Test with an external USB 24-bit soundcard, and software calibrated to the sound card inputs:
Test conditions:
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test signal: 984.350Hz, 48KHz-16 bit wav file, 50% FS, 1.01Vrms measured at the DAC+ output
source: RuneAudio, HW volume control (or disabled) at 100, HiFiBerry DAC+ I2S
input: SB X-Fi HD, ~12k-ohm impedance, 96K-24bit resolution
software: Daquarta for Windows v9.10, calibrated to sound card inputs at 1V rms
Disclaimer: Everything was adjusted to give the best results. Distortion and noise would be higher in normal use, with normal recorded music, and at normal listening volumes.
@Rikardo: Same interconnect cables used for this test, except HDMI cable NOT plugged, and a shorter better quality RCA cable (still under $10...

)
@[deleted]: If you keep noise sources away from your Pi, and use your battery bank with no connections to the mains except your power amp, you should be able to come close to the same low noise and THD.