You would replace

if ( $row =~ $re )
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with

while ( $row =~ /$re/g )
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Certain flags control how a pattern is parsed or compiled. Since these are associated with the pattern, they can be provided to qr// and (?:).

These are: msixpodualn.

(It's surprising to find "p" on this list. It's weird. But "p" doesn't do anything since 5.20, so we can pretend it's not there.)

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Certain flag affects how the operator itself works. These are provided to the operator itself.

For m//, these are: gc.

For s///, these are: gcer.

msixpodualn can also be provided to these, but they won't be recursively applied to embedded compiled patterns. (The same goes for qr//.)

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Therefore, you want to add "g" to the match operator implied by $row =~ $re, and it would result in using $row =~ /$re/g.

Note that /$re/ doesn't cause the pattern to be stringified and re-compiled as it would be if it was interpolated into a larger pattern.