forked from OSchip/llvm-project
82d6e77048
Implement tanf function correctly rounded for all rounding modes.
We use the range reduction that is shared with `sinf`, `cosf`, and `sincosf`:
```
k = round(x * 32/pi) and y = x * (32/pi) - k.
```
Then we use the tangent of sum formula:
```
tan(x) = tan((k + y)* pi/32) = tan((k mod 32) * pi / 32 + y * pi/32)
= (tan((k mod 32) * pi/32) + tan(y * pi/32)) / (1 - tan((k mod 32) * pi/32) * tan(y * pi/32))
```
We need to make a further reduction when `k mod 32 >= 16` due to the pole at `pi/2` of `tan(x)` function:
```
if (k mod 32 >= 16): k = k - 31, y = y - 1.0
```
And to compute the final result, we store `tan(k * pi/32)` for `k = -15..15` in a table of 32 double values,
and evaluate `tan(y * pi/32)` with a degree-11 minimax odd polynomial generated by Sollya with:
```
> P = fpminimax(tan(y * pi/32)/y, [|0, 2, 4, 6, 8, 10|], [|D...|], [0, 1.5]);
```
Performance benchmark using `perf` tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh tanf
CORE-MATH reciprocal throughput : 18.586
System LIBC reciprocal throughput : 50.068
LIBC reciprocal throughput : 33.823
LIBC reciprocal throughput : 25.161 (with `-msse4.2` flag)
LIBC reciprocal throughput : 19.157 (with `-mfma` flag)
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh tanf --latency
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH latency : 55.630
System LIBC latency : 106.264
LIBC latency : 96.060
LIBC latency : 90.727 (with `-msse4.2` flag)
LIBC latency : 82.361 (with `-mfma` flag)
```
Reviewed By: orex
Differential Revision: https://reviews.llvm.org/D131715
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| .. | ||
| _static | ||
| CMakeLists.txt | ||
| README.txt | ||
| api_test.rst | ||
| build_system.rst | ||
| clang_tidy_checks.rst | ||
| conf.py | ||
| entrypoints.rst | ||
| fuzzing.rst | ||
| ground_truth_specification.rst | ||
| header_gen_scheme.svg | ||
| header_generation.rst | ||
| implementation_standard.rst | ||
| index.rst | ||
| layering.rst | ||
| math.rst | ||
| mechanics_of_public_api.rst | ||
| redirectors.rst | ||
| redirectors_schematic.svg | ||
| runtimes_build.rst | ||
| source_layout.rst | ||
| stdio.rst | ||
| strings.rst | ||
README.txt
libc Documentation ================== The libc documentation is written using the Sphinx documentation generator. It is currently tested with Sphinx 1.1.3. To build the documents into html configure libc with the following cmake options: * -DLLVM_ENABLE_SPHINX=ON * -DLIBC_INCLUDE_DOCS=ON After configuring libc with these options the make rule `docs-libc-html` should be available.