runtime: redo insert/remove of large spans

Currently for spans with up to 1 MBytes (128 pages) we
maintain an array indexed by the number of pages in the
span. This is efficient both in terms of space as well
as time to insert or remove a span of a particular size.

Unfortunately for spans larger than 1 MByte we currently
place them on a separate linked list. This results in
O(n) behavior. Now that we are seeing heaps approaching
100 GBytes n is large enough to be noticed in real programs.

This change replaces the linked list now used with a balanced
binary tree structure called a treap. A treap is a
probabilistically balanced tree offering O(logN) behavior for
inserting and removing spans.

To verify that this approach will work we start with noting
that only spans with sizes > 1MByte will be put into the treap.
This means that to support 1 TByte a treap will need at most
1 million nodes and can ideally be held in a treap with a
depth of 20. Experiments with adding and removing randomly
sized spans from the treap seem to result in treaps with
depths of about twice the ideal or 40. A petabyte would
require a tree of only twice again that depth again so this
algorithm should last well into the future.

Fixes #19393

Go1 benchmarks indicate this is basically an overall wash.
Tue Mar 28 21:29:21 EDT 2017
name                     old time/op    new time/op    delta
BinaryTree17-4              2.42s ± 1%     2.42s ± 1%    ~     (p=0.980 n=21+21)
Fannkuch11-4                3.00s ± 1%     3.18s ± 4%  +6.10%  (p=0.000 n=22+24)
FmtFprintfEmpty-4          40.5ns ± 1%    40.3ns ± 3%    ~     (p=0.692 n=22+25)
FmtFprintfString-4         65.9ns ± 3%    64.6ns ± 1%  -1.98%  (p=0.000 n=24+23)
FmtFprintfInt-4            69.6ns ± 1%    68.0ns ± 7%  -2.30%  (p=0.001 n=21+22)
FmtFprintfIntInt-4          102ns ± 2%      99ns ± 1%  -3.07%  (p=0.000 n=23+23)
FmtFprintfPrefixedInt-4     126ns ± 0%     125ns ± 0%  -0.79%  (p=0.000 n=19+17)
FmtFprintfFloat-4           206ns ± 2%     205ns ± 1%    ~     (p=0.671 n=23+21)
FmtManyArgs-4               441ns ± 1%     445ns ± 1%  +0.88%  (p=0.000 n=22+23)
GobDecode-4                5.73ms ± 1%    5.86ms ± 1%  +2.37%  (p=0.000 n=23+22)
GobEncode-4                4.51ms ± 1%    4.89ms ± 1%  +8.32%  (p=0.000 n=22+22)
Gzip-4                      197ms ± 0%     202ms ± 1%  +2.75%  (p=0.000 n=23+24)
Gunzip-4                   32.9ms ± 8%    32.7ms ± 2%    ~     (p=0.466 n=23+24)
HTTPClientServer-4         57.3µs ± 1%    56.7µs ± 1%  -0.94%  (p=0.000 n=21+22)
JSONEncode-4               13.8ms ± 1%    13.9ms ± 2%  +1.14%  (p=0.000 n=22+23)
JSONDecode-4               47.4ms ± 1%    48.1ms ± 1%  +1.49%  (p=0.000 n=23+23)
Mandelbrot200-4            3.92ms ± 0%    3.92ms ± 1%  +0.21%  (p=0.000 n=22+22)
GoParse-4                  2.89ms ± 1%    2.87ms ± 1%  -0.68%  (p=0.000 n=21+22)
RegexpMatchEasy0_32-4      73.6ns ± 1%    72.0ns ± 2%  -2.15%  (p=0.000 n=21+22)
RegexpMatchEasy0_1K-4       173ns ± 1%     173ns ± 1%    ~     (p=0.847 n=22+24)
RegexpMatchEasy1_32-4      71.9ns ± 1%    69.8ns ± 1%  -2.99%  (p=0.000 n=23+20)
RegexpMatchEasy1_1K-4       314ns ± 1%     308ns ± 1%  -1.91%  (p=0.000 n=22+23)
RegexpMatchMedium_32-4      106ns ± 0%     105ns ± 1%  -0.58%  (p=0.000 n=19+21)
RegexpMatchMedium_1K-4     34.3µs ± 1%    34.3µs ± 1%    ~     (p=0.871 n=23+22)
RegexpMatchHard_32-4       1.67µs ± 1%    1.67µs ± 7%    ~     (p=0.224 n=22+23)
RegexpMatchHard_1K-4       51.5µs ± 1%    50.4µs ± 1%  -1.99%  (p=0.000 n=22+23)
Revcomp-4                   383ms ± 1%     415ms ± 0%  +8.51%  (p=0.000 n=22+22)
Template-4                 51.5ms ± 1%    51.5ms ± 1%    ~     (p=0.555 n=20+23)
TimeParse-4                 279ns ± 2%     277ns ± 1%  -0.95%  (p=0.000 n=24+22)
TimeFormat-4                294ns ± 1%     296ns ± 1%  +0.58%  (p=0.003 n=24+23)
[Geo mean]                 43.7µs         43.8µs       +0.32%

