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Author SHA1 Message Date
Austin Clements 1d20a362d0 math: avoid assembly stubs
Currently almost all math functions have the following pattern:

func Sin(x float64) float64

func sin(x float64) float64 {
    // ... pure Go implementation ...
}

Architectures that implement a function in assembly provide the
assembly implementation directly as the exported function (e.g., Sin),
and architectures that don't implement it in assembly use a small stub
to jump back to the Go code, like:

TEXT ·Sin(SB), NOSPLIT, $0
	JMP ·sin(SB)

However, most functions are not implemented in assembly on most
architectures, so this jump through assembly is a waste. It defeats
compiler optimizations like inlining. And, with regabi, it actually
adds a small but non-trivial overhead because the jump from assembly
back to Go must go through an ABI0->ABIInternal bridge function.

Hence, this CL reorganizes this structure across the entire package.
It now leans on inlining to achieve peak performance, but allows the
compiler to see all the way through the pure Go implementation.

Now, functions follow this pattern:

func Sin(x float64) float64 {
	if haveArchSin {
		return archSin(x)
	}
	return sin(x)
}

func sin(x float64) float64 {
    // ... pure Go implementation ...
}

Architectures that have assembly implementations use build-tagged
files to set haveArchX to true an provide an archX implementation.
That implementation can also still call back into the Go
implementation (some of them do this).

Prior to this change, enabling ABI wrappers results in a geomean
slowdown of the math benchmarks of 8.77% (full results:
https://perf.golang.org/search?q=upload:20210415.6) and of the Tile38
benchmarks by ~4%. After this change, enabling ABI wrappers is
completely performance-neutral on Tile38 and all but one math
benchmark (full results:
https://perf.golang.org/search?q=upload:20210415.7). ABI wrappers slow
down SqrtIndirectLatency-12 by 2.09%, which makes sense because that
call must still go through an ABI wrapper.

With ABI wrappers disabled (which won't be an option on amd64 much
longer), on linux/amd64, this change is largely performance-neutral
and slightly improves the performance of a few benchmarks:

(Because there are so many benchmarks, I've applied the Šidák
correction to the alpha threshold. It makes relatively little
difference in which benchmarks are statistically significant.)

