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mirror of https://github.com/golang/go synced 2024-11-19 15:54:46 -07:00
go/src/runtime/iface.go
Josh Bleecher Snyder 504bc3ed24 cmd/compile, runtime: specialize convT2x, don't alloc for zero vals
Prior to this CL, all runtime conversions
from a concrete value to an interface went
through one of two runtime calls: convT2E or convT2I.
However, in practice, basic types are very common.
Specializing convT2x for those basic types allows
for a more efficient implementation for those types.
For basic scalars and strings, allocation and copying
can use the same methods as normal code.
For pointer-free types, allocation can occur without
zeroing, and copying can take place without GC calls.
For slices, copying is cheaper and simpler.

This CL adds twelve runtime routines:

convT2E16, convT2I16
convT2E32, convT2I32
convT2E64, convT2I64
convT2Estring, convT2Istring
convT2Eslice, convT2Islice
convT2Enoptr, convT2Inoptr

While compiling make.bash, 93% of all convT2x calls
are now to one of these specialized convT2x call.

Within specialized convT2x routines, it is cheap to check
for a zero value, in a way that it is not in general.
When we detect a zero value there, we return a pointer
to zeroVal, rather than allocating.

name                         old time/op  new time/op  delta
ConvT2Ezero/zero/16-8        17.9ns ± 2%   3.0ns ± 3%  -83.20%  (p=0.000 n=56+56)
ConvT2Ezero/zero/32-8        17.8ns ± 2%   3.0ns ± 3%  -83.15%  (p=0.000 n=59+60)
ConvT2Ezero/zero/64-8        20.1ns ± 1%   3.0ns ± 2%  -84.98%  (p=0.000 n=57+57)
ConvT2Ezero/zero/str-8       32.6ns ± 1%   3.0ns ± 4%  -90.70%  (p=0.000 n=59+60)
ConvT2Ezero/zero/slice-8     36.7ns ± 2%   3.0ns ± 2%  -91.78%  (p=0.000 n=59+59)
ConvT2Ezero/zero/big-8       91.9ns ± 2%  85.9ns ± 2%   -6.52%  (p=0.000 n=57+57)
ConvT2Ezero/nonzero/16-8     17.7ns ± 2%  12.7ns ± 3%  -28.38%  (p=0.000 n=55+60)
ConvT2Ezero/nonzero/32-8     17.8ns ± 1%  12.7ns ± 1%  -28.44%  (p=0.000 n=54+57)
ConvT2Ezero/nonzero/64-8     20.0ns ± 1%  15.0ns ± 1%  -24.90%  (p=0.000 n=56+58)
ConvT2Ezero/nonzero/str-8    32.6ns ± 1%  25.7ns ± 1%  -21.17%  (p=0.000 n=58+55)
ConvT2Ezero/nonzero/slice-8  36.8ns ± 2%  30.4ns ± 1%  -17.32%  (p=0.000 n=60+52)
ConvT2Ezero/nonzero/big-8    92.1ns ± 2%  85.9ns ± 2%   -6.70%  (p=0.000 n=57+59)

Benchmarks on a real program (the compiler):

name       old time/op      new time/op      delta
Template        227ms ± 5%       221ms ± 2%  -2.48%  (p=0.000 n=30+26)
Unicode         102ms ± 5%       100ms ± 3%  -1.30%  (p=0.009 n=30+26)
GoTypes         656ms ± 5%       659ms ± 4%    ~     (p=0.208 n=30+30)
Compiler        2.82s ± 2%       2.82s ± 1%    ~     (p=0.614 n=29+27)
Flate           128ms ± 2%       128ms ± 5%    ~     (p=0.783 n=27+28)
GoParser        158ms ± 3%       158ms ± 3%    ~     (p=0.261 n=28+30)
Reflect         408ms ± 7%       401ms ± 3%    ~     (p=0.075 n=30+30)
Tar             123ms ± 6%       121ms ± 8%    ~     (p=0.287 n=29+30)
XML             220ms ± 2%       220ms ± 4%    ~     (p=0.805 n=29+29)

