[all-commits] [llvm/llvm-project] 1c89ae: [libc][math] Improve sinhf and coshf performance.

[lntue via All-commits]

  Branch: refs/heads/main
  Home:   https://github.com/llvm/llvm-project
  Commit: 1c89ae71ea69a9203b35a9d96328f1c7ca54994c
      https://github.com/llvm/llvm-project/commit/1c89ae71ea69a9203b35a9d96328f1c7ca54994c
  Author: Tue Ly <lntue at google.com>
  Date:   2022-09-15 (Thu, 15 Sep 2022)

  Changed paths:
    M libc/docs/math.rst
    M libc/src/math/generic/CMakeLists.txt
    M libc/src/math/generic/coshf.cpp
    M libc/src/math/generic/exp2f.cpp
    M libc/src/math/generic/explogxf.h
    M libc/src/math/generic/sinhf.cpp

  Log Message:
  -----------
  [libc][math] Improve sinhf and coshf performance.

Optimize `sinhf` and `coshf` by computing exp(x) and exp(-x) simultaneously.

Currently `sinhf` and `coshf` are implemented using the following formulas:
```
  sinh(x) = 0.5 *(exp(x) - 1) - 0.5*(exp(-x) - 1)
  cosh(x) = 0.5*exp(x) + 0.5*exp(-x)
```
where `exp(x)` and `exp(-x)` are calculated separately using the formula:
```
  exp(x) ~ 2^hi * 2^mid * exp(dx)
         ~ 2^hi * 2^mid * P(dx)
```
By expanding the polynomial `P(dx)` into even and odd parts
```
  P(dx) = P_even(dx) + dx * P_odd(dx)
```
we can see that the computations of `exp(x)` and `exp(-x)` have many things in common,
namely:
```
  exp(x)  ~ 2^(hi + mid) * (P_even(dx) + dx * P_odd(dx))
  exp(-x) ~ 2^(-(hi + mid)) * (P_even(dx) - dx * P_odd(dx))
```
Expanding `sinh(x)` and `cosh(x)` with respect to the above formulas, we can compute
these two functions as follow in order to maximize the sharing parts:
```
  sinh(x) = (e^x - e^(-x)) / 2
          ~ 0.5 * (P_even * (2^(hi + mid) - 2^(-(hi + mid))) +
                  dx * P_odd * (2^(hi + mid) + 2^(-(hi + mid))))
  cosh(x) = (e^x + e^(-x)) / 2
          ~ 0.5 * (P_even * (2^(hi + mid) + 2^(-(hi + mid))) +
                  dx * P_odd * (2^(hi + mid) - 2^(-(hi + mid))))
```
So in this patch, we perform the following optimizations for `sinhf` and `coshf`:
  # Use the above formulas to maximize sharing intermediate results,
  # Apply similar optimizations from https://reviews.llvm.org/D133870

Performance benchmark using `perf` tool from the CORE-MATH project on Ryzen 1700:
For `sinhf`:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinhf
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput   : 16.718
System LIBC reciprocal throughput : 63.151

BEFORE:
LIBC reciprocal throughput        : 90.116
LIBC reciprocal throughput        : 28.554    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 22.577    (with `-mfma` flag)

AFTER:
LIBC reciprocal throughput        : 36.482
LIBC reciprocal throughput        : 16.955    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 13.943    (with `-mfma` flag)

$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinhf --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency   : 48.821
System LIBC latency : 137.019

BEFORE
LIBC latency        : 97.122
LIBC latency        : 84.214    (with `-msse4.2` flag)
LIBC latency        : 71.611    (with `-mfma` flag)

AFTER
LIBC latency        : 54.555
LIBC latency        : 50.865    (with `-msse4.2` flag)
LIBC latency        : 48.700    (with `-mfma` flag)
```
For `coshf`:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh coshf
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput   : 16.939
System LIBC reciprocal throughput : 19.695

BEFORE:
LIBC reciprocal throughput        : 52.845
LIBC reciprocal throughput        : 29.174    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 22.553    (with `-mfma` flag)

AFTER:
LIBC reciprocal throughput        : 37.169
LIBC reciprocal throughput        : 17.805    (with `-msse4.2` flag)
LIBC reciprocal throughput        : 14.691    (with `-mfma` flag)

$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh coshf --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency   : 48.478
System LIBC latency : 48.044

BEFORE
LIBC latency        : 99.123
LIBC latency        : 85.595    (with `-msse4.2` flag)
LIBC latency        : 72.776    (with `-mfma` flag)

AFTER
LIBC latency        : 57.760
LIBC latency        : 53.967    (with `-msse4.2` flag)
LIBC latency        : 50.987    (with `-mfma` flag)
```

Reviewed By: orex, zimmermann6

Differential Revision: https://reviews.llvm.org/D133913