NUMA architectures: Foundations — Hinglish deep dive

6.1.7 · D1 · Hardware › Parallelism & Multicore › NUMA architectures

Is page pe assume kiya gaya hai ki aapne parent note ki notation mein se kuch bhi nahi dekha. Hum har letter, har symbol, har fraction ko ground up se banate hain, ek aisi order mein jahan har idea apne pehle waale idea pe lean karta hai. Jab bhi NUMA architectures pe koi symbol confuse kare, yahan wapas aao.

0. Har cheez ke peeche ki picture

Kisi bhi letter se pehle, machine ka map dekho. Yeh image apne dimag mein rakh lo — baad ke saare symbols is picture pe sirf ek distance ya ek count hain.

1. Processor, core, node — teen "cheezein"

Topic ko yeh words kyun chahiye: NUMA ko ek node ke relative define kiya jaata hai. "Local" ka matlab hai "same node", "remote" ka matlab hai "different node". Agar aapke paas node word nahi hai, toh aap keh bhi nahi sakte ki local ka matlab kya hai.

Hum nodes ko ek letter se count karenge. Maano

$N_{n o d es} = how many nodes (desks) the machine has.$

Chhota subscript $nodes$ bas ek label hai jo yaad dilata hai hum kya count kar rahe hain — yeh multiplication nahi hai, power nahi hai, bas apne aap ko chhota note likha gaya hai. Ise zor se "N-nodes" padho.

2. Memory, address, aur DRAM

Picture: socho ki har shelf pe har book pe ek unique sticker number laga hai. $A$ woh sticker number hai. Poori shelf, node by node, ek lamba numbered strip hai — lekin pieces mein kaata gaya, ek piece per desk.

Topic ko $A$ kyun chahiye: yeh decide karne ke liye ki kaunsi desk pe koi book hai, machine uska sticker number $A$ dekhti hai aur uspe arithmetic karti hai. Woh arithmetic "address mapping" formulas hain jo parent page pe hain — hum §6 mein unke liye taiyaari karte hain.

3. Time aur letter $t$

NUMA mein jo bhi expensive hai woh time mein measure hota hai. Hum letter $t$ use karte hain "kisi cheez mein kitna time lagta hai" ke liye, hamesha ek chhota label ke saath jo batata hai kaun si cheez:

Picture: ek stopwatch jise aap tab shuru karte ho jab processor ek book maangta hai aur tab rokta hai jab book aati hai. Alag alag journeys → alag stopwatch readings → alag $t$ 's. Yahi difference hai NUMA mein "Non-Uniform".

4. Local vs remote — aur "cases" bracket ${$

Parent access time ko ek badi curly brace ke saath likhta hai. Pehle, access time kya hai?

$t_{a ccess} = {t_{l oc a l} t_{r e m o t e} if memory in same node if memory in different node$

Topic ko yeh kyun chahiye: memory access ka ab ek cost nahi hai — iske do cases hain. Bracket yeh honestly likhne ka tarika hai ki "yeh depend karta hai".

5. Fractions, ratios, aur " $\times$ faster" idea

Parent kehta hai remote "1.3x to 3x slower" hai aur ek NUMA factor define karta hai. Dono ratios hain — ek number divided by doosra.

6. Floor, modulo, aur address mapping

Yeh decide karne ke liye ki address $A$ kaun sa node hold karta hai, parent do operators use karta hai jo zyaatar 12-saal ke bacchon ne nahi dekhe: floor $⌊ ⌋$ aur mod.

Topic ko floor & mod kyun chahiye: yeh sirf wahi tools hain jo addresses ki smooth stream ko node numbers ke repeating pattern mein turn karte hain. Woh repeating pattern exactly hai jaise hardware memory ko desks mein split karta hai.

7. Remote accesses ka fraction $f$ , aur average $t_{a v g}$

Parent ka performance model local aur remote trips ko ek fraction $f$ se mix karta hai.

8. Speedup $S$ — ratio kya compare kar raha hai

Prerequisite map

Har arrow ka matlab hai "pehle yeh chahiye". Notice karo ki node aur address do twin roots hain; baaki sab yeh jaanne se barta hai ki desk kya hoti hai aur book ka number uski desk kaise choose karta hai.

Connected notes

Parent: NUMA architectures
Same idea in Hinglish: 6.1.07 NUMA architectures (Hinglish)
"Coherence" aur shared memory actually kya promise karte hain: 6.1.05-memory-consistencymodels
Cores ko ek doosre pe step karne se rokna: 6.1.06-multicore-synchronization
Yeh decide karna ki kaunsi desk pe thread baithta hai: 6.2.03-thread-scheduling
Practice mein fast jaane ke liye yeh sab use karna: 6.3.01-parallel-algorithms

Equipment checklist

Cover the right side; can you answer before revealing?

Ek node physically kya contain karta hai?

Ek ya zyada cores + ek local memory bank + ek memory controller — ek "desk".

Address

A

kya hai?

Memory ke ek box ka unique house-number.

Memory controller (clerk) kya karta hai?

Requested memory ka box kholta hai aur uska content wapas deta hai; har desk ka apna hota hai.

t_{a ccess}

kya hai?

Woh total time jo ek processor ek box maangne se lekar uska content aane tak wait karta hai.

t_{l oc a l}

zor se padho — kya yeh ek product hai?

"Local time"; yeh ek single quantity hai,

t

times "local" nahi.

t_{r e m o t e_co n t r o l l er}

kya hai?

Door wale desk ke memory controller ka apna box kholne ka wait, ek remote trip mein extra legs mein se ek.

t_{r e m o t e}

kabhi

t_{l oc a l}

se kam kyun nahi ho sakta?

Ek remote trip woh sab kuch karta hai jo local trip karta hai plus extra wire aur far-clerk time — aap sirf legs add karte ho.

"Cases" bracket ka matlab kya hai?

Ek written-out if/else: woh line choose karo jiska condition true ho.

⌊ 3.9 ⌋

aur

6 mod 4

compute karo.

3

aur

2

Interleaved mapping mein pehle

A

L_{c a c h e l in e}

se kyun divide karte hain?

Books ek cache-line ke saath ek saath chalti hain, isliye hum node choose karte hain per line-slot, per byte nahi.

F_{N U M A}

ko words mein define karo.

Remote latency divided by local latency — ek remote trip kitni times slower hai.

Agar

f = 0.2

hai, toh trips ka kitna fraction local hai?

1 - f = 0.8

, yaani

80%

f = 0.2, F_{N U M A} = 2

ke liye

t_{a v g}

t_{l oc a l}

ke units mein do.

1.2 t_{l oc a l}

S

un same numbers ke liye do.

2.0/1.2 = 1.67 \times

Kya

F_{N U M A}

aur

S

ek hi cheez hain?

Nahi — ek per-trip slowness hai, doosra locality se whole-program gain hai.

Recall Self-test: ONE core idea ek sentence mein batao

Memory per-node piles mein split hai; apna pile fast hai, baaki slower hain kyunki interconnect cross karna padta hai — woh gap hi woh hai jo saare symbols measure karte hain. One-sentence answer ::: NUMA = local memory fast, remote memory slow, aur topic uss gap ka arithmetic hai.