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
One should be able to do a cross build of the libc now. For example, using
clang on a x86_64 linux host, one can build for an aarch64 linux target by
specifying -DLIBC_TARGET_TRIPLE=aarch64-linux-gnu.
Follow up changes will add a baremetal config and also appropriate
documentation about cross compiling the libc for CPU targets.
Reviewed By: jhuber6
Differential Revision: https://reviews.llvm.org/D140351
This patch introduces documentation for the new GPU mode added in
D138608. The documentation includes instructions for building and using
the library, along with a description of the supported functions and
headers.
Reviewed By: sivachandra, lntue, michaelrj
Differential Revision: https://reviews.llvm.org/D138856
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
Switch from green checkmarks to the following legend:
X = x86_64
A = aarch64
a = arm32
Reviewed By: lntue
Differential Revision: https://reviews.llvm.org/D136020
* Make consistent heading names
* Factor out |check| into an include for reuse
* Use it everywhere (No more YES or UTF-8)
* Remove unneeded summary from pages. People know why they're there.
* Ensure source location headers everywhere.
Differential Revision: https://reviews.llvm.org/D136016
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
Reduce the number of subintervals that need lookup table and optimize
the evaluation steps.
Currently, `exp2f` is computed by reducing to `2^hi * 2^mid * 2^lo` where
`-16/32 <= mid <= 15/32` and `-1/64 <= lo <= 1/64`, and `2^lo` is then
approximated by a degree 6 polynomial.
Experiment with Sollya showed that by using a degree 6 polynomial, we
can approximate `2^lo` for a bigger range with reasonable errors:
```
> P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/64, 1/64]);
> dirtyinfnorm(2^x - 1 - x*P, [-1/64, 1/64]);
0x1.e18a1bc09114def49eb851655e2e5c4dd08075ac2p-63
> P = fpminimax((2^x - 1)/x, 5, [|D...|], [-1/32, 1/32]);
> dirtyinfnorm(2^x - 1 - x*P, [-1/32, 1/32]);
0x1.05627b6ed48ca417fe53e3495f7df4baf84a05e2ap-56
```
So we can optimize the implementation a bit with:
# Reduce the range to `mid = i/16` for `i = 0..15` and `-1/32 <= lo <= 1/32`
# Store the table `2^mid` in bits, and add `hi` directly to its exponent field to compute `2^hi * 2^mid`
# Rearrange the order of evaluating the polynomial approximating `2^lo`.
Performance benchmark using perf tool from the CORE-MATH project on Ryzen 1700:
```
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp2f
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH reciprocal throughput : 9.534
System LIBC reciprocal throughput : 6.229
BEFORE:
LIBC reciprocal throughput : 21.405
LIBC reciprocal throughput : 15.241 (with `-msse4.2` flag)
LIBC reciprocal throughput : 11.111 (with `-mfma` flag)
AFTER:
LIBC reciprocal throughput : 18.617
LIBC reciprocal throughput : 12.852 (with `-msse4.2` flag)
LIBC reciprocal throughput : 9.253 (with `-mfma` flag)
$ CORE_MATH_PERF_MODE="rdtsc" ./perf.sh exp2f --latency
GNU libc version: 2.35
GNU libc release: stable
CORE-MATH latency : 40.869
System LIBC latency : 30.580
BEFORE
LIBC latency : 64.888
LIBC latency : 61.027 (with `-msse4.2` flag)
LIBC latency : 48.778 (with `-mfma` flag)
AFTER
LIBC latency : 48.803
LIBC latency : 45.047 (with `-msse4.2` flag)
LIBC latency : 37.487 (with `-mfma` flag)
```
Reviewed By: sivachandra, orex
Differential Revision: https://reviews.llvm.org/D133870
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
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
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
Add "using" and "status" sections to the sidebar to make getting these
easier.
Fixed mobile formatting not overflow left and right.
Tested:
Chrome on Desktop, using mobile restrictions in devtools.
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D131369
This design is borrowed from the lldb folks (thank you!) to declutter
the page.
* The version number at the top is removed.
* Links are pushed over to a sidebar
* The sidebar has headings
There are other minor changes:
* The warning about this project not being ready is now an RST "warning"
* Links to the Bug Reports and the Source Code are Added
* Refer to this project as either "The LLVM C LIbrary" or "The libc"
Tested:
Built locally
Reviewed By: sivachandra
Differential Revision: https://reviews.llvm.org/D131242
New exp2 function algorithm:
1) Improved performance: 8.176 vs 15.270 by core-math perf tool.
2) Improved accuracy. Only two special values left.
3) Lookup table size reduced twice.
Differential Revision: https://reviews.llvm.org/D129005
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
