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[dev.ssa] cmd/compile: add complex arithmetic

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Still to do:
details, more testing corner cases. (e.g. negative zero)
Includes small cleanups for previous CL.

Note: complex division is currently done in the runtime,
so the division code here is apparently not yet necessary
and also not tested.  Seems likely better to open code
division and expose the widening/narrowing to optimization.

Complex64 multiplication and division is done in wide
format to avoid cancellation errors; for division, this
also happens to be compatible with pre-SSA practice
(which uses a single complex128 division function).

It would-be-nice to widen for complex128 multiplication
intermediates as well, but that is trickier to implement
without a handy wider-precision format.

Change-Id: I595a4300f68868fb7641852a54674c6b2b78855e
Reviewed-on: https://go-review.googlesource.com/14028
Reviewed-by: Keith Randall <khr@golang.org>
This commit is contained in:
David Chase 2015-08-28 14:24:10 -04:00
parent 65677cabfd
commit 3a9d0ac3c8
10 changed files with 325 additions and 23 deletions
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153
src/cmd/compile/internal/gc/ssa.go
View File

@ -747,14 +747,16 @@ var opToSSA = map[opAndType]ssa.Op{
opAndType{ONOT, TBOOL}: ssa.OpNot,
opAndType{OMINUS, TINT8}: ssa.OpNeg8,
opAndType{OMINUS, TUINT8}: ssa.OpNeg8,
opAndType{OMINUS, TINT16}: ssa.OpNeg16,
opAndType{OMINUS, TUINT16}: ssa.OpNeg16,
opAndType{OMINUS, TINT32}: ssa.OpNeg32,
opAndType{OMINUS, TUINT32}: ssa.OpNeg32,
opAndType{OMINUS, TINT64}: ssa.OpNeg64,
opAndType{OMINUS, TUINT64}: ssa.OpNeg64,
opAndType{OMINUS, TINT8}: ssa.OpNeg8,
opAndType{OMINUS, TUINT8}: ssa.OpNeg8,
opAndType{OMINUS, TINT16}: ssa.OpNeg16,
opAndType{OMINUS, TUINT16}: ssa.OpNeg16,
opAndType{OMINUS, TINT32}: ssa.OpNeg32,
opAndType{OMINUS, TUINT32}: ssa.OpNeg32,
opAndType{OMINUS, TINT64}: ssa.OpNeg64,
opAndType{OMINUS, TUINT64}: ssa.OpNeg64,
opAndType{OMINUS, TFLOAT32}: ssa.OpNeg32F,
opAndType{OMINUS, TFLOAT64}: ssa.OpNeg64F,
opAndType{OCOM, TINT8}: ssa.OpCom8,
opAndType{OCOM, TUINT8}: ssa.OpCom8,
@ -953,6 +955,14 @@ func (s *state) ssaOp(op uint8, t *Type) ssa.Op {
return x
}
func floatForComplex(t *Type) *Type {
if t.Size() == 8 {
return Types[TFLOAT32]
} else {
return Types[TFLOAT64]
}
}
type opAndTwoTypes struct {
op uint8
etype1 uint8
@ -1394,7 +1404,24 @@ func (s *state) expr(n *Node) *ssa.Value {
}
return s.newValue1(op, n.Type, x)
}
// TODO: Still lack complex conversions.
if ft.IsComplex() && tt.IsComplex() {
var op ssa.Op
if ft.Size() == tt.Size() {
op = ssa.OpCopy
