Numerics

These topics check that the arithmetic gives the answer you expect:

• exactly how the PE rounds, and how to write a reference that matches it;
• shifts, bit patterns and integers wider than 16 bits;
• the hardware random-number generators.

Each topic is a complete program, and each opens with the lessons and topics it needs. Read a topic once you have read everything on its Needs line.

Topic	What it teaches
Precision: how the PE rounds, and references that match	HP, EP and SP, fused multiply-add, the dot-product unit, math fast, and an exact reference
Bits and wide integers	Shifts, precedence and sign extension, Keccak-f[400] on 16-bit lanes, and 64-bit arithmetic in 16-bit limbs
Hardware random numbers	The four generators, seeding, choosing a recurrence, and the instruction spacing that writes to the generator registers need