inv sqrt implementation

README.md

@@ -88,6 +88,12 @@ The `DDMath` static class provides:
   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.
+- `InvSqrt(DoubleDouble)`: computes the reciprocal square root with power-of-two
+  scaling and a compensated Newton step, avoiding double-double division and its
+  allocating boundary paths. The estimate's squared-product residual is retained
+  with FMA. Signed zeros map to correspondingly signed infinities; positive infinity
+  maps to positive zero; negative nonzero inputs and NaN return canonical NaN.
+  This is a dedicated algorithm, not a claim of measured speedup over `1.0 / Sqrt(x)`.
 - `Pow(DoubleDouble, int)`: exponentiation by squaring with a separately tracked
   binary exponent. Supports the full `int` domain, including `int.MinValue`, and
   reciprocates a bounded significand before final scaling for negative exponents.
@@ -115,6 +121,7 @@ The `DDMath` static class provides:
 using Just.PreciseMath;
 
 DoubleDouble root = DDMath.Sqrt(new DoubleDouble(2.0));
+DoubleDouble inverseRoot = DDMath.InvSqrt(new DoubleDouble(2.0));
 DoubleDouble magnitude = DDMath.Abs(-root);
 DoubleDouble smallPower = DDMath.Pow(new DoubleDouble(2.0), -1024);
 DoubleDouble exponential = DDMath.Exp(new DoubleDouble(1.0));
@@ -124,10 +131,12 @@ DoubleDouble preciseExponent = DoubleDouble.FromComponents(0.5, 1e-30);
 DoubleDouble precisePower = DDMath.Pow(new DoubleDouble(2.0), preciseExponent);
 ```
 
-Square-root tests compare the exact component sum against a `2^-100` relative
-error bound using integer inequalities. They include samples at every binary64
+Square-root and inverse-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
+squares/powers of four. Square-root tests also bracket exact root-rounding midpoints;
+both suites exercise half-ulp low-component normalization boundaries.
+This is a tested approximate-accuracy contract, not exhaustive coverage
 of all component pairs or a guarantee of correctly rounded results.
 
 Logarithm tests compare exact component sums with independently generated