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"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
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// Copyright 2018 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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package codegen
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// This file contains codegen tests related to arithmetic
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// simplifications and optimizations on integer types.
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// For codegen tests on float types, see floats.go.
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// ----------------- //
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// Subtraction //
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// ----------------- //
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var ef int
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func SubMem(arr []int, b, c, d int) int {
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// 386:`SUBL\s[A-Z]+,\s8\([A-Z]+\)`
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// amd64:`SUBQ\s[A-Z]+,\s16\([A-Z]+\)`
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arr[2] -= b
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// 386:`SUBL\s[A-Z]+,\s12\([A-Z]+\)`
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// amd64:`SUBQ\s[A-Z]+,\s24\([A-Z]+\)`
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arr[3] -= b
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// 386:`DECL\s16\([A-Z]+\)`
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arr[4]--
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// 386:`ADDL\s[$]-20,\s20\([A-Z]+\)`
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arr[5] -= 20
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// 386:`SUBL\s\([A-Z]+\)\([A-Z]+\*4\),\s[A-Z]+`
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ef -= arr[b]
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// 386:`SUBL\s[A-Z]+,\s\([A-Z]+\)\([A-Z]+\*4\)`
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arr[c] -= b
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// 386:`ADDL\s[$]-15,\s\([A-Z]+\)\([A-Z]+\*4\)`
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arr[d] -= 15
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// 386:`DECL\s\([A-Z]+\)\([A-Z]+\*4\)`
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arr[b]--
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// amd64:`DECQ\s64\([A-Z]+\)`
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arr[8]--
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// 386:"SUBL\t4"
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// amd64:"SUBQ\t8"
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return arr[0] - arr[1]
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}
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// -------------------- //
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// Multiplication //
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// -------------------- //
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func Pow2Muls(n1, n2 int) (int, int) {
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// amd64:"SHLQ\t[$]5",-"IMULQ"
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// 386:"SHLL\t[$]5",-"IMULL"
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// arm:"SLL\t[$]5",-"MUL"
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// arm64:"LSL\t[$]5",-"MUL"
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// ppc64:"SLD\t[$]5",-"MUL"
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// ppc64le:"SLD\t[$]5",-"MUL"
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a := n1 * 32
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// amd64:"SHLQ\t[$]6",-"IMULQ"
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// 386:"SHLL\t[$]6",-"IMULL"
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// arm:"SLL\t[$]6",-"MUL"
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// arm64:`NEG\sR[0-9]+<<6,\sR[0-9]+`,-`LSL`,-`MUL`
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// ppc64:"SLD\t[$]6","NEG\\sR[0-9]+,\\sR[0-9]+",-"MUL"
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// ppc64le:"SLD\t[$]6","NEG\\sR[0-9]+,\\sR[0-9]+",-"MUL"
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b := -64 * n2
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return a, b
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}
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func Mul_96(n int) int {
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// amd64:`SHLQ\t[$]5`,`LEAQ\t\(.*\)\(.*\*2\),`,-`IMULQ`
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// 386:`SHLL\t[$]5`,`LEAL\t\(.*\)\(.*\*2\),`,-`IMULL`
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// arm64:`LSL\t[$]5`,`ADD\sR[0-9]+<<1,\sR[0-9]+`,-`MUL`
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// arm:`SLL\t[$]5`,`ADD\sR[0-9]+<<1,\sR[0-9]+`,-`MUL`
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return n * 96
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}
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func MulMemSrc(a []uint32, b []float32) {
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// 386:`IMULL\s4\([A-Z]+\),\s[A-Z]+`
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a[0] *= a[1]
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// 386/sse2:`MULSS\s4\([A-Z]+\),\sX[0-9]+`
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// amd64:`MULSS\s4\([A-Z]+\),\sX[0-9]+`
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b[0] *= b[1]
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}
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// Multiplications merging tests
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func MergeMuls1(n int) int {
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// amd64:"IMUL3Q\t[$]46"
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// 386:"IMUL3L\t[$]46"
