_scaled res nu x flags

arb_fpwrap_cdouble_bessel_k_scaled :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_bessel_k_scaled res nu x flags

arb_fpwrap_double_airy_ai :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_ai res x flags

arb_fpwrap_cdouble_airy_ai :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_airy_ai res x flags

arb_fpwrap_double_airy_ai_prime :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_ai_prime res x flags

arb_fpwrap_cdouble_airy_ai_prime :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_airy_ai_prime res x flags

arb_fpwrap_double_airy_bi :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_bi res x flags

arb_fpwrap_cdouble_airy_bi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_airy_bi res x flags

arb_fpwrap_double_airy_bi_prime :: Ptr CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_bi_prime res x flags

arb_fpwrap_cdouble_airy_bi_prime :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_airy_bi_prime res x flags

arb_fpwrap_double_airy_ai_zero :: Ptr CDouble -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_ai_zero res n flags

arb_fpwrap_double_airy_ai_prime_zero :: Ptr CDouble -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_ai_prime_zero res n flags

arb_fpwrap_double_airy_bi_zero :: Ptr CDouble -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_bi_zero res n flags

arb_fpwrap_double_airy_bi_prime_zero :: Ptr CDouble -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_airy_bi_prime_zero res n flags

arb_fpwrap_double_coulomb_f :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_coulomb_f res l eta x flags

arb_fpwrap_cdouble_coulomb_f :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_coulomb_f res l eta x flags

arb_fpwrap_double_coulomb_g :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_coulomb_g res l eta x flags

arb_fpwrap_cdouble_coulomb_g :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_coulomb_g res l eta x flags

arb_fpwrap_cdouble_coulomb_hpos :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_coulomb_hpos res l eta x flags

arb_fpwrap_cdouble_coulomb_hneg :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_coulomb_hneg res l eta x flags

Orthogonal polynomials

arb_fpwrap_double_chebyshev_t :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_chebyshev_t res n x flags

arb_fpwrap_cdouble_chebyshev_t :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_chebyshev_t res n x flags

arb_fpwrap_double_chebyshev_u :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_chebyshev_u res n x flags

arb_fpwrap_cdouble_chebyshev_u :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_chebyshev_u res n x flags

arb_fpwrap_double_jacobi_p :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_jacobi_p res n a b x flags

arb_fpwrap_cdouble_jacobi_p :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_jacobi_p res n a b x flags

arb_fpwrap_double_gegenbauer_c :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_gegenbauer_c res n m x flags

arb_fpwrap_cdouble_gegenbauer_c :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_gegenbauer_c res n m x flags

arb_fpwrap_double_laguerre_l :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_laguerre_l res n m x flags

arb_fpwrap_cdouble_laguerre_l :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_laguerre_l res n m x flags

arb_fpwrap_double_hermite_h :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hermite_h res n x flags

arb_fpwrap_cdouble_hermite_h :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hermite_h res n x flags

arb_fpwrap_double_legendre_p :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_legendre_p res n m x type flags

arb_fpwrap_cdouble_legendre_p :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_legendre_p res n m x type flags

arb_fpwrap_double_legendre_q :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_legendre_q res n m x type flags

arb_fpwrap_cdouble_legendre_q :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_legendre_q res n m x type flags

arb_fpwrap_double_legendre_root :: Ptr CDouble -> Ptr CDouble -> CULong -> CULong -> CInt -> IO FpWrapReturn

arb_fpwrap_double_legendre_root res1 res2 n k flags

Sets res1 to the index k root of the Legendre polynomial \(P_n(x)\), and simultaneously sets res2 to the corresponding weight for Gauss-Legendre quadrature.

arb_fpwrap_cdouble_spherical_y :: Ptr (Complex CDouble) -> CLong -> CLong -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_spherical_y res n m x1 x2 flags

