Processing-in-memory (PIM): Foundations — Hinglish deep dive

6.5.5 · D1 · Hardware › Advanced & Emerging Architectures › Processing-in-memory (PIM)

Isse pehle ki tum Processing-in-memory (PIM) enjoy kar sako, tumhe usmein aane wale har word aur symbol ko samajhna hoga. Ye page har ek cheez ko zero se build karta hai — pehle plain words, phir ek picture, phir kyun ye topic uski zaroorat hai. Upar se neeche padho; har block sirf upar wale blocks par rely karta hai.

1. Numbers kahan rehte hain aur kahan use hote hain

Ek table par do boxes socho jinhe ek lambi wire se joda gaya hai.

Figure s01 — processor (left, yellow) aur memory (right, blue) do alag boxes ki tarah draw kiye gaye hain jo ek patli "bus" wire se jude hain; pink double-arrow us slow traffic path ko mark karta hai jise har number cross karna padta hai.

2. Bus aur uski bandwidth $B$

3. Kaam count karna: $N$ , $C$ , aur rate $R$

Figure s02 — do stacked time-bars. Upar (data-hungry job): blue move-term $N / B$ dominate karta hai jabki pink think-term $C / R$ ek sliver hai. Neeche (compute-heavy job): pink $C / R$ dominate karta hai. Picture dikhati hai ki kaunsa term jeeeta hai wahi matter karta hai.

4. Arithmetic intensity $I = C / N$

Low $I$ → bandwidth-bound → wire limit karta hai → PIM bahut help karta hai.
High $I$ → compute-bound → chef limit karta hai → PIM thoda help karta hai.

Yeh single ratio woh "80/20 test" hai jo parent note pehle run karta hai. Yeh Roofline Model ko bhi feed karta hai, jo performance ko $I$ ke against plot karta hai.

5. Banks aur internal parallelism: $k$ , $B_{bank}$ , $B_{in t}$

Figure s03 — $k$ banks (blue, left) har ek ek wide internal flow (yellow arrows) ek merge point mein feed karte hain, jo phir ek single thin pink "bus $B$ " arrow par squeeze hota hai. Visually: huge internal bandwidth $B_{in t}$ narrow external bottleneck $B$ se hokar funnel hota hai.

6. Energy: $E_{o p}$ vs $E_{m o v e}$

7. "Memory use karne" (PUM) ke liye physics tools

Parent ka crossbar example electricity ke do laws borrow karta hai. Dono ko yahan samajhna zaroori hai.

Figure s04 — ek crossbar grid. Blue vertical wires input voltages $V_{1}, V_{2}, V_{3}$ carry karte hain; crosspoints par yellow dots stored conductances $G_{ij}$ hain; har horizontal wire Kirchhoff's law se cell currents sum karta hai aur ek row current $I_{i}$ (pink arrows) emit karta hai — ek dot product per row, poora matrix–vector multiply ek analog step mein.

Processor (math karta hai) aur memory (bits store karta hai), bus se join kiye hue (slow wire).

Bandwidth

B

kya measure karta hai, aur kaunsi everyday picture fit hoti hai?

Bytes per second jo bus carry kar sakti hai — ek pipe ki thickness, paani ki speed nahi.

Classic time equation likho aur batao har term ka kya matlab hai.

T_{v N} = N / B + C / R

: move-time (bytes ÷ bandwidth) plus think-time (ops ÷ rate).

Arithmetic intensity define karo aur batao low vs high

I

kya imply karta hai.

I = C / N

ops per byte; low

I

= bandwidth-bound (PIM ke liye great), high

I

= compute-bound (PIM kam help karta hai).

Bank kya hai, aur kyun

B_{in t} = k \cdot B_{bank}

B

se better hai?

Bank ek independent DRAM sub-grid hai; bahut saare parallel mein run karte hain, toh total internal bandwidth single external bus se kaafi zyaada hoti hai.

E_{o p}

aur

E_{m o v e}

ke units kya hain, aur woh compare kaise karte hain?

E_{o p}

joules per op mein (pJ order ka),

E_{m o v e}

joules per bit/access mein;

E_{m o v e} \approx 100 - 1000 \times E_{o p}

, toh movement energy dominate karta hai.

Ohm's law aur Kirchhoff's current law ek-ek line mein batao.

Ohm:

I = G V

(current = conductance × voltage). KCL: shared wire par currents add up hote hain.

Symbol

\sum_{j} x_{j}

ka kya matlab hai?

Saare

x_{j}

ko add karo jab index

j

apni values par run kare — ek compact "+ + +" chain.

Woh do laws mil kar matrix–vector multiply kaise bante hain?

Ohm har product

G_{ij} V_{j}

deta hai; KCL unhe per row sum karta hai ek dot product mein, toh

I = G V

ek analog step mein.

Amdahl's Law likho aur uski ceiling batao.

S_{t o t a l} = 1/ ((1 - p) + p / S)

; jab

S \to \infty

toh yeh

1/ (1 - p)

par saturate hota hai, toh un-sped fraction poore speedup ko cap kar deta hai.

Foundations — Processing-in-memory (PIM)

1. Numbers kahan rehte hain aur kahan use hote hain

2. Bus aur uski bandwidth $B$

3. Kaam count karna: $N$ , $C$ , aur rate $R$

4. Arithmetic intensity $I = C / N$

5. Banks aur internal parallelism: $k$ , $B_{bank}$ , $B_{in t}$

6. Energy: $E_{o p}$ vs $E_{m o v e}$

7. "Memory use karne" (PUM) ke liye physics tools

8. Amdahl's Law — reality check

Prerequisite map

Equipment checklist