Use asymptotic expansion for very large a,b and add test cases.
Add some corrections to improve numeric stability.
Add better error handling of cases that explode so we get evaluation_error's.
* Make the library modular usable.
* Fix -Wundef warnings
* Switch to library requirements instead of source. As source puts extra source in install targets.
* Add missing NO_LIB usage requirements.
* Remove boost-root relative include path.
* Add missing import-search for cconfig/predef checks.
* Add requires-b2 check to top-level build file.
* Sync upstream.
* Fix typo in test framework reference.
* Bump B2 require to 5.2
* Update copyright dates.
* Move inter-lib dependencies to a project variable and into the build targets.
* Switch to /boost/test//included target for header only mode of Boost.Test.
* Adjust doc build to avoid boost-root references.
* Update build deps.
* Fix project props not applying to the no_eh.obj compile.
* Update build deps.
* Add missing import-search.
* Fix float128_type checks to actually disable tests. Problem was that build is a non-free feature. Which can't be acquired through a usage requirement.
* GPU Batch 7
Fix igamma_large support on device
Add GPU support to toms748
Add GPU support to igamma_inv
Add GPU markers to gamma_inva
Add GPU Markers to lgamma_small
Remove STL usage from gamma
Remove NVRTC workaround
Fix fraction use of STL headers
Mark gamma functions in fwd
Disable declval on all GPU platforms
Disable more unneeded code on device
Add forward decl for NVRTC tgamma
Disable unneeded items for all GPU
Change workaround for missing overloads
Rearrange definition location
Add include path to cuda now that workaround is removed
Fix NVRTC incompatibility with recursion and forward decls
Add tgamma_ratio CUDA and NVRTC testing
Fix NVRTC handling of gamma_p_derivative
Add gamma_p_derivative CUDA and NVRTC testing
Remove recursion from gamma_incomplete_imp
Add SYCL testing of igamma, igamma_inv, and igamma_inva
Ignore literal-range warnings
Remove use of static const char* for function name
Fix missing CUDA header
Remove calls under NVRTC to fwd decl
Add more nvrtc workarounds
Use builtin erfc instead of header cycle
Add CUDA and NVRTC testing of gamma_p_inv
Adjust tolerances
Add GPU support to chi squared dist
Fix static local variable
Add chi squared dist SYCL testing
Add chi squared dist CUDA testing
Add chi squared dist NVRTC testing
Add GPU support to weibull dist
Add weibull dist SYCL testing
Add weibull dist CUDA testing
Add weibull dist NVRTC testing
* Fix policy macro definition for MSVC platforms
* Don't add quadmath lib for has_128bit_floatmax_t check. It was accidentally copy+pasted.
* Fix incorrect name for float128 type check that caused it to not apear.
---------
Co-authored-by: Matt Borland <matt@mattborland.com>
* Remove tests we don't need right now.
!!!REVERT THIS COMMIT BEFORE MERGING!!!
* Add s390x testing to drone.
* Correct drone file.
* Correct drone file (again)
* Prevent complete cancellation in bessel_jy logic.
* Correct testing for 128-bit floats.
* Make some more tests 128-bit long double safe.
* Make more tests 128-bit float safe.
* Fix some more 128-bit testing issues.
* More 128-bit float fixes.
* Make more tests 128-bit float safe.
* Fix up remaining tests for 128-bit floats.
* Yet more 128-bit float test case fixes.
* Fix up more tests for 128-bit floats and non-intel platforms.
* Fix up more tests to be 128-bit long double safe.
* More test case adjustments.
* More 128-bit float error rate adjustments.
* Fixes for autodiff tests
* Two more test fixes.
* Fix up daubechies_scaling_test.cpp and reinstate full CI.
Co-authored-by: Matt Borland <matt@mattborland.com>
To test over a wider range of values, otherwise precision tails off for middling values of z - 100 < z < 300. Also prints out conditioning on the near-1 or 2 approximations.
Update lanczos.hpp with the new approximations, removed 80-100 digit approximation because it basically doesn't work well.
Modified lanczos.hpp and lgamma_small.hpp to have separate lanczos g values for the near 1 or 2 approximations.
This addresses issues discussed in https://github.com/boostorg/multiprecision/pull/327.
* Jacobi Theta functions
Implementations, tests, and ULP plotting programs are provided for the
four Jacobi Theta functions per #373. Twenty-four public C++ functions
are provided in all, covering various precision-preserving scenarios.
Documentation for collaborators is provided in the code comments. Proper
documentation for end users will be provided when the implementation and
APIs are finalized.
Some tests are failing; this implementation is meant to start a
conversation. The core dilemma faced by the author was that large values
of |q| resulted in slow convergence, and sometimes wildly inaccurate
results. Following the implementation note in DLMF 20.14, I added code
to switch over to the imaginary versions of the theta functions when |q|
> 0.85. This restored accuracy such that all of the identity tests
passed for a loose-enough epsilon, but then lost precision to the point
that the Wolfram Alpha spot checks failed. It is the author's hope that
someone with floating-point experience can tame the exponential dragons
and squeeze the ULPs back down to a reasonable range when |q| is large.
When #392 is merged I will add more thorough value tests, although I
fully expect them to fail until the underlying precision issues are
resolved.
