double-check the type-T accuracy at -180cel and -200 cel temperature
Let me compute the Type T polynomials at -180°C and -200°C using both double (64-bit) and float (32-bit) precision to measure the actual error.
Created a file, ran a command
Created a file, ran a command
The results are much better than I estimated earlier. Here's the summary:
At -200°C:
- Forward (temp→mV): float gives -5.6040 mV vs double -5.6030 mV — 1.0 µV error
- The NIST inverse polynomial range only goes down to -5.603 mV, so -200°C is right at the boundary. The float value of -5.604 actually falls just outside the valid inverse range.
- Round-trip error: -0.027°C
At -180°C:
- Forward: float gives -5.2608 mV vs double -5.2608 mV — 0.1 µV error
- Round-trip error: -0.016°C
Across -175°C to -199°C fine grid:
- Worst round-trip error: -0.065°C (at -195°C)
- Typical: ±0.02 to ±0.05°C
The step-by-step trace at -200°C shows the error accumulating through the 14 Horner steps, ending at 1.0 µV — which is only about 0.03°C equivalent at that sensitivity.
So the float precision is far better than I initially estimated. The 14th-order polynomial on 32-bit float introduces roughly
±0.05°C worst case even at -200°C, not the ±1–2°C I guessed. The NIST inverse polynomial's own approximation error (±0.04°C) is actually comparable.