Наш не­со­вер­шен­ный мир: про­цес­со­ры

В но­вой руб­ри­ке «Наш не­со­вер­шен­ный мир» бу­ду из­ред­ка рас­ска­зы­вать про тот иди­о­тизм, ко­то­рый нас окру­жа­ет. Нач­ну, по­жа­луй, с про­цес­со­ров. Быст­ро­дей­ствие и раз­ме­ры со­вре­мен­ных мик­ро­про­цес­со­ров очень до­стой­ные да­же с мо­ей при­ве­ред­ли­вой точ­ки зре­ния. А вот их энер­го­по­треб­ле­ние остав­ля­ет же­лать луч­ше­го.

Про­цес­сор — са­мое не­эф­фек­тив­ное устрой­ство из всех устройств, ко­гда-ли­бо со­здан­ных че­ло­ве­ком. КПД про­цес­со­ра прак­ти­че­ски точ­но ра­вен ну­лю.

Про­ве­дём не­ко­то­рые оцен­ки (не вы­хо­дя за рам­ки школь­но­го кур­са фи­зи­ки) на при­ме­ре двухъ­ядер­но­го про­цес­со­ра, имею­ще­го 600 мил­ли­о­нов тран­зи­сто­ров и так­то­вую ча­сто­ту 3 ги­га­гер­ца. Не бу­дем тре­бо­вать от про­цес­со­ра че­го-то не­ре­аль­но­го: об­ра­ти­мой ло­ги­ки[1],[2] и ра­бо­ты при тем­пе­ра­ту­ре аб­со­лют­ный ноль. Оце­ним, ка­кое долж­но быть энер­го­по­треб­ле­ние про­цес­со­ра с не­об­ра­ти­мой ло­ги­кой при ком­нат­ной тем­пе­ра­ту­ре.

Рас­смот­рим худ­ший ва­ри­ант: на каж­дом тран­зи­сто­ре за один такт те­ря­ет­ся один бит ин­фор­ма­ции. Это озна­ча­ет, что эн­тро­пия про­цес­со­ра воз­рас­та­ет[1] как ми­ни­мум на k\cdot\ln\left(2\right) джо­у­лей на кель­вин, где k = 1.38 \cdot 10^{-23} — по­сто­ян­ная Больц­ма­на. Эн­тро­пия не мо­жет бес­ко­неч­но на­кап­ли­вать­ся в про­цес­со­ре, и долж­на быть пе­ре­да­на внеш­ней сре­де в ви­де теп­ла. То­гда тран­зи­стор за один такт дол­жен от­дать внеш­ней сре­де энер­гию E_1 = T \cdot k \cdot \ln\left(2\right), где T — тем­пе­ра­ту­ра внеш­ней сре­ды.

Тран­зи­сто­ров у нас n = 600 \cdot 10^6. Каж­дый тран­зи­стор те­ря­ет в се­кун­ду m = 3 \cdot 10^9 бит (так­то­вая ча­сто­та 3 ГГц). То­гда вы­де­ля­е­мая за се­кун­ду (и, зна­чит, по­треб­ля­е­мая за се­кун­ду) про­цес­со­ром энер­гия бу­дет рав­на:

E = n\cdot m\cdot E_1 = m\cdot n\cdot T\cdot k\cdot ln\left(2\right).
(1)

Пусть внеш­няя сре­да име­ет тем­пе­ра­ту­ру T = 27 гра­ду­сов Цель­сия {} = 300 кель­ви­нов, то­гда, под­став­ляя чис­ло­вые дан­ные в фор­му­лу (1), по­лу­чим:

E = 600\cdot 10^6\cdot 3\cdot 10^9\cdot 300\cdot 1.38\cdot 10^{-23}\cdot \ln\left(2\right) \approx 0.005
(2)

джо­у­лей за се­кун­ду {} = 5 мил­ли­ватт.

Итак, не­об­ра­ти­мый про­цес­сор, ра­бо­таю­щий при ком­нат­ной тем­пе­ра­ту­ре, дол­жен по­треб­лять мощ­ность 5 мил­ли­ватт.

