Flynn's taxonomy (SISD - SIMD - MIMD): Foundations

6.1.1 · D1 · Hardware › Parallelism & Multicore › Flynn's taxonomy (SISD - SIMD - MIMD)

Parent note use karne se pehle, tumhe uske andar har word ko earn karna hoga. Yeh page har symbol aur har concept ko bilkul zero se banata hai — pehle plain words, phir ek picture, phir kyun topic ko uski zaroorat hai. Upar se neeche padho; har block uske upar wale par tikaa hua hai.

Parent topic: Flynn's taxonomy.

1. "Instruction" kya hota hai?

Picture. Ek cooking recipe socho. Har line — "egg todo", "hilaao", "daalo" — ek instruction hai. Recipe hi program hai.

Figure — Flynn's taxonomy (SISD - SIMD - MIMD)

Topic ko iske kyun zaroorat hai. Flynn ka pehla axis instruction streams count karta hai. Tum kisi cheez ko count nahi kar sakte jab tak uska naam nahi jaante. Figure mein red line dekho — woh single command "ADD" exactly wahi hai jo ek instruction ka matlab hai.

2. "Stream" kya hota hai?

Picture. Ek conveyor belt imagine karo. Items ek worker ke paas se ek ek karke guzarti hain — woh ordered flow hi stream hai. Worker processor hai; commands ki belt instruction stream hai; numbers ki doosri belt data stream hai.

Topic ko iske kyun zaroorat hai. Poori taxonomy sirf do words "instruction stream" aur "data stream" par bani hai. Flynn jo bhi kehta hai woh yeh hai: tumhare paas kitni belts hain?

3. Single (S) vs Multiple (M)

Picture. Ek conveyor belt versus kaafi belts side by side, sab saath chalti hain.

Topic ko iske kyun zaroorat hai. Do axes, har ek ya to S ya M, $2 \times 2 = 4$ boxes deta hai. Yahi poori taxonomy hai. Neeche wali figure grid dikhati hai.

4. Teen machine parts: CU, PU, ALU, Memory

Picture. CU ek foreman hai clipboard ke saath; PU ek worker hai; memory warehouse shelf hai. Foreman ek command chillata hai; worker shelf se number uthata hai aur process karta hai.

Topic ko iske kyun zaroorat hai. Parent note har architecture ko boxes ki tarah draw karta hai: "CU → PU → Memory". Kitne CUs hain count karna instruction axis batata hai; kitne PUs alag-alag data feed ho rahe hain count karna data axis batata hai. SIMD = ek CU, kaafi PUs. MIMD = kaafi CUs, kaafi PUs.

5. "Broadcast" aur "lockstep"

Picture. Ek foreman megaphone mein "ADD!" chillata hai; chaar workers sab ek hi waqt add karte hain.

Topic ko iske kyun zaroorat hai. Yahi SIMD ka exact mechanism hai: ek instruction, broadcast, multiple data par lockstep mein execute. Inhe jaane bina, "SIMD" ek mystery hai.

6. "Independent" data aur dependencies

Picture. Independent: do log apni apni plate dho rahe hain — order matter nahi karta. Dependent: egg pehle todna zaroori hai tab hi hila sakte ho.

Worked example Dependency dhundho

a[0] = a[0] + 1;   // agle line se independent
a[1] = a[1] + 1;   // independent — ek saath chal sakta hai  ✅ SIMD-able
 
sum = sum + x;     // har step ko pichla sum chahiye
sum = sum + y;     // DEPENDENT — order mein chalna chahiye       ❌

Topic ko iske kyun zaroorat hai. SIMD sirf tab speed up karta hai jab data elements independent hon. Parent ka mistake callout ("SIMD always N× faster nahi hota") poora hidden dependencies ke baare mein hai. Yahi concept speedup ko possible ya impossible banata hai.

7. Clock cycle aur symbol $T$

Picture. Ek stopwatch jo tick karta hai; har tick par, ek chhota kaam ho jaata hai.

Topic ko iske kyun zaroorat hai. $T$ woh unit hai jismein har speedup formula measure hota hai. Tum " $Speedup = \frac{N \cdot T}{T} = N$ " nahi padh sakte jab tak yeh nahi jaante ki $T$ matlab "ek operation ka time" hai.

8. Letter $N$ aur "speedup"

Picture. Agar koi kaam akele 100 seconds leta tha aur helpers ke saath 25 seconds, speedup $= 100/25 = 4$ : yeh 4× faster hai.

Topic ko iske kyun zaroorat hai. Parent ka SIMD formula $\frac{N \cdot T}{T} = N$ aur Amdahl's Law dono ek speedup number output karte hain. Ab unke har letter ki definition ho gayi.

9. Fraction $P$ (parallelizable portion)

Picture. 1 ki length wali ek bar ko do pieces mein kato: $P$ length ka red piece share ho sakta hai; $1 - P$ length ka black piece nahi ho sakta.

Har case matter karta hai.

Agar $P = 0$ (kuch bhi parallel nahi): $S (N) = \frac{1}{1} = 1$ — kabhi speedup nahi.
Agar $P = 1$ (fully parallel): $S (N) = \frac{1}{0 + 1/ N} = N$ — perfect, SIMD se match karta hai.
Jab $N \to \infty$ : $S \to \frac{1}{1 - P}$ — ek hard ceiling jo serial part set karta hai. Infinite cores ke saath bhi ise beat nahi kar sakte.

Topic ko iske kyun zaroorat hai. Yeh MIMD par honest reality-check hai. $P$ ke bina, tum galat sochte ki "zyada cores = proportionally faster" hamesha hoga.

Prerequisite map

Equipment checklist

Khud ko test karo — right side dhako aur reveal karne se pehle jawab do.

Ek instruction kya hai ek sentence mein?

Ek chhota sa command jo machine perform kar sakti hai, jaise ADD ya LOAD.

Stream kya hota hai?

Cheezein (instructions ya data) ka ek ordered sequence jo ek ke baad ek time ke saath flow karta hai.

S aur M letters ka kya matlab hai?

S = Single (exactly ek stream), M = Multiple (ek se zyada streams ek saath).

Flynn name ke kaunse do letters instruction axis hain?

Pehle do (jaise SISD / SIMD mein "SI").

Control Unit (CU) kya karta hai versus Processing Unit (PU)?

CU instructions issue karta hai (boss); PU actually data par operation karta hai (haath).

"Broadcast in lockstep" ka matlab kya hai?

Ek CU same instruction ko kaafi PUs ko bhejta hai, aur woh sab ek hi clock cycle mein execute karte hain.

Do operations ek saath kab chal sakte hain?

Jab woh independent hon — kisi ko doosre ka result nahi chahiye.

T

kya represent karta hai?

Ek operation mein laga time (ek clock ka kaam).

Speedup kya hai, ek formula ki tarah?

Speedup = (serial time) / (parallel time) = kitna zyada fast hai.

Amdahl's Law mein

P

ka kya matlab hai, aur

1 - P

kya hai?

P

= program ka woh fraction jo parallelize ho sakta hai;

1 - P

= serial fraction jo ek core par atka rehta hai.

Jab

N \to \infty

, Amdahl's Law kya approach karta hai?

\frac{1}{1 - P}

— serial fraction se set hone wali ek hard ceiling.