[all-commits] [llvm/llvm-project] e6226e: [libc][math] Improve exp2f performance.

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: e6226e6b7234e5fce5a928861541cec3a519f379
      https://github.com/llvm/llvm-project/commit/e6226e6b7234e5fce5a928861541cec3a519f379
  Author: Tue Ly <lntue at google.com>
  Date:   2022-09-14 (Wed, 14 Sep 2022)

  Changed paths:
    M libc/docs/math.rst
    M libc/src/math/generic/CMakeLists.txt
    M libc/src/math/generic/exp2f.cpp
    M libc/src/math/generic/explogxf.h
    M libc/test/src/math/exhaustive/exp2f_test.cpp
    M libc/test/src/math/explogxf_test.cpp

  Log Message:
  -----------
  [libc][math] Improve exp2f performance.

Reduce the number of subintervals that need lookup table and optimize
the evaluation steps.

Currently, `exp2f` is computed by reducing to `2^hi * 2^mid * 2^lo` where
`-16/32 <= mid <= 15/32` and `-1/64 <= lo <= 1/64`, and `2^lo` is then
approximated by a degree 6 polynomial.

Experiment with Sollya showed that by using a degree 6 polynomial, we
can approximate `2^lo` for a bigger range with reasonable errors:
```
> P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/64, 1/64]);
> dirtyinfnorm(2^x - 1 - x*P, [-1/64, 1/64]);
0x1.e18a1bc09114def49eb851655e2e5c4dd08075ac2p-63

> P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32, 1/32]);
> dirtyinfnorm(2^x - 1 - x*P, [-1/32, 1/32]);
0x1.05627b6ed48ca417fe53e3495f7df4baf84a05e2ap-56
```
So we can optimize the implementation a bit with:
# Reduce the range to `mid = i/16` for `i = 0..15` and `-1/32 <= lo <= 1/32`
# Store the table `2^mid` in bits, and add `hi` directly to its exponent field to compute `2^hi * 2^mid`
# Rearrange the order of evaluating the polynomial approximating `2^lo`.

Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp2f
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput   : 9.534
System LIBC reciprocal throughput : 6.229

BEFORE:
LIBC reciprocal throughput        : 21.405
LIBC reciprocal throughput        : 15.241    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 11.111    (with `-mfma` flag)

AFTER:
LIBC reciprocal throughput        : 18.617
LIBC reciprocal throughput        : 12.852    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 9.253     (with `-mfma` flag)

$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp2f --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency   : 40.869
System LIBC latency : 30.580

BEFORE
LIBC latency        : 64.888
LIBC latency        : 61.027    (with `-msse4.2` flag)
LIBC latency        : 48.778    (with `-mfma` flag)

AFTER
LIBC latency        : 48.803
LIBC latency        : 45.047    (with `-msse4.2` flag)
LIBC latency        : 37.487    (with `-mfma` flag)
```

Reviewed By: sivachandra, orex

Differential Revision: https://reviews.llvm.org/D133870