mirror of
https://github.com/golang/go
synced 2024-11-27 01:21:18 -07:00
4d9dd35806
"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 add 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 needed. 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. On amd64, the divisibility check is 30-45% faster. name old time/op new time/op delta` DivisiblePow2constI64-4 0.83ns ± 1% 0.82ns ± 0% ~ (p=0.079 n=5+4) DivisibleconstI64-4 2.68ns ± 1% 1.87ns ± 0% -30.33% (p=0.000 n=5+4) DivisibleWDivconstI64-4 2.69ns ± 1% 2.71ns ± 3% ~ (p=1.000 n=5+5) DivisiblePow2constI32-4 1.15ns ± 1% 1.15ns ± 0% ~ (p=0.238 n=5+4) DivisibleconstI32-4 2.24ns ± 1% 1.20ns ± 0% -46.48% (p=0.016 n=5+4) DivisibleWDivconstI32-4 2.27ns ± 1% 2.27ns ± 1% ~ (p=0.683 n=5+5) DivisiblePow2constI16-4 0.81ns ± 1% 0.82ns ± 1% ~ (p=0.135 n=5+5) DivisibleconstI16-4 2.11ns ± 2% 1.20ns ± 1% -42.99% (p=0.008 n=5+5) DivisibleWDivconstI16-4 2.23ns ± 0% 2.27ns ± 2% +1.79% (p=0.029 n=4+4) DivisiblePow2constI8-4 0.81ns ± 1% 0.81ns ± 1% ~ (p=0.286 n=5+5) DivisibleconstI8-4 2.13ns ± 3% 1.19ns ± 1% -43.84% (p=0.008 n=5+5) DivisibleWDivconstI8-4 2.23ns ± 1% 2.25ns ± 1% ~ (p=0.183 n=5+5) Fixes #30282 Fixes #15806 Change-Id: Id20d78263a4fdfe0509229ae4dfa2fede83fc1d0 Reviewed-on: https://go-review.googlesource.com/c/go/+/173998 Run-TryBot: Brian Kessler <brian.m.kessler@gmail.com> TryBot-Result: Gobot Gobot <gobot@golang.org> Reviewed-by: Keith Randall <khr@golang.org>
444 lines
10 KiB
Go
444 lines
10 KiB
Go
// asmcheck
|
|
|
|
// Copyright 2018 The Go Authors. All rights reserved.
|
|
// Use of this source code is governed by a BSD-style
|
|
// license that can be found in the LICENSE file.
|
|
|
|
package codegen
|
|
|
|
// This file contains codegen tests related to arithmetic
|
|
// simplifications and optimizations on integer types.
|
|
// For codegen tests on float types, see floats.go.
|
|
|
|
// ----------------- //
|
|
// Subtraction //
|
|
// ----------------- //
|
|
|
|
var ef int
|
|
|
|
func SubMem(arr []int, b, c, d int) int {
|
|
// 386:`SUBL\s[A-Z]+,\s8\([A-Z]+\)`
|
|
// amd64:`SUBQ\s[A-Z]+,\s16\([A-Z]+\)`
|
|
arr[2] -= b
|
|
// 386:`SUBL\s[A-Z]+,\s12\([A-Z]+\)`
|
|
// amd64:`SUBQ\s[A-Z]+,\s24\([A-Z]+\)`
|
|
arr[3] -= b
|
|
// 386:`DECL\s16\([A-Z]+\)`
|
|
arr[4]--
|
|
// 386:`ADDL\s[$]-20,\s20\([A-Z]+\)`
|
|
arr[5] -= 20