Hypergeometric functions

arb_fpwrap_double_hypgeom_0f1 :: Ptr CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hypgeom_0f1 res a x regularized flags

arb_fpwrap_cdouble_hypgeom_0f1 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hypgeom_0f1 res a x regularized flags

arb_fpwrap_double_hypgeom_1f1 :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hypgeom_1f1 res a b x regularized flags

arb_fpwrap_cdouble_hypgeom_1f1 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hypgeom_1f1 res a b x regularized flags

arb_fpwrap_double_hypgeom_u :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hypgeom_u res a b x flags

arb_fpwrap_cdouble_hypgeom_u :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hypgeom_u res a b x flags

arb_fpwrap_double_hypgeom_2f1 :: Ptr CDouble -> CDouble -> CDouble -> CDouble -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hypgeom_2f1 res a b c x regularized flags

arb_fpwrap_cdouble_hypgeom_2f1 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hypgeom_2f1 res a b c x regularized flags

arb_fpwrap_double_hypgeom_pfq :: Ptr CDouble -> Ptr CDouble -> CLong -> Ptr CDouble -> CLong -> CDouble -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_double_hypgeom_pfq res a p b q z regularized flags

arb_fpwrap_cdouble_hypgeom_pfq :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CLong -> Ptr (Complex CDouble) -> CLong -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_hypgeom_pfq res a p b q z regularized flags

Elliptic integrals, elliptic functions and modular forms

arb_fpwrap_double_agm :: Ptr CDouble -> CDouble -> CDouble -> CInt -> IO FpWrapReturn

arb_fpwrap_double_agm res x y flags

arb_fpwrap_cdouble_agm :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_agm res x y flags

Arithmetic-geometric mean.

arb_fpwrap_cdouble_elliptic_k :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_k res m flags

arb_fpwrap_cdouble_elliptic_e :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_e res m flags

arb_fpwrap_cdouble_elliptic_pi :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_pi res n m flags

arb_fpwrap_cdouble_elliptic_f :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_f res phi m pi flags

arb_fpwrap_cdouble_elliptic_e_inc :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_e_inc res phi m pi flags

arb_fpwrap_cdouble_elliptic_pi_inc :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_pi_inc res n phi m pi flags

Complete and incomplete elliptic integrals.

arb_fpwrap_cdouble_elliptic_rf :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_rf res x y z option flags

arb_fpwrap_cdouble_elliptic_rg :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_rg res x y z option flags

arb_fpwrap_cdouble_elliptic_rj :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_rj res x y z w option flags

Carlson symmetric elliptic integrals.

arb_fpwrap_cdouble_elliptic_p :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_p res z tau flags

arb_fpwrap_cdouble_elliptic_p_prime :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_p_prime res z tau flags

arb_fpwrap_cdouble_elliptic_inv_p :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_inv_p res z tau flags

arb_fpwrap_cdouble_elliptic_zeta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_zeta res z tau flags

arb_fpwrap_cdouble_elliptic_sigma :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_elliptic_sigma res z tau flags

Weierstrass elliptic functions.

arb_fpwrap_cdouble_jacobi_theta_1 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_jacobi_theta_1 res z tau flags

arb_fpwrap_cdouble_jacobi_theta_2 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_jacobi_theta_2 res z tau flags

arb_fpwrap_cdouble_jacobi_theta_3 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_jacobi_theta_3 res z tau flags

arb_fpwrap_cdouble_jacobi_theta_4 :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_jacobi_theta_4 res z tau flags

Jacobi theta functions.

arb_fpwrap_cdouble_dedekind_eta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_dedekind_eta res tau flags

arb_fpwrap_cdouble_modular_j :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_modular_j res tau flags

arb_fpwrap_cdouble_modular_lambda :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_modular_lambda res tau flags

arb_fpwrap_cdouble_modular_delta :: Ptr (Complex CDouble) -> Ptr (Complex CDouble) -> CInt -> IO FpWrapReturn

arb_fpwrap_cdouble_modular_delta res tau flags