name       old user-ns/op   new user-ns/op   delta
Template   281user-ms ± 4%  279user-ms ± 3%  -0.87%  (p=0.044 n=28+28)
Unicode    142user-ms ± 4%  141user-ms ± 3%  -1.04%  (p=0.015 n=30+27)
GoTypes    884user-ms ± 3%  886user-ms ± 2%    ~     (p=0.532 n=30+30)
Compiler   3.94user-s ± 3%  3.92user-s ± 1%    ~     (p=0.185 n=30+28)
Flate      165user-ms ± 2%  165user-ms ± 4%    ~     (p=0.780 n=27+29)
GoParser   209user-ms ± 2%  208user-ms ± 3%    ~     (p=0.453 n=28+30)
Reflect    533user-ms ± 6%  526user-ms ± 3%    ~     (p=0.057 n=30+30)
Tar        156user-ms ± 6%  154user-ms ± 6%    ~     (p=0.133 n=29+30)
XML        288user-ms ± 4%  288user-ms ± 4%    ~     (p=0.633 n=30+30)

name       old alloc/op     new alloc/op     delta
Template       41.0MB ± 0%      40.9MB ± 0%  -0.11%  (p=0.000 n=29+29)
Unicode        32.6MB ± 0%      32.6MB ± 0%    ~     (p=0.572 n=29+30)
GoTypes         122MB ± 0%       122MB ± 0%  -0.10%  (p=0.000 n=30+30)
Compiler        482MB ± 0%       481MB ± 0%  -0.07%  (p=0.000 n=30+29)
Flate          26.6MB ± 0%      26.6MB ± 0%    ~     (p=0.096 n=30+30)
GoParser       32.7MB ± 0%      32.6MB ± 0%  -0.06%  (p=0.011 n=28+28)
Reflect        84.2MB ± 0%      84.1MB ± 0%  -0.17%  (p=0.000 n=29+30)
Tar            27.7MB ± 0%      27.7MB ± 0%  -0.05%  (p=0.032 n=27+28)
XML            44.7MB ± 0%      44.7MB ± 0%    ~     (p=0.131 n=28+30)

name       old allocs/op    new allocs/op    delta
Template         373k ± 1%        370k ± 1%  -0.76%  (p=0.000 n=30+30)
Unicode          325k ± 1%        325k ± 1%    ~     (p=0.383 n=29+30)
GoTypes         1.16M ± 0%       1.15M ± 0%  -0.75%  (p=0.000 n=29+30)
Compiler        4.15M ± 0%       4.13M ± 0%  -0.59%  (p=0.000 n=30+29)
Flate            238k ± 1%        237k ± 1%  -0.62%  (p=0.000 n=30+30)
GoParser         304k ± 1%        302k ± 1%  -0.64%  (p=0.000 n=30+28)
Reflect         1.00M ± 0%       0.99M ± 0%  -1.10%  (p=0.000 n=29+30)
Tar              245k ± 1%        244k ± 1%  -0.59%  (p=0.000 n=27+29)
XML              391k ± 1%        389k ± 1%  -0.59%  (p=0.000 n=29+30)

Change-Id: Id7f456d690567c2b0a96b0d6d64de8784b6e305f
Reviewed-on: https://go-review.googlesource.com/36476
Run-TryBot: Josh Bleecher Snyder <josharian@gmail.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Keith Randall <khr@golang.org>
2017-02-28 19:23:33 +00:00

