stillwater-sc / universal / 37928965054

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feat(utility): precision-vs-magnitude profiles and the DSP type comparison (#1650)

* feat(utility): precision-vs-magnitude profiles and the DSP type comparison

precision_profile_of<T> computes Gustafson's decimals of accuracy,
-log10(ulp / (2|x|)), and the fraction bits log2(|x| / ulp), at every
magnitude of any Universal type or native float or integer type.
- Types of up to 16 bits are exhaustive: every encoding is decoded with
  setbits and the positive values are sorted, so the next encoding is
  the next value whatever the encoding order (lns's ++ is not monotone
  across its exponent sign).
- Wider types are sampled per binade, with the spacing from ++ or
  nextafter, or from below where ++ does not land above x.
- write_precision_csv writes one CSV per type, and
  print_precision_table gives the text view for terminals and CI.
- Only the worst case is computed: averaged over an ulp, the curve is
  shifted up by exactly log10(2) and has the same shape.

applications/mixed-precision/dsp/precision_profiles.cpp compares int,
fixed-point, float, lns and bposit at 16 and 32 bits for DSP and FFT
pipelines: the signal band [0.5, 1), small coefficients at 2^-15, and
FFT growth to 2^10. With an output directory it also writes the CSVs.
- The DSP-sized bposit<16,5,2> (range 2^+-20) beats fp16 in the band,
  3.61 against 3.31 decimals, never has fewer than 8 fraction bits, and
  covers 4096-point FFT growth.
- At 32 bits bposit<32,5,2> beats float in the band, 8.43 against 7.22,
  with a 24-bit floor.
- The standard bposit<16,6,5> trails fp16 in the band.
- Q15 is the most precise in the band but has no headroom and one bit
  left at 2^-15.
- bposit<16,3,1> spans only 2^+-6.

tools/notebooks/plot_precision_profiles.py overlays the CSVs (matplotlib).
--dsp shades the signal band, marks FFT growth and adds an SQNR axis.

Tests (static/utility/test_precision_profile.cpp):
- exhaustive profiles of six 8-bit types against an independent decode;
- closed forms... (continued)

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