What is strange to me the phone with that app reports it's getting 1900mA when I use an old HTC charger capable of 1A (1000mA) @ 5V when using the OEM USB cable. Either that HTC charger's specs were grossly understated or the phone itself tries to sense electrical properties of the USB cable? Not sure if that last bit is even possible.
Anyone with knowledge on how the phone determines how much current to draw on a lower level? Kinda curious.
Also, there are sellers on eBay for the original S4 charging cable for something like $7, or same charging cable and 2A wall adapter for $10.
See for example:
http://www.ebay.com/itm/230980370756
The part number they list (ETA-U90JWE) is the same as my OEM charger, that can do 2A @ 5 V.