runtime: compute size classes statically

No point in computing this info on startup.
Compute it at build time.
This lets us spend more time computing & checking the size classes.

Improve the div magic for rounding to the start of an object.
We can now use 32-bit multiplies & shifts, which should help
32-bit platforms.

The static data is <1KB.

The actual size classes are not changed by this CL.

Change-Id: I6450cec7d1b2b4ad31fd3f945f504ed2ec6570e7
Reviewed-on: https://go-review.googlesource.com/32219
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Austin Clements <austin@google.com>

src/runtime/malloc.go

@@ -102,28 +102,13 @@ const (
 	mSpanInUse = _MSpanInUse
 
 	concurrentSweep = _ConcurrentSweep
-)
 
-const (
-	_PageShift = 13
-	_PageSize  = 1 << _PageShift
-	_PageMask  = _PageSize - 1
-)
+	_PageSize = 1 << _PageShift
+	_PageMask = _PageSize - 1
 
-const (
 	// _64bit = 1 on 64-bit systems, 0 on 32-bit systems
 	_64bit = 1 << (^uintptr(0) >> 63) / 2
 
-	// Computed constant. The definition of MaxSmallSize and the
-	// algorithm in msize.go produces some number of different allocation
-	// size classes. NumSizeClasses is that number. It's needed here
-	// because there are static arrays of this length; when msize runs its
-	// size choosing algorithm it double-checks that NumSizeClasses agrees.
-	_NumSizeClasses = 67
-
-	// Tunable constants.
-	_MaxSmallSize = 32 << 10
-
 	// Tiny allocator parameters, see "Tiny allocator" comment in malloc.go.
 	_TinySize      = 16
 	_TinySizeClass = 2
@@ -169,9 +154,9 @@ const (
 	// on the hardware details of the machine. The garbage
 	// collector scales well to 32 cpus.
 	_MaxGcproc = 32
-)
 
-const _MaxArena32 = 1<<32 - 1
+	_MaxArena32 = 1<<32 - 1
+)
 
 // physPageSize is the size in bytes of the OS's physical pages.
 // Mapping and unmapping operations must be done at multiples of
@@ -220,12 +205,17 @@ var physPageSize uintptr
 // if accessed. Used only for debugging the runtime.
 
 func mallocinit() {
-	initSizes()
-
 	if class_to_size[_TinySizeClass] != _TinySize {
 		throw("bad TinySizeClass")
 	}
 
+	testdefersizes()
+
+	// Copy class sizes out for statistics table.
+	for i := range class_to_size {
+		memstats.by_size[i].size = uint32(class_to_size[i])
+	}
+
 	// Check physPageSize.
 	if physPageSize == 0 {
 		// The OS init code failed to fetch the physical page size.

src/runtime/mbitmap.go

@@ -439,7 +439,7 @@ func heapBitsForObject(p, refBase, refOff uintptr) (base uintptr, hbits heapBits
 	if s.baseMask != 0 {
 		// optimize for power of 2 sized objects.
 		base = s.base()
-		base = base + (p-base)&s.baseMask
+		base = base + (p-base)&uintptr(s.baseMask)
 		objIndex = (base - s.base()) >> s.divShift
 		// base = p & s.baseMask is faster for small spans,
 		// but doesn't work for large spans.
@@ -448,7 +448,7 @@ func heapBitsForObject(p, refBase, refOff uintptr) (base uintptr, hbits heapBits
 		base = s.base()
 		if p-base >= s.elemsize {
 			// n := (p - base) / s.elemsize, using division by multiplication
-			objIndex = uintptr(uint64(p-base) >> s.divShift * uint64(s.divMul) >> s.divShift2)
+			objIndex = uintptr(p-base) >> s.divShift * uintptr(s.divMul) >> s.divShift2
 			base += objIndex * s.elemsize
 		}
 	}

