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
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`.
Implements the functions `roundeven()`, `roundevenf()`, `roundevenl()`
from the roundeven family of functions introduced in C23. Also
implements `roundevenf128()`.
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.
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.
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.
This one might be a bit controversial since the terminology has been
introduced from the start but I think `FRACTION_LEN` is a better name
here. AFAICT it really is "the number of bits after the decimal dot when
the number is in normal form."
`MANTISSA_WIDTH` is less precise as it's unclear whether we take the
leading bit into account.
This patch also renames most of the properties to use the `_LEN` suffix
and fixes useless casts or variables.
According to [wikipedia](https://en.wikipedia.org/wiki/Exponent_bias)
the "biased exponent" is the encoded form that is always positive
whereas the unbiased form is the actual "real" exponent that can be
positive or negative.
`FPBits` seems to be using `unbiased_exponent` to describe the encoded
form (unsigned). This patch simply use `biased` instead of `unbiased`.
`PlatformDefs.h` does not bring a lot of value as a separate file.
It is transitively included in `FloatProperties.h` and `FPBits.h`. This
patch sinks it into `FloatProperties.h` and removes the associated build
targets.
We compute `pow(x, y)` using the formula
```
pow(x, y) = x^y = 2^(y * log2(x))
```
We follow similar steps as in `log2f(x)` and `exp2f(x)`, by breaking
down into `hi + mid + lo` parts, in which `hi` parts are computed using
the exponent field directly, `mid` parts will use look-up tables, and
`lo` parts are approximated by polynomials.
We add some speedup for common use-cases:
```
pow(2, y) = exp2(y)
pow(10, y) = exp10(y)
pow(x, 2) = x * x
pow(x, 1/2) = sqrt(x)
pow(x, -1/2) = rsqrt(x) - to be added
```
This patch fixes a couple of warnings when compiling with gcc 13:
* CPP/type_traits_test.cpp: 'apply' overrides a member function but is
not marked 'override'
* UnitTest/LibcTest.cpp:98: control reaches end of non-void function
* MPFRWrapper/MPFRUtils.cpp:75: control reaches end of non-void function
* smoke/FrexpTest.h:92: backslash-newline at end of file
* __support/float_to_string.h:118: comparison of unsigned expression in ‘>= 0’ is always true
* test/src/__support/CPP/bitset_test.cpp:197: comparison of unsigned expression in ‘>= 0’ is always true
---------
Signed-off-by: Mikhail R. Gadelha <mikhail@igalia.com>
The accuracy for the MPFR numbers in the strtofloat fuzz test was set
too high, causing rounding issues when rounding to a smaller final
result.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D154150
str method of FPBits class is only used for pretty printing its objects
in tests. It brings cpp::string dependency to FPBits class, which is not ideal
for embedded use case. We move str method to a free function in test utils and
remove this dependency of FPBits class.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D152607
The previous string to float tests didn't check correctness, but due to
the atof differential test proving unreliable the strtofloat fuzz test
has been changed to use MPFR for correctness checking. Some minor bugs
have been found and fixed as well.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D150905
Unit tests for the str() method have also been added.
Previously, a separate test only helper function was being used by the
test matchers which has regressed over many cleanups. Moreover, being a
test only utility, it was not tested separately (and hence the
regression).
Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D150906
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.
Implement exp10f function correctly rounded to all rounding modes.
Algorithm: perform range reduction to reduce
```
10^x = 2^(hi + mid) * 10^lo
```
where:
```
hi is an integer,
0 <= mid * 2^5 < 2^5
-log10(2) / 2^6 <= lo <= log10(2) / 2^6
```
Then `2^mid` is stored in a table of 32 entries and the product `2^hi * 2^mid` is
performed by adding `hi` into the exponent field of `2^mid`.
`10^lo` is then approximated by a degree-5 minimax polynomials generated by Sollya with:
```
> P = fpminimax((10^x - 1)/x, 4, [|D...|], [-log10(2)/64. log10(2)/64]);
```
Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp10f
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput : 10.215
System LIBC reciprocal throughput : 7.944
LIBC reciprocal throughput : 38.538
LIBC reciprocal throughput : 12.175 (with `-msse4.2` flag)
LIBC reciprocal throughput : 9.862 (with `-mfma` flag)
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp10f --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency : 40.744
System LIBC latency : 37.546
BEFORE
LIBC latency : 48.989
LIBC latency : 44.486 (with `-msse4.2` flag)
LIBC latency : 40.221 (with `-mfma` flag)
```
This patch relies on https://reviews.llvm.org/D134002
Reviewed By: orex, zimmermann6
Differential Revision: https://reviews.llvm.org/D134104
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