Ре­аль­ный же про­цес­сор с ука­зан­ны­ми ха­рак­те­ри­сти­ка­ми по­треб­ля­ет мощ­ность по­ряд­ка 50-ти ватт. Та­ким об­ра­зом, мы при­хо­дим к вы­во­ду, что про­цес­сор по­треб­ля­ет в 10 ты­сяч раз боль­ше энер­гии, чем дол­жен по­треб­лять для про­ве­де­ния вы­чис­ле­ний!

И по­сле это­го лю­ди удив­ля­ют­ся, что за­ря­да ак­ку­му­ля­то­ра в но­ут­бу­ке не хва­та­ет на сут­ки ра­бо­ты. Хо­тя ещё дис­плей мно­го по­треб­ля­ет, но об этом мы по­го­во­рим как-ни­будь в сле­дую­щий раз.

По­че­му ре­аль­но­му про­цес­со­ру тре­бу­ет­ся так мно­го энер­гии? Де­ло в том, что все про­вод­ни­ки про­цес­со­ра име­ют ём­кость и со­про­тив­ле­ние. Ло­ги­че­ское со­стоя­ние про­вод­ни­ка («0» или «1») ко­ди­ру­ет­ся на­пря­же­ни­ем, при­сут­ствую­щем на этом про­вод­ни­ке. Сме­на ло­ги­че­ско­го со­стоя­ния при­во­дит к не­об­хо­ди­мо­сти сме­ны на­пря­же­ния на этом про­вод­ни­ке; сме­на на­пря­же­ния тре­бу­ет пе­ре­за­ряд­ки ём­ко­сти про­вод­ни­ка[8]; за­ряд­ка ём­ко­сти при­во­дит к на­ли­чию то­ка; ток, те­ку­щий че­рез про­вод­ник с со­про­тив­ле­ни­ем, при­во­дит к вы­де­ле­нию теп­ла. Кро­ме то­го, не­боль­шая часть энер­гии ухо­дит из про­цес­со­ра в ви­де элек­тро­маг­нит­но­го из­лу­че­ния.

Пред­ста­вим, что не­ко­то­рый ло­ги­че­ский эле­мент про­цес­со­ра име­ет ём­кость C, и на не­го по­да­ёт­ся сиг­нал f\left(t\right) че­рез про­вод­ник с со­про­тив­ле­ни­ем R. То­гда ток за­ряд­ки кон­ден­са­то­ра ра­вен: I\left(t\right) = C\cdot df\left(t\right)/dt. Мощ­ность, вы­де­ля­е­мая на про­вод­ни­ке, рав­на: P\left(t\right) = I^2\left(t\right)\cdot R. От­сю­да:

P\left(t\right) = \left(C\cdot \frac{df\left(t\right)}{dt}\right)^2 \cdot R.
(3)

Из фор­му­лы сле­ду­ют пу­ти сни­же­ния вы­де­ля­е­мой (а, зна­чит, и по­треб­ля­е­мой) мощ­но­сти:

  • Умень­ше­ние раз­ме­ра про­цес­со­ра: ём­кость кон­ден­са­то­ра пря­мо про­пор­цио­наль­на его раз­ме­ру, а со­про­тив­ле­ние про­вод­ни­ка об­рат­но про­пор­цио­наль­но его раз­ме­ру. Но ём­кость в фор­му­ле (3) воз­во­дит­ся в квад­рат, по­это­му при про­чих рав­ных усло­ви­ях по­треб­ля­е­мая про­цес­со­ром мощ­ность про­пор­цио­наль­на его раз­ме­ру. Раз­мер за­ви­сит от ис­поль­зу­е­мой тех­но­ло­гии из­го­тов­ле­ния, по­это­му про­из­во­ди­те­ли по­сто­ян­но ста­ра­ют­ся усо­вер­шен­ство­вать тех­но­ло­гию из­го­тов­ле­ния про­цес­со­ров.

