Yes the volume processing in the DS is lossless - all bits of the input are kept no matter what the volume is set to and have the correct theoretical effect on the output level. I don’t know what their processing is, but if the DAC ultimately uses a DAC chip then their processing can’t be better numerically than the DS - even if you only lower the level by one bit then the bottom bit can’t be kept. But let me be clear - under any reasonable circumstances I know you can’t measure this loss and I seriously doubt that anyone could hear this loss. I’m not sure what any algorithm could add compared to just doing the volume correctly with a full digital multiply. If hardware is involved they may well have a reasonable cost good volume for those systems that can’t do a full digital multiply with their own hardware.
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