fix(presolve): prevent floating-point underflow in dynamism-scaled tolerances

[HuAliAsu]

Problem

When solving MILP models containing large matrix coefficients (such as micrometer dimensions 10^12 or large Big-M indicators), HiGHS Presolve can incorrectly declare feasible models as Infeasible or fail to reduce valid forcing rows and columns.

Technical Root Cause

In HPresolve.cpp (lines 4300 and 4587), primal_feasibility_tolerance and dual_feasibility_tolerance are scaled by dividing by the matrix dynamism ratio.

When dynamism is high (>= 10^8), tolerance / dynamism underflows below the IEEE 754 double precision machine epsilon (2.22e-16). For example, 1e-7 / 10^12 = 1e-19.

As a result, comparisons like std::abs(bound) <= 1e-19 fail due to standard floating-point noise (~10^-15), causing valid presolve reductions to fail and leading to false Infeasible status returns.

The Fix

Clamp the dynamism-scaled tolerances to a lower bound of 1e-15 (IEEE 754 machine epsilon safeguard):

std::max(double(primal_feastol / dynamism), 1e-15)
std::max(double(options->dual_feasibility_tolerance / dynamism), 1e-15)

Reproducible LP Benchmark

Minimize
  obj: 2976800000000 x1 + 1000 y1
Subject To
  c1: 480000000000 z1 + 600000000000 z2 <= 2976800000000 x1
  c2: pos_x1 + 600000 - pos_x2 - 3000000 delta1 <= 0
Bounds
  0 <= pos_x1 <= 2440000
Binary
  x1 z1 z2 delta1
End

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 73.16%. Comparing base (df4f2cd) to head (f55037b).
⚠️ Report is 415 commits behind head on latest.

Additional details and impacted files

@@           Coverage Diff           @@
##           latest    #3203   +/-   ##
=======================================
  Coverage   73.16%   73.16%           
=======================================
  Files         430      430           
  Lines      103967   103967           
  Branches    16719    16719           
=======================================
+ Hits        76067    76069    +2     
+ Misses      27624    27622    -2     
  Partials      276      276           

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[Opt-Mucca]

I don't see how this change can hurt. It needs to be formatted correctly though. Nice spot!

[fwesselm]

I don't really like hard-coding 1e-15, and I would prefer something like std::numeric_limits<double>::epsilon().

[jajhall]

I don't really like hard-coding 1e-15, and I would prefer something like std::numeric_limits<double>::epsilon().

Agreed