SetPrecision with Manipulate using variable number of controls

Question

I want to convert inputs from controls in Manipulate into exact numbers and have two kinds of inputs:

• parameters: there are a fixed number of these
• rates: the number of rates is controlled by the parameter n

To do this, I package the parameters into a list of rules and use SetPrecision to translate the inputs to exact numbers. But that approach doesn't see to work for rates.

You can see that I tried twice to set the precision of the rates:

1. With (rate[mode]=SetPrecision[#,Infinity])&
2. With SetPrecision[rate /@ Range[n],Infinity]

The figure shows that the rates -- the top line -- are not exact numbers. The parameter p is an exact number. How to get the rates to be exact?

``` 
With[{maxModes = 5},
  Manipulate[
    Manipulate[
        Evaluate[
           With[{rates = Thread[Rule[Range[n], SetPrecision[rate /@ Range[n],Infinity]]],
                 params = {p ->SetPrecision[pval, Infinity]}},
              Column[{rates,params}]]],
        Evaluate[
                 Sequence @@ (With[{mode = #},{{rate[mode], mode, Row[{"Rate ", mode}]},-10, 10,
                              Row[{Manipulator[##]," ", InputField[Dynamic[rate[mode],(rate[mode]=SetPrecision[#,Infinity])&],Appearance->"Frameless",BaseStyle->"Label"]}]&}] & /@ Range[n])]],

    {{n, 3, "Number of Modes"}, Range[maxModes], Control->SetterBar},
    {{pval, 1, "Parameter"}, -1, 1, Appearance->"Labeled"}]]

[![Precision of Rates vs Parameters][1]][1]


  [1]: https://i.stack.imgur.com/eN6Gn.png

Answer 1

Ah, I see at least part of the answer. Dynamic[rate[mode],(rate[mode]=SetPrecision[#,Infinity])&] Sets the precision of inputs to the InputField. Repeating that construction in the Manipulator sets the precision of the inputs via that control. I still do not understand why SetPrecision[rate /@ Range[n],Infinity] had no effect.