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Add ellipke for simultaneous K(m) and E(m) computation #510

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Add ellipke for simultaneous K(m) and E(m) computation #510

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089e285
Optimize ellipk and ellipe with binary tree branching
mgyoo86 Jan 5, 2026
f946cfa
Add comprehensive edge case tests for elliptic integrals
mgyoo86 Jan 6, 2026
9247c4e
Refactor ellipk: extract _ellipk_horner_table
mgyoo86 Jan 6, 2026
bad749d
Refactor ellipe: extract _ellipe_horner_table
mgyoo86 Jan 6, 2026
50b979f
Rename _ellipk_core/_ellipe_core to _ellipk_nonneg/_ellipe_nonneg
mgyoo86 Jan 6, 2026
162e569
Simplify elliptic functions: inline horner tables into core functions
mgyoo86 Jan 6, 2026
5bd6d70
Revert "Simplify elliptic functions: inline horner tables into core f…
mgyoo86 Jan 6, 2026
2e5db7b
Add bounds checking and optimize ellipe idx=9 case
mgyoo86 Jan 6, 2026
f2466d2
Revert elseif idx==9 to else for better LLVM optimization
mgyoo86 Jan 6, 2026
2a3afe3
Add ellipke function for simultaneous K(m) and E(m) computation
mgyoo86 Jan 6, 2026
05428c6
Add missing propagation for ellipke
mgyoo86 Jan 6, 2026
0b1ea29
Optimize ellipke for m >= 0.9 by sharing log calculation
mgyoo86 Jan 6, 2026
49b3a54
Add tests for Float16 and Float32 support in ellipke
mgyoo86 Jan 6, 2026
ea1673d
Add ellipke to documentation
mgyoo86 Jan 6, 2026
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1 change: 1 addition & 0 deletions docs/src/functions_list.md
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Expand Up @@ -143,6 +143,7 @@ jinc
```@docs
ellipk
ellipe
ellipke
```

## Zeta and Related Functions
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1 change: 1 addition & 0 deletions docs/src/functions_overview.md
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Expand Up @@ -108,6 +108,7 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
|:-------- |:----------- |
| [`ellipk(m)`](@ref SpecialFunctions.ellipk) | [complete elliptic integral of 1st kind](https://en.wikipedia.org/wiki/Elliptic_integral#Notational_variants) ``K(m)`` |
| [`ellipe(m)`](@ref SpecialFunctions.ellipe) | [complete elliptic integral of 2nd kind](https://en.wikipedia.org/wiki/Elliptic_integral#Complete_elliptic_integral_of_the_second_kind) ``E(m)`` |
| [`ellipke(m)`](@ref SpecialFunctions.ellipke) | complete elliptic integrals ``K(m)`` and ``E(m)`` simultaneously |


## Zeta and Related Functions
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1 change: 1 addition & 0 deletions src/SpecialFunctions.jl
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Expand Up @@ -47,6 +47,7 @@ export
dawson,
ellipk,
ellipe,
ellipke,
erf,
erfc,
erfcinv,
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