[all-commits] [llvm/llvm-project] 434bf1: [libc][math] Implement double precision exp functi...

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: 434bf1608445fd4b529ac4a3a43f1351dc657ab6
      https://github.com/llvm/llvm-project/commit/434bf1608445fd4b529ac4a3a43f1351dc657ab6
  Author: Tue Ly <lntue at google.com>
  Date:   2023-08-24 (Thu, 24 Aug 2023)

  Changed paths:
    M libc/config/darwin/arm/entrypoints.txt
    M libc/config/linux/aarch64/entrypoints.txt
    M libc/config/linux/riscv64/entrypoints.txt
    M libc/config/linux/x86_64/entrypoints.txt
    M libc/config/windows/entrypoints.txt
    M libc/docs/math/index.rst
    M libc/spec/stdc.td
    M libc/src/__support/FPUtil/PolyEval.h
    M libc/src/__support/FPUtil/double_double.h
    M libc/src/__support/FPUtil/dyadic_float.h
    M libc/src/__support/FPUtil/multiply_add.h
    M libc/src/math/CMakeLists.txt
    A libc/src/math/exp.h
    M libc/src/math/generic/CMakeLists.txt
    A libc/src/math/generic/exp.cpp
    M libc/test/src/math/CMakeLists.txt
    A libc/test/src/math/exp_test.cpp
    M libc/test/src/math/log10_test.cpp

  Log Message:
  -----------
  [libc][math] Implement double precision exp function correctly rounded for all rounding modes.

Implement double precision exp function correctly rounded for all
rounding modes.  Using 4 stages:
- Range reduction: reduce to `exp(x) = 2^hi * 2^mid1 * 2^mid2 * exp(lo)`.
- Use 64 + 64 LUT for 2^mid1 and 2^mid2, and use cubic Taylor polynomial to
approximate `(exp(lo) - 1) / lo` in double precision.  Relative error in this
step is bounded by 1.5 * 2^-63.
- If the rounding test fails, use degree-6 Taylor polynomial to approximate
`exp(lo)` in double-double precision.  Relative error in this step is bounded by
2^-99.
- If the rounding test still fails, use degree-7 Taylor polynomial to compute
`exp(lo)` in ~128-bit precision.

Reviewed By: zimmermann6

Differential Revision: https://reviews.llvm.org/D158551