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 PR implements the following 8 functions along with the tests.
```c++
int idivr(fract, fract);
long int idivlr(long fract, long fract);
int idivk(accum, accum);
long int idivlk(long accum, long accum);
unsigned int idivur(unsigned fract, unsigned fract);
unsigned long int idivulr(unsigned long fract, unsigned long fract);
unsigned int idivuk(unsigned accum, unsigned accum);
unsigned long int idivulk(unsigned long accum, unsigned long accum);
```
ref: https://www.iso.org/standard/51126.htmlFixes#129125
---------
Signed-off-by: krishna2803 <kpandey81930@gmail.com>
Summary:
This patch moves the RPC server handling to be a header only utility
stored in the `shared/` directory. This is intended to be shared within
LLVM for the loaders and `offload/` handling.
Generally, this makes it easier to share code without weird
cross-project binaries being plucked out of the build system. It also
allows us to soon move the loader interface out of the `libc` project so
that we don't need to bootstrap those and can build them in LLVM.
Summary:
Currently we dispatch the writing mode off of a runtime enum passed in
by the constructor. This causes very unfortunate codegen for the GPU
targets where we get worst-case codegen because of the unused function
pointer for `sprintf`. Instead, this patch moves all of this to a
template so it can be masked out. This results in no dynamic stack and
uses 60 VGPRs instead of 117. It also compiles about 5x as fast.
The docs build action was failing with libc due to checks.rst not
existing in the expected path. This patch adjusts the path to the actual
path which seems to make everything happy. It seems like this did not
show up before as stdfix.rst was not included in a place that actually
caused it to get picked up by sphinx.
Move the hdrgen code under a subdirectory to treat it as a Python
module.
This mimics the structure used by llvm/utils/lit and
llvm/utils/mlgo-utils and simplifies integration of hdrgen to the build
system which rely on Python modules. In addition to that, it clarifies
which imports are coming from the hdrgen-specific helpers (e.g. "from
type import ..." becomes "from hdrgen.type import ...".
Leave the entrypoints (top-level main.py and yaml_to_classes.py) as-is:
they can keep being referred by the CMake build system w/o any changes.
Implements the posix-specified strftime conversions for the default
locale, along with comprehensive unit tests. This reuses a lot of design
from printf, as well as the printf writer.
Roughly based on #111305, but with major rewrites.
By far the most important part of this patch is updating
GettingInvolved.rst to include the invite link, but I've grepped for any
other discord.com links.
I'm no Discord expert, but from my experience (confirmed via @preames
kindly testing as well) the direct channel links provide a confusing
experience if you haven't already found and used an invite link to the
LLVM Discord server. If you're logged into Discord but not a member of
LLVM's sever, the web app opens and then...nothing. No channel opens, no
prompt to join the server or even a hint that you need to find an invite
link (and if you're not used to Discord, you likely don't even know
that's necessary).
This patch addresses the issue by providing the invite link where
Discord is mentioned.
This reverts commit bada9220b87e73c0f4a498b82f883e17eda928d1.
Revert "[libc][stdfix] Implement fixed point `countlsfx` functions in llvm-libc (#125356)"
This reverts commit f2a1103b323492160d7d27a1575fbda709b49036.
The existing options for bin→dec float conversion are all based on the
Ryū algorithm, which generates 9 output digits at a time using a table
lookup. For users who can't afford the space cost of the table, the
table-lookup subroutine is replaced with one that computes the needed
table entry on demand, but the algorithm is otherwise unmodified.
The performance problem with computing table entries on demand is that
now you need to calculate a power of 10 for each 9 digits you output.
But if you're calculating a custom power of 10 anyway, it's easier to
just compute one, and multiply the _whole_ mantissa by it.
This patch adds a header file alongside `float_dec_converter.h`, which
replaces the whole Ryū system instead of just the table-lookup routine,
implementing this alternative simpler algorithm. The result is accurate
enough to satisfy (minimally) the accuracy demands of IEEE 754-2019 even
in 128-bit long double. The new float128 test cases demonstrate this by
testing the cases closest to the 39-digit rounding boundary.
In my tests of generating 39 output digits (the maximum number supported
by this algorithm) this code is also both faster and smaller than the
USE_DYADIC_FLOAT version of the existing Ryū code.
Summary:
This introduces libc cache files and adds one for building the GPU
support. The cache files will set defaults for these arguments which can
be overridden if the user needs to. They also serve as documentation for
how the builid is expected to look.
[libc][docs] add cpio to documentation and include related functi…
These changes ensure that the cpio header is documented properly
with respect to the issue
(https://github.com/llvm/llvm-project/issues/122006 ).
**Changes:**
1. **cpio.yaml**: Created a new YAML file for cpio with functions
and related macros.
2. **CMakeLists.txt**: Added cpio to the documentation
directories.
3. **index.rst**: Included `cpio` in the documentation index.
---------
Co-authored-by: siya <siya@Siya.com>