|
|
// 386:`SUBL\s\([A-Z]+\)\([A-Z]+\*4\),\s[A-Z]+`
|
|
ef -= arr[b]
|
|
// 386:`SUBL\s[A-Z]+,\s\([A-Z]+\)\([A-Z]+\*4\)`
|
|
arr[c] -= b
|
|
// 386:`ADDL\s[$]-15,\s\([A-Z]+\)\([A-Z]+\*4\)`
|
|
arr[d] -= 15
|
|
// 386:`DECL\s\([A-Z]+\)\([A-Z]+\*4\)`
|
|
arr[b]--
|
|
// amd64:`DECQ\s64\([A-Z]+\)`
|
|
arr[8]--
|
|
// 386:"SUBL\t4"
|
|
// amd64:"SUBQ\t8"
|
|
return arr[0] - arr[1]
|
|
}
|
|
|
|
// -------------------- //
|
|
// Multiplication //
|
|
// -------------------- //
|
|
|
|
func Pow2Muls(n1, n2 int) (int, int) {
|
|
// amd64:"SHLQ\t[$]5",-"IMULQ"
|
|
// 386:"SHLL\t[$]5",-"IMULL"
|
|
// arm:"SLL\t[$]5",-"MUL"
|
|
// arm64:"LSL\t[$]5",-"MUL"
|
|
// ppc64:"SLD\t[$]5",-"MUL"
|
|
// ppc64le:"SLD\t[$]5",-"MUL"
|
|
a := n1 * 32
|
|
|
|
// amd64:"SHLQ\t[$]6",-"IMULQ"
|
|
// 386:"SHLL\t[$]6",-"IMULL"
|
|
// arm:"SLL\t[$]6",-"MUL"
|
|
// arm64:`NEG\sR[0-9]+<<6,\sR[0-9]+`,-`LSL`,-`MUL`
|
|
// ppc64:"SLD\t[$]6","NEG\\sR[0-9]+,\\sR[0-9]+",-"MUL"
|
|
// ppc64le:"SLD\t[$]6","NEG\\sR[0-9]+,\\sR[0-9]+",-"MUL"
|
|
b := -64 * n2
|
|
|
|
return a, b
|
|
}
|
|
|
|
func Mul_96(n int) int {
|
|
// amd64:`SHLQ\t[$]5`,`LEAQ\t\(.*\)\(.*\*2\),`,-`IMULQ`
|
|
// 386:`SHLL\t[$]5`,`LEAL\t\(.*\)\(.*\*2\),`,-`IMULL`
|
|
// arm64:`LSL\t[$]5`,`ADD\sR[0-9]+<<1,\sR[0-9]+`,-`MUL`
|
|
// arm:`SLL\t[$]5`,`ADD\sR[0-9]+<<1,\sR[0-9]+`,-`MUL`
|
|
return n * 96
|
|
}
|
|
|
|
func MulMemSrc(a []uint32, b []float32) {
|
|
// 386:`IMULL\s4\([A-Z]+\),\s[A-Z]+`
|
|
a[0] *= a[1]
|
|
// 386/sse2:`MULSS\s4\([A-Z]+\),\sX[0-9]+`
|
|
// amd64:`MULSS\s4\([A-Z]+\),\sX[0-9]+`
|
|
b[0] *= b[1]
|
|
}
|
|
|
|
// Multiplications merging tests
|
|
|
|
func MergeMuls1(n int) int {
|
|
// amd64:"IMUL3Q\t[$]46"
|
|
// 386:"IMUL3L\t[$]46"
|
|
return 15*n + 31*n // 46n
|
|
}
|
|
|
|
func MergeMuls2(n int) int {
|
|
// amd64:"IMUL3Q\t[$]23","ADDQ\t[$]29"
|
|
// 386:"IMUL3L\t[$]23","ADDL\t[$]29"
|
|
return 5*n + 7*(n+1) + 11*(n+2) // 23n + 29
|
|
}
|
|
|
|
func MergeMuls3(a, n int) int {
|
|
// amd64:"ADDQ\t[$]19",-"IMULQ\t[$]19"
|
|
// 386:"ADDL\t[$]19",-"IMULL\t[$]19"
|
|
return a*n + 19*n // (a+19)n
|
|
}
|
|
|
|
func MergeMuls4(n int) int {
|
|
// amd64:"IMUL3Q\t[$]14"
|
|
// 386:"IMUL3L\t[$]14"
|
|
return 23*n - 9*n // 14n
|
|
}
|
|
|
|
func MergeMuls5(a, n int) int {
|
|
// amd64:"ADDQ\t[$]-19",-"IMULQ\t[$]19"
|
|