  • Умень­ше­ние на­пря­же­ния пи­та­ния при­во­дит к про­пор­цио­наль­но­му умень­ше­нию функ­ции f\left(t\right) (а, зна­чит, и её про­из­вод­ной) в фор­му­ле (3). Так как эта функ­ция воз­во­дит­ся в квад­рат, то по­треб­ля­е­мая мощ­ность сни­жа­ет­ся про­пор­цио­наль­но квад­ра­ту сни­же­ния на­пря­же­ния. По­это­му про­цес­сор, пи­таю­щий­ся от на­пря­же­ния 1.5 воль­та, по­треб­ля­ет в 4 ра­за мень­шую мощ­ность, чем про­цес­сор, пи­таю­щий­ся от на­пря­же­ния 3 воль­та. К со­жа­ле­нию, умень­ше­ние на­пря­же­ния сни­жа­ет устой­чи­вость про­цес­со­ра к по­ме­хам и по­вы­ша­ет тре­бо­ва­ния к ка­че­ству его из­го­тов­ле­ния. Ещё 20 лет на­зад все про­цес­со­ры пи­та­лись от 5-ти вольт, сей­час встре­ча­ют­ся про­цес­со­ры, тре­бую­щие ме­нее од­но­го воль­та для сво­ей ста­биль­ной ра­бо­ты.

    На сни­же­нии на­пря­же­ния пи­та­ния про­цес­со­ра ос­но­ван энер­го­сбе­ре­гаю­щий ре­жим в но­ут­бу­ках. При этом, что­бы про­цес­сор не за­глю­чил, так­же сни­жа­ет­ся его так­то­вая ча­сто­та, что да­ёт до­пол­ни­тель­ное умень­ше­ние по­треб­ля­е­мой мощ­но­сти (смот­ри­те сле­дую­щий пункт).

  • Умень­ше­ние так­то­вой ча­сто­ты при­во­дит к про­пор­цио­наль­но­му умень­ше­нию ско­ро­сти из­ме­не­ния всех на­пря­же­ний в про­цес­со­ре. Так как ско­рость из­ме­не­ния на­пря­же­ния в фор­му­ле (3) воз­во­дит­ся в квад­рат, то, в иде­а­ле, энер­го­по­треб­ле­ние про­цес­со­ра па­да­ет про­пор­цио­наль­но квад­ра­ту умень­ше­ния так­то­вой ча­сто­ты. На прак­ти­ке си­ту­а­ция ху­же, и за­кон сни­же­ния энер­го­по­треб­ле­ния мо­жет ока­зать­ся бли­же к ли­ней­но­му, чем к квад­ра­тич­но­му (из-за рез­ко­сти сме­ны на­пря­же­ния в про­вод­ни­ках про­цес­со­ра). До­пол­ни­тель­но ухуд­ша­ет си­ту­а­цию то, что при сни­же­нии ча­сто­ты про­пор­цио­наль­но сни­жа­ет­ся быст­ро­дей­ствие про­цес­со­ра. При этом у нас есть два вы­хо­да:

    • Мы мо­жем доль­ше ждать ре­ше­ния за­да­чи. При этом за­тра­чен­ная энер­гия про­пор­цио­наль­на вре­ме­ни ра­бо­ты про­цес­со­ра, ко­то­рое, в свою оче­редь, об­рат­но про­пор­цио­наль­но так­то­вой ча­сто­те. По­лу­ча­ем, что при умень­ше­нии так­то­вой ча­сто­ты в k раз по­треб­ля­е­мая мощ­ность па­да­ет в k^2 раз, од­на­ко в k раз уве­ли­чи­ва­ет­ся вре­мя, в те­че­ние ко­то­ро­го эта мощ­ность по­треб­ля­ет­ся. В ито­ге, при сни­же­нии ча­сто­ты в k раз, энер­гия не­об­хо­ди­мая для ре­ше­ния за­да­чи, то­же умень­ша­ет­ся в k раз (это в тео­рии, на прак­ти­ке вы­иг­рыш зна­чи­тель­но ни­же).

