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Algorithm:
```
1) atan(x) = sign(x) * atan(|x|)
2) If |x| > 1 + 1/32, atan(|x|) = pi/2 - atan(1/|x|)
3) For 1/16 < |x| < 1 + 1/32, we find k such that: | |x| - k/16 | <= 1/32.
Let y = |x| - k/16, then using the angle summation formula, we have:
atan(|x|) = atan(k/16) + atan( (|x| - k/16) / (1 + |x| * k/16) )
= atan(k/16) + atan( y / (1 + (y + k/16) * k/16 )
= atan(k/16) + atan( y / ((1 + k^2/256) + y * k/16) )
4) Let u = y / (1 + k^2/256), then we can rewritten the above as:
atan(|x|) = atan(k/16) + atan( u / (1 + u * k/16) )
~ atan(k/16) + (u - k/16 * u^2 + (k^2/256 - 1/3) * u^3 +
+ (k/16 - (k/16)^3) * u^4) + O(u^5)
```
With all the computations are done in single precision (float), the
total of approximation errors and rounding errors is bounded by 4 ULPs.
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This is one more follow-up to PR
https://github.com/llvm/llvm-project/pull/157517 that cleans up the
usage of
libc_errno in math unit-tests (non-smoke). It follows the same rule:
* if you use libc_errno in code literally, include
src/__support/libc_errno.h
* if you only rely on errno constants, include hdr/errno_macros.h
Several tests for exp/log still retain the direct libc_errno usage,
since in some cases they skip doing any validation if the error was
raised. But the direct usage of libc_errno is removed from all other
cases.
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<stdint.h> includes. (#150303)
https://github.com/llvm/llvm-project/issues/149993
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LIBC_ERRNO_MODE_SYSTEM to be header-only. (#143187)
This is the first step 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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(#88816)
Adds more FP test macros for the upcoming test adds for #61092 and the
issues opened from it: #88768, #88769, #88770, #88771, #88772.
Fix bug in `{EXPECT,ASSERT}_FP_EXCEPTION`. `EXPECT_FP_EXCEPTION(0)`
seems to be used to test that an exception did not happen, but it always
does `EXPECT_GE(... & 0, 0)` which never fails.
Update and refactor tests that break after the above bug fix. An
interesting way things broke after the above change is that
`ForceRoundingMode` and `quick_get_round()` were raising the inexact
exception, breaking a lot of the `atan*` tests.
The changes for all files other than `FPMatcher.h` and
`libc/test/src/math/smoke/RoundToIntegerTest.h` should have the same
semantics as before. For `RoundToIntegerTest.h`, lines 56-58 before the
changes do not always hold since this test is used for functions with
different exception and errno behavior like `lrint` and `lround`. I've
deleted those lines for now, but tests for those cases should be added
for the different nearest int functions to account for this.
Adding @nickdesaulniers for review.
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Context: https://github.com/llvm/llvm-project/pull/87017
- Add proxy header `libc/hdr/math_macros.h` that will:
- include `<math.h>` in overlay mode,
- include `"include/llvm-libc-macros/math-macros.h"` in full build mode.
- Its corresponding CMake target `libc.hdr.math_macros` will only depend
on `libc.include.math` and `libc.include.llvm-libc-macros.math_macros`
in full build mode.
- Replace all `#include "include/llvm-libc-macros/math-macros.h"` with
`#include "hdr/math_macros.h"`.
- Add dependency to `libc.hdr.math_macros` CMake target when using
`add_fp_unittest`.
- Update the remaining dependency.
- Update bazel overlay: add `libc:hdr_math_macros` target, and replacing
all dependency on `libc:llvm_libc_macros_math_macros` with
`libc:hdr_math_macros`.
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We compute atan2f(y, x) in 2 stages:
- Fast step: perform computations in double precision , with relative
errors < 2^-50
- Accurate step: if the result from the Fast step fails Ziv's rounding
test, then we perform computations in double-double precision, with
relative errors < 2^-100.
On Ryzen 5900X, worst-case latency is ~ 200 clocks, compared to average
latency ~ 60 clocks, and average reciprocal throughput ~ 20 clocks.
