Cache coherence at scale (directory-based): Foundations

6.1.6 · D1 · Hardware › Parallelism & Multicore › Cache coherence at scale (directory-based)

Parent note Cache coherence at scale (directory-based) padhne se pehle, tumhe har woh word aur symbol samajhna hoga jo woh use karta hai. Hum har cheez ko zero se build karte hain — pehle picture, phir meaning, phir kyun is topic ko uski zaroorat hai.

1. Ek core, aur kyun uske paas private cache hai

Figure s01 mein, upar violet boxes follow karo — woh cores hain. Har ek ke neeche seedha uski khud ki orange cache hanging hai; notice karo ki char alag orange boxes hain, ek shared nahi. Woh alag-alag hona hi poora point hai: magenta arrow trace karo aur tum dekhoge ki same address ek saath do alag orange caches mein copy ho gayi hai. Sab neeche ek single navy bar — shared main memory — se connect hain.

2. Memory blocks, addresses, aur symbols $A$ , $B$ , $N$ , $M$

Parent note mein "block $B$ at address $A$ " jaisi cheezein likhi hain. Har letter earn karte hain.

Recall

Ek block physically kya represent karta hai? ::: Memory ka ek fixed-size chunk (e.g. 64 bytes) jise caches ek single unit ki tarah move aur track karte hain. Byte address $A$ se block number $B$ kaise milta hai? ::: $B = ⌊ A / BlockSize ⌋$ — block size se divide karo aur round down karo; remainder (offset) discard ho jaata hai. $M \times (2 + N)$ mein, $N$ kya count kar raha hai? ::: $N$ cores mein se har ek ke liye ek bit — sharer bit-vector.

3. State: words Uncached, Shared, Modified — aur " $2$ " bits

Ek block ki har copy kisi state mein hoti hai. Parent teen use karta hai. Block ko ek shared library book ki tarah socho.

Figure s03 mein teen coloured boxes teen states hain side by side; har ek ke neeche chhota navy caption padho jo main memory ke baare mein kya kehta hai (valid vs. stale).

4. Sharers, bit-vector, aur symbol $⟨ \cdot, \cdot ⟩$

Figure s04 mein, har square ek core ka bit hai; magenta squares 1 hain (copy hai) aur pale ones 0 hain. Magenta squares count karo — woh sharers set ka size hai. Caption off karta hai ki woh cores kaun se hain.

5. Home node / Home Directory (HD)

6. Snooping, messages, hops, aur O(N) vs O(N²)

Protocol cores ke ek doosre ko mail karne se kaam karta hai. Mail aur counting ko naam dete hain — lekin pehle woh purana approach jo directories replace karti hain.

Intuition Har bound actually kahan se aata hai (per operation, worst case)

Ek cache miss ke liye messages count karo:

Snooping: ek miss ek broadcast force karta hai jise har doosra core receive karna padta hai — yeh ek single operation ke liye $N - 1$ messages hain. Agar sab $N$ cores miss kar rahe hain, total traffic $N \times (N - 1) \approx N^{2}$ hai. Yeh worst case aur typical case bhi hai, kyunki broadcast hamesha sabke paas pahunchta hai chahe actually koi care kare ya nahi.
Directory: ek miss home ko 1 message bhejta hai, phir home sirf sharers ko message karta hai. Average case mein ek block ke sirf 1–3 sharers hote hain, toh woh ek chhota constant hai — roughly $O (1)$ per operation, aur $O (N)$ $N$ simultaneously-missing cores mein. Worst case woh block hai jo sab $N$ cores share karte hain aur write ho raha hai: home ko $N - 1$ invalidates bhejna padta hai — lekin yeh rare hai, jabki broadcast har baar poori price pay karta hai. $N = 64$ par ek broadcast round ~4000 messages hai jahan directory typically handful bhejti hai. Yahi gap hai pura reason ki directories exist karti hain.

7. Invalidate, Ack, aur Write-Back

Prerequisite map

Ise top-down padho: private caches wale cores duplicate copies create karte hain (problem); state (2 bits) + sharers ( $N$ bits) har copy describe karte hain; home directory unhe ek entry mein store karta hai; messages entries par act karte hain; traffic count (snooping vs directory) poore design ko justify karta hai.

Equipment checklist

Right side cover karo aur zor se answer karo. Agar kar sako, tum parent note ke liye ready ho.

Ek core kya hai, aur kyun har ek ka apna cache hona ek problem create karta hai?

Core ek independent instruction-runner hai; kyunki har ek ke paas private cache hai, ek address ek saath kai caches mein reh sakta hai aur unki copies disagree kar sakti hain.

Byte address

A

ko block number

B

mein kaise convert karo?

B = ⌊ A / BlockSize ⌋

— block size se divide karo aur round down karo; bacha hua offset bits discard ho jaata hai.

State field exactly 2 bits kyun cost karti hai?

Teen states (Uncached/Shared/Modified) ke liye kam se kam 2 bits chahiye, kyunki 1 bit sirf 2 patterns deta hai aur 2 bits 4 dete hain (teen use, ek spare).

Block Uncached hone par directory entry kya hold karti hai?

State bits

= 00

aur sharer bit-vector sab zeros hai — kisi ke paas copy nahi.

4 cores ke liye bit-vector 0101 mein, kis ke paas copies hain?

Cores 0 aur 2 (rightmost bit = core 0).

⟨ State, Owner/Sharers ⟩

ka kya matlab hai?

Ek directory entry: block ki state aur ya toh uske single owner (Modified) ya uske sharers ke set (Shared) ka paired bundle.

Snooping kya hai, aur yeh directory se kaise differ karta hai?

Snooping broadcast coherence hai jahan sab cores ek shared bus sun te hain aur har miss sab ke paas jaata hai; directory ki jagah record karti hai kis ke paas kaun sa block hai aur sirf unhe message karta hai.

Home node (HD) kya hai aur iski zaroorat kyun hai?

Woh fixed jagah jo ek diye gaye address ki directory row store karti hai — ek jaana-pehchaana desk jisse har core poochh sake "is block ke paas kaun hai?"

Broadcast

O (N^{2})

kyun hai lekin directory

O (N)

Broadcast:

N

cores mein se har ek baaki

N - 1

ko message karta hai → ~

N^{2}

, har baar. Directory: har request 1 home + kuch sharers (avg 1–3) tak jaati hai →

N

ke saath badhti hai.

Directory write grant karne se pehle Invalidate-Acks kyun count karta hai?

Guarantee karne ke liye ki har purane reader ne pehle apni copy maar di, taaki do caches ek address ke liye alag-alag values hold na karein.