name                    old time/op  new time/op  delta
Acos-12                 22.3ns ± 0%  18.8ns ± 1%  -15.44%  (p=0.000 n=18+16)
Acosh-12                28.2ns ± 0%  28.2ns ± 0%     ~     (p=0.404 n=18+20)
Asin-12                 18.1ns ± 0%  18.2ns ± 0%   +0.20%  (p=0.000 n=18+16)
Asinh-12                32.8ns ± 0%  32.9ns ± 1%     ~     (p=0.891 n=18+20)
Atan-12                 9.92ns ± 0%  9.90ns ± 1%   -0.24%  (p=0.000 n=17+16)
Atanh-12                27.7ns ± 0%  27.5ns ± 0%   -0.72%  (p=0.000 n=16+20)
Atan2-12                18.5ns ± 0%  18.4ns ± 0%   -0.59%  (p=0.000 n=19+19)
Cbrt-12                 22.1ns ± 0%  22.1ns ± 0%     ~     (p=0.804 n=16+17)
Ceil-12                 0.84ns ± 0%  0.84ns ± 0%     ~     (p=0.663 n=18+16)
Copysign-12             0.84ns ± 0%  0.84ns ± 0%     ~     (p=0.762 n=16+19)
Cos-12                  12.7ns ± 0%  12.7ns ± 1%     ~     (p=0.145 n=19+18)
Cosh-12                 22.2ns ± 0%  22.5ns ± 0%   +1.60%  (p=0.000 n=17+19)
Erf-12                  11.1ns ± 1%  11.1ns ± 1%     ~     (p=0.010 n=19+19)
Erfc-12                 12.6ns ± 1%  12.7ns ± 0%     ~     (p=0.066 n=19+15)
Erfinv-12               16.1ns ± 0%  16.1ns ± 0%     ~     (p=0.462 n=17+20)
Erfcinv-12              16.0ns ± 1%  16.0ns ± 1%     ~     (p=0.015 n=17+16)
Exp-12                  16.3ns ± 0%  16.5ns ± 1%   +1.25%  (p=0.000 n=19+16)
ExpGo-12                36.2ns ± 1%  36.1ns ± 1%     ~     (p=0.242 n=20+18)
Expm1-12                18.6ns ± 0%  18.7ns ± 0%   +0.25%  (p=0.000 n=16+19)
Exp2-12                 34.7ns ± 0%  34.6ns ± 1%     ~     (p=0.010 n=19+18)
Exp2Go-12               34.8ns ± 1%  34.8ns ± 1%     ~     (p=0.372 n=19+19)
Abs-12                  0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.766 n=18+16)
Dim-12                  0.84ns ± 1%  0.84ns ± 1%     ~     (p=0.167 n=17+19)
Floor-12                0.84ns ± 0%  0.84ns ± 0%     ~     (p=0.993 n=18+16)
Max-12                  3.35ns ± 0%  3.35ns ± 0%     ~     (p=0.894 n=17+19)
Min-12                  3.35ns ± 0%  3.36ns ± 1%     ~     (p=0.214 n=18+18)
Mod-12                  35.2ns ± 0%  34.7ns ± 0%   -1.45%  (p=0.000 n=18+17)
Frexp-12                5.31ns ± 0%  4.75ns ± 0%  -10.51%  (p=0.000 n=19+18)
Gamma-12                14.8ns ± 0%  16.2ns ± 1%   +9.21%  (p=0.000 n=20+19)
Hypot-12                6.16ns ± 0%  6.17ns ± 0%   +0.26%  (p=0.000 n=19+20)
HypotGo-12              7.79ns ± 1%  7.78ns ± 0%     ~     (p=0.497 n=18+17)
Ilogb-12                4.47ns ± 0%  4.47ns ± 0%     ~     (p=0.167 n=19+19)
J0-12                   76.0ns ± 0%  76.3ns ± 0%   +0.35%  (p=0.000 n=19+18)
J1-12                   76.8ns ± 1%  75.9ns ± 0%   -1.14%  (p=0.000 n=18+18)
Jn-12                    167ns ± 1%   168ns ± 1%     ~     (p=0.038 n=18+18)
Ldexp-12                6.98ns ± 0%  6.43ns ± 0%   -7.97%  (p=0.000 n=17+18)
Lgamma-12               15.9ns ± 0%  16.0ns ± 1%     ~     (p=0.011 n=20+17)
Log-12                  13.3ns ± 0%  13.4ns ± 1%   +0.37%  (p=0.000 n=15+18)
Logb-12                 4.75ns ± 0%  4.75ns ± 0%     ~     (p=0.831 n=16+18)
Log1p-12                19.5ns ± 0%  19.5ns ± 1%     ~     (p=0.851 n=18+17)
Log10-12                15.9ns ± 0%  14.0ns ± 0%  -11.92%  (p=0.000 n=17+16)
Log2-12                 7.88ns ± 1%  8.01ns ± 0%   +1.72%  (p=0.000 n=20+20)
Modf-12                 4.75ns ± 0%  4.34ns ± 0%   -8.66%  (p=0.000 n=19+17)
Nextafter32-12          5.31ns ± 0%  5.31ns ± 0%     ~     (p=0.389 n=17+18)
Nextafter64-12          5.03ns ± 1%  5.03ns ± 0%     ~     (p=0.774 n=17+18)
PowInt-12               29.9ns ± 0%  28.5ns ± 0%   -4.69%  (p=0.000 n=18+19)
PowFrac-12              91.0ns ± 0%  91.1ns ± 0%     ~     (p=0.029 n=19+19)
Pow10Pos-12             1.12ns ± 0%  1.12ns ± 0%     ~     (p=0.363 n=20+20)
Pow10Neg-12             3.90ns ± 0%  3.90ns ± 0%     ~     (p=0.921 n=17+18)
Round-12                2.31ns ± 0%  2.31ns ± 1%     ~     (p=0.390 n=18+18)
RoundToEven-12          0.84ns ± 0%  0.84ns ± 0%     ~     (p=0.280 n=18+19)
Remainder-12            31.6ns ± 0%  29.6ns ± 0%   -6.16%  (p=0.000 n=18+17)
Signbit-12              0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.385 n=19+18)
Sin-12                  12.5ns ± 0%  12.5ns ± 0%     ~     (p=0.080 n=18+18)
Sincos-12               16.4ns ± 2%  16.4ns ± 2%     ~     (p=0.253 n=20+19)
Sinh-12                 26.1ns ± 0%  26.1ns ± 0%   +0.18%  (p=0.000 n=17+19)
SqrtIndirect-12         3.91ns ± 0%  3.90ns ± 0%     ~     (p=0.133 n=19+19)
SqrtLatency-12          2.79ns ± 0%  2.79ns ± 0%     ~     (p=0.226 n=16+19)
SqrtIndirectLatency-12  6.68ns ± 0%  6.37ns ± 2%   -4.66%  (p=0.000 n=17+20)
SqrtGoLatency-12        49.4ns ± 0%  49.4ns ± 0%     ~     (p=0.289 n=18+16)
SqrtPrime-12            3.18µs ± 0%  3.18µs ± 0%     ~     (p=0.084 n=17+18)
Tan-12                  13.8ns ± 0%  13.9ns ± 2%     ~     (p=0.292 n=19+20)
Tanh-12                 25.4ns ± 0%  25.4ns ± 0%     ~     (p=0.101 n=17+17)
Trunc-12                0.84ns ± 0%  0.84ns ± 0%     ~     (p=0.765 n=18+16)
Y0-12                   75.8ns ± 0%  75.9ns ± 1%     ~     (p=0.805 n=16+18)
Y1-12                   76.3ns ± 0%  75.3ns ± 1%   -1.34%  (p=0.000 n=19+17)
Yn-12                    164ns ± 0%   164ns ± 2%     ~     (p=0.356 n=18+20)
Float64bits-12          0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.383 n=18+18)
Float64frombits-12      0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.066 n=18+19)
Float32bits-12          0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.889 n=16+19)
Float32frombits-12      0.56ns ± 0%  0.56ns ± 0%     ~     (p=0.007 n=18+19)
FMA-12                  23.9ns ± 0%  24.0ns ± 0%   +0.31%  (p=0.000 n=16+17)
[Geo mean]              9.86ns       9.77ns        -0.87%

