T27: a number format of our own
You will learn
How three trits give more levels than a 4-bit float, and what that costs in plain bits.
A 4-bit float such as E2M1, the element of NVFP4 and MXFP4, has 16 codes, and two of them are zero. Three balanced trits have 3 x 3 x 3 = 27 states. T27 is our format that uses all of them: 27 levels placed where a trained network's weights actually fall, and one shared scale per block of weights. On ternary storage that is more levels in the same room. Packed into plain binary bits it is larger, not smaller, and the widget shows both counts.
Try it
Move the weight across the range and find where E2M1 rounds worse than T27; then read the storage table in bits.
All lessons
Module 1 · The chip
What an FPGA is, which chip we use, and how its pins meet the board.
Module 2 · Numbers in hardware
Bits, trits and number formats, and what arithmetic costs in logic.
Module 3 · Your t27 program
Write a spec, test it, and see why compiling is not the same as being right.
Module 4 · Inside t27c
How the compiler reads a spec and what it writes, including the native t27b.
Module 5 · From spec to hardware
The Verilog t27c writes, the cells it becomes, and what one LUT does.
Module 6 · Reading synthesis
What yosys reports about your design, and which warnings matter.
Module 7 · Place, route, timing
Where the cells land on the die, and whether the clock is met.
Module 8 · The bitstream
How a routed design becomes the bits the chip loads, with no Vivado.
Module 9 · On the board
Ask the chip who it is, load the bits, and check them.
Module 10 · Lab: our own research
A number format of our own, an honest scoreboard, and a model's tables multiplied on the board.