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cmd/compile: add unsigned divisibility rules
"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>
This commit is contained in:
Brian Kessler
Keith Randall
parent
f67f5511ee
commit
a28a942768
24 changed files with 9927 additions and 24 deletions
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@ -18,11 +18,29 @@ func BenchmarkDivconstI64(b *testing.B) {
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}
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}
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func BenchmarkModconstI64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i64res = int64(i) % 7
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}
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}
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func BenchmarkDivisiblePow2constI64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int64(i)%16 == 0
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}
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}
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func BenchmarkDivisibleconstI64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int64(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstI64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i64res = int64(i) / 7
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boolres = int64(i)%7 == 0
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}
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}
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var u64res uint64
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@ -32,6 +50,25 @@ func BenchmarkDivconstU64(b *testing.B) {
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}
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}
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func BenchmarkModconstU64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u64res = uint64(i) % 7
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}
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}
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func BenchmarkDivisibleconstU64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = uint64(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstU64(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u64res = uint64(i) / 7
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boolres = uint64(i)%7 == 0
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}
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}
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var i32res int32
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func BenchmarkDivconstI32(b *testing.B) {
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@ -40,12 +77,31 @@ func BenchmarkDivconstI32(b *testing.B) {
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}
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}
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func BenchmarkModconstI32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i32res = int32(i) % 7
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}
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}
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func BenchmarkDivisiblePow2constI32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int32(i)%16 == 0
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}
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}
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func BenchmarkDivisibleconstI32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int32(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstI32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i32res = int32(i) / 7
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boolres = int32(i)%7 == 0
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}
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}
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var u32res uint32
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func BenchmarkDivconstU32(b *testing.B) {
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@ -54,6 +110,25 @@ func BenchmarkDivconstU32(b *testing.B) {
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}
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}
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func BenchmarkModconstU32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u32res = uint32(i) % 7
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}
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}
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func BenchmarkDivisibleconstU32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = uint32(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstU32(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u32res = uint32(i) / 7
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boolres = uint32(i)%7 == 0
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}
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}
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var i16res int16
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func BenchmarkDivconstI16(b *testing.B) {
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@ -62,12 +137,31 @@ func BenchmarkDivconstI16(b *testing.B) {
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}
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}
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func BenchmarkModconstI16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i16res = int16(i) % 7
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}
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}
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func BenchmarkDivisiblePow2constI16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int16(i)%16 == 0
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}
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}
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func BenchmarkDivisibleconstI16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int16(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstI16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i16res = int16(i) / 7
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boolres = int16(i)%7 == 0
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}
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}
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var u16res uint16
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func BenchmarkDivconstU16(b *testing.B) {
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@ -76,6 +170,25 @@ func BenchmarkDivconstU16(b *testing.B) {
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}
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}
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func BenchmarkModconstU16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u16res = uint16(i) % 7
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}
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}
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func BenchmarkDivisibleconstU16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = uint16(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstU16(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u16res = uint16(i) / 7
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boolres = uint16(i)%7 == 0
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}
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}
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var i8res int8
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func BenchmarkDivconstI8(b *testing.B) {
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@ -84,12 +197,31 @@ func BenchmarkDivconstI8(b *testing.B) {
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}
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}
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func BenchmarkModconstI8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i8res = int8(i) % 7
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}
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}
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func BenchmarkDivisiblePow2constI8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int8(i)%16 == 0
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}
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}
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func BenchmarkDivisibleconstI8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = int8(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstI8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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i8res = int8(i) / 7
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boolres = int8(i)%7 == 0
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}
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}
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var u8res uint8
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func BenchmarkDivconstU8(b *testing.B) {
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@ -97,3 +229,22 @@ func BenchmarkDivconstU8(b *testing.B) {
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u8res = uint8(i) / 7
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}
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}
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func BenchmarkModconstU8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u8res = uint8(i) % 7
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}
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}
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func BenchmarkDivisibleconstU8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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boolres = uint8(i)%7 == 0
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}
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}
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func BenchmarkDivisibleWDivconstU8(b *testing.B) {
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for i := 0; i < b.N; i++ {
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u8res = uint8(i) / 7
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boolres = uint8(i)%7 == 0
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}
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}
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