} else if ft.Size() == 8 && tt.Size() == 16 {
op = ssa.OpCvt32Fto64F
} else if ft.Size() == 16 && tt.Size() == 8 {
op = ssa.OpCvt64Fto32F
} else {
s.Fatalf("weird complex conversion %s -> %s", ft, tt)
}
ftp := floatForComplex(ft)
ttp := floatForComplex(tt)
return s.newValue2(ssa.OpComplexMake, tt,
s.newValue1(op, ttp, s.newValue1(ssa.OpComplexReal, ftp, x)),
s.newValue1(op, ttp, s.newValue1(ssa.OpComplexImag, ftp, x)))
}
s.Unimplementedf("unhandled OCONV %s -> %s", Econv(int(n.Left.Type.Etype), 0), Econv(int(n.Type.Etype), 0))
return nil
@ -1404,7 +1431,97 @@ func (s *state) expr(n *Node) *ssa.Value {
a := s.expr(n.Left)
b := s.expr(n.Right)
return s.newValue2(s.ssaOp(n.Op, n.Left.Type), Types[TBOOL], a, b)
case OADD, OAND, OMUL, OOR, OSUB, ODIV, OMOD, OHMUL, OXOR:
case OMUL:
a := s.expr(n.Left)
b := s.expr(n.Right)
if n.Type.IsComplex() {
mulop := ssa.OpMul64F
addop := ssa.OpAdd64F
subop := ssa.OpSub64F
pt := floatForComplex(n.Type) // Could be Float32 or Float64
wt := Types[TFLOAT64] // Compute in Float64 to minimize cancellation error
areal := s.newValue1(ssa.OpComplexReal, pt, a)
breal := s.newValue1(ssa.OpComplexReal, pt, b)
aimag := s.newValue1(ssa.OpComplexImag, pt, a)
bimag := s.newValue1(ssa.OpComplexImag, pt, b)
if pt != wt { // Widen for calculation
areal = s.newValue1(ssa.OpCvt32Fto64F, wt, areal)
breal = s.newValue1(ssa.OpCvt32Fto64F, wt, breal)
aimag = s.newValue1(ssa.OpCvt32Fto64F, wt, aimag)
bimag = s.newValue1(ssa.OpCvt32Fto64F, wt, bimag)
}
xreal := s.newValue2(subop, wt, s.newValue2(mulop, wt, areal, breal), s.newValue2(mulop, wt, aimag, bimag))
ximag := s.newValue2(addop, wt, s.newValue2(mulop, wt, areal, bimag), s.newValue2(mulop, wt, aimag, breal))
if pt != wt { // Narrow to store back
xreal = s.newValue1(ssa.OpCvt64Fto32F, pt, xreal)
ximag = s.newValue1(ssa.OpCvt64Fto32F, pt, ximag)
}
return s.newValue2(ssa.OpComplexMake, n.Type, xreal, ximag)
}
return s.newValue2(s.ssaOp(n.Op, n.Type), a.Type, a, b)
case ODIV:
a := s.expr(n.Left)
b := s.expr(n.Right)
if n.Type.IsComplex() {
// TODO this is not executed because the front-end substitutes a runtime call.
// That probably ought to change; with modest optimization the widen/narrow
// conversions could all be elided in larger expression trees.
mulop := ssa.OpMul64F
addop := ssa.OpAdd64F
subop := ssa.OpSub64F
divop := ssa.OpDiv64F
pt := floatForComplex(n.Type) // Could be Float32 or Float64
wt := Types[TFLOAT64] // Compute in Float64 to minimize cancellation error
areal := s.newValue1(ssa.OpComplexReal, pt, a)
breal := s.newValue1(ssa.OpComplexReal, pt, b)
aimag := s.newValue1(ssa.OpComplexImag, pt, a)
bimag := s.newValue1(ssa.OpComplexImag, pt, b)
if pt != wt { // Widen for calculation
