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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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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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Add tests for signaling NaNs, and fix function behavior for handling
signaling NaN input.
Fixes https://github.com/llvm/llvm-project/issues/124812
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LIBC_MATH_SKIP_ACCURATE_PASS is set. (#130811)
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(#130700)
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This is a part of #97655.
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declaration" (#98593)
Reverts llvm/llvm-project#98075
bots are broken
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This is a part of #97655.
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- [libc][NFC] Rename FPBits nan functions
- rename build_signaling_nan in signaling_nan
- rename build_quiet_nan to quiet_nan
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- reland #79113
- Fix aarch64 RISC-V build
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Reverts llvm/llvm-project#79113
It broke aarch64 build bot machines.
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This patch reduces the surface of `FPBits`.
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Another patch is needed to cover `DyadicFloat` and `NormalFloat`
constructors.
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This is step 4 of
https://discourse.llvm.org/t/rfc-customizable-namespace-to-allow-testing-the-libc-when-the-system-libc-is-also-llvms-libc/73079
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Many math functions need to check for floating point rounding modes to
return correct values. Currently most of them use the internal implementation
of `fegetround`, which is platform-dependent and blocking math functions to be
enabled on platforms with unimplemented `fegetround`. In this change, we add
platform independent rounding mode checks and switching math functions to use
them instead. https://github.com/llvm/llvm-project/issues/63016
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D152280
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Differential Revision: https://reviews.llvm.org/D146738
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floating point exceptions.
Switch math functions to use libc_errno and fix some errno and
floating point exceptions
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D145349
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Set FE_OVERFLOW and FE_UNDERFLOW for expf, exp2f, exp10f, expm1f, sinhf
and coshf.
Reviewed By: sivachandra, renyichen
Differential Revision: https://reviews.llvm.org/D144340
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This implements the same behavior as D141997 but makes sure that the same detection mechanism is used between CMake and source code.
Reviewed By: sivachandra, lntue
Differential Revision: https://reviews.llvm.org/D142108
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try_compile instead of try_run."
The build bots are failing.
This reverts commit c84d74f5bfe810744de1268eb0516a6622e4aa73.
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try_run.
This implements the same behavior as D141997 but makes sure that the same detection mechanism is used between CMake and source code.
Differential Revision: https://reviews.llvm.org/D142108
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instead of try_run."
Build bots are failing.
https://lab.llvm.org/buildbot/#/builders/90/builds/44634
This reverts commit 9acc2f37bdfce08ca0c2faec03392db10d1bb7a9.
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This implements the same behavior as D141997 but makes sure that the same detection mechanism is used between CMake and source code.
Differential Revision: https://reviews.llvm.org/D142108
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Change sinf/cosf range reduction to mod pi/32 to be shared with tanf,
since polynomial approximations for tanf on subintervals of length pi/16 do not
provide enough accuracy.
Reviewed By: orex
Differential Revision: https://reviews.llvm.org/D131652
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Refactor common range reductions and evaluations for sinf, cosf, and
sincosf. Added exhaustive tests for sincosf.
Performance before the patch:
```
System LIBC reciprocal throughput : 30.205
LIBC reciprocal throughput : 30.533
System LIBC latency : 67.961
LIBC latency : 61.564
```
Performance after the patch:
```
System LIBC reciprocal throughput : 30.409
LIBC reciprocal throughput : 20.273
System LIBC latency : 67.527
LIBC latency : 61.959
```
Reviewed By: orex
Differential Revision: https://reviews.llvm.org/D130901
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Change `sinf` range reduction to mod pi/16 to be shared with `cosf`.
Previously, `sinf` used range reduction `mod pi`, but this cannot be used to implement `cosf` since the minimax algorithm for `cosf` does not converge due to critical points at `pi/2`. In order to be able to share the same range reduction functions for both `sinf` and `cosf`, we change the range reduction to `mod pi/16` for the following reasons:
- The table size is sufficiently small: 32 entries for `sin(k * pi/16)` with `k = 0..31`. It could be reduced to 16 entries if we treat the final sign separately, with an extra multiplication at the end.
- The polynomials' degrees are reduced to 7/8 from 15, with extra computations to combine `sin` and `cos` with trig sum equality.
- The number of exceptional cases reduced to 2 (with FMA) and 3 (without FMA).
- The latency is reduced while maintaining similar throughput as before.
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D130629
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Implement sinf function that is correctly rounded to all rounding modes.
- We use a simple range reduction for `pi/16 < |x|` :
Let `k = round(x / pi)` and `y = (x/pi) - k`.
So `k` is an integer and `-0.5 <= y <= 0.5`.
Then
```
sin(x) = sin(y*pi + k*pi)
= (-1)^(k & 1) * sin(y*pi)
~ (-1)^(k & 1) * y * P(y^2)
```
where `y*P(y^2)` is a degree-15 minimax polynomial generated by Sollya with:
```
> P = fpminimax(sin(x*pi)/x, [|0, 2, 4, 6, 8, 10, 12, 14|], [|D...|], [0, 0.5]);
```
- Performance benchmark using perf tool from CORE-MATH project
(https://gitlab.inria.fr/core-math/core-math/-/tree/master) on Ryzen 1700:
Before this patch (not correctly rounded):
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinf
CORE-MATH reciprocal throughput : 17.892
System LIBC reciprocal throughput : 25.559
LIBC reciprocal throughput : 29.381
```
After this patch (correctly rounded):
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh sinf
CORE-MATH reciprocal throughput : 17.896
System LIBC reciprocal throughput : 25.740
LIBC reciprocal throughput : 27.872
LIBC reciprocal throughput : 20.012 (with `-msse4.2` flag)
LIBC reciprocal throughput : 14.244 (with `-mfma` flag)
```
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D123154
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Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D117645
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This patch applies the lint rules described in the previous patch. There
was also a significant amount of effort put into manually fixing things,
since all of the templated functions, or structs defined in /spec, were
not updated and had to be handled manually.
Reviewed By: sivachandra, lntue
Differential Revision: https://reviews.llvm.org/D114302
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This expands the pattern suggest in https://reviews.llvm.org/D95850 to all
math functions.
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