TSO 等のメモリ・モデルは、 global visible order *3 に関する規則です。にも関わらず、例えば、load がいつの時点で global visible になるのか、そもそも、global visible とはなんなのか？という記述なしに、 TSO の説明が始まっているように見えます。

なぜなら、TSO メモリ・モデル全体が、global visible order を定義するからです。特定のインプリメントに依存しないように global visible order を定義する方法は、これしか無いように思われます。

Global visible order について、 TSO のようなメモリ・モデルなしに（自明な事実として）合意されるであろう事柄は、「ストアが global visible になった後でなければ、そのストア値は他の CPU からは見えない (load できない）」だけでしょう。

この順序は、以下のようなプログラム片を用いて観測することが可能です。(以降、メモリの初期値は 0 とします。）

 Processor-1            Processor-2
 1: Store [X] = 1    2: Load r1 = [X]

実行結果として、r1 = 1 が得られれば、（ソフトウエアから観測される、（以下わざわざ書かない））global visible order は、 1: → 2: となります。r1 = 0 だったなら、2: → 1:。

意外かもしれませんが、TSO 等のメモリ・モデルなしに推定できる順序（ソフトウエアによって観測される振る舞い）はこれだけです。

たとえば、次のようなプログラム片を実行した結果、 r1 = 1, r2 = 1 が得られたとしましょう。

 Processor-1            Processor-2
 1: Store [X] = 1    3: Load r1 = [X]
 2: Store [Y] = 1    4: Load r2 = [Y]

このとき観測された global visible order は、 1: → 3: かつ 2: → 4: です。1:, 2:, 3:, 4: の 4 つすべての global visible order として考えられる候補 (3! 通り）のうちどれだったのかは、ソフトウエアには観測できないことになります。たとえば、2: → 4: → 1: → 3: だったのかも知れない。

ここで、TSO を仮定すると、1: → 2:, 3: → 4: の制約が加わるため、考えられる組み合わせはもっと減ることになります。

再び、問題のケース

問題のプログラム片を再び持ち出してみましょう。ただし、組み合わせを減らすために、Processor-2 の方に少し細工をしました。メモリ・モデルは、TSO を仮定します。

 Processor-1         Processor-2
 1: Store [X] = 1    4: Store [Y] = 1
 2: Load r1 = [X]       Membar #StoreLoad
 3: Load r2 = [Y]    5: Load r3 = [Y]
                        Membar #LoadLoad ; TSO なら不要だが念のため
                     6: Load r4 = [X]

ここで、実行結果 r1 = r3 = 1, r2 = r4 = 0　のとき、ソフトウエアから観測された global visible order がどのようなものだったか考えてみます。

まず、r2 = r4 = 0 と、「ストアが global visible になった後でなければ、そのストア値は他の CPU からは見えない (load できない）」という自明な規則から、

 6: → 1:
 3: → 4:

が判明します。

今回、Processor-2 の方は、シーケンシャル・オーダーになるよう細工してあるので、

 4: → 5: → 6:

となっています。

ここまでで確定したのは、

 3: → 4: → 5: → 6: → 1:

です。まだ 2: の場所がきまっていません。（★）

ここで注意すべきなのは、観測結果 r1 = 1 から global visible order について推定できることがらは存在しないという点です。自明な規則は、「ストアが global visible になった後でなければ、そのストア値は他の CPU からは見えない (load できない）」でしたが、これでは Processor-1 内部に閉じた 1:, 2: 間の順序を確定することはできません。

しかしここで、TSO のメモリモデルより、

 2: → 3:

が決まります。

したがって、global visible order としては

 2: → 3: → 4: → 5: → 6: → 1:

が観測されたことになります。

Processor-1 の分だけとりだすと、

 2: → 3: → 1:

となっていますが、これは TSO メモリ・モデルを違反していません。

一方、3: → 1: → 2: 案は？

一方、3: → 1: → 2: とする案では、どのような推定が行われたのことになるでしょうか？

上で（★）印をつけたところまでは共通でしょう。つまり、

 3: → 4: → 5: → 6: → 1:

までが確定していて、2: の位置が決まっていない。

ここで、nminoru さんは、どこからともなく

 1: → 2:

という規則を持ち出してきています。

どこにも書かれていない規則を適用し、「3: → 1: → 2: になってしまった、TSO 違反だ！」と主張しているように、私には思えます。

*1 SPARC-V9 の TSO 定義はこう読むべきですとしなかったのは、自信のなさの現れだったり。

*2 SPARC-V9 の TSO 定義はこう読むべきですとしなかったのは、自信のなさの現れだったり。

*3 英語的には globally visible order と書くべきでしょうか。

◆ π秒は 1 ナノ世紀

http://njb.virtualave.net/nmain0216.html#nmain20060922095828

もしかすると google 様が教えてくれるのではないかと思い、聞いてみました。

http://www.google.co.jp/search?q=pi+second+in+century&lr=lang_ja

おお。

本日のツッコミ(全185件) [ツッコミを入れる]

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