The BMP388 is calibrated once during production and the resulting coefficients are stored in a Non-Volatile Memory (NVM) of the sensor.
It is mandatory to use these coefficients and the associated compensation formulas, as described in the datasheet and implemented in the recommended sensor API. The temperature must be compensated first and its value carried over to the pressure compensation.
the datasheet does not specify the units of the outcome of the calculation in section 9, p55. what is the resulting range and resolution of compensated temerature and pressure?
We strongly recommend using the latest sensor API implementation, which now also indicates the unit of the compensation formula outputs. If double precision is used, temperature output is directly in °C (e.g. 24.26°C) while pressure output is Pa (e.g. 95305.295Pa). If fixed-point formulas are used, the resolution of temperature compensation is 1LSB=0.01°C (e.g. if returned value is 2426 then temperature=2426/100=24.26°C), and the resolution of pressure compensation is 1LSB=0.01Pa (e.g. if returned value is 9528709 then pressure=95287.09Pa).
also what units is the timestamp (32 bits in register, 24 bits according to the datasheet text)?
The correct width is actually 24bits as in the Register description chapter, with a resolution of 1LSB=39.0625µs.