Suspicious definition of erlang distribution in Verilog-2005 spec

Question

The $dist_erlang function in Verilog-2005 takes an argument called mean. Some information about the mean argument of $dist_erlang is found in this paragraph from section 17.9.2 of the spec:

They also provide C code for how simulators ought to internally implement $dist_erlang (from page 320 of the spec). This code implements a formula that can be found on Wikipedia for sampling an Erlang distribution.

erlangian(seed, k, mean)
long *seed, k, mean;
{
    double x, log(), a, b;
    long i;
    x = 1.0;
    for(i = 1; i <= k; i++)
    {
        x = x * uniform(seed, 0, 1);
    }
    a = (double)mean;
    b = (double)k;
    x = -a * log(x)/b;
    return(x);
}

I'm no expert on statistics, but I'm pretty sure that the multiplication by mean / a at the very end of this function is not gonna result in a distribution whose mean is mean. This would imply that every Erlang distribution sampled from using the equation on Wikipedia has a mean of 1, which definitely isn't true.

Am I missing something here, or is this an honest to goodness error in the Verilog spec?

This question may get better answers on math.SE instead of here. I'm not familiar with the Erlang distribution, at least. — Hearth, Jul 16 '20 at 17:37
Thanks for the advice! Anyways, after staring at it for another 10 minutes, I found my error, so I'm going to delete this question. — John M, Jul 16 '20 at 17:40
Before you do that, consider a self-answer. It may be useful to others. — Hearth, Jul 16 '20 at 17:40
BTW the Verilog-2005 LRM is obsolete. Please use the [IEEE 1800-2017 SystemVerilog LRM](https://ieeexplore.ieee.org/document/8299595). This is now section 20.15.2 — dave_59, Jul 16 '20 at 17:57
AFAIK, the tools I'm using (yosys) don't support SystemVerilog. That's why I'm looking at the 2005 document. — John M, Jul 16 '20 at 18:04
OK, but do check the latest spec for any corrections that might have been made, next time. — dave_59, Jul 16 '20 at 18:58

score 1 · Accepted Answer · answered Jul 16 '20 at 17:48

I was confused about this because I was confused by the parameter naming in the Verilog spec and I made a basic algebra error.

The mean can be given by k / lambda. The sampling formula requires 1 / lambda, which is the same as (k / lambda) / k.

Taking mean as an argument instead of lambda might have been considered more user friendly.

Suspicious definition of erlang distribution in Verilog-2005 spec

1 Answers1