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I don't think Softasilk is self-rising. I think it's just plain cake flour and you still need to add your own baking soda/baking powder.
No. It is not the same.
Softasilk is not self-rising. To make "self-rising" cake flour, add 1 1/2 teaspoons of baking powder and 1/2 teaspoon of salt for every cup of flour.
It is usually best to use the right flour for the right purpose. "All purpose flour" (of which self-rising is a type of AP flour -- with rising agents and salt added as plainhomecook notes) is half-way between the high protein count of a "bread flour" and the low protein count of a "cake flour". Adding baking soda and salt to cake flour will yield "self-rising cake flour" (quite a hybrid if there ever was one!) which is still not likely the best choice for whatever you are making. For example, if you are looking for self-rising flour to make biscuits, chances are that a modified cake flour just won't give you the consistency you expect (including that they will likely be flatter).
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