arithmetic.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]
}

func SubFromConst(a int) int {
	// ppc64le: `SUBC\tR[0-9]+,\s[$]40,\sR`
	// ppc64: `SUBC\tR[0-9]+,\s[$]40,\sR`
	b := 40 - a
	return b
}

func SubFromConstNeg(a int) int {
	// ppc64le: `ADD\t[$]40,\sR[0-9]+,\sR`
	// ppc64: `ADD\t[$]40,\sR[0-9]+,\sR`
	c := 40 - (-a)
	return c
}

func SubSubFromConst(a int) int {
	// ppc64le: `ADD\t[$]20,\sR[0-9]+,\sR`
	// ppc64: `ADD\t[$]20,\sR[0-9]+,\sR`
	c := 40 - (20 - a)
	return c
}

func AddSubFromConst(a int) int {
	// ppc64le: `SUBC\tR[0-9]+,\s[$]60,\sR`
	// ppc64: `SUBC\tR[0-9]+,\s[$]60,\sR`
	c := 40 + (20 - a)
	return c
}

func NegSubFromConst(a int) int {
	// ppc64le: `ADD\t[$]-20,\sR[0-9]+,\sR`
	// ppc64: `ADD\t[$]-20,\sR[0-9]+,\sR`
	c := -(20 - a)
	return c
}

func NegAddFromConstNeg(a int) int {
	// ppc64le: `SUBC\tR[0-9]+,\s[$]40,\sR`
	// ppc64: `SUBC\tR[0-9]+,\s[$]40,\sR`
	c := -(-40 + a)
	return c
}

// -------------------- //
//    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`
	// s390x:`SLD\t[$]5`,`SLD\t[$]6`,-`MULLD`
	return n * 96
}

func Mul_n120(n int) int {
	// s390x:`SLD\t[$]3`,`SLD\t[$]7`,-`MULLD`
	return n * -120
}

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)|(LEAQ\t29)"
	// 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(n1, n2 int) (bool, 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"
	a := n1%64 == 0 // signed divisible

	// 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"
	b := n2%64 != 0 // signed indivisible

	return a, b
}

// 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/power8:"MULLD","ADD","ROTL\t[$]63"
	// ppc64le/power8:"MULLD","ADD","ROTL\t[$]63"
	// ppc64/power9:"MADDLD","ROTL\t[$]63"
	// ppc64le/power9:"MADDLD","ROTL\t[$]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/power8:"MULLD","ADD",-"ROTL"
	// ppc64/power9:"MADDLD",-"ROTL"
	// ppc64le/power8:"MULLD","ADD",-"ROTL"
	// ppc64le/power9:"MADDLD",-"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"
		// The following statement is to avoid conflict between the above check
		// and the normal JMP generated at the end of the block.
		d += e
	}
	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"
		d += e
	}
	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
		d += e
	}
	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
		d += e
	}
	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
		d += e
	}
	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
		d += e
	}
	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
}

// Divide -> shift rules usually require fixup for negative inputs.
// If the input is non-negative, make sure the fixup is eliminated.
func divInt(v int64) int64 {
	if v < 0 {
		return 0
	}
	// amd64:-`.*SARQ.*63,`, -".*SHRQ", ".*SARQ.*[$]9,"
	return v / 512
}

// The reassociate rules "x - (z + C) -> (x - z) - C" and
// "(z + C) -x -> C + (z - x)" can optimize the following cases.
func constantFold1(i0, j0, i1, j1, i2, j2, i3, j3 int) (int, int, int, int) {
	// arm64:"SUB","ADD\t[$]2"
	r0 := (i0 + 3) - (j0 + 1)
	// arm64:"SUB","SUB\t[$]4"
	r1 := (i1 - 3) - (j1 + 1)
	// arm64:"SUB","ADD\t[$]4"
	r2 := (i2 + 3) - (j2 - 1)
	// arm64:"SUB","SUB\t[$]2"
	r3 := (i3 - 3) - (j3 - 1)
	return r0, r1, r2, r3
}

// The reassociate rules "x - (z + C) -> (x - z) - C" and
// "(C - z) - x -> C - (z + x)" can optimize the following cases.
func constantFold2(i0, j0, i1, j1 int) (int, int) {
	// arm64:"ADD","MOVD\t[$]2","SUB"
	r0 := (3 - i0) - (j0 + 1)
	// arm64:"ADD","MOVD\t[$]4","SUB"
	r1 := (3 - i1) - (j1 - 1)
	return r0, r1
}

func constantFold3(i, j int) int {
	// arm64: "MOVD\t[$]30","MUL",-"ADD",-"LSL"
	r := (5 * i) * (6 * j)
	return r
}