areal = s.newValue1(ssa.OpCvt32Fto64F, wt, areal)
breal = s.newValue1(ssa.OpCvt32Fto64F, wt, breal)
aimag = s.newValue1(ssa.OpCvt32Fto64F, wt, aimag)
bimag = s.newValue1(ssa.OpCvt32Fto64F, wt, bimag)
}
denom := s.newValue2(addop, wt, s.newValue2(mulop, wt, breal, breal), s.newValue2(mulop, wt, bimag, bimag))
xreal := s.newValue2(addop, wt, s.newValue2(mulop, wt, areal, breal), s.newValue2(mulop, wt, aimag, bimag))
ximag := s.newValue2(subop, wt, s.newValue2(mulop, wt, aimag, breal), s.newValue2(mulop, wt, areal, bimag))
// TODO not sure if this is best done in wide precision or narrow
// Double-rounding might be an issue.
// Note that the pre-SSA implementation does the entire calculation
// in wide format, so wide is compatible.
xreal = s.newValue2(divop, wt, xreal, denom)
ximag = s.newValue2(divop, wt, ximag, denom)
if pt != wt { // Narrow to store back
xreal = s.newValue1(ssa.OpCvt64Fto32F, pt, xreal)
ximag = s.newValue1(ssa.OpCvt64Fto32F, pt, ximag)
}
return s.newValue2(ssa.OpComplexMake, n.Type, xreal, ximag)
}
return s.newValue2(s.ssaOp(n.Op, n.Type), a.Type, a, b)
case OADD, OSUB:
a := s.expr(n.Left)
b := s.expr(n.Right)
if n.Type.IsComplex() {
pt := floatForComplex(n.Type)
op := s.ssaOp(n.Op, pt)
return s.newValue2(ssa.OpComplexMake, n.Type,
s.newValue2(op, pt, s.newValue1(ssa.OpComplexReal, pt, a), s.newValue1(ssa.OpComplexReal, pt, b)),
s.newValue2(op, pt, s.newValue1(ssa.OpComplexImag, pt, a), s.newValue1(ssa.OpComplexImag, pt, b)))
}
return s.newValue2(s.ssaOp(n.Op, n.Type), a.Type, a, b)
case OAND, OOR, OMOD, OHMUL, OXOR:
a := s.expr(n.Left)
b := s.expr(n.Right)
return s.newValue2(s.ssaOp(n.Op, n.Type), a.Type, a, b)
@ -1464,8 +1581,18 @@ func (s *state) expr(n *Node) *ssa.Value {
s.startBlock(bResult)
return s.variable(n, Types[TBOOL])
// unary ops
case ONOT, OMINUS, OCOM:
// unary ops
case OMINUS:
a := s.expr(n.Left)
if n.Type.IsComplex() {
tp := floatForComplex(n.Type)
negop := s.ssaOp(n.Op, tp)
return s.newValue2(ssa.OpComplexMake, n.Type,
s.newValue1(negop, tp, s.newValue1(ssa.OpComplexReal, tp, a)),
s.newValue1(negop, tp, s.newValue1(ssa.OpComplexImag, tp, a)))
}
return s.newValue1(s.ssaOp(n.Op, n.Type), a.Type, a)
case ONOT, OCOM:
a := s.expr(n.Left)
return s.newValue1(s.ssaOp(n.Op, n.Type), a.Type, a)
@ -2551,7 +2678,7 @@ func genValue(v *ssa.Value) {
ssa.OpAMD64ORQ, ssa.OpAMD64ORL, ssa.OpAMD64ORW, ssa.OpAMD64ORB,
ssa.OpAMD64XORQ, ssa.OpAMD64XORL, ssa.OpAMD64XORW, ssa.OpAMD64XORB,
ssa.OpAMD64MULQ, ssa.OpAMD64MULL, ssa.OpAMD64MULW, ssa.OpAMD64MULB,
ssa.OpAMD64MULSS, ssa.OpAMD64MULSD:
ssa.OpAMD64MULSS, ssa.OpAMD64MULSD, ssa.OpAMD64PXOR:
r := regnum(v)
x := regnum(v.Args[0])
y := regnum(v.Args[1])