src/runtime/mheap.go

@@ -234,7 +234,8 @@ type mspan struct {
 	// h->sweepgen is incremented by 2 after every GC
 
 	sweepgen    uint32
-	divMul      uint32     // for divide by elemsize - divMagic.mul
+	divMul      uint16     // for divide by elemsize - divMagic.mul
+	baseMask    uint16     // if non-0, elemsize is a power of 2, & this will get object allocation base
 	allocCount  uint16     // capacity - number of objects in freelist
 	sizeclass   uint8      // size class
 	incache     bool       // being used by an mcache
@@ -248,7 +249,6 @@ type mspan struct {
 	limit       uintptr    // end of data in span
 	speciallock mutex      // guards specials list
 	specials    *special   // linked list of special records sorted by offset.
-	baseMask    uintptr    // if non-0, elemsize is a power of 2, & this will get object allocation base
 }
 
 func (s *mspan) base() uintptr {

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.
+
+// +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).
+//
+// TODO(rsc): Compute max waste for any given size.
+
+package main
+
+import (
+	"bytes"
+	"flag"
+	"fmt"
+	"go/format"
+	"io"
+	"io/ioutil"
+	"log"
+	"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, "// AUTO-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()
+
+	printClasses(&b, classes)
+
+	out, err := format.Source(b.Bytes())
+	if err != nil {
+		log.Fatal(err)
+	}
+	if *stdout {
+		_, err = os.Stdout.Write(out)
+	} else {
+		err = ioutil.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
+
+	mul    int
+	shift  uint
+	shift2 uint
+	mask   int
+}
+
+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 >= 16 {
+				align = 16 // required for x86 SSE instructions, if we want to use them
+			}
+		}
+		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) != 67 {
+		panic("number of size classes has changed")
+	}
+
+	for i := range classes {
+		computeDivMagic(&classes[i])
+	}
+
+	return classes
+}
+
+// computeDivMagic computes some magic constants to implement
+// the division required to compute object number from span offset.
+// n / c.size is implemented as n >> c.shift * c.mul >> c.shift2
+// 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 - 1
+
+	if powerOfTwo(d) {
+		// If the size is a power of two, heapBitsForObject can divide even faster by masking.
+		// Compute this mask.
+		if max >= 1<<16 {
+			panic("max too big for power of two size")
+		}
+		c.mask = 1<<16 - d
+	}
+
+	// Compute pre-shift by factoring power of 2 out of d.
+	for d%2 == 0 {
+		c.shift++
+		d >>= 1
+		max >>= 1
+	}
+
+	// Find the smallest k that works.
+	// A small k allows us to fit the math required into 32 bits
+	// so we can use 32-bit multiplies and shifts on 32-bit platforms.
+nextk:
+	for k := uint(0); ; k++ {
+		mul := (int(1)<<k + d - 1) / d //  ⌈2^k / d⌉
+
+		// Test to see if mul works.
+		for n := 0; n <= max; n++ {
+			if n*mul>>k != n/d {
+				continue nextk
+			}
+		}
+		if mul >= 1<<16 {
+			panic("mul too big")
+		}
+		if uint64(mul)*uint64(max) >= 1<<32 {
+			panic("mul*max too big")
+		}
+		c.mul = mul
+		c.shift2 = k
+		break
+	}
+
+	// double-check.
+	for n := 0; n <= max; n++ {
+		if n*c.mul>>c.shift2 != n/d {
+			fmt.Printf("d=%d max=%d mul=%d shift2=%d n=%d\n", d, max, c.mul, c.shift2, n)
+			panic("bad multiply magic")
+		}
+		// Also check the exact computations that will be done by the runtime,
+		// for both 32 and 64 bit operations.
+		if uint32(n)*uint32(c.mul)>>uint8(c.shift2) != uint32(n/d) {
+			fmt.Printf("d=%d max=%d mul=%d shift2=%d n=%d\n", d, max, c.mul, c.shift2, n)
+			panic("bad 32-bit multiply magic")
+		}
+		if uint64(n)*uint64(c.mul)>>uint8(c.shift2) != uint64(n/d) {
+			fmt.Printf("d=%d max=%d mul=%d shift2=%d n=%d\n", d, max, c.mul, c.shift2, n)
+			panic("bad 64-bit multiply magic")
+		}
+	}
+}
+
+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.Fprintln(w, "type divMagic struct {")
+	fmt.Fprintln(w, "  shift uint8")
+	fmt.Fprintln(w, "  shift2 uint8")
+	fmt.Fprintln(w, "  mul uint16")
+	fmt.Fprintln(w, "  baseMask uint16")
+	fmt.Fprintln(w, "}")
+	fmt.Fprint(w, "var class_to_divmagic = [_NumSizeClasses]divMagic {")
+	for _, c := range classes {
+		fmt.Fprintf(w, "{%d,%d,%d,%d},", c.shift, c.shift2, c.mul, c.mask)
+	}
+	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, "}")
+}

