Closes#159614
**Changes:**
- Initial implementation of rsqrt for single precision float
**Some small unrelated style changes to this PR (that I missed in my
rsqrtf16 PR):**
- Added extra - to the top comments to make it look nicer in
libc/shared/math/rsqrtf16.h
- Put rsqrtf16 inside of libc/src/__support/math/CMakeLists.txt in
sorted order
- Rearanged libc_math_function rsqrtf16 in Bazel to match alphabetical
order
This patch enhances the GPU support documentation page (`support.html`)
by adding a new, detailed section for `math.h`. This new section
presents the results of the GPU math conformance tests, providing
quantitative data on the accuracy of the supported higher math
functions.
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- scalbnbf16
- scalblnbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- totalorderbf16
- totalordermagbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- canonicalizebf16
- iscanonicalbf16
- fdimbf16
- copysignbf16
- issignalingbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- modfbf16
- remainderbf16
- remquobf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
Co-authored-by: OverMighty <its.overmighty@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- frexpbf16
- ilobbf16
- ldexpbf16
- llogbbf16
- logbbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- nearbyintbf16
- rintbf16
- lrintbf16
- llrintbf16
- lroundbf16
- llroundbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- getpayloadbf16
- setpayloadbf16
- setpayloadsigbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- nextafterbf16
- nextdownbf16
- nexttowardbf16
- nextupbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
Co-authored-by: OverMighty <its.overmighty@gmail.com>
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- fromfpbf16
- fromfpxbf16
- ufromfpbf16
- ufromfpxbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
Reverts llvm/llvm-project#146226
The MPFR test uses `mpfr_asinpi` which requires MPFR 4.2.0 or later, but
the Buildbots are running an older version of MPFR.
See https://lab.llvm.org/buildbot/#/builders/104/builds/27743 for
example.
I said I was going to revert the PR until we have a workaround for older
versions of MPFR, but then I forgot and I just disabled the entrypoints
which doesn't fix the Buildbot builds.
The function is implemented using the following Taylor series that's
generated using [python-sympy](https://www.sympy.org/en/index.html), and
it is very accurate for |x| $$\in [0, 0.5]$$ and has been verified using
Geogebra. The range reduction is used for the rest range (0.5, 1].
$$
\frac{\arcsin(x)}{\pi} \approx
\begin{aligned}[t]
& 0.318309886183791x \\
& + 0.0530516476972984x^3 \\
& + 0.0238732414637843x^5 \\
& + 0.0142102627760621x^7 \\
& + 0.00967087327815336x^9 \\
& + 0.00712127941391293x^{11} \\
& + 0.00552355646848375x^{13} \\
& + 0.00444514782463692x^{15} \\
& + 0.00367705242846804x^{17} \\
& + 0.00310721681820837x^{19} + O(x^{21})
\end{aligned}
$$
## Geogebra graph
Closes#132210
Main algorithm:
The Taylor series expansion of `asin(x)` is:
```math
\begin{align*}
asin(x) &= x + x^3 / 6 + 3x^5 / 40 + ... \\
&= x \cdot P(x^2) \\
&= x \cdot P(u) &\text{, where } u = x^2.
\end{align*}
```
For the fast path, we perform range reduction mod 1/64 and use degree-7
(minimax + Taylor) polynomials to approximate `P(x^2)`.
When `|x| >= 0.5`, we use the transformation:
```math
u = \frac{1 + x}{2}
```
and apply half-angle formula to reduce `asin(x)` to:
```math
\begin{align*}
asin(x) &= sign(x) \cdot \left( \frac{\pi}{2} - 2 \cdot asin(\sqrt{u}) \right) \\
&= sign(x) \cdot \left( \frac{\pi}{2} - 2 \cdot \sqrt{u} \cdot P(u) \right).
\end{align*}
```
Since `0.5 <= |x| <= 1`, `|u| <= 0.5`. So we can reuse the polynomial
evaluation of `P(u)` when `|x| < 0.5`.
For the accurate path, we redo the computations in 128-bit precision
with degree-15 (minimax + Taylor) polynomials to approximate `P(u)`.
This reverts commit bada9220b87e73c0f4a498b82f883e17eda928d1.
Revert "[libc][stdfix] Implement fixed point `countlsfx` functions in llvm-libc (#125356)"
This reverts commit f2a1103b323492160d7d27a1575fbda709b49036.
This commit does a few things:
* creates libc/docs/headers/ and moves all user API related headers under it.
* updates paths and docgen
* updates the top level index to put these headers under a new "Implementation
Status" tab.
* rename some of the files to be foo.rst for foo.h (except strings, which is
currently a mix of string.h and stdlib.h)
* update the heading of some files to be in the form foo.h.
