Implement acosf function correctly rounded for all rounding modes.
We perform range reduction as follows:
- When `|x| < 2^(-10)`, we use cubic Taylor polynomial:
```
acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 / 6.
```
- When `2^(-10) <= |x| <= 0.5`, we use the same approximation that is used for `asinf(x)` when `|x| <= 0.5`:
```
acos(x) = pi/2 - asin(x) ~ pi/2 - x - x^3 * P(x^2).
```
- When `0.5 < x <= 1`, we use the double angle formula: `cos(2y) = 1 - 2 * sin^2 (y)` to reduce to:
```
acos(x) = 2 * asin( sqrt( (1 - x)/2 ) )
```
- When `-1 <= x < -0.5`, we reduce to the positive case above using the formula:
```
acos(x) = pi - acos(-x)
```
Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh acosf
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput : 28.613
System LIBC reciprocal throughput : 29.204
LIBC reciprocal throughput : 24.271
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh asinf --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency : 55.554
System LIBC latency : 76.879
LIBC latency : 62.118
```
Reviewed By: orex, zimmermann6
Differential Revision: https://reviews.llvm.org/D133550
This function cannot have any instrumentation because it's
assembly must match exactly what the debugger is expecting.
Previously it was just a list of what sanitizers we expect
libc would be sanitized with but this is untenable.
Update the utility functions for checking exceptional values of math
functions to use cpp::optional return values.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D133134
This adds division and power implementations to UInt. Modulo and
division are handled by the same function. These are necessary for some
higher order mathematics, often involving large floating point numbers.
Reviewed By: sivachandra, lntue
Differential Revision: https://reviews.llvm.org/D132184
builtin_wrappers contains the wrappers for the clz builtins, which do
not depend on anything in fputil. This patch moves the file out of
FPUtil. The location is updated as appropriate.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D133035
The implementation currently supports only non-thumb mode. As a test for
the implementation, mmap and munmap functions have been enabled.
Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D132825
The libc.src.__support.FPUtil.fputil target encompassed many unrelated
files, and provided a lot of hidden dependencies. This patch splits out
all of these files into component parts and cleans up the cmake files
that used them. It does not touch any source files for simplicity, but
there may be changes made to them in future patches.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D132980
Performance by core-math (core-math/glibc 2.31/current llvm-14):
10.845/43.174/13.467
The review is done on top of D132809.
Differential Revision: https://reviews.llvm.org/D132811
1) `double log2_eval(double)` function added with better than float precision is added.
2) Some refactoring done to put all auxiliary functions and corresponding data
to one place to reuse the code.
3) Added tests for new functions.
4) Performance and precision tests of the function shows, that it more precise than exiting log2,
(no exceptional cases), but timing is ~5% higer that on current one.
Differential Revision: https://reviews.llvm.org/D132809
This patch allows for adjusting the size of the array that printf uses
to track the types of arguments in index mode. This is useful for
optimizing the tradeoff between memory usage and performance.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D131993
The FormatSection and the writer functions both previously took a char*
and a length to represent a string. Now they use the StringView class to
represent that more succinctly. This change also required fixing
everywhere these were used, so it touches a lot of files.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D131994
