Add support for the half-precision complementary error function
`erfcf16``, using a Sollya generated polynomial implementation with
proper handling of special cases.
Extend the MPFR utilities with erfc support to allow tests.
closes: #180927
closes#180171
part of #177259
Here are some extra changes apart from the usual which were needed
1. `libc/src/__support/FPUtil/generic/add_sub.h` → +0 -0 error
2. `libc/src/__support/FPUtil/generic/FMA.h` → implemented to handle
fmabf16(Normal,Normal,+/-INF)
```jsx
/home/runner/work/llvm-project/llvm-project/libc/test/src/math/fmabf16_test.cpp:62: FAILURE
Failed to match __llvm_libc_23_0_0_git::fmabf16(x, y, z) against LIBC_NAMESPACE::testing::mpfr::get_mpfr_matcher<mpfr::Operation::Fma>( input, __llvm_libc_23_0_0_git::fmabf16(x, y, z), 0.5, mpfr::RoundingMode::Nearest).
Input decimal: x: 338953138925153547590470800371487866880.00000000000000000000000000000000000000000000000000 y: 338953138925153547590470800371487866880.00000000000000000000000000000000000000000000000000 z: -inf
First input bits: 0x7F7F = (S: 0, E: 0x00FE, M: 0x007F)
Second input bits: 0x7F7F = (S: 0, E: 0x00FE, M: 0x007F)
Third input bits: (-Infinity)
Libc result: nan
MPFR result: -inf
Libc floating point result bits: (NaN)
MPFR rounded bits: (-Infinity)
```
1. ~~`libc/src/__support/FPUtil/bfloat16.h` → to handle *= operator for
Bfloat16 ( uses the already available mult operator)~~
moved to #182882
The exhaustive test currently includes subnormal range and for checking
for specific edge cases . This is due to the repeated failure at <2^32
input space specifically only for ubuntu 24.04 and 24.04-arm
The removed tests included -> PositiveRange and NegativeRange for
Normals and an extra positive test for subnormals/Denormals
Let me know if there are any changes expected or anything I missed in
this .
cc: @lntue @krishna2803 @overmighty
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:
- bf16fma
- bf16fmaf
- bf16fmal
- bf16fmaf128
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
This PR adds implements following basic math functions for BFloat16 type
along with the tests:
- bf16add
- bf16addf
- bf16addl
- bf16addf128
- bf16sub
- bf16subf
- bf16subl
- bf16subf128
---------
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
Fixes incorrect logic that went unnoticed until the function was tested
with output and input types that have the same underlying floating-point
format.
This PR aims to add the groundwork to test the precision of libc complex
functions against MPC. I took `cargf` as a test to verify that the infra
works fine.
- Implementation of `tan` for 16-bit floating point inputs scaled by pi.
i.e,. `tanpif16()`
- Implementation of Tanpi in MPFRWrapper for MPFR versions < 4.2
- Exhaustive tests for `tanpif16()`
Implementation of `cos` for half precision floating point inputs scaled
by pi (i.e., `cospi`), correctly rounded for all rounding modes.
---------
Co-authored-by: OverMighty <its.overmighty@gmail.com>
- added all variations of ffma and fdiv
- will add all new headers into yaml for next patch
- only fsub is left then all basic operations for float is complete
---------
Co-authored-by: OverMighty <its.overmighty@gmail.com>
Fixes https://github.com/llvm/llvm-project/issues/92874
Algorithm: Let `x = (-1)^s * 2^e * (1 + m)`.
- Step 1: Range reduction: reduce the exponent with:
```
y = cbrt(x) = (-1)^s * 2^(floor(e/3)) * 2^((e % 3)/3) * (1 + m)^(1/3)
```
- Step 2: Use the first 4 bit fractional bits of `m` to look up for a
degree-7 polynomial approximation to:
```
(1 + m)^(1/3) ~ 1 + m * P(m).
```
- Step 3: Perform the multiplication:
```
2^((e % 3)/3) * (1 + m)^(1/3).
```
- Step 4: Check for exact cases to prevent rounding and clear
`FE_INEXACT` floating point exception.
- Step 5: Combine with the exponent and sign before converting down to
`float` and return.
I also fixed a comment in sinpif.cpp in the first commit. Should this be
included in this PR?
All tests were passed, including the exhaustive test.
CC: @lntue
