initial DDMath implementation

README.md

@@ -75,8 +75,32 @@ DoubleDouble quarterTurn = DoubleDouble.PiOver2;
 The factors avoid deriving constants at runtime; the multiplication itself remains
 approximate DD arithmetic, so conversions are not guaranteed exact round trips.
 The list is mathematical and dimensionless, not a table of unit-dependent physical
-constants. Precomputed roots/logarithms do not imply general `Sqrt`/`Log` functions
-are implemented.
+constants. Precomputed logarithms do not imply a general `Log` function is implemented.
+
+## Mathematical functions
+
+The initial `DDMath` static class provides:
+
+- `Abs(DoubleDouble)`: preserves both components, maps either signed zero to
+  positive zero and either infinity to positive infinity, and returns canonical NaN.
+  It shares the existing `DoubleDouble.Abs` implementation.
+- `Sqrt(DoubleDouble)`: uses power-of-two scaling and an FMA-based Newton correction
+  to retain extended precision, including for subnormal inputs, without squaring
+  an unscaled estimate near the exponent limits. Signed zero and positive infinity
+  are preserved; negative nonzero inputs and NaN return canonical NaN.
+
+```csharp
+using Just.PreciseMath;
+
+DoubleDouble root = DDMath.Sqrt(new DoubleDouble(2.0));
+DoubleDouble magnitude = DDMath.Abs(-root);
+```
+
+Square-root tests compare the exact component sum against a `2^-100` relative
+error bound using integer inequalities. They include samples at every binary64
+exponent, boundary neighbors, both signs of the low component, and exact binary
+squares. This is a tested approximate-accuracy contract, not exhaustive coverage
+of all component pairs or a guarantee of correctly rounded results.
 
 ## Conversions and formatting
 
@@ -165,8 +189,8 @@ bool success = DoubleDouble.TryParse("1.25e-2".AsSpan(), CultureInfo.InvariantCu
 
 ## Deferred scope
 
-The planned `PreciseMath` static class and its `Abs`, `Sqrt`, `Pow`, `Exp`, and
-`Log` functions are not implemented. Generic-math interfaces beyond `ISignedNumber`,
+The `DDMath.Pow`, `DDMath.Exp`, and `DDMath.Log` functions remain unimplemented.
+Generic-math interfaces beyond `ISignedNumber`,
 additional text formats/general round-trip formatting, and non-arithmetic performance
 benchmarks remain deferred.
 Replacing allocating arithmetic boundary fallbacks is also deferred; the current