[all-commits] [llvm/llvm-project] f320fe: [libc][math] Implement erff function correctly rou...

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: f320fefc4ad0516bb13af8ce0189fc64a3879275
      https://github.com/llvm/llvm-project/commit/f320fefc4ad0516bb13af8ce0189fc64a3879275
  Author: Tue Ly <lntue at google.com>
  Date:   2023-06-28 (Wed, 28 Jun 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/math/CMakeLists.txt
    A libc/src/math/erff.h
    M libc/src/math/generic/CMakeLists.txt
    A libc/src/math/generic/erff.cpp
    M libc/test/src/math/CMakeLists.txt
    A libc/test/src/math/erff_test.cpp
    M libc/test/src/math/exhaustive/CMakeLists.txt
    A libc/test/src/math/exhaustive/erff_test.cpp
    M libc/utils/MPFRWrapper/MPFRUtils.cpp
    M libc/utils/MPFRWrapper/MPFRUtils.h
    M utils/bazel/llvm-project-overlay/libc/BUILD.bazel

  Log Message:
  -----------
  [libc][math] Implement erff function correctly rounded to all rounding modes.

Implement correctly rounded `erff` functions.

For `x >= 4`, `erff(x) = 1` for `FE_TONEAREST` or `FE_UPWARD`, `0x1.ffffep-1` for `FE_DOWNWARD` or `FE_TOWARDZERO`.

For `0 <= x < 4`, we divide into 32 sub-intervals of length `1/8`, and use a degree-15 odd polynomial to approximate `erff(x)` in each sub-interval:
```
  erff(x) ~ x * (c0 + c1 * x^2 + c2 * x^4 + ... + c7 * x^14).
```

For `x < 0`, we can use the same formula as above, since the odd part is factored out.

Performance tested with `perf.sh` tool from the CORE-MATH project on AMD Ryzen 9 5900X:

Reciprocal throughput (clock cycles / op)
```
$ ./perf.sh erff --path2
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH reciprocal throughput --  with -march=native      (with FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 11.790 + 0.182 clc/call; Median-Min = 0.154 clc/call; Max = 12.255 clc/call;
-- CORE-MATH reciprocal throughput --  with -march=x86-64-v2      (without FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 14.205 + 0.151 clc/call; Median-Min = 0.159 clc/call; Max = 15.893 clc/call;

-- System LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 45.519 + 0.445 clc/call; Median-Min = 0.552 clc/call; Max = 46.345 clc/call;

-- LIBC reciprocal throughput --  with -mavx2 -mfma     (with FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 9.595 + 0.214 clc/call; Median-Min = 0.220 clc/call; Max = 9.887 clc/call;
-- LIBC reciprocal throughput --  with -msse4.2     (without FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 10.223 + 0.190 clc/call; Median-Min = 0.222 clc/call; Max = 10.474 clc/call;
```

and latency (clock cycles / op):
```
$ ./perf.sh erff --path2
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH latency --  with -march=native      (with FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 38.566 + 0.391 clc/call; Median-Min = 0.503 clc/call; Max = 39.170 clc/call;
-- CORE-MATH latency --  with -march=x86-64-v2      (without FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 43.223 + 0.667 clc/call; Median-Min = 0.680 clc/call; Max = 43.913 clc/call;

-- System LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 111.613 + 1.267 clc/call; Median-Min = 1.696 clc/call; Max = 113.444 clc/call;

-- LIBC latency --  with -mavx2 -mfma     (with FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 40.138 + 0.410 clc/call; Median-Min = 0.536 clc/call; Max = 40.729 clc/call;
-- LIBC latency --  with -msse4.2     (without FMA instructions)
[####################] 100 %
Ntrial = 20 ; Min = 44.858 + 0.872 clc/call; Median-Min = 0.814 clc/call; Max = 46.019 clc/call;
```

Reviewed By: michaelrj

Differential Revision: https://reviews.llvm.org/D153683