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
Performance by core-math (core-math/glibc 2.31/current llvm-14):
10.845/43.174/13.467
The review is done on top of D132809.
Differential Revision: https://reviews.llvm.org/D132811
Migrating all private STL code to the standard STL case but keeping it under the CPP namespace to avoid confusion. Starting with the type_traits header.
Differential Revision: https://reviews.llvm.org/D130727
The specified rounding mode will be used and restored
to what it was before the test ran.
Additionally, it moves ForceRoundingMode and RoundingMode
out of MPFRUtils to be used in more places.
Differential Revision: https://reviews.llvm.org/D129685
This is a implementation of find remainder fmod function from standard libm.
The underline algorithm is developed by myself, but probably it was first
invented before.
Some features of the implementation:
1. The code is written on more-or-less modern C++.
2. One general implementation for both float and double precision numbers.
3. Spitted platform/architecture dependent and independent code and tests.
4. Tests covers 100% of the code for both float and double numbers. Tests cases with NaN/Inf etc is copied from glibc.
5. The new implementation in general 2-4 times faster for “regular” x,y values. It can be 20 times faster for x/y huge value, but can also be 2 times slower for double denormalized range (according to perf tests provided).
6. Two different implementation of division loop are provided. In some platforms division can be very time consuming operation. Depend on platform it can be 3-10 times slower than multiplication.
Performance tests:
The test is based on core-math project (https://gitlab.inria.fr/core-math/core-math). By Tue Ly suggestion I took hypot function and use it as template for fmod. Preserving all test cases.
`./check.sh <--special|--worst> fmodf` passed.
`CORE_MATH_PERF_MODE=rdtsc ./perf.sh fmodf` results are
```
GNU libc version: 2.35
GNU libc release: stable
21.166 <-- FPU
51.031 <-- current glibc
37.659 <-- this fmod version.
```
Based on RLIBM implementation similar to logf and log2f. Most of the exceptional inputs are the exact powers of 10.
Reviewed By: sivachandra, zimmermann6, santoshn, jpl169
Differential Revision: https://reviews.llvm.org/D118093
Add an extra argument for rounding mode to EXPECT_MPFR_MATCH and ASSERT_MPFR_MATCH macros.
Reviewed By: sivachandra, michaelrj
Differential Revision: https://reviews.llvm.org/D116777
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
Fix a bug in MPFRUtils making ULP values off by 2^(-mantissaWidth) and incorrect eps for denormal numbers.
Differential Revision: https://reviews.llvm.org/D114878
We may want to restrict the detected platforms to only `x86_64` and `aarch64`.
There are still custom detection in api.td but I don't think we can handle these:
- config/linux/api.td:205
- config/linux/api.td:199
Differential Revision: https://reviews.llvm.org/D112818
We may want to restrict the detected platforms to only `x86_64` and `aarch64`.
There are still custom detection in api.td but I don't think we can handle these:
- config/linux/api.td:205
- config/linux/api.td:199
Differential Revision: https://reviews.llvm.org/D112818
The idea is to move all pieces related to the actual libc sources to the
"src" directory. This allows downstream users to ship and build just the
"src" directory.
Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D112653
These functions will be used in a future patch to implement
trigonometric functions. Unit tests have been added but to the
libc-long-running-tests suite. The unit tests long running because we
compare against MPFR computations performed at 1280 bits of precision.
Some cleanups or elimination of repeated patterns can be done as follow
up changes.
Differential Revision: https://reviews.llvm.org/D104817
Some ctype functions are called from other libc functions (e.g. isspace
is used in atoi). By moving ctype_utils.h to __support it becomes easier
to include just the implementations of these functions. For these
reasons the implementation for isspace was moved into
ctype_utils as well.
FPUtils was moved to simplify the build order, and to clarify which
files are a part of the actual libc.
Many files were modified to accomodate these changes, mostly changing
the #include paths.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D107600
Use expm1f(x) = exp(x) - 1 for |x| > ln(2).
For |x| <= ln(2), divide it into 3 subintervals: [-ln2, -1/8], [-1/8, 1/8], [1/8, ln2]
and use a degree-6 polynomial approximation generated by Sollya's fpminmax for each interval.
Errors < 1.5 ULPs when we use fma to evaluate the polynomials.
Differential Revision: https://reviews.llvm.org/D101134
The implementations use the x86_64 FPU instructions. These instructions
are extremely slow compared to a polynomial based software
implementation. Also, their accuracy falls drastically once the input
goes beyond 2PI. To improve both the speed and accuracy, we will be
taking the following approach going forward:
1. As a follow up to this CL, we will implement a range reduction algorithm
which will expand the accuracy to the entire double precision range.
2. After that, we will replace the HW instructions with a polynomial
implementation to improve the run time.
After step 2, the implementations will be accurate, performant and target
architecture independent.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D102384
This helps us avoid the uncomfortable reinterpret-casts. Avoiding the
reinterpret casts prevents us from tripping the sanitizers as well.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D100360
This class is to serve as a replacement for llvm::StringRef as part of
the plans to limit dependency on other parts of LLVM. One use of
llvm::StringRef in MPFRWrapper has been replaced with the new class.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D97330
A new function to MPFRWrapper has been added, which is used to set up
the unit tests.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D93007
Tue Ly