102
src/cmd/compile/internal/gc/testdata/fp_ssa.go vendored
View File

@ -1306,7 +1306,7 @@ func fail32bool(s string, f func(a, b float32) bool, a, b float32, e bool) int {
func expect64(s string, x, expected float64) int {
if x != expected {
println("Expected", expected, "for", s, ", got", x)
println("F64 Expected", expected, "for", s, ", got", x)
return 1
}
return 0
@ -1314,7 +1314,7 @@ func expect64(s string, x, expected float64) int {
func expect32(s string, x, expected float32) int {
if x != expected {
println("Expected", expected, "for", s, ", got", x)
println("F32 Expected", expected, "for", s, ", got", x)
return 1
}
return 0
@ -1322,7 +1322,7 @@ func expect32(s string, x, expected float32) int {
func expectUint64(s string, x, expected uint64) int {
if x != expected {
fmt.Printf("%s: Expected 0x%016x, got 0x%016x\n", s, expected, x)
fmt.Printf("U64 Expected 0x%016x for %s, got 0x%016x\n", expected, s, x)
return 1
}
return 0
@ -1435,6 +1435,100 @@ func cmpOpTest(s string,
return fails
}
func expectCx128(s string, x, expected complex128) int {
if x != expected {
println("Cx 128 Expected", expected, "for", s, ", got", x)
return 1
}
return 0
}
func expectCx64(s string, x, expected complex64) int {
if x != expected {
println("Cx 64 Expected", expected, "for", s, ", got", x)
return 1
}
return 0
}
func cx128sum_ssa(a, b complex128) complex128 {
return a + b
}
func cx128diff_ssa(a, b complex128) complex128 {
return a - b
}
func cx128prod_ssa(a, b complex128) complex128 {
return a * b
}
func cx128quot_ssa(a, b complex128) complex128 {
return a / b
}
func cx128neg_ssa(a complex128) complex128 {
return -a
}
func cx64sum_ssa(a, b complex64) complex64 {
return a + b
}
func cx64diff_ssa(a, b complex64) complex64 {
return a - b
}
func cx64prod_ssa(a, b complex64) complex64 {
return a * b
}
func cx64quot_ssa(a, b complex64) complex64 {
return a / b
}
func cx64neg_ssa(a complex64) complex64 {
return -a
}
func complexTest128() int {
fails := 0
var a complex128 = 1 + 2i
var b complex128 = 3 + 6i
sum := cx128sum_ssa(b, a)
diff := cx128diff_ssa(b, a)
prod := cx128prod_ssa(b, a)
quot := cx128quot_ssa(b, a)
neg := cx128neg_ssa(a)
fails += expectCx128("sum", sum, 4+8i)
fails += expectCx128("diff", diff, 2+4i)
fails += expectCx128("prod", prod, -9+12i)
fails += expectCx128("quot", quot, 3+0i)
fails += expectCx128("neg", neg, -1-2i)
return fails
}
func complexTest64() int {
fails := 0
var a complex64 = 1 + 2i
var b complex64 = 3 + 6i
sum := cx64sum_ssa(b, a)
diff := cx64diff_ssa(b, a)
prod := cx64prod_ssa(b, a)
quot := cx64quot_ssa(b, a)
neg := cx64neg_ssa(a)
fails += expectCx64("sum", sum, 4+8i)
fails += expectCx64("diff", diff, 2+4i)
fails += expectCx64("prod", prod, -9+12i)
fails += expectCx64("quot", quot, 3+0i)
fails += expectCx64("neg", neg, -1-2i)
return fails
}
func main() {
a := 3.0
@ -1523,6 +1617,8 @@ func main() {
}
fails += floatingToIntegerConversionsTest()
fails += complexTest128()
fails += complexTest64()
if fails > 0 {
fmt.Printf("Saw %v failures\n", fails)