(https://perf.golang.org/search?q=upload:20210415.5)

For #40724.

Change-Id: I44fbba2a17be930ec9daeb0a8222f55cd50555a0
Reviewed-on: https://go-review.googlesource.com/c/go/+/310331
Trust: Austin Clements <austin@google.com>
Reviewed-by: Cherry Zhang <cherryyz@google.com>
2021-04-15 15:48:19 +00:00
Bill O'Farrell 88672de7af math: use SIMD to accelerate additional scalar math functions on s390x
As necessary, math functions were structured to use stubs, so that they can
be accelerated with assembly on any platform.

Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.

Benchmark         New     Old     Speedup
BenchmarkAcos     12.2    47.5    3.89
BenchmarkAcosh    18.5    56.2    3.04
BenchmarkAsin     13.1    40.6    3.10
BenchmarkAsinh    19.4    62.8    3.24
BenchmarkAtan     10.1    23      2.28
BenchmarkAtanh    19.1    53.2    2.79
BenchmarkAtan2    16.5    33.9    2.05
BenchmarkCbrt     14.8    58      3.92
BenchmarkErf      10.8    20.1    1.86
BenchmarkErfc     11.2    23.5    2.10
BenchmarkExp      8.77    53.8    6.13
BenchmarkExpm1    10.1    38.3    3.79
BenchmarkLog      13.1    40.1    3.06
BenchmarkLog1p    12.7    38.3    3.02
BenchmarkPowInt   31.7    40.5    1.28
BenchmarkPowFrac  33.1    141     4.26
BenchmarkTan      11.5    30      2.61

Accuracy was tested against a high precision
reference function to determine maximum error.
Note: ulperr is error in "units in the last place"

       max
      ulperr
Acos  1.15
Acosh 1.07
Asin  2.22
Asinh 1.72
Atan  1.41
Atanh 3.00
Atan2 1.45
Cbrt  1.18
Erf   1.29
Erfc  4.82
Exp   1.00
Expm1 2.26
Log   0.94
Log1p 2.39
Tan   3.14

Pow will have 99.99% correctly rounded results with reasonable inputs
producing numeric (non Inf or NaN) results

Change-Id: I850e8cf7b70426e8b54ec49d74acd4cddc8c6cb2
Reviewed-on: https://go-review.googlesource.com/38585
Reviewed-by: Michael Munday <munday@ca.ibm.com>
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
2017-05-08 19:52:30 +00:00
Brad Fitzpatrick 5fea2ccc77 all: single space after period.
The tree's pretty inconsistent about single space vs double space
after a period in documentation. Make it consistently a single space,
per earlier decisions. This means contributors won't be confused by
misleading precedence.

This CL doesn't use go/doc to parse. It only addresses // comments.
It was generated with:

$ perl -i -npe 's,^(\s*// .+[a-z]\.)  +([A-Z]),$1 $2,' $(git grep -l -E '^\s*//(.+\.)  +([A-Z])')
$ go test go/doc -update

Change-Id: Iccdb99c37c797ef1f804a94b22ba5ee4b500c4f7
Reviewed-on: https://go-review.googlesource.com/20022
Reviewed-by: Rob Pike <r@golang.org>
Reviewed-by: Dave Day <djd@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
2016-03-02 00:13:47 +00:00
Russ Cox c007ce824d build: move package sources from src/pkg to src
Preparation was in CL 134570043.
This CL contains only the effect of 'hg mv src/pkg/* src'.
For more about the move, see golang.org/s/go14nopkg.
2014-09-08 00:08:51 -04:00