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The manual says under 'package.loaded':

    When you require a module modname and package.loaded[modname] is
not false, require simply returns the value stored there.

This formulation is precise and correct.

Under 'require', it says:

   The function starts by looking into the package.loaded table to
determine whether modname is already loaded.

This formulation is less precise but not incorrect.

And under luaL_requiref:

    "If modname is not already present in package.loaded, calls
function openf .."

This formulation is wrong. If modname is present but false, openf is not called.