EnzymeAD / EnzymeAD/Reactant.jl

SpecialFunctions meta-issue

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Description

Each of the following functions from the SpecialFunctions.jl package should have a method added here that handles TracedRNumber or TracedRArray inputs (depending on whether the expected input is a scalar or vector). This should be implemented using corresponding calls to stablehlo methods https://github.com/openxla/stablehlo/blob/c2fccec9f02daa2d709001ed5f37924d2526676f/stablehlo/dialect/StablehloOps.td#L938 or chlo methods https://github.com/openxla/stablehlo/blob/c2fccec9f02daa2d709001ed5f37924d2526676f/stablehlo/dialect/ChloOps.td . Ideally it should directly call operations within Ops.jl which wrap these stablehlo and chlo utilities. If one needs to call a stablehlo or chlo method which doesn't have an interface in Ops, it should be added to Ops, with a corresponding test, and then use that new Ops.jl method.

- [ ] [SpecialFunctions.gamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma)
- [ ] [SpecialFunctions.loggamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.loggamma)
- [ ] [SpecialFunctions.logabsgamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logabsgamma)
- [ ] [SpecialFunctions.loggamma1p](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.loggamma1p)
- [ ] [SpecialFunctions.logfactorial](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logfactorial)
- [ ] [SpecialFunctions.digamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.digamma)
- [ ] [SpecialFunctions.invdigamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.invdigamma)
- [ ] [SpecialFunctions.trigamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.trigamma)
- [ ] [SpecialFunctions.polygamma](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.polygamma)
- [ ] [SpecialFunctions.gamma_inc](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc)
- [ ] [SpecialFunctions.gamma_inc_inv](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_inv)
- [ ] [SpecialFunctions.loggammadiv](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.loggammadiv)
- [ ] [SpecialFunctions.gammax](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gammax)
- [ ] [SpecialFunctions.rgammax](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.rgammax)
- [ ] [SpecialFunctions.rgamma1pm1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.rgamma1pm1)
- [ ] [SpecialFunctions.gamma_inc_asym](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_asym)
- [ ] [SpecialFunctions.gamma_inc_cf](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_cf)
- [ ] [SpecialFunctions.gamma_inc_fsum](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_fsum)
- [ ] [SpecialFunctions.gamma_inc_minimax](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_minimax)
- [ ] [SpecialFunctions.gamma_inc_taylor](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_taylor)
- [ ] [SpecialFunctions.gamma_inc_taylor_x](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_taylor_x)
- [ ] [SpecialFunctions.gamma_inc_temme](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_temme)
- [ ] [SpecialFunctions.gamma_inc_temme_1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_temme_1)
- [ ] [SpecialFunctions.gamma_inc_inv_psmall](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_inv_psmall)
- [ ] [SpecialFunctions.gamma_inc_inv_qsmall](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_inv_qsmall)
- [ ] [SpecialFunctions.gamma_inc_inv_alarge](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc_inv_alarge)
- [ ] [SpecialFunctions.auxgam](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.auxgam)
- [ ] [SpecialFunctions.beta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta)
- [ ] [SpecialFunctions.logbeta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logbeta)
- [ ] [SpecialFunctions.logabsbeta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logabsbeta)
- [ ] [SpecialFunctions.logabsbinomial](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logabsbinomial)
- [ ] [SpecialFunctions.beta_inc](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc)
- [ ] [SpecialFunctions.beta_inc_inv](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_inv)
- [ ] [SpecialFunctions.ncbeta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ncbeta)
- [ ] [SpecialFunctions.ncbeta_poisson](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ncbeta_poisson)
- [ ] [SpecialFunctions.ncbeta_tail](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ncbeta_tail)
- [ ] [SpecialFunctions.beta_inc_power_series1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_power_series1)
- [ ] [SpecialFunctions.beta_inc_power_series2](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_power_series2)
- [ ] [SpecialFunctions.beta_inc_asymptotic_asymmetric](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_asymptotic_asymmetric)
- [ ] [SpecialFunctions.beta_inc_asymptotic_symmetric](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_asymptotic_symmetric)
- [ ] [SpecialFunctions.beta_inc_power_series](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_power_series)
- [ ] [SpecialFunctions.beta_inc_diff](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_diff)
- [ ] [SpecialFunctions.beta_inc_cont_fraction](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_inc_cont_fraction)
- [ ] [SpecialFunctions.beta_integrand](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.beta_integrand)
- [ ] [SpecialFunctions.chepolsum](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.chepolsum)
