PYTHON · NUMPY

The bill is data movement, not arithmetic

Build the energy ledger of a small workload and find out which side it is actually on. This is the fact that decides what a cheaper computer must look like.

01Challenge

Model a thousand multiply-accumulates, vary how far the operands travel, and find the point where arithmetic stops mattering.

Predict firstIn a workload with no off-chip fetches at all, what share of the energy is the arithmetic?

02Model

Fetching a number from off-chip DRAM costs roughly a hundred picojoules. The multiply it feeds costs a fraction of one. So a machine that computes brilliantly and fetches carelessly is paying a hundred times over for the privilege. This is the memory wall, and it is why the serious escape routes all share one move: stop moving the data. Compute inside the memory, settle in place, or remove the multiply entirely.

03Guided practice

1. Build the ledger. Price a workload of 1,000 MACs where a fraction f of operands come from DRAM and the rest from on-chip SRAM.

2. Sweep f. Run it from 0% to 100% and print the share of energy spent on movement.

3. Find the crossover. Notice how little DRAM traffic it takes before movement owns the bill. That number is the design constraint.

04Feedback

PASS WHEN PASS when your sweep shows movement above 90% of the bill even at 0% DRAM, rising toward 99%+ as DRAM traffic grows.

If your run fails, check:

If arithmetic looks dominant, check your units: SRAM is 5e-12 J, not 5e-15.
The lesson is in the first row of the sweep. At zero DRAM traffic the arithmetic is still outweighed — that is the memory wall in one number.

05Retrieve & space

Roughly how many times the arithmetic does a DRAM fetch cost?
At 0% DRAM traffic, is arithmetic or movement the larger share?
Name one architectural move that reduces movement rather than arithmetic.

06Mastery & project

You can build an energy ledger for a workload and say which side of it any proposed optimisation actually touches.

Take any efficiency claim you have read this year and ask which side of this ledger it improves. Most improve the smaller side.

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PYTHON · NUMPY

The bill is data movement, not arithmetic

Price a workload honestly and watch the arithmetic stop mattering.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you