Change system options in package

Question

I use Mathematica mostly for numerical calculations, and sometimes the performance of numerical calculations can be greatly improved if the high-precision arithmetic can be switched off by

Developer`SetSystemOptions["CatchMachineUnderflow" -> False]

As suggested in this post, when one want to switch off the high-precision arithmetic, one can usually do something like

With[{cmuopt = SystemOptions["CatchMachineUnderflow"]},
 Internal`WithLocalSettings[
  SetSystemOptions["CatchMachineUnderflow" -> False],
  (* put your own code here; for example: *)
  SetSystemOptions[cmuopt]
 ]
]

Consider now I have a package that I want to run at the machine precision. This is fine for one function, but for a package containing many functions, adding those pieces of code to each function would be a pain. So I'm wondering whether there are ways to switch off the high precision at package wise, for all the functions in the package. Or in other words, can we change the "CatchMachineUnderflow" settings by context?

Answer 1

If you're willing to overload SetDelayed (and/or Set) inside the package for the sake of defining functions inside the package, you could automatically add a wrapper offCMU that turns off "CatchMachineUnderflow" if it is on. This is quite like what Albert Retey recommended in a comment. The main difference is that SetDelayed is changed to do the wrapping. A minor difference is that a Condition is added to the wrapper so that the underflow option is turned off only once.

Here's the idea applied to a dummy package:

BeginPackage["foo`"];

minsquared::usage = "minsquared[] yields 0. if underflow";
expmax::usage = "expmax[] yields 0. if underflow";

Begin["`Private`"];

ClearAll[offCMU];
SetAttributes[offCMU, HoldAll];
offCMU[expr_] := 
  With[{cmuopt = SystemOptions["CatchMachineUnderflow"]}, 
   Internal`WithLocalSettings[
     SetSystemOptions["CatchMachineUnderflow" -> False],
     expr,
     SetSystemOptions[cmuopt]
     ] /; ("CatchMachineUnderflow" /. cmuopt)];
offCMU[expr_] := expr;  (* CMU already off *)

Internal`InheritedBlock[{SetDelayed},

  Unprotect@SetDelayed;
  SetDelayed[lhs_, rhs_] /; ! TrueQ[$in] := Block[{$in = True},
    SetDelayed[lhs, offCMU@rhs]
    ];

  minsquared[] := $MinMachineNumber^2;
  expmax[] := Exp[-$MaxMachineNumber];

  ];

End[ ];

EndPackage[ ]

Examples:

minsquared[]
$MinMachineNumber^2

(*
  0.
  4.95095367581213*10^-616
*)

expmax[]
Exp[-$MaxMachineNumber]

(*  0.  *)

General::unfl: Underflow occurred in computation. >>

(*  Underflow[]  *)