src/runtime/msize.go

@@ -5,60 +5,22 @@
 // Malloc small 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).
-//
-// TODO(rsc): Compute max waste for any given size.
+// See also mksizeclasses.go for how we decide what size classes to use.
 
 package runtime
 
-// Size classes. Computed and initialized by InitSizes.
-//
-// SizeToClass(0 <= n <= MaxSmallSize) returns the size class,
+// sizeToClass(0 <= n <= MaxSmallSize) returns the size class,
 //	1 <= sizeclass < NumSizeClasses, for n.
 //	Size class 0 is reserved to mean "not small".
 //
-// class_to_size[i] = largest size in class i
-// class_to_allocnpages[i] = number of pages to allocate when
-//	making new objects in class i
-
-// The SizeToClass lookup is implemented using two arrays,
+// The sizeToClass lookup is implemented using two arrays,
 // one mapping sizes <= 1024 to their class and one mapping
 // sizes >= 1024 and <= MaxSmallSize to their class.
 // All objects are 8-aligned, so the first array is indexed by
 // the size divided by 8 (rounded up).  Objects >= 1024 bytes
 // are 128-aligned, so the second array is indexed by the
-// size divided by 128 (rounded up).  The arrays are filled in
-// by InitSizes.
-
-const (
-	smallSizeDiv = 8
-	smallSizeMax = 1024
-	largeSizeDiv = 128
-)
-
-var class_to_size [_NumSizeClasses]uint32
-var class_to_allocnpages [_NumSizeClasses]uint32
-var class_to_divmagic [_NumSizeClasses]divMagic
-
-var size_to_class8 [smallSizeMax/smallSizeDiv + 1]uint8
-var size_to_class128 [(_MaxSmallSize-smallSizeMax)/largeSizeDiv + 1]uint8
-
+// size divided by 128 (rounded up).  The arrays are constants
+// in sizeclass.go generated by mksizeclass.go.
 func sizeToClass(size uint32) uint32 {
 	if size > _MaxSmallSize {
 		throw("invalid size")
@@ -69,147 +31,6 @@ func sizeToClass(size uint32) uint32 {
 	return uint32(size_to_class8[(size+smallSizeDiv-1)/smallSizeDiv])
 }
 