// 386:"ADDL\t[$]-19",-"IMULL\t[$]19"
|
|
return a*n - 19*n // (a-19)n
|
|
}
|
|
|
|
// -------------- //
|
|
// Division //
|
|
// -------------- //
|
|
|
|
func DivMemSrc(a []float64) {
|
|
// 386/sse2:`DIVSD\s8\([A-Z]+\),\sX[0-9]+`
|
|
// amd64:`DIVSD\s8\([A-Z]+\),\sX[0-9]+`
|
|
a[0] /= a[1]
|
|
}
|
|
|
|
func Pow2Divs(n1 uint, n2 int) (uint, int) {
|
|
// 386:"SHRL\t[$]5",-"DIVL"
|
|
// amd64:"SHRQ\t[$]5",-"DIVQ"
|
|
// arm:"SRL\t[$]5",-".*udiv"
|
|
// arm64:"LSR\t[$]5",-"UDIV"
|
|
// ppc64:"SRD"
|
|
// ppc64le:"SRD"
|
|
a := n1 / 32 // unsigned
|
|
|
|
// amd64:"SARQ\t[$]6",-"IDIVQ"
|
|
// 386:"SARL\t[$]6",-"IDIVL"
|
|
// arm:"SRA\t[$]6",-".*udiv"
|
|
// arm64:"ASR\t[$]6",-"SDIV"
|
|
// ppc64:"SRAD"
|
|
// ppc64le:"SRAD"
|
|
b := n2 / 64 // signed
|
|
|
|
return a, b
|
|
}
|
|
|
|
// Check that constant divisions get turned into MULs
|
|
func ConstDivs(n1 uint, n2 int) (uint, int) {
|
|
// amd64:"MOVQ\t[$]-1085102592571150095","MULQ",-"DIVQ"
|
|
// 386:"MOVL\t[$]-252645135","MULL",-"DIVL"
|
|
// arm64:`MOVD`,`UMULH`,-`DIV`
|
|
// arm:`MOVW`,`MUL`,-`.*udiv`
|
|
a := n1 / 17 // unsigned
|
|
|
|
// amd64:"MOVQ\t[$]-1085102592571150095","IMULQ",-"IDIVQ"
|
|
// 386:"MOVL\t[$]-252645135","IMULL",-"IDIVL"
|
|
// arm64:`MOVD`,`SMULH`,-`DIV`
|
|
// arm:`MOVW`,`MUL`,-`.*udiv`
|
|
b := n2 / 17 // signed
|
|
|
|
return a, b
|
|
}
|
|
|
|
func FloatDivs(a []float32) float32 {
|
|
// amd64:`DIVSS\s8\([A-Z]+\),\sX[0-9]+`
|
|
// 386/sse2:`DIVSS\s8\([A-Z]+\),\sX[0-9]+`
|
|
return a[1] / a[2]
|
|
}
|
|
|
|
func Pow2Mods(n1 uint, n2 int) (uint, int) {
|
|
// 386:"ANDL\t[$]31",-"DIVL"
|
|
// amd64:"ANDQ\t[$]31",-"DIVQ"
|
|
// arm:"AND\t[$]31",-".*udiv"
|
|
// arm64:"AND\t[$]31",-"UDIV"
|
|
// ppc64:"ANDCC\t[$]31"
|
|
// ppc64le:"ANDCC\t[$]31"
|
|
a := n1 % 32 // unsigned
|
|
|
|
// 386:"SHRL",-"IDIVL"
|
|
// amd64:"SHRQ",-"IDIVQ"
|
|
// arm:"SRA",-".*udiv"
|
|
// arm64:"ASR",-"REM"
|
|
// ppc64:"SRAD"
|
|
// ppc64le:"SRAD"
|
|
b := n2 % 64 // signed
|
|
|
|
return a, b
|
|
}
|
|
|
|
// Check that signed divisibility checks get converted to AND on low bits
|
|
func Pow2DivisibleSigned(n int) bool {
|
|
// 386:"TESTL\t[$]63",-"DIVL",-"SHRL"
|
|
// amd64:"TESTQ\t[$]63",-"DIVQ",-"SHRQ"
|
|
// arm:"AND\t[$]63",-".*udiv",-"SRA"
|
|
// arm64:"AND\t[$]63",-"UDIV",-"ASR"
|
|
// ppc64:"ANDCC\t[$]63",-"SRAD"
|