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return 15*n + 31*n // 46n
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}
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func MergeMuls2(n int) int {
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// amd64:"IMUL3Q\t[$]23","ADDQ\t[$]29"
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// 386:"IMUL3L\t[$]23","ADDL\t[$]29"
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return 5*n + 7*(n+1) + 11*(n+2) // 23n + 29
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}
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func MergeMuls3(a, n int) int {
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// amd64:"ADDQ\t[$]19",-"IMULQ\t[$]19"
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// 386:"ADDL\t[$]19",-"IMULL\t[$]19"
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return a*n + 19*n // (a+19)n
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}
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func MergeMuls4(n int) int {
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// amd64:"IMUL3Q\t[$]14"
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// 386:"IMUL3L\t[$]14"
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return 23*n - 9*n // 14n
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}
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func MergeMuls5(a, n int) int {
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// amd64:"ADDQ\t[$]-19",-"IMULQ\t[$]19"
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// 386:"ADDL\t[$]-19",-"IMULL\t[$]19"
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return a*n - 19*n // (a-19)n
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}
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// -------------- //
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// Division //
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// -------------- //
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func DivMemSrc(a []float64) {
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// 386/sse2:`DIVSD\s8\([A-Z]+\),\sX[0-9]+`
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// amd64:`DIVSD\s8\([A-Z]+\),\sX[0-9]+`
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a[0] /= a[1]
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}
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func Pow2Divs(n1 uint, n2 int) (uint, int) {
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// 386:"SHRL\t[$]5",-"DIVL"
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// amd64:"SHRQ\t[$]5",-"DIVQ"
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// arm:"SRL\t[$]5",-".*udiv"
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// arm64:"LSR\t[$]5",-"UDIV"
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// ppc64:"SRD"
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// ppc64le:"SRD"
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a := n1 / 32 // unsigned
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// amd64:"SARQ\t[$]6",-"IDIVQ"
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// 386:"SARL\t[$]6",-"IDIVL"
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// arm:"SRA\t[$]6",-".*udiv"
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// arm64:"ASR\t[$]6",-"SDIV"
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// ppc64:"SRAD"
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// ppc64le:"SRAD"
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b := n2 / 64 // signed
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return a, b
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}
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// Check that constant divisions get turned into MULs
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func ConstDivs(n1 uint, n2 int) (uint, int) {
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// amd64:"MOVQ\t[$]-1085102592571150095","MULQ",-"DIVQ"
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// 386:"MOVL\t[$]-252645135","MULL",-"DIVL"
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// arm64:`MOVD`,`UMULH`,-`DIV`
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// arm:`MOVW`,`MUL`,-`.*udiv`
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a := n1 / 17 // unsigned
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// amd64:"MOVQ\t[$]-1085102592571150095","IMULQ",-"IDIVQ"
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// 386:"MOVL\t[$]-252645135","IMULL",-"IDIVL"
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// arm64:`MOVD`,`SMULH`,-`DIV`
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// arm:`MOVW`,`MUL`,-`.*udiv`
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b := n2 / 17 // signed
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return a, b
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}
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func FloatDivs(a []float32) float32 {
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// amd64:`DIVSS\s8\([A-Z]+\),\sX[0-9]+`
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// 386/sse2:`DIVSS\s8\([A-Z]+\),\sX[0-9]+`
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return a[1] / a[2]
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}
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func Pow2Mods(n1 uint, n2 int) (uint, int) {
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// 386:"ANDL\t[$]31",-"DIVL"
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// amd64:"ANDQ\t[$]31",-"DIVQ"
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// arm:"AND\t[$]31",-".*udiv"
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// arm64:"AND\t[$]31",-"UDIV"
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// ppc64:"ANDCC\t[$]31"
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// ppc64le:"ANDCC\t[$]31"
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a := n1 % 32 // unsigned
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// 386:"SHRL",-"IDIVL"