-func initSizes() {
-	// Initialize the runtime·class_to_size table (and choose class sizes in the process).
-	class_to_size[0] = 0
-	sizeclass := 1 // 0 means no class
-	align := 8
-	for size := align; size <= _MaxSmallSize; size += align {
-		if size&(size-1) == 0 { // bump alignment once in a while
-			if size >= 2048 {
-				align = 256
-			} else if size >= 128 {
-				align = size / 8
-			} else if size >= 16 {
-				align = 16 // required for x86 SSE instructions, if we want to use them
-			}
-		}
-		if align&(align-1) != 0 {
-			throw("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 >> _PageShift
-
-		// 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 sizeclass > 1 && npages == int(class_to_allocnpages[sizeclass-1]) && allocsize/size == allocsize/int(class_to_size[sizeclass-1]) {
-			class_to_size[sizeclass-1] = uint32(size)
-			continue
-		}
-
-		class_to_allocnpages[sizeclass] = uint32(npages)
-		class_to_size[sizeclass] = uint32(size)
-		sizeclass++
-	}
-	if sizeclass != _NumSizeClasses {
-		print("runtime: sizeclass=", sizeclass, " NumSizeClasses=", _NumSizeClasses, "\n")
-		throw("bad NumSizeClasses")
-	}
-
-	// 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 := 1; i < _NumSizeClasses; i++ {
-		npages := class_to_allocnpages[i]
-		psize := npages * _PageSize
-		size := class_to_size[i]
-		new_size := (psize / (psize / size)) &^ (largeSizeDiv - 1)
-		if new_size > size {
-			class_to_size[i] = new_size
-		}
-	}
-
-	// Check maxObjsPerSpan => number of objects invariant.
-	for i, size := range class_to_size {
-		if i != 0 && class_to_size[i-1] >= size {
-			throw("non-monotonic size classes")
-		}
-
-		if size != 0 && class_to_allocnpages[i]*pageSize/size > maxObjsPerSpan {
-			throw("span contains too many objects")
-		}
-		if size == 0 && i != 0 {
-			throw("size is 0 but class is not 0")
-		}
-	}
-	// Initialize the size_to_class tables.
-	nextsize := 0
-	for sizeclass = 1; sizeclass < _NumSizeClasses; sizeclass++ {
-		for ; nextsize < 1024 && nextsize <= int(class_to_size[sizeclass]); nextsize += 8 {
-			size_to_class8[nextsize/8] = uint8(sizeclass)
-		}
-		if nextsize >= 1024 {
-			for ; nextsize <= int(class_to_size[sizeclass]); nextsize += 128 {
-				size_to_class128[(nextsize-1024)/128] = uint8(sizeclass)
-			}
-		}
-	}
-
-	// Double-check SizeToClass.
-	if false {
-		for n := uint32(0); n < _MaxSmallSize; n++ {
-			sizeclass := sizeToClass(n)
-			if sizeclass < 1 || sizeclass >= _NumSizeClasses || class_to_size[sizeclass] < n {
-				print("runtime: size=", n, " sizeclass=", sizeclass, " runtime·class_to_size=", class_to_size[sizeclass], "\n")
-				print("incorrect SizeToClass\n")
-				goto dump
-			}
-			if sizeclass > 1 && class_to_size[sizeclass-1] >= n {
-				print("runtime: size=", n, " sizeclass=", sizeclass, " runtime·class_to_size=", class_to_size[sizeclass], "\n")
-				print("SizeToClass too big\n")
-				goto dump
-			}
-		}
-	}
-
-	testdefersizes()
-
-	// Copy out for statistics table.
-	for i := 0; i < len(class_to_size); i++ {