    • Мы мо­жем ис­поль­зо­вать для ре­ше­ния за­да­чи не­сколь­ко ядер/про­цес­со­ров. До­пол­ни­тель­ные яд­ра тре­бу­ют до­пол­ни­тель­ной энер­гии, од­на­ко их на­ли­чие поз­во­ля­ет сни­зить так­то­вую ча­сто­ту, не­об­хо­ди­мую для до­сти­же­ния тре­бу­е­мой про­из­во­ди­тель­но­сти. Рас­суж­дая ана­ло­гич­но рас­суж­де­ни­ям преды­ду­ще­го пунк­та, по­лу­чим, что нам энер­ге­ти­че­ски в 2 ра­за вы­год­нее ре­шить за­да­чу на двух мед­лен­ных яд­рах, чем на од­ном в 2 ра­за бо­лее быст­ром яд­ре. По­это­му про­из­во­ди­те­ли ре­кла­ми­ру­ют, что с по­вы­ше­ни­ем ко­ли­че­ства ядер уве­ли­чи­ва­ет­ся вре­мя ра­бо­ты но­ут­бу­ка от ба­та­реи. Де­ло в том, что на про­цес­со­ре с бо́льшим чис­лом ядер мож­но ис­поль­зо­вать бо­лее су­ще­ствен­ное сни­же­ние так­то­вой ча­сто­ты в ре­жи­ме энер­го­сбе­ре­же­ния, не до­став­ляя дис­ком­фор­та поль­зо­ва­те­лю. Важ­ным усло­ви­ем здесь яв­ля­ет­ся за­груз­ка всех имею­щих­ся ядер (па­ра­л­лель­ная ра­бо­та про­грамм), что не все­гда бы­ва­ет на прак­ти­ке.

    Ес­те­ствен­но, про­из­во­ди­те­ли стре­мят­ся по­вы­сить, а не по­ни­зить ча­сто­ту про­цес­со­ров, так как быст­ро­дей­ствие обыч­но счи­та­ет­ся бо­лее важ­ным, чем энер­го­по­треб­ле­ние.

  • На­ко­нец, в фор­му­ле (3) остал­ся по­след­ний па­ра­метр: R. Его мож­но сни­жать ли­бо пу­тём ис­поль­зо­ва­ния бо­лее ка­че­ствен­ных ма­те­ри­а­лов при из­го­тов­ле­нии мик­ро­схем (тут пре­дел дав­но до­стиг­нут), ли­бо пе­ре­во­дом ма­те­ри­а­лов в сверх­про­во­дя­щее со­стоя­ние.

    Сверх­про­во­дя­щие по­лу­про­вод­ни­ки уже изоб­ре­те­ны. До­ста­точ­но сде­лать про­цес­сор из под­хо­дя­щих ма­те­ри­а­лов, охла­дить его до по­ло­ви­ны гра­ду­са Кель­ви­на — и со­про­тив­ле­ние упа­дёт до ну­ля. По­сле это­го про­цес­сор пе­ре­ста­нет греть­ся во­об­ще. Но и ра­бо­тать он то­же пе­ре­ста­нет: во всех це­пях про­цес­со­ра воз­ник­нут ко­ле­ба­ния, ко­то­рые бу­дут за­ту­хать толь­ко за счёт элек­тро­маг­нит­но­го из­лу­че­ния. При­дёт­ся су­ще­ствен­но сни­зить так­то­вую ча­сто­ту про­цес­со­ра, что­бы все ко­ле­ба­ния успе­ли за­тух­нуть, при этом энер­гия всё рав­но бу­дет тра­тить­ся впу­стую.

Мы убе­ди­лись, что про­цес­сор не­со­вер­ше­нен. Но не на­шли спо­со­ба ра­ди­каль­но улуч­шить си­ту­а­цию. При­ни­маю ва­ши пред­ло­же­ния по из­го­тов­ле­нию про­цес­со­ра, пус­каю­ще­го всю энер­гию «в де­ло»!

Ссыл­ки по те­ме

  1. Фи­зи­че­ская ин­фор­ма­ция — ин­фор­ма­ция фи­зи­че­ской си­сте­мы.

  2. Об­ра­ти­мые вы­чис­ле­ния — вы­чис­ле­ния, осу­ществ­ляе­мые без по­те­ри ин­фор­ма­ции.

  3. Ло­ги­че­ский эле­мент Тоф­фо­ли — об­ра­ти­мый ло­ги­че­ский эле­мент, функ­цио­ни­рую­щий без по­те­ри ин­фор­ма­ции и, зна­чит, та­кой эле­мент мо­жет не вы­де­лять теп­ло при сво­ей ра­бо­те (и не по­треб­лять энер­гию).

