# Equivalence summary

Every comparison below is a byte compare of printed output: each number at 17 significant digits and as a
hex float. "same" means byte-identical between the official QuantLib 1.43 build and the TAKT build.

## C++ (one driver, library swapped), 867 printed results per run

Identical on: AMD Zen 3 (glibc 2.39), a glibc 2.28 reference system, and AMD Zen 4 (glibc 2.41).
The matrix covers:
- six markets: flat (Act/365F, TARGET), flat (Act/360, NYSE), a bootstrapped curve with a dividend curve
  and a variance term structure, a zero curve (Act/Act ISDA), a zero-spreaded curve, a volatility surface;
- European: pseudo-random over 1/7/52 steps x antithetic x two seeds; Sobol with and without Brownian
  bridge; steps-per-year;
- Asian (arithmetic with/without control variate x antithetic, geometric), American LSM (antithetic x two
  basis systems), barrier (down-out/up-in x biased), digital;
- Greeks by bumping the spot, the volatility and a rate spread;
- notification edge cases: updates disabled then recalculated, deferred updates, evaluation date moved and
  restored, a non-observing curve handle, extrapolation toggled (with the original exception reproduced);
- direct process use: a path generator with antithetic paths; evolve/variance/stdDeviation/drift/diffusion
  at arbitrary and repeated times;
- the whole Black process family, forced discretization, external local volatility, empty handles;
- Heston in six schemes and Broadie-Kaya, Bates;
- baskets (pseudo-random and Sobol, with a spot bump);
- non-Monte-Carlo engines on the same processes: analytic, CRR/JR/Tian trees, finite-difference
  Black-Scholes (with and without local vol), Barone-Adesi-Whaley, analytic and finite-difference Heston.

## Python (official wheel vs TAKT wheel), 270 printed results plus every workload

Identical on: Python 3.12 (glibc 2.28 and 2.39), Python 3.13 (Zen 4), and free-threaded Python 3.14t with
the GIL off (including a four-thread run, each thread's result equal to the single-threaded value). The
Python output is byte-identical to the C++ driver's.

## QuantLib's own test suites

- C++ test suite (QuantLib 1.43): 1,339 test cases pass with the TAKT library; the detailed reports are
  identical to the official library except for the total-time line.
- QuantLib-SWIG Python test suite: 211 passed, 1 skipped, with both the official and the TAKT wheel.

## Note on bit-identity across systems

QuantLib's results come from the system maths library, so the official build itself prints slightly
different last bits on different glibc versions (205 of the 867 values differ between glibc 2.28 and 2.39,
by at most 1.5e-6 relative). The TAKT build reproduces the official build's output on the same system.