src/runtime/mksizeclasses.go - go - Git at Google

 // 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

 // 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 maxObjsPerSpan(classes []class) int {
 	max := 0
 	for _, c := range classes[1:] {
 		n := c.npages * pageSize / c.size
 		if n > max {
 			max = n
 		}
 	}
 	return max
 }

 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.Fprintf(w, "maxObjsPerSpan = %d\n", maxObjsPerSpan(classes))
 	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, "}")
 }
	// 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

	// 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 maxObjsPerSpan(classes []class) int {
	max := 0
	for _, c := range classes[1:] {
	n := c.npages * pageSize / c.size
	if n > max {
	max = n
	}
	}
	return max
	}

	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.Fprintf(w, "maxObjsPerSpan = %d\n", maxObjsPerSpan(classes))
	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, "}")
	}