Op-amp as an inverting amplifier with diode on OUT, circuit close to precision rectifier
This is a full-wave precision rectifier. When a negative voltage is applied to the input it acts as an inverting amplifier, so Vout = -Vin. When a positive voltage is applied, the op-amp rails near the negative supply rail and the positive voltage finds it's way to the output, Vout = +Vin (if loading is minimal on the output).
The op-amp output has to slew all the way from near the negative rail to +0.6V at the negative-going zero crossings so it's not going to be great at high frequency. The capacitor also doesn't help with high frequency response but it may help with stability. Op-amps which are railed don't necessarily come out of saturation, and start slewing, as quickly as one might hope- and any measure of that is often omitted from the datasheet information, particularly if it is bad.
Also, some op-amps behave differently in this configuration because of protection diodes between the inverting and non-inverting inputs, so current flows through R31.
Edit: See below for simulation of this working.



simulate this circuit &ndash; Schematic created using CircuitLab