|
// ppc64le:"ANDCC\t[$]63",-"SRAD"
|
|
return n%64 == 0 // signed
|
|
}
|
|
|
|
// Check that constant modulo divs get turned into MULs
|
|
func ConstMods(n1 uint, n2 int) (uint, int) {
|
|
// amd64:"MOVQ\t[$]-1085102592571150095","MULQ",-"DIVQ"
|
|
// 386:"MOVL\t[$]-252645135","MULL",-"DIVL"
|
|
// arm64:`MOVD`,`UMULH`,-`DIV`
|
|
// arm:`MOVW`,`MUL`,-`.*udiv`
|
|
a := n1 % 17 // unsigned
|
|
|
|
// amd64:"MOVQ\t[$]-1085102592571150095","IMULQ",-"IDIVQ"
|
|
// 386:"MOVL\t[$]-252645135","IMULL",-"IDIVL"
|
|
// arm64:`MOVD`,`SMULH`,-`DIV`
|
|
// arm:`MOVW`,`MUL`,-`.*udiv`
|
|
b := n2 % 17 // signed
|
|
|
|
return a, b
|
|
}
|
|
|
|
// Check that divisibility checks x%c==0 are converted to MULs and rotates
|
|
func Divisible(n1 uint, n2 int) (bool, bool, bool, bool) {
|
|
// amd64:"MOVQ\t[$]-6148914691236517205","IMULQ","ROLQ\t[$]63",-"DIVQ"
|
|
// 386:"IMUL3L\t[$]-1431655765","ROLL\t[$]31",-"DIVQ"
|
|
// arm64:"MOVD\t[$]-6148914691236517205","MUL","ROR",-"DIV"
|
|
// arm:"MUL","CMP\t[$]715827882",-".*udiv"
|
|
// ppc64:"MULLD","ROTL\t[$]63"
|
|
// ppc64le:"MULLD","ROTL\t[$]63"
|
|
evenU := n1%6 == 0
|
|
|
|
// amd64:"MOVQ\t[$]-8737931403336103397","IMULQ",-"ROLQ",-"DIVQ"
|
|
// 386:"IMUL3L\t[$]678152731",-"ROLL",-"DIVQ"
|
|
// arm64:"MOVD\t[$]-8737931403336103397","MUL",-"ROR",-"DIV"
|
|
// arm:"MUL","CMP\t[$]226050910",-".*udiv"
|
|
// ppc64:"MULLD",-"ROTL"
|
|
// ppc64le:"MULLD",-"ROTL"
|
|
oddU := n1%19 == 0
|
|
|
|
// amd64:"IMULQ","ADD","ROLQ\t[$]63",-"DIVQ"
|
|
// 386:"IMUL3L\t[$]-1431655765","ADDL\t[$]715827882","ROLL\t[$]31",-"DIVQ"
|
|
// arm64:"MUL","ADD\t[$]3074457345618258602","ROR",-"DIV"
|
|
// arm:"MUL","ADD\t[$]715827882",-".*udiv"
|
|
// ppc64:"MULLD","ADD","ROTL\t[$]63"
|
|
// ppc64le:"MULLD","ADD","ROTL\t[$]63"
|
|
evenS := n2%6 == 0
|
|
|
|
// amd64:"IMULQ","ADD",-"ROLQ",-"DIVQ"
|
|
// 386:"IMUL3L\t[$]678152731","ADDL\t[$]113025455",-"ROLL",-"DIVQ"
|
|
// arm64:"MUL","ADD\t[$]485440633518672410",-"ROR",-"DIV"
|
|
// arm:"MUL","ADD\t[$]113025455",-".*udiv"
|
|
// ppc64:"MULLD","ADD",-"ROTL"
|
|
// ppc64le:"MULLD","ADD",-"ROTL"
|
|
oddS := n2%19 == 0
|
|
|
|
return evenU, oddU, evenS, oddS
|
|
}
|
|
|
|
// Check that fix-up code is not generated for divisions where it has been proven that
|
|
// that the divisor is not -1 or that the dividend is > MinIntNN.