-		memstats.by_size[i].size = uint32(class_to_size[i])
-	}
-
-	for i := 1; i < len(class_to_size); i++ {
-		class_to_divmagic[i] = computeDivMagic(uint32(class_to_size[i]))
-	}
-
-	return
-
-dump:
-	if true {
-		print("runtime: NumSizeClasses=", _NumSizeClasses, "\n")
-		print("runtime·class_to_size:")
-		for sizeclass = 0; sizeclass < _NumSizeClasses; sizeclass++ {
-			print(" ", class_to_size[sizeclass], "")
-		}
-		print("\n\n")
-		print("runtime: size_to_class8:")
-		for i := 0; i < len(size_to_class8); i++ {
-			print(" ", i*8, "=>", size_to_class8[i], "(", class_to_size[size_to_class8[i]], ")\n")
-		}
-		print("\n")
-		print("runtime: size_to_class128:")
-		for i := 0; i < len(size_to_class128); i++ {
-			print(" ", i*128, "=>", size_to_class128[i], "(", class_to_size[size_to_class128[i]], ")\n")
-		}
-		print("\n")
-	}
-	throw("InitSizes failed")
-}
-
 // Returns size of the memory block that mallocgc will allocate if you ask for the size.
 func roundupsize(size uintptr) uintptr {
 	if size < _MaxSmallSize {
@@ -224,66 +45,3 @@ func roundupsize(size uintptr) uintptr {
 	}
 	return round(size, _PageSize)
 }
-
-// divMagic holds magic constants to implement division
-// by a particular constant as a shift, multiply, and shift.
-// That is, given
-//	m = computeMagic(d)
-// then
-//	n/d == ((n>>m.shift) * m.mul) >> m.shift2
-//
-// The magic computation picks m such that
-//	d = d₁*d₂
-//	d₂= 2^m.shift
-//	m.mul = ⌈2^m.shift2 / d₁⌉
-//
-// The magic computation here is tailored for malloc block sizes
-// and does not handle arbitrary d correctly. Malloc block sizes d are
-// always even, so the first shift implements the factors of 2 in d
-// and then the mul and second shift implement the odd factor
-// that remains. Because the first shift divides n by at least 2 (actually 8)
-// before the multiply gets involved, the huge corner cases that
-// require additional adjustment are impossible, so the usual
-// fixup is not needed.
-//
-// For more details see Hacker's Delight, Chapter 10, and
-// http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
-// http://ridiculousfish.com/blog/posts/labor-of-division-episode-iii.html
-type divMagic struct {
-	shift    uint8
-	mul      uint32
-	shift2   uint8
-	baseMask uintptr
-}
-
-func computeDivMagic(d uint32) divMagic {
-	var m divMagic
-
-	// If the size is a power of two, heapBitsForObject can divide even faster by masking.
-	// Compute this mask.
-	if d&(d-1) == 0 {
-		// It is a power of 2 (assuming dinptr != 1)
-		m.baseMask = ^(uintptr(d) - 1)
-	} else {
-		m.baseMask = 0
-	}
-
-	// Compute pre-shift by factoring power of 2 out of d.
-	for d&1 == 0 {
-		m.shift++
-		d >>= 1
-	}
-
-	// Compute largest k such that ⌈2^k / d⌉ fits in a 32-bit int.
-	// This is always a good enough approximation.
-	// We could use smaller k for some divisors but there's no point.
-	k := uint8(63)
-	d64 := uint64(d)
-	for ((1<<k)+d64-1)/d64 >= 1<<32 {
-		k--
-	}
-	m.mul = uint32(((1 << k) + d64 - 1) / d64) //  ⌈2^k / d⌉
-	m.shift2 = k
-
-	return m
-}

