Simplify the range reduction steps by choosing the reduction constants
carefully so that the reduced arguments v = r*m_x - 1 and v^2 are exact in double
precision, even without FMA instructions, and -2^-8 <= v < 2^-7. This allows the
polynomial evaluations to be parallelized more efficiently.
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D147676
Implement double precision log10 function correctly rounded for all
rounding modes. This implementation currently needs FMA instructions for
correctness.
Use 2 passes:
Fast pass:
- 1 step range reduction with a lookup table of `2^7 = 128` elements to reduce the ranges to `[-2^-7, 2^-7]`.
- Use a degree-7 minimax polynomial generated by Sollya, evaluated using a mixed of double-double and double precisions.
- Apply Ziv's test for accuracy.
Accurate pass:
- Apply 5 more range reduction steps to reduce the ranges further to [-2^-27, 2^-27].
- Use a degree-4 minimax polynomial generated by Sollya, evaluated using 192-bit precisions.
- By the result of Lefevre (add quote), this is more than enough for correct rounding to all rounding modes.
In progress: Adding detail documentations about the algorithm.
Depend on: https://reviews.llvm.org/D136799
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D139846
