This is done by decomposing the number to be divided in 32-bit
components and using the 32-bit magic multiply. For the lowering to be
effective the constant must fit in 16 bits.
On ARM the expression n / 5 compiles to 25 instructions.
Benchmark for GOARCH=arm (Cortex-A53)
name old time/op new time/op delta
DivconstU64/3-6 1.19µs ± 0% 0.03µs ± 1% -97.40% (p=0.000 n=9+9)
DivconstU64/5-6 1.18µs ± 1% 0.03µs ± 1% -97.38% (p=0.000 n=10+8)
DivconstU64/37-6 1.13µs ± 1% 0.04µs ± 1% -96.51% (p=0.000 n=10+8)
DivconstU64/1234567-6 852ns ± 0% 901ns ± 1% +5.73% (p=0.000 n=8+9)
Benchmark for GOARCH=386 (Haswell)
name old time/op new time/op delta
DivconstU64/3-4 18.0ns ± 2% 5.6ns ± 1% -69.06% (p=0.000 n=10+10)
DivconstU64/5-4 17.8ns ± 1% 5.5ns ± 1% -68.87% (p=0.000 n=9+10)
DivconstU64/37-4 17.8ns ± 1% 7.3ns ± 0% -58.90% (p=0.000 n=10+10)
DivconstU64/1234567-4 17.5ns ± 1% 16.0ns ± 0% -8.55% (p=0.000 n=10+9)
Change-Id: I38a19b4d59093ec021ef2e5241364a3dad4eae73
Reviewed-on: https://go-review.googlesource.com/c/go/+/264683
Run-TryBot: Emmanuel Odeke <emmanuel@orijtech.com>
TryBot-Result: Go Bot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
Trust: Emmanuel Odeke <emmanuel@orijtech.com>
"Division by invariant integers using multiplication" paper
by Granlund and Montgomery contains a method for directly computing
divisibility (x%c == 0 for c constant) by means of the modular inverse.
The method is further elaborated in "Hacker's Delight" by Warren Section 10-17
This general rule can compute divisibilty by one multiplication and a compare
for odd divisors and an additional rotate for even divisors.
To apply the divisibility rule, we must take into account
the rules to rewrite x%c = x-((x/c)*c) and (x/c) for c constant on the first
optimization pass "opt". This complicates the matching as we want to match
only in the cases where the result of (x/c) is not also available.
So, we must match on the expanded form of (x/c) in the expression x == c*(x/c)
in the "late opt" pass after common subexpresion elimination.
Note, that if there is an intermediate opt pass introduced in the future we
could simplify these rules by delaying the magic division rewrite to "late opt"
and matching directly on (x/c) in the intermediate opt pass.
Additional rules to lower the generic RotateLeft* ops were also applied.
On amd64, the divisibility check is 25-50% faster.
name old time/op new time/op delta
DivconstI64-4 2.08ns ± 0% 2.08ns ± 1% ~ (p=0.881 n=5+5)
DivisibleconstI64-4 2.67ns ± 0% 2.67ns ± 1% ~ (p=1.000 n=5+5)
DivisibleWDivconstI64-4 2.67ns ± 0% 2.67ns ± 0% ~ (p=0.683 n=5+5)
DivconstU64-4 2.08ns ± 1% 2.08ns ± 1% ~ (p=1.000 n=5+5)
DivisibleconstU64-4 2.77ns ± 1% 1.55ns ± 2% -43.90% (p=0.008 n=5+5)
DivisibleWDivconstU64-4 2.99ns ± 1% 2.99ns ± 1% ~ (p=1.000 n=5+5)
DivconstI32-4 1.53ns ± 2% 1.53ns ± 0% ~ (p=1.000 n=5+5)
DivisibleconstI32-4 2.23ns ± 0% 2.25ns ± 3% ~ (p=0.167 n=5+5)
DivisibleWDivconstI32-4 2.27ns ± 1% 2.27ns ± 1% ~ (p=0.429 n=5+5)
DivconstU32-4 1.78ns ± 0% 1.78ns ± 1% ~ (p=1.000 n=4+5)
DivisibleconstU32-4 2.52ns ± 2% 1.26ns ± 0% -49.96% (p=0.000 n=5+4)
DivisibleWDivconstU32-4 2.63ns ± 0% 2.85ns ±10% +8.29% (p=0.016 n=4+5)
DivconstI16-4 1.54ns ± 0% 1.54ns ± 0% ~ (p=0.333 n=4+5)
DivisibleconstI16-4 2.10ns ± 0% 2.10ns ± 1% ~ (p=0.571 n=4+5)
DivisibleWDivconstI16-4 2.22ns ± 0% 2.23ns ± 1% ~ (p=0.556 n=4+5)
DivconstU16-4 1.09ns ± 0% 1.01ns ± 1% -7.74% (p=0.000 n=4+5)
DivisibleconstU16-4 1.83ns ± 0% 1.26ns ± 0% -31.52% (p=0.008 n=5+5)
DivisibleWDivconstU16-4 1.88ns ± 0% 1.89ns ± 1% ~ (p=0.365 n=5+5)
DivconstI8-4 1.54ns ± 1% 1.54ns ± 1% ~ (p=1.000 n=5+5)
DivisibleconstI8-4 2.10ns ± 0% 2.11ns ± 0% ~ (p=0.238 n=5+4)
DivisibleWDivconstI8-4 2.22ns ± 0% 2.23ns ± 2% ~ (p=0.762 n=5+5)
DivconstU8-4 0.92ns ± 1% 0.94ns ± 1% +2.65% (p=0.008 n=5+5)
DivisibleconstU8-4 1.66ns ± 0% 1.26ns ± 1% -24.28% (p=0.008 n=5+5)
DivisibleWDivconstU8-4 1.79ns ± 0% 1.80ns ± 1% ~ (p=0.079 n=4+5)
A follow-up change will address the signed division case.
