Re: Short Vectors Versus Long Vectors

On 4/23/2024 7:34 PM, MitchAlsup1 wrote:

Lawrence D'Oliveiro wrote:
 

On Tue, 23 Apr 2024 18:36:49 -0500, BGB wrote:

 

DIV:
Didn't bother with this.
Typically faked using multiply-by-reciprocal and taking the high result.

 

Another Cray-ism! ;)

 Not IEEE 754 legal.

The multiply and take high result:
   This is for Packed Integer SIMD.
For Packed-Float SIMD:
   Multiply by reciprocal.
There is an instruction to calculate an approximate reciprocal (say, for dividing two FP-SIMD vectors), at which a person can use Newton-Raphson to either get a more accurate version, or use it directly (possibly using N-R to fix up the result of the division).
For some use-cases with Binary16, directly using the approximate version may be "good enough". Algorithm for Binary16 being, roughly: 0x7800-Val.
If N-R is used, there is often some wonk needed with the first stage, since as the values often aren't close enough for N-R to reliably converge if used directly (for whatever reason this may happen; it seems one needs to be fairly close to the true reciprocal for N-R to be reliable).
But, for some algorithms, if one only needs "throwing darts at a dartboard" levels of accuracy, the N-R can be skipped.
Note that the default case (if one just divides two FP-SIMD vectors in C) will be handled using a runtime call (which will use N-R to find the vector reciprocal and then multiply by it); so faster cases would require either an inline ASM blob or an intrinsic.