[dv,cip] Rewrite `_DV_MUBI_DIST to avoid warnings

[rswarbrick]

It turns out that randomising with a distribution like this

  if (0) {
    XYZ dist { [1:0] := 1; };
  }

generates a runtime warning from Xcelium (even though the distribution expression isn't actually used).

Fortunately, range endpoints can be general expressions, so we can do everything with ternary operators instead. We can also avoid repeating stuff if we define MIN / MAX macros.

This commit also fixes the weighting for true/false. Suppose we want to distribute with weights ZeroW, OneW, OtherW for 0, 1, other in a way that e.g. the fraction of ones is OneW / (ZeroW + OneW + OtherW).

The following would definitely be wrong:

 value dist { 0      := ZeroW,
              1      := OneW,
              [2:9] := OtherW };

Because there are eight "other" values, the fractions end up looking like OneW / (ZeroW + OneW + 8 * OtherW). Oops!

To make everything line up properly, we multiply by 8:

 value dist { 0      := 8 * ZeroW,
              1      := 8 * OneW,
              [2:9] := OtherW };

and will now have fractions like

 8 * OneW / (8 * ZeroW + 8 * OneW + 8 * OtherW
  =
 OneW / (ZeroW + OneW + OtherW)

Generalising to the macro, there are (MAX_ - 1) possible values (instead of 10), so we need to scale up by (MAX_ - 3).

[rswarbrick]

Dammit! Just realised that I had an off-by-one error in the commit message. Take 2 3...

[marnovandermaas]

I think it's not quite right, so I've made a suggestion.

[marnovandermaas]

Suggested change

	VAR_ dist { \
	TRUE_ := (T_WEIGHT_) * ((MAX_) - 3), \
	FALSE_ := (F_WEIGHT_) * ((MAX_) - 3), \
	[0 : `DV_TERNARY_MIN(TRUE_, FALSE_)-1] := (OTHER_WEIGHT_), \
	[(`DV_TERNARY_MIN(TRUE_, FALSE_)+1) : \
	(`DV_TERNARY_MAX(TRUE_, FALSE_)-1)] := (OTHER_WEIGHT_), \
	[(`DV_TERNARY_MAX(TRUE_, FALSE_)+1):(MAX_)] := (OTHER_WEIGHT_) \
	};
	VAR_ dist { \
	TRUE_ :/ T_WEIGHT_, \
	FALSE_ :/ F_WEIGHT_, \
	[0 : `DV_TERNARY_MIN(TRUE_, FALSE_)-1] :/ (OTHER_WEIGHT_) * (`DV_TERNARY_MIN(TRUE_, FALSE_) / MAX_), \
	[(`DV_TERNARY_MIN(TRUE_, FALSE_)+1) : \
	(`DV_TERNARY_MAX(TRUE_, FALSE_)-1)] :/ (OTHER_WEIGHT_) / ((MAX_ - 2) / (2*MAX_)), \
	[(`DV_TERNARY_MAX(TRUE_, FALSE_)+1):(MAX_)] :/ (OTHER_WEIGHT_) / ((MAX_-`DV_TERNARY_MAX(TRUE_, FALSE_)) / MAX_) \
	};

I think it may be simpler to use the proportional distribution :/ instead of the weighted distribution. Also I think there is an error with the other weight, shouldn't this be split among the three other values? I've tried to add a proportion to the expression, although admittedly the code is a bit ugly.

[rswarbrick]

Ahah: that was the whole reason for Matutem's original change. The problem is that I might have e.g. MAX=9, True=0, False=2. Then I'd end up with something like

var dist {
  0      :/ T_WEIGHT,
  2      :/ F_WEIGHT,
  [1:1] :/ OTHER_WEIGHT,
  [3:9] :/ OTHER_WEIGHT

This doesn't balance out properly (factor of two because there are two "other" ranges). But the "other" values also are biased because the ranges are different lengths. I think you have to use := to solve the latter problem.

[rswarbrick]

Sorry: I hadn't read your suggestion properly. Is your proposal to weight the ranges by their lengths? In which case, I guess it would work, except for the fact that I think the weights have to be integral. I think the end result is probably a bit more complicated than what we've got (possibly why Matute did it that way).