chore: justify ill-condition tolerance

Author: Alvaro-Kothe

pandas/_libs/window/aggregations.pyx

@@ -62,6 +62,12 @@ cdef:
     float64_t MAXfloat64 = np.inf
 
     float64_t NaN = <float64_t>np.nan
+    float64_t EpsF64 = np.finfo(np.float64).eps
+
+    # Consider an operation ill-conditioned if
+    # it will only have up to 3 significant digits in base 10 remaining.
+    # https://en.wikipedia.org/wiki/Condition_number
+    float64_t InvConditionNumber = EpsF64 * 1e3
 
 cdef bint is_monotonic_increasing_start_end_bounds(
     ndarray[int64_t, ndim=1] start, ndarray[int64_t, ndim=1] end
@@ -532,7 +538,7 @@ cdef void add_skew(float64_t val, int64_t *nobs,
     cdef:
         float64_t n, delta, delta_n, term1, m3_update, new_m3
 
-    # This formulas are adapted from
+    # Formulas adapted from
     # https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Higher-order_statistics
 
     # Not NaN
@@ -545,7 +551,7 @@ cdef void add_skew(float64_t val, int64_t *nobs,
 
         m3_update = delta_n * fma(term1, n - 2.0, -3.0 * m2[0])
         new_m3 = m3[0] + m3_update
-        if fabs(m3_update) + fabs(m3[0]) > 1e10 * fabs(new_m3):
+        if (fabs(m3_update) + fabs(m3[0])) * InvConditionNumber > fabs(new_m3):
             # possible catastrophic cancellation
             numerically_unstable[0] = True
 
@@ -591,7 +597,7 @@ cdef void remove_skew(float64_t val, int64_t *nobs,
         m3_update = delta_n * fma(term1, n + 2.0, -3.0 * m2[0])
         new_m3 = m3[0] - m3_update
 
-        if fabs(m3_update) + fabs(m3[0]) > 1e10 * fabs(new_m3):
+        if (fabs(m3_update) + fabs(m3[0])) * InvConditionNumber > fabs(new_m3):
             # possible catastrophic cancellation
             numerically_unstable[0] = True