When dealing with a code that produces too small numbers (in a complicated way) like

0.33691 4.015757066049965*10^-330

I get the following warning

General::munfl: 0.00530878/1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 is too small to represent as a normalized machine number; precision may be lost.

Is there any tricky way to ensure that too small resulting numbers in my function are well handled by MMA (12.1)?

Note that I had a look at General::munfl and tried some proposed ideas (e.g SetPrecision, Rationalize,..), but I didn't get any solution.

  • 2
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    – bbgodfrey
    Commented Jul 10, 2021 at 0:17
  • $\begingroup$ @bbgodfrey Thank you. Done! $\endgroup$
    – S. Euler
    Commented Jul 10, 2021 at 6:00
  • $\begingroup$ Do you have any idea on my question? $\endgroup$
    – S. Euler
    Commented Jul 10, 2021 at 14:45
  • 3
    $\begingroup$ SetPrecision[ 0.33691 4.015757066049965*10^-300, $MachinePrecision] 10^-30 works, but to say more I would need to know how you generated this number and what you are trying to accomplish. $\endgroup$
    – bbgodfrey
    Commented Jul 10, 2021 at 15:24
  • 2
    $\begingroup$ I recommend that you add to your question a simple version of your code that still produces an underflow. Then, perhaps readers can provide useful answers. In the meantime, consider x = SetPrecision[1.1 10^-10, $MachinePrecision] followed by x^400. The point is, you need to set the Precision appropriately before the underflow occurs, not after. $\endgroup$
    – bbgodfrey
    Commented Jul 10, 2021 at 16:33


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