|
|
func NoFix64A(divr int64) (int64, int64) {
|
|
var d int64 = 42
|
|
var e int64 = 84
|
|
if divr > 5 {
|
|
d /= divr // amd64:-"JMP"
|
|
e %= divr // amd64:-"JMP"
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
func NoFix64B(divd int64) (int64, int64) {
|
|
var d int64
|
|
var e int64
|
|
var divr int64 = -1
|
|
if divd > -9223372036854775808 {
|
|
d = divd / divr // amd64:-"JMP"
|
|
e = divd % divr // amd64:-"JMP"
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
func NoFix32A(divr int32) (int32, int32) {
|
|
var d int32 = 42
|
|
var e int32 = 84
|
|
if divr > 5 {
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
d /= divr
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
e %= divr
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
func NoFix32B(divd int32) (int32, int32) {
|
|
var d int32
|
|
var e int32
|
|
var divr int32 = -1
|
|
if divd > -2147483648 {
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
d = divd / divr
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
e = divd % divr
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
func NoFix16A(divr int16) (int16, int16) {
|
|
var d int16 = 42
|
|
var e int16 = 84
|
|
if divr > 5 {
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
d /= divr
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
e %= divr
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
func NoFix16B(divd int16) (int16, int16) {
|
|
var d int16
|
|
var e int16
|
|
var divr int16 = -1
|
|
if divd > -32768 {
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
d = divd / divr
|
|
// amd64:-"JMP"
|
|
// 386:-"JMP"
|
|
e = divd % divr
|
|
}
|
|
return d, e
|
|
}
|
|
|
|
// Check that len() and cap() calls divided by powers of two are
|
|
// optimized into shifts and ands
|
|
|
|
func LenDiv1(a []int) int {
|
|
// 386:"SHRL\t[$]10"
|
|
// amd64:"SHRQ\t[$]10"
|
|
// arm64:"LSR\t[$]10",-"SDIV"
|
|
// arm:"SRL\t[$]10",-".*udiv"
|
|
// ppc64:"SRD"\t[$]10"
|
|
// ppc64le:"SRD"\t[$]10"
|
|
return len(a) / 1024
|
|
}
|
|
|
|
func LenDiv2(s string) int {
|
|
// 386:"SHRL\t[$]11"
|
|
// amd64:"SHRQ\t[$]11"
|
|
// arm64:"LSR\t[$]11",-"SDIV"
|
|
// arm:"SRL\t[$]11",-".*udiv"
|
|
// ppc64:"SRD\t[$]11"
|
|
