runtime: replace division by span element size by multiply and shifts

Divisions are generally slow. The compiler can optimize a division
to use a sequence of faster multiplies and shifts (magic constants)
if the divisor is not know at compile time.

The value of the span element size in mcentral.grow is not known at
compile time but magic constants to compute n / span.elementsize
are already stored in class_to_divmagic and mspan.
They however need to be adjusted to work for
(0 <= n <= span.npages * pagesize) instead of
(0 <= n <  span.npages * pagesize).

Change-Id: Ieea59f1c94525a88d012f2557d43691967900deb
Reviewed-on: https://go-review.googlesource.com/c/go/+/148057
Run-TryBot: Martin Möhrmann <moehrmann@google.com>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Austin Clements <austin@google.com>
Reviewed-by: Keith Randall <khr@golang.org>

src/runtime/mcentral.go

@@ -251,16 +251,16 @@ func (c *mcentral) freeSpan(s *mspan, preserve bool, wasempty bool) bool {
 func (c *mcentral) grow() *mspan {
 	npages := uintptr(class_to_allocnpages[c.spanclass.sizeclass()])
 	size := uintptr(class_to_size[c.spanclass.sizeclass()])
-	n := (npages << _PageShift) / size
 
 	s := mheap_.alloc(npages, c.spanclass, false, true)
 	if s == nil {
 		return nil
 	}
 
-	p := s.base()
-	s.limit = p + size*n
-
+	// Use division by multiplication and shifts to quickly compute:
+	// n := (npages << _PageShift) / size
+	n := (npages << _PageShift) >> s.divShift * uintptr(s.divMul) >> s.divShift2
+	s.limit = s.base() + size*n
 	heapBitsForAddr(s.base()).initSpan(s)
 	return s
 }

src/runtime/mksizeclasses.go

@@ -171,7 +171,7 @@ func makeClasses() []class {
 // 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
+// for all 0 <= n <= c.npages * pageSize
 func computeDivMagic(c *class) {
 	// divisor
 	d := c.size
@@ -180,7 +180,7 @@ func computeDivMagic(c *class) {
 	}
 
 	// maximum input value for which the formula needs to work.
-	max := c.npages*pageSize - 1
+	max := c.npages * pageSize
 
 	if powerOfTwo(d) {
 		// If the size is a power of two, heapBitsForObject can divide even faster by masking.

src/runtime/sizeclasses.go

@@ -90,6 +90,6 @@ type divMagic struct {
 	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 class_to_divmagic = [_NumSizeClasses]divMagic{{0, 0, 0, 0}, {3, 0, 1, 65528}, {4, 0, 1, 65520}, {5, 0, 1, 65504}, {4, 11, 683, 0}, {6, 0, 1, 65472}, {4, 10, 205, 0}, {5, 9, 171, 0}, {4, 11, 293, 0}, {7, 0, 1, 65408}, {4, 13, 911, 0}, {5, 10, 205, 0}, {4, 12, 373, 0}, {6, 9, 171, 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, 9, 103, 0}, {6, 11, 187, 0}, {8, 7, 43, 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}