Fix low precision for BigFloats in ExpMethodGeneric (Issue #44)#205
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ChrisRackauckas merged 2 commits intoSciML:masterfrom Jan 12, 2026
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The `ExpMethodGeneric` exponential implementation was using a fixed (13,13) Padé approximant regardless of the floating-point precision, which is only appropriate for Float64 (~53 bits). For BigFloat with default 256-bit precision, this resulted in errors of ~10^42 eps instead of machine precision. Changes: - Add `pade_order_for_type(T)` to compute the minimum Padé order k needed for machine-precision accuracy for a given floating-point type - Automatically detect high-precision types (BigFloat, etc.) and use the appropriate Padé order when `ExpMethodGeneric()` is called - Add `ExpMethodGeneric(k)` constructor to manually specify order - Add `ExpMethodGeneric(T)` constructor to select order based on type - Add tests verifying machine-precision accuracy for BigFloat with various precision settings (128, 256, 512 bits) The fix computes k based on the error bound for (k,k) Padé approximants: (x/2)^(2k+1) / (2k+1)! < 2^(-precision_bits) Results: - Float64: k=13 (unchanged, ~10 eps error) - BigFloat 128-bit: k=15 - BigFloat 256-bit: k=25 - BigFloat 512-bit: k=43 - BigFloat 1024-bit: k=76 Fixes SciML#44 cc @ChrisRackauckas 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
- Create test/jet directory with its own Project.toml for JET dependencies - Move JET tests from qa.jl to test/jet/jet.jl - Add activate_jet_env() function to runtests.jl following GPU pattern - Remove JET from main Project.toml extras, compat, and test targets - JET tests now run with GROUP=JET environment variable This follows the same pattern as GPU tests, allowing JET to have its own dependency resolution separate from the main test suite. Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>
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JET Test SeparationAdded commit to split JET tests into a separate test group with its own environment, following the same pattern as GPU tests. Changes:
How to run JET tests:GROUP=JET julia --project -e 'using Pkg; Pkg.test()'This follows the pattern from OrdinaryDiffEq.jl and DelayDiffEq.jl for separating heavy analysis tools like JET into their own test environments. |
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Summary
ExpMethodGeneric(Fixes exp_generic has low precision for BigFloats #44)pade_order_for_type(T)to compute the minimum Padé order needed for machine-precision accuracyProblem
The
ExpMethodGenericexponential implementation was using a fixed (13,13) Padé approximant regardless of the floating-point precision. This is only appropriate for Float64 (~53 bits). For BigFloat with default 256-bit precision, this resulted in errors of ~10^42 eps instead of machine precision.Solution
The fix computes k based on the error bound for (k,k) Padé approximants:
(x/2)^(2k+1) / (2k+1)! < 2^(-precision_bits)Results:
Test plan
cc @ChrisRackauckas
🤖 Generated with Claude Code