// ppc64le:"SRD\t[$]11"
|
|
return len(s) / (4097 >> 1)
|
|
}
|
|
|
|
func LenMod1(a []int) int {
|
|
// 386:"ANDL\t[$]1023"
|
|
// amd64:"ANDQ\t[$]1023"
|
|
// arm64:"AND\t[$]1023",-"SDIV"
|
|
// arm/6:"AND",-".*udiv"
|
|
// arm/7:"BFC",-".*udiv",-"AND"
|
|
// ppc64:"ANDCC\t[$]1023"
|
|
// ppc64le:"ANDCC\t[$]1023"
|
|
return len(a) % 1024
|
|
}
|
|
|
|
func LenMod2(s string) int {
|
|
// 386:"ANDL\t[$]2047"
|
|
// amd64:"ANDQ\t[$]2047"
|
|
// arm64:"AND\t[$]2047",-"SDIV"
|
|
// arm/6:"AND",-".*udiv"
|
|
// arm/7:"BFC",-".*udiv",-"AND"
|
|
// ppc64:"ANDCC\t[$]2047"
|
|
// ppc64le:"ANDCC\t[$]2047"
|
|
return len(s) % (4097 >> 1)
|
|
}
|
|
|
|
func CapDiv(a []int) int {
|
|
// 386:"SHRL\t[$]12"
|
|
// amd64:"SHRQ\t[$]12"
|
|
// arm64:"LSR\t[$]12",-"SDIV"
|
|
// arm:"SRL\t[$]12",-".*udiv"
|
|
// ppc64:"SRD\t[$]12"
|
|
// ppc64le:"SRD\t[$]12"
|
|
return cap(a) / ((1 << 11) + 2048)
|
|
}
|
|
|
|
func CapMod(a []int) int {
|
|
// 386:"ANDL\t[$]4095"
|
|
// amd64:"ANDQ\t[$]4095"
|
|
// arm64:"AND\t[$]4095",-"SDIV"
|
|
// arm/6:"AND",-".*udiv"
|
|
// arm/7:"BFC",-".*udiv",-"AND"
|
|
// ppc64:"ANDCC\t[$]4095"
|
|
// ppc64le:"ANDCC\t[$]4095"
|
|
return cap(a) % ((1 << 11) + 2048)
|
|
}
|
|
|
|
func AddMul(x int) int {
|
|
// amd64:"LEAQ\t1"
|
|
return 2*x + 1
|
|
}
|
|
|
|
func MULA(a, b, c uint32) (uint32, uint32, uint32) {
|
|
// arm:`MULA`,-`MUL\s`
|
|
// arm64:`MADDW`,-`MULW`
|
|
r0 := a*b + c
|
|
// arm:`MULA`,-`MUL\s`
|
|
// arm64:`MADDW`,-`MULW`
|
|
r1 := c*79 + a
|
|
// arm:`ADD`,-`MULA`,-`MUL\s`
|
|
// arm64:`ADD`,-`MADD`,-`MULW`
|
|
r2 := b*64 + c
|
|
return r0, r1, r2
|
|
}
|
|
|
|
func MULS(a, b, c uint32) (uint32, uint32, uint32) {
|
|
// arm/7:`MULS`,-`MUL\s`
|
|
// arm/6:`SUB`,`MUL\s`,-`MULS`
|
|
// arm64:`MSUBW`,-`MULW`
|
|
r0 := c - a*b
|
|
// arm/7:`MULS`,-`MUL\s`
|
|
// arm/6:`SUB`,`MUL\s`,-`MULS`
|
|
// arm64:`MSUBW`,-`MULW`
|
|
r1 := a - c*79
|
|
// arm/7:`SUB`,-`MULS`,-`MUL\s`
|
|
// arm64:`SUB`,-`MSUBW`,-`MULW`
|
|
r2 := c - b*64
|
|
return r0, r1, r2
|
|
}
|
|
|
|
func addSpecial(a, b, c uint32) (uint32, uint32, uint32) {
|
|
// amd64:`INCL`
|
|
a++
|
|
// amd64:`DECL`
|
|
b--
|
|
// amd64:`SUBL.*-128`
|
|
c += 128
|
|
return a, b, c
|
|
}
|