9
src/cmd/compile/internal/ssa/decompose.go
View File

@ -77,12 +77,13 @@ func decomposeSlicePhi(v *Value) {
func decomposeComplexPhi(v *Value) {
fe := v.Block.Func.Config.fe
var partType Type
if v.Type.Size() == 8 {
switch z := v.Type.Size(); z {
case 8:
partType = fe.TypeFloat32()
} else if v.Type.Size() == 16 {
case 16:
partType = fe.TypeFloat64()
} else {
panic("Whoops, are sizes in bytes or bits?")
default:
v.Fatalf("decomposeComplexPhi: bad complex size %d", z)
}
real := v.Block.NewValue0(v.Line, OpPhi, partType)

2
src/cmd/compile/internal/ssa/gen/AMD64.rules
View File

@ -81,6 +81,8 @@
(Neg32 x) -> (NEGL x)
(Neg16 x) -> (NEGW x)
(Neg8 x) -> (NEGB x)
(Neg32F x) -> (PXOR x (MOVSSconst <config.Frontend().TypeFloat32()> {math.Copysign(0, -1)}))
(Neg64F x) -> (PXOR x (MOVSDconst <config.Frontend().TypeFloat64()> {math.Copysign(0, -1)}))
(Com64 x) -> (NOTQ x)
(Com32 x) -> (NOTL x)

2
src/cmd/compile/internal/ssa/gen/AMD64Ops.go
View File

@ -354,6 +354,8 @@ func init() {
{name: "CVTSD2SS", reg: fp11, asm: "CVTSD2SS"}, // convert float64 to float32
{name: "CVTSS2SD", reg: fp11, asm: "CVTSS2SD"}, // convert float32 to float64
{name: "PXOR", reg: fp21, asm: "PXOR"}, // exclusive or, applied to X regs for float negation.
{name: "LEAQ", reg: gp11sb}, // arg0 + auxint + offset encoded in aux
{name: "LEAQ1", reg: gp21sb}, // arg0 + arg1 + auxint
{name: "LEAQ2", reg: gp21sb}, // arg0 + 2*arg1 + auxint

7
src/cmd/compile/internal/ssa/gen/genericOps.go
View File

@ -24,7 +24,6 @@ var genericOps = []opData{
{name: "SubPtr"},
{name: "Sub32F"},
{name: "Sub64F"},
// TODO: Sub64C, Sub128C
{name: "Mul8"}, // arg0 * arg1
{name: "Mul16"},
@ -225,6 +224,8 @@ var genericOps = []opData{
{name: "Neg16"},
{name: "Neg32"},
{name: "Neg64"},
{name: "Neg32F"},
{name: "Neg64F"},
{name: "Com8"}, // ^arg0
{name: "Com16"},
@ -336,8 +337,8 @@ var genericOps = []opData{
// Complex (part/whole)
{name: "ComplexMake"}, // arg0=real, arg1=imag
{name: "ComplexReal"}, // real_part(arg0)
{name: "ComplexImag"}, // imaginary_part(arg0)
{name: "ComplexReal"}, // real(arg0)
{name: "ComplexImag"}, // imag(arg0)
// Strings
{name: "StringMake"}, // arg0=ptr, arg1=len

3
src/cmd/compile/internal/ssa/gen/rulegen.go
View File

@ -142,6 +142,9 @@ func genRules(arch arch) {
if *genLog {
fmt.Fprintln(w, "import \"fmt\"")
}
fmt.Fprintln(w, "import \"math\"")
fmt.Fprintln(w, "var _ = math.MinInt8 // in case not otherwise used")
fmt.Fprintf(w, "func rewriteValue%s(v *Value, config *Config) bool {\n", arch.name)
fmt.Fprintln(w, "b := v.Block")