As a final note, the precision issues do not affect the z=0 case - the
ULP plots indicate these return values within 2 ULP across all valid
|q|. So that's a start.
* [CI SKIP] Jacobi theta: Add special-value tests and more
* Add tests covering z=0 special values from MathWorld
* Add missing real_concept header
* Replace M_PI and friends with constants::pi etc
* Use BOOST_MATH_STD_USING in more places
* Jacobi theta: Test two more of Watson's identities [CI SKIP]
See https://mathworld.wolfram.com/JacobiThetaFunctions.html
(Equations 48 and 49)
* Improve precision of Jacobi theta functions [CI SKIP]
Rewrite the private imaginary versions to use double-sided summations
following DLMF 20.13.4 and 20.13.5. This cuts down the worst of the
precision issues by a factor of 10, and gets more of the tests to pass.
I am confident enough in the code path to eliminate the compile-time
__JACOBI_THETA_USE_IMAGINARY flag. In fact the imaginary-z code paths
are now enabled for all |q| > 0.04, i.e. most legal values of q.
More extensive tests will be needed to illuminate any remaining
precision issues.
* Jacobi theta: Make changes suggested in #394 [CI SKIP]
* Add LICENSE notice to main file
* Document convergence criteria
* Eliminate eps*eps = 0 logic. This causes some disagreement with the
zero returned by Wolfram Alpha for z=0, q > 0.99 in the fourth function.
Mathematically, the fourth function is never exactly zero, so I don't
trust Wolfram here.
* Per code-review comments, remove multiplications by floating-point 2.
* Tweak the plotting programs to display their titles, and to uniformly
use `float` as their CoarseType and `long double` as their
`PreciseType`.
* Add quadrature tests to Jacobi theta functions [CI SKIP]
The quadrature tests revealed a problem in the m1 functions: they too
should switch to the _IMAGINARY logic for q > exp(-pi), or will suffer
from slow convergence. Fix them.
Also tighten tolerances for many tests from sqrt(eps) to 100 * eps.
* Test Jacobi thetas against elliptic functions and elliptic integrals [CI SKIP]
See:
* https://dlmf.nist.gov/22.2
* https://dlmf.nist.gov/20.9#i
* Test Jacobi Thetas against their Laplace transforms [CI SKIP]
See:
* https://dlmf.nist.gov/20.10#ii
I did find some disagreement, and dropped the negative sign from the
theta1 equation. DLMF's theta2 and theta3 Laplace transform equations do
not agree at all with the computed values - will need to investigate.
In the meantime, the two implemented equations agree to 4 EPS so I am
keeping them.
* Add a note on using log1p with Jacobi theta functions [CI SKIP]
See discussion:
* https://github.com/boostorg/math/pull/394#issuecomment-655871762
* Add random data tests to Jacobi Theta functions [CI SKIP]
Add a test data generator program for the Jacobi theta functions.
This program will produce data for the tau parameterization, so that
precision isn't lost during the log-transformation. This distinguishes
it from the Wolfram Alpha data, which is parameterized by q.
A few of these new random-data tests are failing, but not by obscene
margins (< 100 EPS). These failures will be addressed when the test
tolerances are finalized.
* Add small-tau tests and simplify Jacobi Theta code [CI SKIP]
Add tests for small tau (i.e. large q). The tests are failing with mean
~ 200 EPS and max ~ 800 EPS. These look like worst-case input, and
should be the focus of future accuracy improvements.
This commit also simplifies the _IMAGINARY code by abstracting all of
the loops into a single svelte function.
* Add user documentation for Jacobi Theta functions [CI SKIP]
* Add function graphs to Jacobi Theta docs [CI SKIP]
* Define Jacobi Theta test tolerances [CI SKIP]
* Add implementation note on Jacobi theta functions [CI SKIP]
* Consolidate Jacobi Theta ULPs plotting programs [CI SKIP]
* Fix q domain checking of jacobi_theta4 [CI SKIP]
* Add ULPs plots to Jacobi Theta docs [CI SKIP]
Also add the built HTML files for easy evaluation. A full rebuild is
needed for the new docs to appear in the indexes.
* Add missing Jacobi Theta ULPs plots [CI SKIP]
* Add LaTeX source for Jacobi Theta equations [CI SKIP]
* Remove unused Jacobi Theta PNG equations [CI SKIP]
* Add Jacobi Theta performance script [CI SKIP]
Provided by @NAThompson.
* Remove vestigial eps*eps check from jacobi_theta3 [CI SKIP]
* Update Jacobi Theta docs per code review comments [CI SKIP]
* Enable arg promotion for Jacobi Theta functions [CI SKIP]
Add Jacobi theta functions to the instantiation tests and fix up
everything needed to make them pass. This changes the function
signatures to use promote_args.
* Fix Jacobi Theta plotting script [CI SKIP]
This script broke when the promote_args API was added.
* Change Jacobi Theta convergence criterion [CI SKIP]
Compare the non-oscillating part of the delta to the previous one.
This avoids some headaches comparing the delta to the partial sum,
because the partial sum can be a small number due to the oscillating
component alternating signs.
Because successive terms involve either q^n^2 or exp(-(pi*n)^2),
convergence should still happen pretty quickly. Graphs have been updated
and tests still passs with no noticeable difference.