- [ ] [SpecialFunctions.lambdaeta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.lambdaeta)
- [ ] [SpecialFunctions.stirling_corr](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.stirling_corr)
- [ ] [SpecialFunctions.stirling_error](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.stirling_error)
- [ ] [SpecialFunctions.esum](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.esum)
- [ ] [SpecialFunctions.coeff1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.coeff1)
- [ ] [SpecialFunctions.coeff2](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.coeff2)
- [ ] [SpecialFunctions.coeff3](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.coeff3)
- [ ] [SpecialFunctions.ncF](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ncF)
- [ ] [SpecialFunctions.expint](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.expint)
- [ ] [SpecialFunctions.expinti](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.expinti)
- [ ] [SpecialFunctions.expintx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.expintx)
- [ ] [SpecialFunctions.sinint](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.sinint)
- [ ] [SpecialFunctions.cosint](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.cosint)
- [ ] [SpecialFunctions.erf](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erf)
- [ ] [SpecialFunctions.erf](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erf-Tuple{Real,%20Real})
- [ ] [SpecialFunctions.erfc](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erfc)
- [ ] [SpecialFunctions.logerf](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logerf)
- [ ] [SpecialFunctions.erfcinv](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erfcinv)
- [ ] [SpecialFunctions.erfcx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erfcx)
- [ ] [SpecialFunctions.logerfc](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logerfc)
- [ ] [SpecialFunctions.logerfcx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.logerfcx)
- [ ] [SpecialFunctions.erfi](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erfi)
- [ ] [SpecialFunctions.erfinv](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.erfinv)
- [ ] [SpecialFunctions.dawson](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.dawson)
- [ ] [SpecialFunctions.faddeeva](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.faddeeva)
- [ ] [SpecialFunctions.airyai](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airyai)
- [ ] [SpecialFunctions.airyaiprime](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airyaiprime)
- [ ] [SpecialFunctions.airybi](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airybi)
- [ ] [SpecialFunctions.airybiprime](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airybiprime)
- [ ] [SpecialFunctions.airyaix](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airyaix)
- [ ] [SpecialFunctions.airyaiprimex](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airyaiprimex)
- [ ] [SpecialFunctions.airybix](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airybix)
- [ ] [SpecialFunctions.airybiprimex](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.airybiprimex)
- [ ] [SpecialFunctions.besselj](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselj)
- [ ] [SpecialFunctions.besselj0](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselj0)
- [ ] [SpecialFunctions.besselj1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselj1)
- [ ] [SpecialFunctions.besseljx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besseljx)
- [ ] [SpecialFunctions.sphericalbesselj](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.sphericalbesselj)
- [ ] [SpecialFunctions.bessely](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.bessely)
- [ ] [SpecialFunctions.bessely0](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.bessely0)
- [ ] [SpecialFunctions.bessely1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.bessely1)
- [ ] [SpecialFunctions.besselyx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselyx)
- [ ] [SpecialFunctions.sphericalbessely](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.sphericalbessely)
- [ ] [SpecialFunctions.besselh](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselh)
- [ ] [SpecialFunctions.besselhx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselhx)
- [ ] [SpecialFunctions.hankelh1](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.hankelh1)
- [ ] [SpecialFunctions.hankelh1x](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.hankelh1x)
- [ ] [SpecialFunctions.hankelh2](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.hankelh2)
- [ ] [SpecialFunctions.hankelh2x](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.hankelh2x)
- [ ] [SpecialFunctions.besseli](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besseli)
- [ ] [SpecialFunctions.besselix](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselix)
- [ ] [SpecialFunctions.besselk](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselk)
- [ ] [SpecialFunctions.besselkx](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.besselkx)
- [ ] [SpecialFunctions.jinc](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.jinc)
- [ ] [SpecialFunctions.ellipk](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ellipk)
- [ ] [SpecialFunctions.ellipe](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.ellipe)
- [ ] [SpecialFunctions.eta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.eta)
- [ ] [SpecialFunctions.zeta](https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.zeta)

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