Another method is to build an analog logarithmic amplifier to measure the voltage across a shunt resistor.
This is not easy to build, but it is straightforward to calibrate the indicated voltage output as a function of input voltage/current.
The ancient (ca. 1970) -hp- 7562A and 7563A logarithmic units can be found at surplus sites: the 7562A includes a true-RMS converter, and is capable of AC or DC input. The 7563A is DC only.
The 7563A has a dynamic range of 110 dB (3.2 x 105 V/V), and a rise time of 2 ms (input < 1 mV) decreasing to 40 us (input > 10 mV) and 2 us (input > 1 V).
It has a single input range, but you need to select positive or negative input voltage.