Scale internal tolerances with working precision (single-precision robustness)

[cl445]

Problem

Three internal tolerances are hard-coded as double literals that sit below the single-precision roundoff floor (float eps is about 1.2e-7). When DAQP is built with -DDAQP_SINGLE_PRECISION (a supported path; it is handled in the MATLAB interface) they misbehave:

• src/utils.c, the daqp_lu singularity check max_val < 1e-12. For a singular matrix the largest pivot is around float-noise magnitude (about 1e-7 for O(1) data), which is larger than 1e-12. The check passes, so the factorization divides by that noise and pushes Inf/NaN into the AVI solve. In single precision, singular matrices are essentially never caught.
• src/api.c, daqp_primal_init_active (tol = 1e-9) and daqp_dual_init_active (tol = 1e-12). These "on-bound" and multiplier-sign bands are below the float floor, so the warm-start active-set heuristics degenerate: almost any nonzero slack or multiplier lands on the wrong side of the band.

Change

Add precision-selected macros in include/constants.h and use them at the three sites:

Macro	double	single
DAQP_LU_SING_TOL	1e-12	1e-6
DAQP_INIT_PRIM_TOL	1e-9	1e-5
DAQP_INIT_DUAL_TOL	1e-12	1e-6

The double-precision values match the previous literals exactly, so default builds are unaffected. Only the DAQP_SINGLE_PRECISION path changes.

Notes

• The single-precision values are picked to sit above the float roundoff floor; treat them as a starting point.
• The user-facing DAQP_DEFAULT_* settings are left alone to keep the scope small, though several of those are double-tuned too and could get the same treatment.

Testing

Builds cleanly in both precisions:

cmake -S . -B build -DCMAKE_BUILD_TYPE=Release && cmake --build build
cmake -S . -B build_sp -DCMAKE_BUILD_TYPE=Release -DCMAKE_C_FLAGS="-DDAQP_SINGLE_PRECISION" && cmake --build build_sp

[darnstrom]

Thank you for starting this PR!

Having different defaults depending on double/single precision makes a lot of sense! When I have used daqp for single-precision scenarios, I have used similar values that you selected here primal, dual, and zero tolerances. But it would definitely be nice to have most default settings be different if the user sets the single-precision flag out of convenience.

I think it would make sense to also select different values for the DAQP_DEFAULT_* values. I suppose the square root of most floating-point tolerances already set should be sufficient as a first attempt. Even better, it would be nice to have some test cases where single precision is used to make sure that the default values for the tolerances in single precision make sense.