added sanity checks

README.md

@@ -24,11 +24,15 @@ not perform double-double arithmetic or allocate on the heap.
   a `double`. Addition retains residuals under cancellation; multiplication uses
   fused multiply-add; division uses residual corrections. Mixed `double` operators
   use specialized scalar paths rather than promoting the scalar to `DoubleDouble`.
-  Their finite fast paths normalize once with a final sum transform; scalar
-  division uses one compensated quotient correction within the error contract below.
+  Division retains the complete first remainder and applies two quotient corrections,
+  normalizing before the final correction. Mixed addition and subtraction also retain
+  intermediate sum residuals through final normalization. Mixed addition, subtraction,
+  and division produce the same component bits as their `DoubleDouble` operations
+  with the scalar represented as a zero-low pair.
 - Exponent boundaries: bounded `BigInteger` calculations avoid intermediate
   overflow and underflow on the exceptional finite path. Ordinary arithmetic uses
-  floating-point transforms without allocations. The stored value remains two
+  floating-point transforms without allocations, although sparse division correction
+  products can also reach a boundary path. The stored value remains two
   doubles; this is not an arbitrary-precision API.
 - Comparisons use both components. `Equals` treats NaNs as equal and signed zeros
   as equal for collections. `CompareTo` orders NaN before other values. Numerical
@@ -107,8 +111,8 @@ The `DDMath` static class provides:
   It shares the existing `DoubleDouble.Abs` implementation.
 - `Reciprocal(DoubleDouble)`: returns exactly the same high and low component bits
   as `1.0 / value`. It specializes scalar/DD division for a numerator of one,
-  omitting only redundant numerator checks while preserving both divisions,
-  the FMA sequence, and normalization. Signed zeros map to signed infinities,
+  omitting redundant numerator checks and sharing the finite scalar-numerator kernel,
+  including both residual corrections and normalization. Signed zeros map to signed infinities,
   signed infinities to signed zeros, and NaN to canonical NaN. The allocating exact boundary
   path handles extreme exponents; finite overflow produces signed infinity.
   No speedup over scalar/DD division has been measured.