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Simplify the range reduction logic and computations. Performance test
using `perf.sh` from CORE-MATH project on Ryzen 5900X:
Before:
```
$ ./perf.sh atanf --rdtsc --path1
LIBC-location: /home/lnt/experiment/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 14.369 + 0.556 clc/call; Median-Min = 0.613 clc/call; Max = 15.061 clc/call;
-- System LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 26.180 + 0.015 clc/call; Median-Min = 0.014 clc/call; Max = 26.260 clc/call;
-- LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 21.237 + 0.022 clc/call; Median-Min = 0.020 clc/call; Max = 21.272 clc/call;
$ ./perf.sh atanf --rdtsc --path1 --latency
LIBC-location: /home/lnt/experiment/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH latency --
[####################] 100 %
Ntrial = 20 ; Min = 50.505 + 0.045 clc/call; Median-Min = 0.037 clc/call; Max = 50.579 clc/call;
-- System LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 62.438 + 0.836 clc/call; Median-Min = 0.049 clc/call; Max = 64.498 clc/call;
-- LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 67.781 + 0.546 clc/call; Median-Min = 0.028 clc/call; Max = 68.844 clc/call;
```
After:
```
$ ./perf.sh atanf --rdtsc --path2
LIBC-location: /home/lnt/experiment/llvm/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 14.400 + 0.353 clc/call; Median-Min = 0.404 clc/call; Max = 14.863 clc/call;
-- System LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 25.247 + 0.783 clc/call; Median-Min = 0.714 clc/call; Max = 26.238 clc/call;
-- LIBC reciprocal throughput --
[####################] 100 %
Ntrial = 20 ; Min = 13.751 + 0.158 clc/call; Median-Min = 0.140 clc/call; Max = 14.006 clc/call;
$ ./perf.sh atanf --rdtsc --path2 --latency
LIBC-location: /home/lnt/experiment/llvm/llvm-project/build/projects/libc/lib/libllvmlibc.a
GNU libc version: 2.35
GNU libc release: stable
-- CORE-MATH latency --
[####################] 100 %
Ntrial = 20 ; Min = 51.837 + 0.073 clc/call; Median-Min = 0.058 clc/call; Max = 52.000 clc/call;
-- System LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 62.487 + 1.878 clc/call; Median-Min = 1.965 clc/call; Max = 64.569 clc/call;
OK
-- LIBC latency --
[####################] 100 %
Ntrial = 20 ; Min = 55.414 + 1.312 clc/call; Median-Min = 0.345 clc/call; Max = 58.362 clc/call;
```
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Reland of #84991
A downstream overlay mode user ran into issues with the isnan macro not
working in our sources with a specific libc configuration. This patch
replaces the last direct includes of math.h with our internal
math_macros.h, along with the necessary build system changes.
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Having libc_errno outside of the namespace causes versioning issues when
trying to link the tests against LLVM-libc. Most of this patch is just
moving libc_errno inside the namespace in tests. This isn't necessary in
the function implementations since those are already inside the
namespace.
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The semantics for casting can range from "bitcast" (same representation)
to "different representation", to "type promotion". Here we remove the
cast operator and force usage of `get_val` as the only function to get
the floating point value, making the intent clearer and more consistent.
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The test for atanf used <initializer_list> to simplify iterating through
an array. This caused issues with the new features.h change by creating
a
libcpp dependency in the test. This change moves the list to an array
variable, removing the need for that dependency.
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(#69558)
Clean up usage of `DECLARE_SPECIAL_CONSTANTS` in global scope.
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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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Fix signed zeros for acosf, acoshf, and atanf in FE_DOWNWARD mode.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D159476
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Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D151798
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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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This part of the effort to make all test related pieces into the `test`
directory. This helps is excluding test related pieces in a straight
forward manner if LLVM_INCLUDE_TESTS is OFF. Future patches will also move
the MPFR wrapper and testutils into the 'test' directory.
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Differential Revision: https://reviews.llvm.org/D134917
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Performance by core-math (core-math/glibc 2.31/current llvm-14):
28.879/20.843/20.15
Differential Revision: https://reviews.llvm.org/D132842
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