Updates #30282
Change-Id: I7e995f167179aa5c76bb10fbcbeb49c520943403
Reviewed-on: https://go-review.googlesource.com/c/go/+/168037
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
For powers of two (c=1<<k), the divisibility check x%c == 0 can be made
just by checking the trailing zeroes via a mask x&(c-1) == 0 even for signed
integers. This avoids division fix-ups when just divisibility check is needed.
To apply this rule, we match on the fixed-up version of the division. This is
neccessary because the mod and division rewrite rules are already applied
during the initial opt pass.
The speed up on amd64 due to elimination of unneccessary fix-up code is ~55%:
name old time/op new time/op delta
DivconstI64-4 2.08ns ± 0% 2.09ns ± 1% ~ (p=0.730 n=5+5)
DivisiblePow2constI64-4 1.78ns ± 1% 0.81ns ± 1% -54.66% (p=0.008 n=5+5)
DivconstU64-4 2.08ns ± 0% 2.08ns ± 0% ~ (p=0.683 n=5+5)
DivconstI32-4 1.53ns ± 0% 1.53ns ± 1% ~ (p=0.968 n=4+5)
DivisiblePow2constI32-4 1.79ns ± 1% 0.81ns ± 1% -54.97% (p=0.008 n=5+5)
DivconstU32-4 1.78ns ± 1% 1.80ns ± 2% ~ (p=0.206 n=5+5)
DivconstI16-4 1.54ns ± 2% 1.54ns ± 0% ~ (p=0.238 n=5+4)
DivisiblePow2constI16-4 1.78ns ± 0% 0.81ns ± 1% -54.72% (p=0.000 n=4+5)
DivconstU16-4 1.00ns ± 5% 1.01ns ± 1% ~ (p=0.119 n=5+5)
DivconstI8-4 1.54ns ± 0% 1.54ns ± 2% ~ (p=0.571 n=4+5)
DivisiblePow2constI8-4 1.78ns ± 0% 0.82ns ± 8% -53.71% (p=0.008 n=5+5)
DivconstU8-4 0.93ns ± 1% 0.93ns ± 1% ~ (p=0.643 n=5+5)
A follow-up CL will address the general case of x%c == 0 for signed integers.
Updates #15806
Change-Id: Iabadbbe369b6e0998c8ce85d038ebc236142e42a
Reviewed-on: https://go-review.googlesource.com/c/go/+/173557
Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
This reverts CL 168038 (git 68819fb6d2)
Reason for revert: Doesn't work on 32 bit archs.
Change-Id: Idec9098060dc65bc2f774c5383f0477f8eb63a3d
Reviewed-on: https://go-review.googlesource.com/c/go/+/173442
Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
For powers of two (c=1<<k), the divisibility check x%c == 0 can be made
just by checking the trailing zeroes via a mask x&(c-1)==0 even for signed
integers. This avoids division fixups when just divisibility check is needed.
To apply this rule the generic divisibility rule for A%B = A-(A/B*B) is disabled
on the "opt" pass, but this does not affect generated code as this rule is applied
later.
The speed up on amd64 due to elimination of unneccessary fixup code is ~55%:
name old time/op new time/op delta
DivconstI64-4 2.08ns ± 0% 2.07ns ± 0% ~ (p=0.079 n=5+5)
DivisiblePow2constI64-4 1.78ns ± 1% 0.81ns ± 1% -54.55% (p=0.008 n=5+5)
DivconstU64-4 2.08ns ± 0% 2.08ns ± 0% ~ (p=1.000 n=5+5)
DivconstI32-4 1.53ns ± 0% 1.53ns ± 0% ~ (all equal)
DivisiblePow2constI32-4 1.79ns ± 1% 0.81ns ± 4% -54.75% (p=0.008 n=5+5)
DivconstU32-4 1.78ns ± 1% 1.78ns ± 1% ~ (p=1.000 n=5+5)
DivconstI16-4 1.54ns ± 2% 1.53ns ± 0% ~ (p=0.333 n=5+4)
DivisiblePow2constI16-4 1.78ns ± 0% 0.79ns ± 1% -55.39% (p=0.000 n=4+5)
DivconstU16-4 1.00ns ± 5% 0.99ns ± 1% ~ (p=0.730 n=5+5)
DivconstI8-4 1.54ns ± 0% 1.53ns ± 0% ~ (p=0.714 n=4+5)
DivisiblePow2constI8-4 1.78ns ± 0% 0.80ns ± 0% -55.06% (p=0.000 n=5+4)
DivconstU8-4 0.93ns ± 1% 0.95ns ± 1% +1.72% (p=0.024 n=5+5)
A follow-up CL will address the general case of x%c == 0 for signed integers.
Updates #15806
Change-Id: I0d284863774b1bc8c4ce87443bbaec6103e14ef4
Reviewed-on: https://go-review.googlesource.com/c/go/+/168038
Reviewed-by: Keith Randall <khr@golang.org>
This is necessary to avoid disrupting the go1 suite and gives
us a place to put other tests of basic compiler function and
correctness.
Change-Id: I36933819ff2bfe6a2121fff2be9a98efd2123d9a
Reviewed-on: https://go-review.googlesource.com/22597
Run-TryBot: David Chase <drchase@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
2016-04-29 16:20:18 +00:00
Renamed from test/bench/go1/divconst_test.go (Browse further)