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// amd64:"SHRQ",-"IDIVQ"
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// arm:"SRA",-".*udiv"
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// arm64:"ASR",-"REM"
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// ppc64:"SRAD"
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// ppc64le:"SRAD"
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b := n2 % 64 // signed
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return a, b
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}
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// Check that signed divisibility checks get converted to AND on low bits
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func Pow2DivisibleSigned(n int) bool {
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// 386:"TESTL\t[$]63",-"DIVL",-"SHRL"
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// amd64:"TESTQ\t[$]63",-"DIVQ",-"SHRQ"
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// arm:"AND\t[$]63",-".*udiv",-"SRA"
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// arm64:"AND\t[$]63",-"UDIV",-"ASR"
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// ppc64:"ANDCC\t[$]63",-"SRAD"
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// ppc64le:"ANDCC\t[$]63",-"SRAD"
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return n%64 == 0 // signed
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}
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// Check that constant modulo divs get turned into MULs
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func ConstMods(n1 uint, n2 int) (uint, int) {
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// amd64:"MOVQ\t[$]-1085102592571150095","MULQ",-"DIVQ"
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// 386:"MOVL\t[$]-252645135","MULL",-"DIVL"
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// arm64:`MOVD`,`UMULH`,-`DIV`
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// arm:`MOVW`,`MUL`,-`.*udiv`
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a := n1 % 17 // unsigned
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// amd64:"MOVQ\t[$]-1085102592571150095","IMULQ",-"IDIVQ"
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// 386:"MOVL\t[$]-252645135","IMULL",-"IDIVL"
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// arm64:`MOVD`,`SMULH`,-`DIV`
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// arm:`MOVW`,`MUL`,-`.*udiv`
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b := n2 % 17 // signed
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return a, b
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}
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// Check that divisibility checks x%c==0 are converted to MULs and rotates
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func Divisible(n1 uint, n2 int) (bool, bool, bool, bool) {
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// amd64:"MOVQ\t[$]-6148914691236517205","IMULQ","ROLQ\t[$]63",-"DIVQ"
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// 386:"IMUL3L\t[$]-1431655765","ROLL\t[$]31",-"DIVQ"
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// arm64:"MOVD\t[$]-6148914691236517205","MUL","ROR",-"DIV"
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// arm:"MUL","CMP\t[$]715827882",-".*udiv"
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// ppc64:"MULLD","ROTL\t[$]63"
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// ppc64le:"MULLD","ROTL\t[$]63"
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evenU := n1%6 == 0
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// amd64:"MOVQ\t[$]-8737931403336103397","IMULQ",-"ROLQ",-"DIVQ"
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// 386:"IMUL3L\t[$]678152731",-"ROLL",-"DIVQ"
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// arm64:"MOVD\t[$]-8737931403336103397","MUL",-"ROR",-"DIV"
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// arm:"MUL","CMP\t[$]226050910",-".*udiv"
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// ppc64:"MULLD",-"ROTL"
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// ppc64le:"MULLD",-"ROTL"
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oddU := n1%19 == 0
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// amd64:"IMULQ","ADD","ROLQ\t[$]63",-"DIVQ"
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// 386:"IMUL3L\t[$]-1431655765","ADDL\t[$]715827882","ROLL\t[$]31",-"DIVQ"
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// arm64:"MUL","ADD\t[$]3074457345618258602","ROR",-"DIV"
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// arm:"MUL","ADD\t[$]715827882",-".*udiv"
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// ppc64:"MULLD","ADD","ROTL\t[$]63"
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// ppc64le:"MULLD","ADD","ROTL\t[$]63"
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evenS := n2%6 == 0
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// amd64:"IMULQ","ADD",-"ROLQ",-"DIVQ"
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// 386:"IMUL3L\t[$]678152731","ADDL\t[$]113025455",-"ROLL",-"DIVQ"
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// arm64:"MUL","ADD\t[$]485440633518672410",-"ROR",-"DIV"
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// arm:"MUL","ADD\t[$]113025455",-".*udiv"
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// ppc64:"MULLD","ADD",-"ROTL"
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// ppc64le:"MULLD","ADD",-"ROTL"
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oddS := n2%19 == 0
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return evenU, oddU, evenS, oddS
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}
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// Check that fix-up code is not generated for divisions where it has been proven that
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// that the divisor is not -1 or that the dividend is > MinIntNN.
