Description:
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The documentation for mb_detect_encoding() fails to note that FALSE is a possible return value from the function if no encoding can be detected. This can be demonstrated trivially with the reproduce code below, and is obviously intended behaviour, looking at ext/mbstring/mbstring.c and ext/mbstring/libmbfl/mbfl/mbfilter.c.

My suggestion would be to replace the Return Values text with the following:

"Returns the detected character encoding, or FALSE if the encoding cannot be detected from the given string."

Reproduce code:
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<?php
// On the off chance you want to see this in action, any high-bit
// character in the input should return false in strict mode when
// ASCII is the only possible encoding.
var_dump(mb_detect_encoding("f??", "ASCII", true));

Expected result:
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bool(false)

Actual result:
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bool(false)