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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
Iskander Sharipov 0fbaf6ca8b math,net: omit explicit true tag expr in switch
Performed `switch true {}` => `switch {}` replacement.

Found using https://go-critic.github.io/overview.html#switchTrue-ref

Change-Id: Ib39ea98531651966a5a56b7bd729b46e4eeb7f7c
Reviewed-on: https://go-review.googlesource.com/123378
Run-TryBot: Iskander Sharipov <iskander.sharipov@intel.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
2018-08-20 22:15:59 +00:00
erifan01 ed6c6c9c11 math: optimize sinh and cosh
Improve performance by reducing unnecessary function calls

Benchmarks:

Tme    old time/op  new time/op  delta
Cosh-8   229ns ± 0%   138ns ± 0%  -39.74%  (p=0.008 n=5+5)
Sinh-8   231ns ± 0%   139ns ± 0%  -39.83%  (p=0.008 n=5+5)

Change-Id: Icab5485849bbfaafca8429d06b67c558101f4f3c
Reviewed-on: https://go-review.googlesource.com/85477
Reviewed-by: Robert Griesemer <gri@golang.org>
2018-02-27 04:34:37 +00:00
Thanabodee Charoenpiriyakij 1124fa300b math: use Abs rather than if x < 0 { x = -x }
This is the benchmark result base on darwin with amd64 architecture:

name     old time/op  new time/op  delta
Cos      10.2ns ± 2%  10.3ns ± 3%  +1.18%  (p=0.032 n=10+10)
Cosh     25.3ns ± 3%  24.6ns ± 2%  -3.00%  (p=0.000 n=10+10)
Hypot    6.40ns ± 2%  6.19ns ± 3%  -3.36%  (p=0.000 n=10+10)
HypotGo  7.16ns ± 3%  6.54ns ± 2%  -8.66%  (p=0.000 n=10+10)
J0       66.0ns ± 2%  63.7ns ± 1%  -3.42%  (p=0.000 n=9+10)

Fixes #21812

Change-Id: I2b88fbdfc250cd548f8f08b44ce2eb172dcacf43
Reviewed-on: https://go-review.googlesource.com/84437
Reviewed-by: Giovanni Bajo <rasky@develer.com>
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
Run-TryBot: Giovanni Bajo <rasky@develer.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
2018-02-13 20:12:23 +00:00
Bill O'Farrell b6a15683f0 math: use SIMD to accelerate some scalar math functions on s390x
Note, most math functions are structured to use stubs, so that they can
be accelerated with assembly on any platform.
Sinh, cosh, and tanh were not structued with stubs, so this CL does
that. This set of routines was chosen as likely to produce good speedups
with assembly on any platform.

Technique used was minimax polynomial approximation using tables of
polynomial coefficients, with argument range reduction.
A table of scaling factors was also used for cosh and log10.

                     before       after      speedup
BenchmarkCos         22.1 ns/op   6.79 ns/op  3.25x
BenchmarkCosh       125   ns/op  11.7  ns/op 10.68x
BenchmarkLog10       48.4 ns/op  12.5  ns/op  3.87x
BenchmarkSin         22.2 ns/op   6.55 ns/op  3.39x
BenchmarkSinh       125   ns/op  14.2  ns/op  8.80x
BenchmarkTanh        65.0 ns/op  15.1  ns/op  4.30x

Accuracy was tested against a high precision
reference function to determine maximum error.
Approximately 4,000,000 points were tested for each function,
producing the following result.
Note: ulperr is error in "units in the last place"

       max
      ulperr
sin    1.43 (returns NaN beyond +-2^50)
cos    1.79 (returns NaN beyond +-2^50)
cosh   1.05
sinh   3.02
tanh   3.69
log10  1.75

Also includes a set of tests to test non-vector functions even
when SIMD is enabled

Change-Id: Icb45f14d00864ee19ed973d209c3af21e4df4edc
Reviewed-on: https://go-review.googlesource.com/32352
Run-TryBot: Michael Munday <munday@ca.ibm.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Michael Munday <munday@ca.ibm.com>
2016-11-11 20:20:23 +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