v0.6.0

Fixed

Core AD (all modes: Dual, DualVec, Reverse, BReverse, bytecode tape)

• Max/Min NaN handling: BReverse::max/min and bytecode eval_forward/reverse_partials now return the non-NaN argument when one input is NaN, matching Float::max/Float::min semantics and the behavior of Dual/Reverse modes.
• atan2(0,0) derivative: returns zero gradient (matching JAX/PyTorch convention) instead of NaN from division by zero in x²+y².
• powf(x, 0) derivative: correctly returns d/db = ln(x) for x > 0 instead of silently dropping the exponent derivative. d/da = 0 was already correct.
• powf(x, y) at x=0: Reverse and bytecode modes now use the y * x^(y-1) form (matching Dual) instead of y * val / x which produces 0/0 = NaN.
• powi_exp_decode: deleted broken generic float round-trip decoder (failed for f32 negative exponents); replaced with powi_exp_decode_raw at both call sites.

Taylor / Laurent series

• Taylor abs(0): Taylor::abs and TaylorDyn::abs now use the first nonzero coefficient's sign instead of signum(+0.0) = 0, preventing the entire jet from being annihilated.
• taylor_cbrt at zero: returns [0, Inf, ...] (signaling the vertical tangent) instead of NaN from ln(0).
• taylor_sqrt at zero: runtime guard returns [0, Inf, ...] instead of silent Inf/NaN from division by 2*sqrt(0).
• Laurent Add/Sub truncation: promoted from debug_assert to assert! — silent coefficient loss when pole-order gap exceeds K-1 is now caught at runtime.

Bytecode tape

• Checkpoint thinning: online checkpoint thinning now maintains uniform spacing after doubling (skip(1).step_by(2) instead of step_by(2)), fixing O(N) recomputation degradation for small checkpoint budgets.
• Abs sparse Hessian: reclassified from UnaryNonlinear to ZeroDerivative — d²|x|/dx² = 0 a.e., reducing spurious Hessian sparsity pattern entries.
• Added debug_assert for tape variable count overflow (u32::MAX) and contiguous input opcodes.

GPU Taylor kernels (CUDA + wgpu, codegen)

• POWI negative bases: GPU Taylor mode now handles negative bases via sign(a)^n * exp(n * ln(|a|)) instead of exp(n * ln(a)) which produced NaN for ln(negative).
• POWF at a≤0: added first-order chain-rule fallback when a ≤ 0 (where ln(a) is undefined).
• REM Taylor coefficients: c1/c2 now pass through a's jet (d(a%b)/da = 1 a.e.) instead of being zeroed.
• _sign in taylor_eval.cu: now matches tape_eval.cu — returns 1 for +0.0 and NaN for NaN (Rust signum semantics).
• ATAN2 at b=0: uses direct derivative formula instead of jet_div(a, b) which divided by zero.
• CBRT at a=0: returns [0, Inf, ...] instead of NaN from ln(0).
• wgpu expm1/ln1p: polynomial approximation for |x| < 1e-4 to avoid catastrophic cancellation.

echidna-optim

• Trust-region min radius: added min_radius field to TrustRegionConfig (default F::epsilon()), preventing silent stall from geometric radius collapse.
• boundary_tau zero direction: guards ||d||² < epsilon to prevent NaN from degenerate CG directions.
• LU singularity threshold: changed from hardcoded 1e-12 to F::epsilon().sqrt(), fixing false negatives for f32 near-singular matrices.
• Piggyback adjoint: extra reverse pass with converged lambda_new eliminates O(tol × ||G_x||) error in parameter gradients.
• Weighted STDE: estimate_weighted skips zero-weight samples to prevent division by zero in West's algorithm.
• Welford accumulator: debug_assert!(sample.is_finite()) catches NaN/Inf inputs in debug builds.

Changed

• GPU STDE test parity: refactored tests/gpu_stde.rs to use a generic opcode_tests_for_backend! macro, running all per-opcode Taylor tests on both wgpu and CUDA backends instead of wgpu-only.
• TrustRegionConfig: added min_radius: F field (breaking change for direct struct construction; Default impls updated).