[libc] Implement sinf function that is correctly rounded to all rounding modes.
authorTue Ly <lntue.h@gmail.com>
Tue, 5 Apr 2022 20:17:18 +0000 (16:17 -0400)
committerTue Ly <lntue@google.com>
Fri, 22 Jul 2022 14:07:31 +0000 (10:07 -0400)
commitd883a4ad02d867e7037bd4ec342016c402484148
treefb4e927170177ab6f6ed1af58e9ea5aa77481250
parent4f2cfbe5314b064625b2c87bde6ce5c8d04004c5
[libc] Implement sinf function that is correctly rounded to all rounding modes.

Implement sinf function that is correctly rounded to all rounding modes.

- We use a simple range reduction for `pi/16 < |x|` :
    Let `k = round(x / pi)` and `y = (x/pi) - k`.
    So `k` is an integer and `-0.5 <= y <= 0.5`.
Then
```
sin(x) = sin(y*pi + k*pi)
          = (-1)^(k & 1) * sin(y*pi)
          ~ (-1)^(k & 1) * y * P(y^2)
```
    where `y*P(y^2)` is a degree-15 minimax polynomial generated by Sollya with:
```
> P = fpminimax(sin(x*pi)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|D...|], [0, 0.5]);
```

- Performance benchmark using perf tool from CORE-MATH project
(https://gitlab.inria.fr/core-math/core-math/-/tree/master) on Ryzen 1700:
Before this patch (not correctly rounded):
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinf
CORE-MATH reciprocal throughput   : 17.892
System LIBC reciprocal throughput : 25.559
LIBC reciprocal throughput        : 29.381
```
After this patch (correctly rounded):
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinf
CORE-MATH reciprocal throughput   : 17.896
System LIBC reciprocal throughput : 25.740

LIBC reciprocal throughput        : 27.872
LIBC reciprocal throughput        : 20.012     (with `-msse4.2` flag)
LIBC reciprocal throughput        : 14.244     (with `-mfma` flag)
```

Reviewed By: zimmermann6

Differential Revision: https://reviews.llvm.org/D123154
12 files changed:
libc/cmake/modules/LLVMLibCObjectRules.cmake
libc/docs/math.rst
libc/src/__support/FPUtil/CMakeLists.txt
libc/src/__support/FPUtil/except_value_utils.h [new file with mode: 0644]
libc/src/math/generic/CMakeLists.txt
libc/src/math/generic/range_reduction.h [new file with mode: 0644]
libc/src/math/generic/range_reduction_fma.h [new file with mode: 0644]
libc/src/math/generic/sinf.cpp
libc/test/src/math/exhaustive/CMakeLists.txt
libc/test/src/math/exhaustive/sinf_test.cpp
libc/test/src/math/sinf_test.cpp
utils/bazel/llvm-project-overlay/libc/BUILD.bazel