578 lines
14 KiB
Go

// Copyright 2014 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 runtime
import (
"runtime/internal/atomic"
"runtime/internal/sys"
"unsafe"
)
const (
hashSize = 1009
)
var (
ifaceLock mutex // lock for accessing hash
hash [hashSize]*itab
)
func itabhash(inter *interfacetype, typ *_type) uint32 {
// compiler has provided some good hash codes for us.
h := inter.typ.hash
h += 17 * typ.hash
// TODO(rsc): h += 23 * x.mhash ?
return h % hashSize
}
func getitab(inter *interfacetype, typ *_type, canfail bool) *itab {
if len(inter.mhdr) == 0 {
throw("internal error - misuse of itab")
}
// easy case
if typ.tflag&tflagUncommon == 0 {
if canfail {
return nil
}
name := inter.typ.nameOff(inter.mhdr[0].name)
panic(&TypeAssertionError{"", typ.string(), inter.typ.string(), name.name()})
}
h := itabhash(inter, typ)
// look twice - once without lock, once with.
// common case will be no lock contention.
var m *itab
var locked int
for locked = 0; locked < 2; locked++ {
if locked != 0 {
lock(&ifaceLock)
}
for m = (*itab)(atomic.Loadp(unsafe.Pointer(&hash[h]))); m != nil; m = m.link {
if m.inter == inter && m._type == typ {
if m.bad {
if !canfail {
// this can only happen if the conversion
// was already done once using the , ok form
// and we have a cached negative result.
// the cached result doesn't record which
// interface function was missing, so try
// adding the itab again, which will throw an error.
additab(m, locked != 0, false)
}
m = nil
}
if locked != 0 {
unlock(&ifaceLock)
}
return m
}
}
}
m = (*itab)(persistentalloc(unsafe.Sizeof(itab{})+uintptr(len(inter.mhdr)-1)*sys.PtrSize, 0, &memstats.other_sys))
m.inter = inter
m._type = typ
additab(m, true, canfail)
unlock(&ifaceLock)
if m.bad {
return nil
}
return m
}
func additab(m *itab, locked, canfail bool) {
inter := m.inter
typ := m._type
x := typ.uncommon()
// both inter and typ have method sorted by name,
// and interface names are unique,
// so can iterate over both in lock step;
// the loop is O(ni+nt) not O(ni*nt).
ni := len(inter.mhdr)
nt := int(x.mcount)
xmhdr := (*[1 << 16]method)(add(unsafe.Pointer(x), uintptr(x.moff)))[:nt:nt]
j := 0
for k := 0; k < ni; k++ {
i := &inter.mhdr[k]
itype := inter.typ.typeOff(i.ityp)
name := inter.typ.nameOff(i.name)
iname := name.name()
ipkg := name.pkgPath()
if ipkg == "" {
ipkg = inter.pkgpath.name()
}
for ; j < nt; j++ {
t := &xmhdr[j]
tname := typ.nameOff(t.name)
if typ.typeOff(t.mtyp) == itype && tname.name() == iname {
pkgPath := tname.pkgPath()
if pkgPath == "" {
pkgPath = typ.nameOff(x.pkgpath).name()
}
if tname.isExported() || pkgPath == ipkg {
if m != nil {
ifn := typ.textOff(t.ifn)
*(*unsafe.Pointer)(add(unsafe.Pointer(&m.fun[0]), uintptr(k)*sys.PtrSize)) = ifn
}
goto nextimethod
}
}
}
// didn't find method
if !canfail {
if locked {
unlock(&ifaceLock)
}
panic(&TypeAssertionError{"", typ.string(), inter.typ.string(), iname})
}
m.bad = true
break
nextimethod:
}
if !locked {
throw("invalid itab locking")
}
h := itabhash(inter, typ)
m.link = hash[h]
m.inhash = true
atomicstorep(unsafe.Pointer(&hash[h]), unsafe.Pointer(m))
}
func itabsinit() {
lock(&ifaceLock)
for _, md := range activeModules() {
for _, i := range md.itablinks {
// itablinks is a slice of pointers to the itabs used in this
// module. A given itab may be used in more than one module
// and thanks to the way global symbol resolution works, the
// pointed-to itab may already have been inserted into the
// global 'hash'.
if !i.inhash {
additab(i, true, false)
}
}
}
unlock(&ifaceLock)
}
// panicdottypeE is called when doing an e.(T) conversion and the conversion fails.
// have = the dynamic type we have.
// want = the static type we're trying to convert to.
// iface = the static type we're converting from.
func panicdottypeE(have, want, iface *_type) {
haveString := ""
if have != nil {
haveString = have.string()
}
panic(&TypeAssertionError{iface.string(), haveString, want.string(), ""})
}
// panicdottypeI is called when doing an i.(T) conversion and the conversion fails.
