Current File : //usr/local/go/src/runtime/mksizeclasses.go
// Copyright 2016 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.
//go:build ignore
// +build ignore
// Generate tables for small malloc size classes.
//
// See malloc.go for overview.
//
// The size classes are chosen so that rounding an allocation
// request up to the next size class wastes at most 12.5% (1.125x).
//
// Each size class has its own page count that gets allocated
// and chopped up when new objects of the size class are needed.
// That page count is chosen so that chopping up the run of
// pages into objects of the given size wastes at most 12.5% (1.125x)
// of the memory. It is not necessary that the cutoff here be
// the same as above.
//
// The two sources of waste multiply, so the worst possible case
// for the above constraints would be that allocations of some
// size might have a 26.6% (1.266x) overhead.
// In practice, only one of the wastes comes into play for a
// given size (sizes < 512 waste mainly on the round-up,
// sizes > 512 waste mainly on the page chopping).
// For really small sizes, alignment constraints force the
// overhead higher.
package main
import (
"bytes"
"flag"
"fmt"
"go/format"
"io"
"log"
"math"
"math/bits"
"os"
)
// Generate msize.go
var stdout = flag.Bool("stdout", false, "write to stdout instead of sizeclasses.go")
func main() {
flag.Parse()
var b bytes.Buffer
fmt.Fprintln(&b, "// Code generated by mksizeclasses.go; DO NOT EDIT.")
fmt.Fprintln(&b, "//go:generate go run mksizeclasses.go")
fmt.Fprintln(&b)
fmt.Fprintln(&b, "package runtime")
classes := makeClasses()
printComment(&b, classes)
printClasses(&b, classes)
out, err := format.Source(b.Bytes())
if err != nil {
log.Fatal(err)
}
if *stdout {
_, err = os.Stdout.Write(out)
} else {
err = os.WriteFile("sizeclasses.go", out, 0666)
}
if err != nil {
log.Fatal(err)
}
}
const (
// Constants that we use and will transfer to the runtime.
maxSmallSize = 32 << 10
smallSizeDiv = 8
smallSizeMax = 1024
largeSizeDiv = 128
pageShift = 13
// Derived constants.
pageSize = 1 << pageShift
)
type class struct {
size int // max size
npages int // number of pages
}
func powerOfTwo(x int) bool {
return x != 0 && x&(x-1) == 0
}
func makeClasses() []class {
var classes []class
classes = append(classes, class{}) // class #0 is a dummy entry
align := 8
for size := align; size <= maxSmallSize; size += align {
if powerOfTwo(size) { // bump alignment once in a while
if size >= 2048 {
align = 256
} else if size >= 128 {
align = size / 8
} else if size >= 32 {
align = 16 // heap bitmaps assume 16 byte alignment for allocations >= 32 bytes.
}
}
if !powerOfTwo(align) {
panic("incorrect alignment")
}
// Make the allocnpages big enough that
// the leftover is less than 1/8 of the total,
// so wasted space is at most 12.5%.
allocsize := pageSize
for allocsize%size > allocsize/8 {
allocsize += pageSize
}
npages := allocsize / pageSize
// If the previous sizeclass chose the same
// allocation size and fit the same number of
// objects into the page, we might as well
// use just this size instead of having two
// different sizes.
if len(classes) > 1 && npages == classes[len(classes)-1].npages && allocsize/size == allocsize/classes[len(classes)-1].size {
classes[len(classes)-1].size = size
continue
}
classes = append(classes, class{size: size, npages: npages})
}
// Increase object sizes if we can fit the same number of larger objects
// into the same number of pages. For example, we choose size 8448 above
// with 6 objects in 7 pages. But we can well use object size 9472,
// which is also 6 objects in 7 pages but +1024 bytes (+12.12%).
// We need to preserve at least largeSizeDiv alignment otherwise
// sizeToClass won't work.
for i := range classes {
if i == 0 {
continue
}
c := &classes[i]
psize := c.npages * pageSize
new_size := (psize / (psize / c.size)) &^ (largeSizeDiv - 1)
if new_size > c.size {
c.size = new_size
}
}
if len(classes) != 68 {
panic("number of size classes has changed")
}
for i := range classes {
computeDivMagic(&classes[i])
}
return classes
}
// computeDivMagic checks that the division required to compute object
// index from span offset can be computed using 32-bit multiplication.
// n / c.size is implemented as (n * (^uint32(0)/uint32(c.size) + 1)) >> 32
// for all 0 <= n <= c.npages * pageSize
func computeDivMagic(c *class) {
// divisor
d := c.size
if d == 0 {
return
}
// maximum input value for which the formula needs to work.
max := c.npages * pageSize
// As reported in [1], if n and d are unsigned N-bit integers, we
// can compute n / d as ⌊n * c / 2^F⌋, where c is ⌈2^F / d⌉ and F is
// computed with:
//
// Algorithm 2: Algorithm to select the number of fractional bits
// and the scaled approximate reciprocal in the case of unsigned
// integers.
//
// if d is a power of two then
// Let F ← log₂(d) and c = 1.
// else
// Let F ← N + L where L is the smallest integer
// such that d ≤ (2^(N+L) mod d) + 2^L.
