legacy units and rounding constants

[cattabiani]

I report a cvf issue here as it is useful to decide how to tackle this problem:

In hippocampus/mod/cagk.mod exposes a new, related, possible missmatch between nmodl and mod2c (or neuron) behaviors.

In that file we find:

UNITS {
	FARADAY = (faraday)  (kilocoulombs)
	R = 8.313424 (joule/degC)
}

Faraday is taken from the internal library while R is set as custom value. If we use legacy units, in mod2c (or neuron) we get in the .c file:

#define FARADAY _nrnunit_FARADAY[_nrnunit_use_legacy_]
static double _nrnunit_FARADAY[2] = {0x1.81f0fae775426p+6, 96.4853}; /* 96.4853321233100303 */
 static double R = 8.313424;

Let's notice that Faraday (96.4853) has 6 digits while R (8.313424) has 7 digits. This is due to the fact that faraday is hard-coded as exactly that number (96.4853) in legacy units and R is kept as a string and copy-pasted in the .c file.

Meanwhile, in nmodl, doubles are stored as doubles and printed using this line (from codegen_c_visitor):

std::string format_string = "static const double {} = {:g};";

In the fmt documentation, for g we get:

'g'	
General format. For a given precision p >= 1, this rounds the number to p significant digits and then formats the result in either fixed-point format or in scientific notation, depending on its magnitude.

As last, note that the standard legacy faraday constant is taken from this value:

static const double FARADAY = 96.4853321233100184

Now, let's check what happens for FARADAY in nmodl:

• the full value is loaded from the library (96.4853321233100184)
• static const double {} = {:g} chops it to 6 digits (default value)
• we get the correct legacy value of 96.4853

For the custom R the process is similar:

• the value is loaded from the mod file (8.313424)
• {quote}static const double {} = {:g}{quote} chops it to 6 digits (default value)
• we get the incorrect legacy value of 8.31342

Unfortunately, this means that we cannot simply tamper with fmt precision like:

std::string format_string = "static const double {} = {:.18g};";

because faraday and R require different precisions: either we chop too much R or we chop too little faraday.

Storing R as a string would help but we need to find a way to chop faraday if legacy units is on