name                     old speed      new speed      delta
GobDecode-4               134MB/s ± 1%   131MB/s ± 1%  -2.32%  (p=0.000 n=23+22)
GobEncode-4               170MB/s ± 1%   157MB/s ± 1%  -7.68%  (p=0.000 n=22+22)
Gzip-4                   98.7MB/s ± 0%  96.1MB/s ± 1%  -2.68%  (p=0.000 n=23+24)
Gunzip-4                  590MB/s ± 7%   593MB/s ± 2%    ~     (p=0.466 n=23+24)
JSONEncode-4              141MB/s ± 1%   139MB/s ± 2%  -1.13%  (p=0.000 n=22+23)
JSONDecode-4             40.9MB/s ± 1%  40.3MB/s ± 0%  -1.47%  (p=0.000 n=23+23)
GoParse-4                20.1MB/s ± 1%  20.2MB/s ± 1%  +0.69%  (p=0.000 n=21+22)
RegexpMatchEasy0_32-4     435MB/s ± 1%   444MB/s ± 2%  +2.21%  (p=0.000 n=21+22)
RegexpMatchEasy0_1K-4    5.89GB/s ± 1%  5.89GB/s ± 1%    ~     (p=0.439 n=22+24)
RegexpMatchEasy1_32-4     445MB/s ± 1%   459MB/s ± 1%  +3.06%  (p=0.000 n=23+20)
RegexpMatchEasy1_1K-4    3.26GB/s ± 1%  3.32GB/s ± 1%  +1.97%  (p=0.000 n=22+23)
RegexpMatchMedium_32-4   9.40MB/s ± 1%  9.44MB/s ± 1%  +0.43%  (p=0.000 n=23+21)
RegexpMatchMedium_1K-4   29.8MB/s ± 1%  29.8MB/s ± 1%    ~     (p=0.826 n=23+22)
RegexpMatchHard_32-4     19.1MB/s ± 1%  19.1MB/s ± 7%    ~     (p=0.233 n=22+23)
RegexpMatchHard_1K-4     19.9MB/s ± 1%  20.3MB/s ± 1%  +2.03%  (p=0.000 n=22+23)
Revcomp-4                 664MB/s ± 1%   612MB/s ± 0%  -7.85%  (p=0.000 n=22+22)
Template-4               37.6MB/s ± 1%  37.7MB/s ± 1%    ~     (p=0.558 n=20+23)
[Geo mean]                134MB/s        133MB/s       -0.76%
Tue Mar 28 22:16:54 EDT 2017

Change-Id: I4a4f5c2b53d3fb85ef76c98522d3ed5cf8ae5b7e
Reviewed-on: https://go-review.googlesource.com/38732
Reviewed-by: Russ Cox <rsc@golang.org>

1 files changed, 5 insertions, 5 deletions

diff --git a/src/runtime/mfixalloc.go b/src/runtime/mfixalloc.go
index fe4b0fcf2a..7496671fbe 100644
--- a/src/runtime/mfixalloc.go
+++ b/src/runtime/mfixalloc.go
@@ -29,7 +29,7 @@ type fixalloc struct {
 	first  func(arg, p unsafe.Pointer) // called first time p is returned
 	arg    unsafe.Pointer
 	list   *mlink
-	chunk  unsafe.Pointer
+	chunk  uintptr // use uintptr instead of unsafe.Pointer to avoid write barriers
 	nchunk uint32
 	inuse  uintptr // in-use bytes now
 	stat   *uint64
@@ -54,7 +54,7 @@ func (f *fixalloc) init(size uintptr, first func(arg, p unsafe.Pointer), arg uns
 	f.first = first
 	f.arg = arg
 	f.list = nil
-	f.chunk = nil
+	f.chunk = 0
 	f.nchunk = 0
 	f.inuse = 0
 	f.stat = stat
@@ -77,15 +77,15 @@ func (f *fixalloc) alloc() unsafe.Pointer {
 		return v
 	}
 	if uintptr(f.nchunk) < f.size {
-		f.chunk = persistentalloc(_FixAllocChunk, 0, f.stat)
+		f.chunk = uintptr(persistentalloc(_FixAllocChunk, 0, f.stat))
 		f.nchunk = _FixAllocChunk
 	}
 
-	v := f.chunk
+	v := unsafe.Pointer(f.chunk)
 	if f.first != nil {
 		f.first(f.arg, v)
 	}
-	f.chunk = add(f.chunk, f.size)
+	f.chunk = f.chunk + f.size
 	f.nchunk -= uint32(f.size)
 	f.inuse += f.size
 	return v