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AFMT_S24_NE is not a new sample format but just a convenience macro that is defined ad AFMT_S24_LE or AFMT_S24_BE depending on the endianess of the processor. It always maps to the native endianess of the system.
This format uses 32 bit integers (int) to store samples. However the permitted value range is limited to -16777216 and 16777215.
AFMT_S24_NE is totally unsuitable to be used as a file or transport format of audio data. It must only be used for samples generated or used locally in the application. AFMT_S24_LE is the recommended external sample format for 24 bit audio data because it's the industry standard.