src/runtime/sizeclasses.go

+// AUTO-GENERATED by mksizeclasses.go; DO NOT EDIT
+//go:generate go run mksizeclasses.go
+
+package runtime
+
+const (
+	_MaxSmallSize   = 32768
+	smallSizeDiv    = 8
+	smallSizeMax    = 1024
+	largeSizeDiv    = 128
+	_NumSizeClasses = 67
+	_PageShift      = 13
+)
+
+var class_to_size = [_NumSizeClasses]uint16{0, 8, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 256, 288, 320, 352, 384, 416, 448, 480, 512, 576, 640, 704, 768, 896, 1024, 1152, 1280, 1408, 1536, 1792, 2048, 2304, 2688, 3072, 3200, 3456, 4096, 4864, 5376, 6144, 6528, 6784, 6912, 8192, 9472, 9728, 10240, 10880, 12288, 13568, 14336, 16384, 18432, 19072, 20480, 21760, 24576, 27264, 28672, 32768}
+var class_to_allocnpages = [_NumSizeClasses]uint8{0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 2, 3, 4, 5, 6, 1, 7, 6, 5, 4, 3, 5, 7, 2, 9, 7, 5, 8, 3, 10, 7, 4}
+
+type divMagic struct {
+	shift    uint8
+	shift2   uint8
+	mul      uint16
+	baseMask uint16
+}
+
+var class_to_divmagic = [_NumSizeClasses]divMagic{{0, 0, 0, 0}, {3, 0, 1, 65528}, {4, 0, 1, 65520}, {5, 0, 1, 65504}, {4, 9, 171, 0}, {6, 0, 1, 65472}, {4, 10, 205, 0}, {5, 9, 171, 0}, {4, 11, 293, 0}, {7, 0, 1, 65408}, {4, 9, 57, 0}, {5, 10, 205, 0}, {4, 12, 373, 0}, {6, 7, 43, 0}, {4, 13, 631, 0}, {5, 11, 293, 0}, {4, 13, 547, 0}, {8, 0, 1, 65280}, {5, 9, 57, 0}, {6, 9, 103, 0}, {5, 12, 373, 0}, {7, 7, 43, 0}, {5, 10, 79, 0}, {6, 10, 147, 0}, {5, 11, 137, 0}, {9, 0, 1, 65024}, {6, 9, 57, 0}, {7, 6, 13, 0}, {6, 11, 187, 0}, {8, 5, 11, 0}, {7, 8, 37, 0}, {10, 0, 1, 64512}, {7, 9, 57, 0}, {8, 6, 13, 0}, {7, 11, 187, 0}, {9, 5, 11, 0}, {8, 8, 37, 0}, {11, 0, 1, 63488}, {8, 9, 57, 0}, {7, 10, 49, 0}, {10, 5, 11, 0}, {7, 10, 41, 0}, {7, 9, 19, 0}, {12, 0, 1, 61440}, {8, 9, 27, 0}, {8, 10, 49, 0}, {11, 5, 11, 0}, {7, 13, 161, 0}, {7, 13, 155, 0}, {8, 9, 19, 0}, {13, 0, 1, 57344}, {8, 12, 111, 0}, {9, 9, 27, 0}, {11, 6, 13, 0}, {7, 14, 193, 0}, {12, 3, 3, 0}, {8, 13, 155, 0}, {11, 8, 37, 0}, {14, 0, 1, 49152}, {11, 8, 29, 0}, {7, 13, 55, 0}, {12, 5, 7, 0}, {8, 14, 193, 0}, {13, 3, 3, 0}, {7, 14, 77, 0}, {12, 7, 19, 0}, {15, 0, 1, 32768}}
+var size_to_class8 = [smallSizeMax/smallSizeDiv + 1]uint8{0, 1, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 27, 27, 27, 27, 27, 27, 27, 28, 28, 28, 28, 28, 28, 28, 28, 29, 29, 29, 29, 29, 29, 29, 29, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31, 31}
+var size_to_class128 = [(_MaxSmallSize-smallSizeMax)/largeSizeDiv + 1]uint8{31, 32, 33, 34, 35, 36, 36, 37, 37, 38, 38, 39, 39, 39, 40, 40, 40, 41, 42, 42, 43, 43, 43, 43, 43, 44, 44, 44, 44, 44, 44, 45, 45, 45, 45, 46, 46, 46, 46, 46, 46, 47, 47, 47, 48, 48, 49, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 51, 51, 51, 51, 51, 51, 51, 51, 51, 51, 52, 52, 53, 53, 53, 53, 54, 54, 54, 54, 54, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 55, 56, 56, 56, 56, 56, 56, 56, 56, 56, 56, 57, 57, 57, 57, 57, 57, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 58, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 59, 60, 60, 60, 60, 60, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 61, 62, 62, 62, 62, 62, 62, 62, 62, 62, 62, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66, 66}