Re: [PATCH] Improve hypot performance

[Paul Zimmermann <Paul.Zimmermann@inria.fr>]

       Dear Wilco,

> Improve hypot performance significantly by using fma when available. The fma
> version has twice the throughput of the previous version and 70% of the latency.
> The non-fma version has 30% higher throughput and 10% higher latency.

I cannot reproduce these figures. On a x86_64 for the fma version I get almost
identical throughput, and only 88% of the previous latency. For the non-fma
version I get 24% smaller throughput (31% larger *reciprocal* throughput),
and 51% higher latency.

With fma:

before:
  "hypot": {
   "workload-random": {
    "duration": 3.31399e+09,
    "iterations": 7.4e+07,
    "reciprocal-throughput": 32.4478,
    "latency": 57.1194,
    "max-throughput": 3.08188e+07,
    "min-throughput": 1.75072e+07
   }

with patch:
  "hypot": {
   "workload-random": {
    "duration": 3.33618e+09,
    "iterations": 8.2e+07,
    "reciprocal-throughput": 31.205,
    "latency": 50.1653,
    "max-throughput": 3.20462e+07,
    "min-throughput": 1.99341e+07
   }

Without fma:

before:
  "hypot": {
   "workload-random": {
    "duration": 3.34724e+09,
    "iterations": 7.4e+07,
    "reciprocal-throughput": 32.9285,
    "latency": 57.5374,
    "max-throughput": 3.03689e+07,
    "min-throughput": 1.738e+07
   }

with patch:
  "hypot": {
   "workload-random": {
    "duration": 3.38571e+09,
    "iterations": 5.2e+07,
    "reciprocal-throughput": 43.1054,
    "latency": 87.1141,
    "max-throughput": 2.31989e+07,
    "min-throughput": 1.14792e+07
   }

> Max ULP error is 0.949 with fma and 0.792 without fma.

I confirm this. More precisely here are the largest errors I find with
corresponding inputs:

Without fma:
hypot 0x0.603e52daf0bfdp-1022,-0x0.a622d0a9a433bp-1022 0.791664

With fma:
hypot -0x0.5a22c27a3893p-1022,0x0.9cfea180c00dap-1022 0.948811

(compared to 0.986776 for the current version, with inputs
-0x0.5a934b7eac967p-1022,-0x0.b5265a7e06b82p-1022).

Best regards,
Paul