Re:Reciprocal Approximation with 1 Subtraction
by mbitsnbites on Thursday January 02, 2025 @02:22AM
(#42572468)
The big cores do. They essentially pump division through something like an FMA (fused multiply-add) unit, possibly the same unit that is used for multiplication and addition. That's for the Newton-Raphson steps, or Goldschmidt steps.
In hardware it's much easier to do a LUT-based approximation for the initial estimate rather than the subtraction trick, though.
It's common for CPUs to give 6-8 accurate bits in the approximation. x86 gives 13 accurate bits. Back in 1975, the Cray 1 gave 30 (!) accurate bits in the first approximation, and it didn't even have a division instruction (everything about that machine was big and fast).
In hardware it's much easier to do a LUT-based approximation for the initial estimate rather than the subtraction trick, though.
It's common for CPUs to give 6-8 accurate bits in the approximation. x86 gives 13 accurate bits. Back in 1975, the Cray 1 gave 30 (!) accurate bits in the first approximation, and it didn't even have a division instruction (everything about that machine was big and fast).