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func NoFix64A(divr int64) (int64, int64) {
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var d int64 = 42
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var e int64 = 84
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if divr > 5 {
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d /= divr // amd64:-"JMP"
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e %= divr // amd64:-"JMP"
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}
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return d, e
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}
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func NoFix64B(divd int64) (int64, int64) {
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var d int64
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var e int64
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var divr int64 = -1
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if divd > -9223372036854775808 {
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d = divd / divr // amd64:-"JMP"
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e = divd % divr // amd64:-"JMP"
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}
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return d, e
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}
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func NoFix32A(divr int32) (int32, int32) {
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var d int32 = 42
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var e int32 = 84
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if divr > 5 {
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// amd64:-"JMP"
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// 386:-"JMP"
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d /= divr
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// amd64:-"JMP"
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// 386:-"JMP"
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e %= divr
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}
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return d, e
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}
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func NoFix32B(divd int32) (int32, int32) {
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var d int32
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var e int32
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var divr int32 = -1
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if divd > -2147483648 {
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// amd64:-"JMP"
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// 386:-"JMP"
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d = divd / divr
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// amd64:-"JMP"
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// 386:-"JMP"
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e = divd % divr
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}
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return d, e
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}
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func NoFix16A(divr int16) (int16, int16) {
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var d int16 = 42
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var e int16 = 84
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if divr > 5 {
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// amd64:-"JMP"
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// 386:-"JMP"
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d /= divr
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// amd64:-"JMP"
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// 386:-"JMP"
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e %= divr
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}
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return d, e
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}
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func NoFix16B(divd int16) (int16, int16) {
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var d int16
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var e int16
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var divr int16 = -1
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if divd > -32768 {
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// amd64:-"JMP"
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// 386:-"JMP"
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d = divd / divr
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// amd64:-"JMP"
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// 386:-"JMP"
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e = divd % divr
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}
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return d, e
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}
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// Check that len() and cap() calls divided by powers of two are
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// optimized into shifts and ands
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func LenDiv1(a []int) int {
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// 386:"SHRL\t[$]10"
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// amd64:"SHRQ\t[$]10"
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// arm64:"LSR\t[$]10",-"SDIV"
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// arm:"SRL\t[$]10",-".*udiv"
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// ppc64:"SRD"\t[$]10"
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// ppc64le:"SRD"\t[$]10"
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return len(a) / 1024
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}
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func LenDiv2(s string) int {
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// 386:"SHRL\t[$]11"
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// amd64:"SHRQ\t[$]11"
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// arm64:"LSR\t[$]11",-"SDIV"
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// arm:"SRL\t[$]11",-".*udiv"
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// ppc64:"SRD\t[$]11"
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// ppc64le:"SRD\t[$]11"
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return len(s) / (4097 >> 1)
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}
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func LenMod1(a []int) int {
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// 386:"ANDL\t[$]1023"
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// amd64:"ANDQ\t[$]1023"
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// arm64:"AND\t[$]1023",-"SDIV"
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// arm/6:"AND",-".*udiv"
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// arm/7:"BFC",-".*udiv",-"AND"
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// ppc64:"ANDCC\t[$]1023"
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// ppc64le:"ANDCC\t[$]1023"
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return len(a) % 1024
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}
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func LenMod2(s string) int {
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// 386:"ANDL\t[$]2047"
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// amd64:"ANDQ\t[$]2047"
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// arm64:"AND\t[$]2047",-"SDIV"
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// arm/6:"AND",-".*udiv"
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// arm/7:"BFC",-".*udiv",-"AND"
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// ppc64:"ANDCC\t[$]2047"
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// ppc64le:"ANDCC\t[$]2047"
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return len(s) % (4097 >> 1)
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}
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func CapDiv(a []int) int {
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// 386:"SHRL\t[$]12"
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// amd64:"SHRQ\t[$]12"
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// arm64:"LSR\t[$]12",-"SDIV"
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// arm:"SRL\t[$]12",-".*udiv"
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// ppc64:"SRD\t[$]12"
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// ppc64le:"SRD\t[$]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
|
|
}
|