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src/__support/math folder. (#162019)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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Optimization flags are now handled through a common flag. These are no
longer necessary.
Fixes #112409
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Based on the double precision's sin/cos fast path algorithm:
Step 1: Perform range reduction `y = x mod pi/8` with target errors <
2^-54.
This is because the worst case mod pi/8 for single precision is ~2^-31,
so to have up to 1 ULP errors from
the range reduction, the targeted errors should `be 2^(-31 - 23) =
2^-54`.
Step 2: Polynomial approximation
We use degree-5 and degree-4 polynomials to approximate sin and cos of
the reduced angle respectively.
Step 3: Combine the results using trig identities
```math
\begin{align*}
\sin(x) &= \sin(y) \cdot \cos(k \cdot \frac{\pi}{8}) + \cos(y) \cdot \sin(k \cdot \frac{\pi}{8}) \\
\cos(x) &= \cos(y) \cdot \cos(k \cdot \frac{\pi}{8}) - \sin(y) \cdot \sin(k \cdot \frac{\pi}{8})
\end{align*}
```
Overall errors: <= 3 ULPs for default rounding modes (tested
exhaustively).
Current limitation: large range reduction requires FMA instructions for
binary32. This restriction will be removed in the followup PR.
---------
Co-authored-by: Petr Hosek <phosek@google.com>
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Closes #164403
GCC fails to compile libc currently. This PR fixes this by capturing
'POLY_COEFFS' by reference.
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src/__support/math folder. (#162017)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#161993)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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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
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src/__support/math folder. (#161992)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#161297)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#161119)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#159897)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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This PR adds log_bf16 higher math function for BFloat16 type along with
the tests.
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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src/__support/math folder. (#154868)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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Addresses #132818
Part of #95250
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This PR adds sqrtbf16 higher math function for BFloat16 type along with
the tests.
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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This PR adds fmodbf16 basic math function for BFloat16 type along with
the tests.
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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This PR implements `atanpif16(x)` which computes
$\frac{\arctan(x)}{\pi}$ for half-precision floating-point numbers using
polynomial approximation with domain reduction.
## Mathematical Implementation
The implementation uses a 15th-degree Taylor polynomial expansion of
$\frac{\arctan(x)}{\pi}$ that's computed using
[`python-sympy`](https://www.sympy.org/en/index.html) and it's accurate
in $|x| \in [0, 0.5)$:
$$
g(x) = \frac{\arctan(x)}{\pi} \approx
\begin{aligned}[t]
& 0.318309886183791x \\
& - 0.106103295394597x^3 \\
& + 0.0636619772367581x^5 \\
& - 0.0454728408833987x^7 \\
& + 0.0353677651315323x^9 \\
& - 0.0289372623803446x^{11} \\
& + 0.0244853758602916x^{13} \\
& - 0.0212206590789194x^{15} + O(x^{17})
\end{aligned}
$$
---
To ensure accuracy across all real inputs, the domain is divided into
three cases with appropriate transformations:
**Case 1: $|x| \leq 0.5$**
Direct polynomial evaluation:
$$\text{atanpi}(x) = \text{sign}(x) \cdot g(|x|)$$
**Case 2: $0.5 < |x| \leq 1$**
Double-angle reduction using:
$$\arctan(x) = 2\arctan\left(\frac{x}{1 + \sqrt{1 + x^2}}\right)$$
$$\text{atanpi}(x) = \text{sign}(x) \cdot 2g\left(\frac{|x|}{1 + \sqrt{1
+ x^2}}\right)$$
**Case 3: $|x| > 1$**
Reciprocal transformation using
$$\arctan(x) = \frac{\pi}{2} - \arctan\left(\frac{1}{x}\right) \
\text{for} \ x \gt 0$$
$$\text{atanpi}(x) = \text{sign}(x) \cdot \left(\frac{1}{2} -
g\left(\frac{1}{|x|}\right)\right)$$
Closes #132212
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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>
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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>
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{canonicalize,iscanonical,fdim,copysign,issignaling}bf16 math functions (#155567)
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>
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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>
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(#154427)
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>
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Compiler runtimes for float16 basic operations might not be correctly
rounded for all rounding modes.
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math functions (#153882)
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>
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This PR adds the nanbf16 basic math function for BFloat16 type along
with the tests.
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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functions (#153994)
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>
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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>
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src/__support/math folder. (#154222)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#154215)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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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>
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src/__support/math folder. (#153582)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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#146226 with fixing asinpi MPFR number function and make it work when
mpfr < `4.2.0`
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src/__support/math folder. (#153427)
Part of #147386
in preparation for:
https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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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>
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src/__support/math folder. (#152871)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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This PR adds the following basic math functions for BFloat16 type along
with the tests:
- bf16div
- bf16divf
- bf16divl
- bf16divf128
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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functions (#152881)
This PR adds the following basic math functions for BFloat16 type along
with the tests:
- fmaximumbf16
- fmaximum_magbf16
- fmaximum_mag_numbf16
- fmaximum_numbf16
- fminimumbf16
- fminimum_magbf16
- fminimum_mag_numbf16
- fminimum_numbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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src/__support/math folder. (#152069)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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This PR adds the following basic math functions for BFloat16 type along
with the tests:
- bf16mul
- bf16mulf
- bf16mull
- bf16mulf128
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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src/__support/math folder. (#151883)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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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>
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src/__support/math folder. (#151846)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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functions (#152352)
This PR implements the following basic math functions for BFloat16 type
along with the tests:
- ceilbf16
- floorbf16
- roundbf16
- roundevenbf16
- truncbf16
---------
Signed-off-by: Krishna Pandey <kpandey81930@gmail.com>
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src/__support/math folder. (#151837)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#151779)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#151399)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#151012)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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src/__support/math folder. (#150993)
Part of #147386
in preparation for: https://discourse.llvm.org/t/rfc-make-clang-builtin-math-functions-constexpr-with-llvm-libc-to-support-c-23-constexpr-math-functions/86450
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