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math/big: optimize shlVU_g and shrVU_g

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Special case shifts by zero.
Provide hints to the compiler that shifts are bounded.

There are no existing benchmarks for shifts,
but the Float implementation uses shifts,
so we can use those.

Benchmarks on amd64 with -tags=math_big_pure_go.

name                  old time/op    new time/op    delta
FloatString/100-8        869ns ± 3%     872ns ± 4%   +0.40%  (p=0.001 n=94+83)
FloatString/1000-8      26.5µs ± 1%    26.4µs ± 1%   -0.46%  (p=0.000 n=87+96)
FloatString/10000-8     2.18ms ± 2%    2.18ms ± 2%     ~     (p=0.687 n=90+89)
FloatString/100000-8     200ms ± 7%     197ms ± 5%   -1.47%  (p=0.000 n=100+90)
FloatAdd/10-8           65.9ns ± 4%    64.0ns ± 4%   -2.94%  (p=0.000 n=92+93)
FloatAdd/100-8          71.3ns ± 4%    67.4ns ± 4%   -5.51%  (p=0.000 n=96+93)
FloatAdd/1000-8          128ns ± 1%     121ns ± 0%   -5.69%  (p=0.000 n=91+80)
FloatAdd/10000-8         718ns ± 4%     626ns ± 4%  -12.83%  (p=0.000 n=99+99)
FloatAdd/100000-8       6.43µs ± 3%    5.50µs ± 1%  -14.50%  (p=0.000 n=98+83)
FloatSub/10-8           57.7ns ± 2%    57.0ns ± 4%   -1.20%  (p=0.000 n=89+96)
FloatSub/100-8          59.9ns ± 3%    58.7ns ± 4%   -2.10%  (p=0.000 n=100+98)
FloatSub/1000-8         94.5ns ± 1%    88.6ns ± 0%   -6.16%  (p=0.000 n=74+70)
FloatSub/10000-8         456ns ± 1%     416ns ± 5%   -8.83%  (p=0.000 n=87+95)
FloatSub/100000-8       4.00µs ± 1%    3.57µs ± 1%  -10.87%  (p=0.000 n=68+85)
FloatSqrt/64-8           585ns ± 1%     579ns ± 1%   -0.99%  (p=0.000 n=92+90)
FloatSqrt/128-8         1.26µs ± 1%    1.23µs ± 2%   -2.42%  (p=0.000 n=91+81)
FloatSqrt/256-8         1.45µs ± 3%    1.40µs ± 1%   -3.61%  (p=0.000 n=96+90)
FloatSqrt/1000-8        4.03µs ± 1%    3.91µs ± 1%   -3.05%  (p=0.000 n=90+93)
FloatSqrt/10000-8       48.0µs ± 0%    47.3µs ± 1%   -1.55%  (p=0.000 n=90+90)
FloatSqrt/100000-8      1.23ms ± 3%    1.22ms ± 4%   -1.00%  (p=0.000 n=99+99)
FloatSqrt/1000000-8     96.7ms ± 4%    98.0ms ±10%     ~     (p=0.322 n=89+99)

Change-Id: I0f941c05b7c324256d7f0674559b6ba906e92ba8
Reviewed-on: https://go-review.googlesource.com/c/go/+/164967
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Robert Griesemer <gri@golang.org>
This commit is contained in:
Josh Bleecher Snyder 2019-03-03 13:08:40 -08:00
parent abf8e355a8
commit 87cc56718a
1 changed files with 34 additions and 20 deletions
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54
src/math/big/arith.go
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@ -204,32 +204,46 @@ func subVW_g(z, x []Word, y Word) (c Word) {
}
func shlVU_g(z, x []Word, s uint) (c Word) {
if n := len(z); n > 0 {
ŝ := _W - s
w1 := x[n-1]
c = w1 >> ŝ
for i := n - 1; i > 0; i-- {
w := w1
w1 = x[i-1]
z[i] = w<<s | w1>>ŝ
}
z[0] = w1 << s
if s == 0 {
copy(z, x)
return
}
if len(z) == 0 {
return
}
s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
ŝ := _W - s
ŝ &= _W - 1 // ditto
w1 := x[len(z)-1]
c = w1 >> ŝ
for i := len(z) - 1; i > 0; i-- {
w := w1
w1 = x[i-1]
z[i] = w<<s | w1>>ŝ
}
z[0] = w1 << s
return
}
func shrVU_g(z, x []Word, s uint) (c Word) {
if n := len(z); n > 0 {
ŝ := _W - s
w1 := x[0]
c = w1 << ŝ
for i := 0; i < n-1; i++ {
w := w1
w1 = x[i+1]
z[i] = w>>s | w1<<ŝ
}
z[n-1] = w1 >> s
if s == 0 {
copy(z, x)
return
}
if len(z) == 0 {
return
}
s &= _W - 1 // hint to the compiler that shifts by s don't need guard code
ŝ := _W - s
ŝ &= _W - 1 // ditto
w1 := x[0]
c = w1 << ŝ
for i := 0; i < len(z)-1; i++ {
w := w1
w1 = x[i+1]
z[i] = w>>s | w1<<ŝ
}
z[len(z)-1] = w1 >> s
return
}