Add lgamma and digamma ops#3181
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Add element-wise lgamma (log-gamma) and digamma (psi) functions as native unary operations across all backends. Metal: Lanczos g=5 approximation for lgamma, asymptotic expansion with recurrence for digamma. CPU: std::lgamma + custom digamma. CUDA: built-in lgamma + custom digamma. Full autograd support: grad(lgamma) returns digamma. Closes ml-explore#2050 Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
Metal Shading Language has no call stack, so the recursive call to lgamma_impl(1-x) in the reflection formula was silently miscompiled, dropping the log(pi) - log(|sin(pi*x)|) terms entirely. Fix: compute the reflection terms first, transform x -> 1-x, then run Lanczos once on the transformed value. No function calls needed. Verified: lgamma(0.001) now returns 6.907 (was -0.000578). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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Summary
Closes #2050 — adds element-wise
lgamma(log-gamma) anddigamma(psi) functions as native unary operations.lgamma.h)std::lgammafor lgamma, custom asymptotic expansion for digamma::lgammafor lgamma, custom digammagrad(lgamma)returnsdigamma. Digamma itself throws on second-order differentiation (trigamma can be a follow-up).mx.lgamma()andmx.digamma()with docstringsThese are needed by probabilistic programming frameworks (PyMC, scVI, GenMLX) that use log-gamma extensively in distribution log-prob computations.
Test plan
lgammaanddigammaadded🤖 Generated with Claude Code