  4. Кван­то­вый ком­пью­тер — он мо­жет функ­цио­ни­ро­вать до тех пор, по­ка не про­изо­шло кван­то­вой де­ко­ге­рен­ции. Ес­ли кван­то­вый ло­ги­че­ский эле­мент бу­дет не­об­ра­тим, то про­изой­дёт по­те­ря ин­фор­ма­ции и де­ко­ге­рен­ция. По­это­му, кван­то­вый ком­пью­тер обя­зан функ­цио­ни­ро­вать без по­те­ри ин­фор­ма­ции, что обу­слав­ли­ва­ет по­пу­ляр­ность ис­сле­до­ва­ний в об­ла­сти об­ра­ти­мых вы­чис­ле­ний.

  5. «Чёр­ная ды­ра не име­ет во­лос» — ги­по­те­за о том, что не­воз­мож­но от­ли­чить две чёр­ных ды­ры, ес­ли они име­ют оди­на­ко­вые мас­су, элек­три­че­ский за­ряд, и уг­ло­вой мо­мент. Из этой ги­по­те­зы сле­ду­ет па­ра­докс:

  6. Ин­фор­ма­ци­он­ный па­ра­докс чёр­ной ды­ры — раз чёр­ные ды­ры не­от­ли­чи­мы, то ку­да де­ва­ет­ся ин­фор­ма­ция, ко­то­рая за­са­сы­ва­ет­ся в них?

  7. Го­ло­гра­фи­че­ский прин­цип — раз­ре­ша­ет ин­фор­ма­ци­он­ный па­ра­докс при по­мо­щи тео­рии струн.

  8. Элек­три­че­ский кон­ден­са­тор — ссыл­ка на вся­кий слу­чай.

116 отзывов о несовершенных процессорах

Про­цес­со­ры — не са­мое боль­шое не­со­вер­шен­ство в на­шем ми­ре. Че­ло­век ку­да бо­лее не­со­вер­ше­нен. Да и что зна­чит са­мо по­ня­тие «со­вер­шен­ный»? Зна­чит ли это, что что-ли­бо долж­но пол­но­стью со­от­вет­ство­вать на­шим о нем пред­став­ле­ни­ям и мо­де­лям? http://ru.wikipedia.org/wiki/Иде­ал А в ка­че­стве за­дач­ки по фи­зи­ке — очень хо­ро­шее упраж­не­ние по­лу­чи­лось
Всё го­раз­до про­ще. Под не­со­вер­шен­ством я по­ни­мал не­эф­фек­тив­ность, низ­кий КПД (смот­ри вто­рой аб­зац). В мо­ём по­ни­ма­нии со­вер­шен­ство — это эф­фек­тив­ность. Чем эф­фек­тив­нее тра­тят­ся имею­щие­ся ре­сур­сы (ве­ще­ство, энер­гия, вре­мя, день­ги) для до­сти­же­ния це­ли, — тем со­вер­шен­нее си­сте­ма. Ес­те­ствен­но, о со­вер­шен­стве в та­ком кон­тек­сте мож­но го­во­рить толь­ко то­гда, ко­гда це­ли функ­цио­ни­ро­ва­ния си­сте­мы яс­но опре­де­ле­ны.
Кста­ти, чёр­ная ды­ра при ис­па­ре­нии воз­вра­ща­ет по­пав­шие в неё ве­ще­ство, энер­гию и, как не­дав­но по­ка­за­но, ин­фор­ма­цию. Воз­вра­ща­ет ли она по­пав­шие в неё день­ги? Хо­тя день­ги — это и есть ин­фор­ма­ция. Они дав­но уже хра­нят­ся не в сей­фах, а в ба­зах дан­ных…
А по мо­е­му са­мое не­со­вер­шен­ное- это об­ще­ство в ко­то­ром мы все с ва­ми жи­вем…. Я по­мо­е­му на­звал са­мо не­овр­шен­ство, кто воз­ра­зит!!!
од­но из ре­ше­ний всем из­вест­но и не кем в пол­ной ме­ре не реа­ли­зо­ва­но — трех­мер­ная ком­по­нов­ка.
дру­гой ва­ри­ант из­ба­вит­ся от не­нуж­ных тран­зи­сто­ров — MISC.
осталь­ное без­мер­но слож­нее…
кста есть ге­те­ро­ген­ные вы­со­ко­тем­пе­ра­тур­ные сверх­про­вод­ни­ки
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