Implement double precision log10 function correctly rounded for all
rounding modes. This implementation currently needs FMA instructions for
correctness.
Use 2 passes:
Fast pass:
- 1 step range reduction with a lookup table of `2^7 = 128` elements to reduce the ranges to `[-2^-7, 2^-7]`.
- Use a degree-7 minimax polynomial generated by Sollya, evaluated using a mixed of double-double and double precisions.
- Apply Ziv's test for accuracy.
Accurate pass:
- Apply 5 more range reduction steps to reduce the ranges further to [-2^-27, 2^-27].
- Use a degree-4 minimax polynomial generated by Sollya, evaluated using 192-bit precisions.
- By the result of Lefevre (add quote), this is more than enough for correct rounding to all rounding modes.
In progress: Adding detail documentations about the algorithm.
Depend on: https://reviews.llvm.org/D136799
Reviewed By: zimmermann6
Differential Revision: https://reviews.llvm.org/D139846
The `assert.h` and `ctype.h` headers are never built despite their
entrypoints being present in the generated library. This patch adds a
dependency on these headers so that they will be built properly.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D138142
Implement gettimeofday per
.../onlinepubs/9699919799/functions/gettimeofday.html.
This call clock_gettime to implement gettimeofday function.
Tested:
Limited unit test: This makes a call and checks that no error was
returned. Used nanosleep for 100 microseconds and verfified it
returns a value that elapses more than 100 microseconds and less
than 300 microseconds.
Co-authored-by: Jeff Bailey <jeffbailey@google.com>
Differential Revision: https://reviews.llvm.org/D137881
Tested:
Limited unit test: This makes a call and checks that no error was
returned, but we currently don't have the ability to ensure that
time has elapsed as expected.
Co-authored-by: Jeff Bailey <jeffbailey@google.com>
Reviewed By: sivachandra, jeffbailey
Differential Revision: https://reviews.llvm.org/D134095
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
To use the FILE data structure, LLVM-libc must be in fullbuild mode
since it expects its own implementation. This means that (f)printf can't
be used without fullbuild, but s(n)printf only uses strings. This patch
adjusts the CMake to allow for this.
Reviewed By: sivachandra, lntue
Differential Revision: https://reviews.llvm.org/D131913
Implement tanf function correctly rounded for all rounding modes.
We use the range reduction that is shared with `sinf`, `cosf`, and `sincosf`:
```
k = round(x * 32/pi) and y = x * (32/pi) - k.
```
Then we use the tangent of sum formula:
```
tan(x) = tan((k + y)* pi/32) = tan((k mod 32) * pi / 32 + y * pi/32)
= (tan((k mod 32) * pi/32) + tan(y * pi/32)) / (1 - tan((k mod 32) * pi/32) * tan(y * pi/32))
```
We need to make a further reduction when `k mod 32 >= 16` due to the pole at `pi/2` of `tan(x)` function:
```
if (k mod 32 >= 16): k = k - 31, y = y - 1.0
```
And to compute the final result, we store `tan(k * pi/32)` for `k = -15..15` in a table of 32 double values,
and evaluate `tan(y * pi/32)` with a degree-11 minimax odd polynomial generated by Sollya with:
```
> P = fpminimax(tan(y * pi/32)/y, [|0, 2, 4, 6, 8, 10|], [|D...|], [0, 1.5]);
```
Performance benchmark using `perf` tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh tanf
CORE-MATH reciprocal throughput : 18.586
System LIBC reciprocal throughput : 50.068
LIBC reciprocal throughput : 33.823
LIBC reciprocal throughput : 25.161 (with `-msse4.2` flag)
LIBC reciprocal throughput : 19.157 (with `-mfma` flag)
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh tanf --latency
GNU libc version: 2.31
GNU libc release: stable
CORE-MATH latency : 55.630
System LIBC latency : 106.264
LIBC latency : 96.060
LIBC latency : 90.727 (with `-msse4.2` flag)
LIBC latency : 82.361 (with `-mfma` flag)
```
Reviewed By: orex
Differential Revision: https://reviews.llvm.org/D131715
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.
```
Not all attributes have been added to phtread_attr_t in this patch. They
will be added gradually in future patches.
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D123423
A simple implementation of the getters and setters has been added. More
logic can be added to them in future as required.
Reviewed By: michaelrj
Differential Revision: https://reviews.llvm.org/D122969