24
src/cmd/compile/internal/ssa/opGen.go
View File

@ -237,6 +237,7 @@ const (
OpAMD64CVTSQ2SD
OpAMD64CVTSD2SS
OpAMD64CVTSS2SD
OpAMD64PXOR
OpAMD64LEAQ
OpAMD64LEAQ1
OpAMD64LEAQ2
@ -435,6 +436,8 @@ const (
OpNeg16
OpNeg32
OpNeg64
OpNeg32F
OpNeg64F
OpCom8
OpCom16
OpCom32
@ -2794,6 +2797,19 @@ var opcodeTable = [...]opInfo{
},
},
},
{
name: "PXOR",
asm: x86.APXOR,
reg: regInfo{
inputs: []inputInfo{
{0, 4294901760}, // .X0 .X1 .X2 .X3 .X4 .X5 .X6 .X7 .X8 .X9 .X10 .X11 .X12 .X13 .X14 .X15
{1, 4294901760}, // .X0 .X1 .X2 .X3 .X4 .X5 .X6 .X7 .X8 .X9 .X10 .X11 .X12 .X13 .X14 .X15
},
outputs: []regMask{
4294901760, // .X0 .X1 .X2 .X3 .X4 .X5 .X6 .X7 .X8 .X9 .X10 .X11 .X12 .X13 .X14 .X15
},
},
},
{
name: "LEAQ",
reg: regInfo{
@ -3743,6 +3759,14 @@ var opcodeTable = [...]opInfo{
name: "Neg64",
generic: true,
},
{
name: "Neg32F",
generic: true,
},
{
name: "Neg64F",
generic: true,
},
{
name: "Com8",
generic: true,

43
src/cmd/compile/internal/ssa/rewriteAMD64.go
View File

@ -2,6 +2,9 @@
// generated with: cd gen; go run *.go
package ssa
import "math"
var _ = math.MinInt8 // in case not otherwise used
func rewriteValueAMD64(v *Value, config *Config) bool {
b := v.Block
switch v.Op {
@ -6059,6 +6062,26 @@ func rewriteValueAMD64(v *Value, config *Config) bool {
goto endce1f7e17fc193f6c076e47d5e401e126
endce1f7e17fc193f6c076e47d5e401e126:
;
case OpNeg32F:
// match: (Neg32F x)
// cond:
// result: (PXOR x (MOVSSconst <config.Frontend().TypeFloat32()> {math.Copysign(0, -1)}))
{
x := v.Args[0]
v.Op = OpAMD64PXOR
v.AuxInt = 0
v.Aux = nil
v.resetArgs()
v.AddArg(x)
v0 := b.NewValue0(v.Line, OpAMD64MOVSSconst, TypeInvalid)
v0.Type = config.Frontend().TypeFloat32()
v0.Aux = math.Copysign(0, -1)
v.AddArg(v0)
return true
}
goto end47074133a76e069317ceca46372cafc3
end47074133a76e069317ceca46372cafc3:
;
case OpNeg64:
// match: (Neg64 x)
// cond:
@ -6075,6 +6098,26 @@ func rewriteValueAMD64(v *Value, config *Config) bool {
goto enda06c5b1718f2b96aba10bf5a5c437c6c
enda06c5b1718f2b96aba10bf5a5c437c6c:
;
case OpNeg64F:
// match: (Neg64F x)
// cond:
// result: (PXOR x (MOVSDconst <config.Frontend().TypeFloat64()> {math.Copysign(0, -1)}))
{
x := v.Args[0]
v.Op = OpAMD64PXOR
v.AuxInt = 0
v.Aux = nil
v.resetArgs()
v.AddArg(x)
v0 := b.NewValue0(v.Line, OpAMD64MOVSDconst, TypeInvalid)
v0.Type = config.Frontend().TypeFloat64()
v0.Aux = math.Copysign(0, -1)
v.AddArg(v0)
return true
}
goto end9240202f5753ebd23f11f982ece3e06e
end9240202f5753ebd23f11f982ece3e06e:
;
case OpNeg8:
// match: (Neg8 x)
// cond:

3
src/cmd/compile/internal/ssa/rewritegeneric.go
View File

@ -2,6 +2,9 @@
// generated with: cd gen; go run *.go
package ssa
import "math"
var _ = math.MinInt8 // in case not otherwise used
func rewriteValuegeneric(v *Value, config *Config) bool {
b := v.Block
switch v.Op {