math/bits: directly calculate quo/rem when hi is zero in Div64

func Div64(hi, lo, y uint64) (quo, rem uint64) {...}

math/bits.Div64 returns the quotient and remainder of (hi, lo) divided
by y. When hi is zero, we can directly return lo/y, lo%y, which can save
a lot of unnecessary calculations.

The performance is measured on arm64 and the changes will only affect
the arch that doesn't have the intrinsic.

name                old time/op    new time/op    delta
DivWVW/1-10         4.62ns ± 1%    2.45ns ± 1%  -46.97%
DivWVW/2-10         12.4ns ± 0%    12.2ns ± 0%   -1.38%
DivWVW/3-10         17.4ns ± 1%    17.2ns ± 0%   -0.88%
DivWVW/4-10         21.4ns ± 1%    21.6ns ± 0%   +0.75%
DivWVW/5-10         22.1ns ± 1%    21.9ns ± 0%   -0.69%
DivWVW/10-10        53.4ns ± 1%    53.0ns ± 1%   -0.69%
DivWVW/100-10        641ns ± 1%     633ns ± 0%   -1.26%
DivWVW/1000-10      5.52µs ± 1%    5.44µs ± 0%   -1.39%
DivWVW/10000-10     54.9µs ± 1%    54.7µs ± 1%   -0.54%
DivWVW/100000-10     646µs ± 1%     643µs ± 1%     ~

name                  old speed      new speed    delta
DivWVW/1-10       13.8GB/s ± 1%  26.1GB/s ± 1%  +88.57%
DivWVW/2-10       10.3GB/s ± 0%  10.5GB/s ± 0%   +1.39%
DivWVW/3-10       11.1GB/s ± 1%  11.2GB/s ± 0%   +0.90%
DivWVW/4-10       12.0GB/s ± 1%  11.9GB/s ± 0%   -0.74%
DivWVW/5-10       14.5GB/s ± 1%  14.6GB/s ± 0%   +0.69%
DivWVW/10-10      12.0GB/s ± 1%  12.1GB/s ± 1%   +0.69%
DivWVW/100-10     10.0GB/s ± 1%  10.1GB/s ± 0%   +1.28%
DivWVW/1000-10    11.6GB/s ± 1%  11.8GB/s ± 0%   +1.41%
DivWVW/10000-10   11.6GB/s ± 1%  11.7GB/s ± 1%   +0.54%
DivWVW/100000-10  9.91GB/s ± 1%  9.95GB/s ± 1%     ~

Change-Id: I12014c2e2cdb2c91608079f7502592307af9e525
Reviewed-on: https://go-review.googlesource.com/c/go/+/449776
Reviewed-by: Keith Randall <khr@google.com>
Run-TryBot: Eric Fang <eric.fang@arm.com>
Reviewed-by: Robert Griesemer <gri@google.com>
TryBot-Result: Gopher Robot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>

diff --git a/src/math/bits/bits.go b/src/math/bits/bits.go
index 6ca4bfe9a60373cff1a2d2f6b1c86656420c6e06..c1c7b7978aceae3bb54b0633caf8c693bec58c73 100644 (file)
--- a/src/math/bits/bits.go
+++ b/src/math/bits/bits.go
@@ -516,10 +516,6 @@ func Div32(hi, lo, y uint32) (quo, rem uint32) {
 // half in parameter hi and the lower half in parameter lo.
 // Div64 panics for y == 0 (division by zero) or y <= hi (quotient overflow).
 func Div64(hi, lo, y uint64) (quo, rem uint64) {
-       const (
-               two32  = 1 << 32
-               mask32 = two32 - 1
-       )
        if y == 0 {
                panic(divideError)
        }
@@ -527,9 +523,18 @@ func Div64(hi, lo, y uint64) (quo, rem uint64) {
                panic(overflowError)
        }
 
+       // If high part is zero, we can directly return the results.
+       if hi == 0 {
+               return lo / y, lo % y
+       }
+
        s := uint(LeadingZeros64(y))
        y <<= s
 
+       const (
+               two32  = 1 << 32
+               mask32 = two32 - 1
+       )
        yn1 := y >> 32
        yn0 := y & mask32
        un32 := hi<<s | lo>>(64-s)