Referencing function value inside CASE..WHEN

Hi,

In the following statement, does the custom function get executed twice?

SELECT
  MY_FUNCTION(...),
  CASE WHEN MY_FUNCTION(...) = '...' THEN '...' ELSE '...' END
...
...


If so, is there a way I can make it execute once?  I tried this but it gave me a "Column my_function does not exist" error.

SELECT
  MY_FUNCTION(...) AS my_function,
  CASE WHEN my_function = '...' THEN '...' ELSE '...' END
...
...


Thank you in advance.