// Same args as panicdottypeE, but "have" is the dynamic itab we have.
func panicdottypeI(have *itab, want, iface *_type) {
var t *_type
if have != nil {
t = have._type
}
panicdottypeE(t, want, iface)
}
// panicnildottype is called when doing a i.(T) conversion and the interface i is nil.
// want = the static type we're trying to convert to.
func panicnildottype(want *_type) {
panic(&TypeAssertionError{"", "", want.string(), ""})
// TODO: Add the static type we're converting from as well.
// It might generate a better error message.
// Just to match other nil conversion errors, we don't for now.
}
// The conv and assert functions below do very similar things.
// The convXXX functions are guaranteed by the compiler to succeed.
// The assertXXX functions may fail (either panicking or returning false,
// depending on whether they are 1-result or 2-result).
// The convXXX functions succeed on a nil input, whereas the assertXXX
// functions fail on a nil input.
func convT2E(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2E))
}
if msanenabled {
msanread(elem, t.size)
}
x := mallocgc(t.size, t, true)
// TODO: We allocate a zeroed object only to overwrite it with actual data.
// Figure out how to avoid zeroing. Also below in convT2Eslice, convT2I, convT2Islice.
typedmemmove(t, x, elem)
e._type = t
e.data = x
return
}
func convT2E16(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2E16))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint16)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(2, t, false)
*(*uint16)(x) = *(*uint16)(elem)
}
e._type = t
e.data = x
return
}
func convT2E32(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2E32))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint32)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(4, t, false)
*(*uint32)(x) = *(*uint32)(elem)
}
e._type = t
e.data = x
return
}
func convT2E64(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2E64))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint64)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(8, t, false)
*(*uint64)(x) = *(*uint64)(elem)
}
e._type = t
e.data = x
return
}
func convT2Estring(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2Estring))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*string)(elem) == "" {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(t.size, t, true)
*(*string)(x) = *(*string)(elem)
}
e._type = t
e.data = x
return
}
func convT2Eslice(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2Eslice))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if v := *(*slice)(elem); uintptr(v.array) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(t.size, t, true)
*(*slice)(x) = *(*slice)(elem)
}
e._type = t
e.data = x
return
}
func convT2Enoptr(t *_type, elem unsafe.Pointer) (e eface) {
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&t)), funcPC(convT2Enoptr))
}
if msanenabled {
msanread(elem, t.size)
}
x := mallocgc(t.size, t, false)
memmove(x, elem, t.size)
e._type = t
e.data = x
return
}
func convT2I(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2I))
}
if msanenabled {
msanread(elem, t.size)
}
x := mallocgc(t.size, t, true)
typedmemmove(t, x, elem)
i.tab = tab
i.data = x
return
}
func convT2I16(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2I16))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint16)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(2, t, false)
*(*uint16)(x) = *(*uint16)(elem)
}
i.tab = tab
i.data = x
return
}
func convT2I32(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2I32))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint32)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(4, t, false)
*(*uint32)(x) = *(*uint32)(elem)
}
i.tab = tab
i.data = x
return
}
func convT2I64(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2I64))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*uint64)(elem) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(8, t, false)
*(*uint64)(x) = *(*uint64)(elem)
}
i.tab = tab
i.data = x
return
}
