Use expm1f(x) = exp(x) - 1 for |x| > ln(2).
For |x| <= ln(2), divide it into 3 subintervals: [-ln2, -1/8], [-1/8, 1/8], [1/8, ln2]
and use a degree-6 polynomial approximation generated by Sollya's fpminmax for each interval.
Errors < 1.5 ULPs when we use fma to evaluate the polynomials.
Differential Revision: https://reviews.llvm.org/D101134
The implementations use the x86_64 FPU instructions. These instructions
are extremely slow compared to a polynomial based software
implementation. Also, their accuracy falls drastically once the input
goes beyond 2PI. To improve both the speed and accuracy, we will be
taking the following approach going forward:
1. As a follow up to this CL, we will implement a range reduction algorithm
which will expand the accuracy to the entire double precision range.
2. After that, we will replace the HW instructions with a polynomial
implementation to improve the run time.
After step 2, the implementations will be accurate, performant and target
architecture independent.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D102384
A new function to MPFRWrapper has been added, which is used to set up
the unit tests.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D93007
Tests for frexp[f|l] now use the new capability. Not all input-output
combinations have been addressed by this change. Support for newer combinations
can be added in future as needed.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D86506
This dramtically reduces the run time of tests. For example,
sincosf_test takes over 25 minutes without this attribute but only 8
seconds with this attribute.
A new test matcher class MPFRMatcher is added along with helper macros
EXPECT|ASSERT_MPFR_MATCH.
New type traits classes RemoveCV and IsFloatingPointType have been
added and used to implement the above class and its helpers.
Reviewers: abrachet, phosek
Differential Revision: https://reviews.llvm.org/D79256
NFC intended in the implementaton. Only mechanical changes to fit the LLVM
libc implementation standard have been done.
Math testing infrastructure has been added. This infrastructure compares the
results produced by the libc with the high precision results from MPFR.
Tests making use of this infrastructure have been added for cosf, sinf and
sincosf.
Reviewers: abrachet, phosek
Differential Revision: https://reviews.llvm.org/D76825
Tue Ly