stillwater-sc / universal / 23282562175

85%

master: 84%

Build Type

push

github

Committed by web-flow

Commit Message

feat(takum): implement linear takum arithmetic per arXiv:2404.18603 (#593)

* feat(takum): implement linear takum arithmetic per arXiv:2404.18603

Rewrite the takum skeleton to implement the linear takum number system
specification by Hunhold (2024). The encoding uses two's complement
storage with monotonic ordering, enabling direct signed integer
comparison.

Key changes:
- Two's complement encoding: zero=0x00, NaR=0x80, negation via ~x+1
- Linear value formula: value = (-1)^sign * (1 + f) * 2^c
- Add rbits template parameter (default 3) for regime width, replacing
  hardcoded LUTs with constexpr functions dr_to_r() and dr_to_c_bias()
- Float-to-takum and takum-to-float conversions with round-to-nearest-even
- Small bit-width support: MSB-aligned truncated C field when r > nbits-overhead
- Arithmetic (+,-,*,/) via double conversion with NaR propagation
- Signed two's complement comparison operators (monotonic property)
- Exhaustive regression tests for takum<6> and takum<8> arithmetic
- Roundtrip and monotonicity verification for conversion

Closes #592

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* feat(takum): add application demos for decimal accuracy and iterative refinement

Two demonstrations of takum's value in scientific computation:

1. takum_decimal_accuracy.cpp: Scans decimal accuracy (correct digits)
   across magnitudes from 10^-30 to 10^+30 for takum, posit, cfloat,
   and lns at 16 bits. Shows takum retains ~2.4 digits at all magnitudes
   while posit drops to 0 beyond 10^+/-18.

2. takum_iterative_refinement.cpp: Mixed-precision iterative refinement
   comparing 16-bit formats on two problems:
   - Hilbert matrix (near 1.0): posit advantage
   - Wide-range matrix (10^-20 to 10^+20): takum advantage
   Shows format choice depends on problem's value distribution.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

* ci: add takum to conventional commit scopes

Co-Authored-By: Claude Opus 4.6 ... (continued)

Coverage Stats

249 of 257 new or added lines in 3 files covered. (96.89%)

7 existing lines in 2 files now uncovered.

44305 of 52521 relevant lines covered (84.36%)

5995774.98 hits per line