// end if
//
// [1] "Faster Remainder by Direct Computation: Applications to
// Compilers and Software Libraries" Daniel Lemire, Owen Kaser,
// Nathan Kurz arXiv:1902.01961
//
// To minimize the risk of introducing errors, we implement the
// algorithm exactly as stated, rather than trying to adapt it to
// fit typical Go idioms.
N := bits.Len(uint(max))
var F int
if powerOfTwo(d) {
F = int(math.Log2(float64(d)))
if d != 1<<F {
panic("imprecise log2")
}
} else {
for L := 0; ; L++ {
if d <= ((1<<(N+L))%d)+(1<<L) {
F = N + L
break
}
}
}
// Also, noted in the paper, F is the smallest number of fractional
// bits required. We use 32 bits, because it works for all size
// classes and is fast on all CPU architectures that we support.
if F > 32 {
fmt.Printf("d=%d max=%d N=%d F=%d\n", c.size, max, N, F)
panic("size class requires more than 32 bits of precision")
}
// Brute force double-check with the exact computation that will be
// done by the runtime.
m := ^uint32(0)/uint32(c.size) + 1
for n := 0; n <= max; n++ {
if uint32((uint64(n)*uint64(m))>>32) != uint32(n/c.size) {
fmt.Printf("d=%d max=%d m=%d n=%d\n", d, max, m, n)
panic("bad 32-bit multiply magic")
}
}
}
func printComment(w io.Writer, classes []class) {
fmt.Fprintf(w, "// %-5s %-9s %-10s %-7s %-10s %-9s %-9s\n", "class", "bytes/obj", "bytes/span", "objects", "tail waste", "max waste", "min align")
prevSize := 0
var minAligns [pageShift + 1]int
for i, c := range classes {
if i == 0 {
continue
}
spanSize := c.npages * pageSize
objects := spanSize / c.size
tailWaste := spanSize - c.size*(spanSize/c.size)
maxWaste := float64((c.size-prevSize-1)*objects+tailWaste) / float64(spanSize)
alignBits := bits.TrailingZeros(uint(c.size))
if alignBits > pageShift {
// object alignment is capped at page alignment
alignBits = pageShift
}
for i := range minAligns {
if i > alignBits {
minAligns[i] = 0
} else if minAligns[i] == 0 {
minAligns[i] = c.size
}
}
prevSize = c.size
fmt.Fprintf(w, "// %5d %9d %10d %7d %10d %8.2f%% %9d\n", i, c.size, spanSize, objects, tailWaste, 100*maxWaste, 1<<alignBits)
}
fmt.Fprintf(w, "\n")
fmt.Fprintf(w, "// %-9s %-4s %-12s\n", "alignment", "bits", "min obj size")
for bits, size := range minAligns {
if size == 0 {
break
}
if bits+1 < len(minAligns) && size == minAligns[bits+1] {
continue
}
fmt.Fprintf(w, "// %9d %4d %12d\n", 1<<bits, bits, size)
}
fmt.Fprintf(w, "\n")
}
func printClasses(w io.Writer, classes []class) {
fmt.Fprintln(w, "const (")
fmt.Fprintf(w, "_MaxSmallSize = %d\n", maxSmallSize)
fmt.Fprintf(w, "smallSizeDiv = %d\n", smallSizeDiv)
fmt.Fprintf(w, "smallSizeMax = %d\n", smallSizeMax)
fmt.Fprintf(w, "largeSizeDiv = %d\n", largeSizeDiv)
fmt.Fprintf(w, "_NumSizeClasses = %d\n", len(classes))
fmt.Fprintf(w, "_PageShift = %d\n", pageShift)
fmt.Fprintln(w, ")")
fmt.Fprint(w, "var class_to_size = [_NumSizeClasses]uint16 {")
for _, c := range classes {
fmt.Fprintf(w, "%d,", c.size)
}
fmt.Fprintln(w, "}")
fmt.Fprint(w, "var class_to_allocnpages = [_NumSizeClasses]uint8 {")
for _, c := range classes {
fmt.Fprintf(w, "%d,", c.npages)
}
fmt.Fprintln(w, "}")
fmt.Fprint(w, "var class_to_divmagic = [_NumSizeClasses]uint32 {")
for _, c := range classes {
if c.size == 0 {
fmt.Fprintf(w, "0,")
continue
}
fmt.Fprintf(w, "^uint32(0)/%d+1,", c.size)
}
fmt.Fprintln(w, "}")
// map from size to size class, for small sizes.
sc := make([]int, smallSizeMax/smallSizeDiv+1)
for i := range sc {
size := i * smallSizeDiv
for j, c := range classes {
if c.size >= size {
sc[i] = j
break
}
}
}
fmt.Fprint(w, "var size_to_class8 = [smallSizeMax/smallSizeDiv+1]uint8 {")
for _, v := range sc {
fmt.Fprintf(w, "%d,", v)
}
fmt.Fprintln(w, "}")
// map from size to size class, for large sizes.
sc = make([]int, (maxSmallSize-smallSizeMax)/largeSizeDiv+1)
for i := range sc {
size := smallSizeMax + i*largeSizeDiv
for j, c := range classes {
if c.size >= size {
sc[i] = j
break
}
}
}
fmt.Fprint(w, "var size_to_class128 = [(_MaxSmallSize-smallSizeMax)/largeSizeDiv+1]uint8 {")
for _, v := range sc {
fmt.Fprintf(w, "%d,", v)
}
fmt.Fprintln(w, "}")
}
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