func convT2Istring(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2Istring))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if *(*string)(elem) == "" {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(t.size, t, true)
*(*string)(x) = *(*string)(elem)
}
i.tab = tab
i.data = x
return
}
func convT2Islice(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2Islice))
}
if msanenabled {
msanread(elem, t.size)
}
var x unsafe.Pointer
if v := *(*slice)(elem); uintptr(v.array) == 0 {
x = unsafe.Pointer(&zeroVal[0])
} else {
x = mallocgc(t.size, t, true)
*(*slice)(x) = *(*slice)(elem)
}
i.tab = tab
i.data = x
return
}
func convT2Inoptr(tab *itab, elem unsafe.Pointer) (i iface) {
t := tab._type
if raceenabled {
raceReadObjectPC(t, elem, getcallerpc(unsafe.Pointer(&tab)), funcPC(convT2Inoptr))
}
if msanenabled {
msanread(elem, t.size)
}
x := mallocgc(t.size, t, false)
memmove(x, elem, t.size)
i.tab = tab
i.data = x
return
}
func convI2I(inter *interfacetype, i iface) (r iface) {
tab := i.tab
if tab == nil {
return
}
if tab.inter == inter {
r.tab = tab
r.data = i.data
return
}
r.tab = getitab(inter, tab._type, false)
r.data = i.data
return
}
func assertI2I(inter *interfacetype, i iface) (r iface) {
tab := i.tab
if tab == nil {
// explicit conversions require non-nil interface value.
panic(&TypeAssertionError{"", "", inter.typ.string(), ""})
}
if tab.inter == inter {
r.tab = tab
r.data = i.data
return
}
r.tab = getitab(inter, tab._type, false)
r.data = i.data
return
}
func assertI2I2(inter *interfacetype, i iface) (r iface, b bool) {
tab := i.tab
if tab == nil {
return
}
if tab.inter != inter {
tab = getitab(inter, tab._type, true)
if tab == nil {
return
}
}
r.tab = tab
r.data = i.data
b = true
return
}
func assertE2I(inter *interfacetype, e eface) (r iface) {
t := e._type
if t == nil {
// explicit conversions require non-nil interface value.
panic(&TypeAssertionError{"", "", inter.typ.string(), ""})
}
r.tab = getitab(inter, t, false)
r.data = e.data
return
}
func assertE2I2(inter *interfacetype, e eface) (r iface, b bool) {
t := e._type
if t == nil {
return
}
tab := getitab(inter, t, true)
if tab == nil {
return
}
r.tab = tab
r.data = e.data
b = true
return
}
//go:linkname reflect_ifaceE2I reflect.ifaceE2I
func reflect_ifaceE2I(inter *interfacetype, e eface, dst *iface) {
*dst = assertE2I(inter, e)
}
func iterate_itabs(fn func(*itab)) {
for _, h := range &hash {
for ; h != nil; h = h.link {
fn(h)
}
}
}
// staticbytes is used to avoid convT2E for byte-sized values.
var staticbytes = [...]byte{
0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07,
0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f,
0x10, 0x11, 0x12, 0x13, 0x14, 0x15, 0x16, 0x17,
0x18, 0x19, 0x1a, 0x1b, 0x1c, 0x1d, 0x1e, 0x1f,
0x20, 0x21, 0x22, 0x23, 0x24, 0x25, 0x26, 0x27,
0x28, 0x29, 0x2a, 0x2b, 0x2c, 0x2d, 0x2e, 0x2f,
0x30, 0x31, 0x32, 0x33, 0x34, 0x35, 0x36, 0x37,
0x38, 0x39, 0x3a, 0x3b, 0x3c, 0x3d, 0x3e, 0x3f,
0x40, 0x41, 0x42, 0x43, 0x44, 0x45, 0x46, 0x47,
0x48, 0x49, 0x4a, 0x4b, 0x4c, 0x4d, 0x4e, 0x4f,
0x50, 0x51, 0x52, 0x53, 0x54, 0x55, 0x56, 0x57,
0x58, 0x59, 0x5a, 0x5b, 0x5c, 0x5d, 0x5e, 0x5f,
0x60, 0x61, 0x62, 0x63, 0x64, 0x65, 0x66, 0x67,
0x68, 0x69, 0x6a, 0x6b, 0x6c, 0x6d, 0x6e, 0x6f,
0x70, 0x71, 0x72, 0x73, 0x74, 0x75, 0x76, 0x77,
0x78, 0x79, 0x7a, 0x7b, 0x7c, 0x7d, 0x7e, 0x7f,
0x80, 0x81, 0x82, 0x83, 0x84, 0x85, 0x86, 0x87,
0x88, 0x89, 0x8a, 0x8b, 0x8c, 0x8d, 0x8e, 0x8f,
0x90, 0x91, 0x92, 0x93, 0x94, 0x95, 0x96, 0x97,
0x98, 0x99, 0x9a, 0x9b, 0x9c, 0x9d, 0x9e, 0x9f,
0xa0, 0xa1, 0xa2, 0xa3, 0xa4, 0xa5, 0xa6, 0xa7,
0xa8, 0xa9, 0xaa, 0xab, 0xac, 0xad, 0xae, 0xaf,
0xb0, 0xb1, 0xb2, 0xb3, 0xb4, 0xb5, 0xb6, 0xb7,
0xb8, 0xb9, 0xba, 0xbb, 0xbc, 0xbd, 0xbe, 0xbf,
0xc0, 0xc1, 0xc2, 0xc3, 0xc4, 0xc5, 0xc6, 0xc7,
0xc8, 0xc9, 0xca, 0xcb, 0xcc, 0xcd, 0xce, 0xcf,
0xd0, 0xd1, 0xd2, 0xd3, 0xd4, 0xd5, 0xd6, 0xd7,
0xd8, 0xd9, 0xda, 0xdb, 0xdc, 0xdd, 0xde, 0xdf,
0xe0, 0xe1, 0xe2, 0xe3, 0xe4, 0xe5, 0xe6, 0xe7,
0xe8, 0xe9, 0xea, 0xeb, 0xec, 0xed, 0xee, 0xef,
0xf0, 0xf1, 0xf2, 0xf3, 0xf4, 0xf5, 0xf6, 0xf7,
0xf8, 0xf9, 0xfa, 0xfb, 0xfc, 0xfd, 0xfe, 0xff,
}