add precomputed mathematical constants and specialize the second division residual

README.md

@@ -16,8 +16,9 @@ for a single `double`, or `DoubleDouble.FromComponents(high, low)` for arbitrary
 components. The factory normalizes finite sums and canonicalizes NaN/infinity
 with a positive-zero low component. The two-component constructor is internal
 and performs no normalization or validation; it is reserved for trusted,
-already-normalized results. The constants `PI`, `E`, and `LN2` include binary64
-residuals checked against independently computed high-precision values.
+already-normalized results. Mathematical constants use precomputed high/low pairs
+checked against independently computed high-precision values; accessing them does
+not perform double-double arithmetic or allocate on the heap.
 
 - Arithmetic: unary `+`/`-`, binary `+`, `-`, `*`, `/`, and both operand orders with
   a `double`. Addition retains residuals under cancellation; multiplication uses
@@ -44,6 +45,39 @@ with exact component checks for selected representable cases. Near underflow,
 extended precision necessarily decreases; overflow produces infinity. Performance
 of the allocating exponent-boundary path is not covered by the basic benchmarks.
 
+## Predefined mathematical constants
+
+All constants below are static `DoubleDouble` properties. Each stores the nearest
+binary64 high component followed by the nearest binary64 residual, rather than
+calculating a ratio, root, or logarithm on access. Names use PascalCase, including
+`Pi`, `E`, and `Ln2`.
+
+| Group | Properties and values |
+|---|---|
+| Circle and common angles | `Pi` (π), `Tau` (2π), `PiOver2`, `PiOver3`, `PiOver4`, `PiOver6` |
+| Angular conversion | `DegToRad` (π/180), `RadToDeg` (180/π), `InvPi` (1/π), `InvTau` (1/(2π), radians to turns) |
+| Exponential and logarithmic | `E`, `InvE` (1/e), `Ln2` (ln 2), `Ln10` (ln 10) |
+| Log-base conversion | `Log2E` (1/ln 2), `Log10E` (1/ln 10), `Log2Of10` (ln 10/ln 2), `Log10Of2` (ln 2/ln 10) |
+| Roots and geometry | `Sqrt2`, `Sqrt3`, `Sqrt5`, `InvSqrt2`, `InvSqrt3`, `GoldenRatio` ((1+√5)/2) |
+| Gaussian and error-function factors | `SqrtPi`, `InvSqrtPi`, `TwoInvSqrtPi` (2/√π), `SqrtTau` (√(2π)), `InvSqrtTau` (1/√(2π)) |
+
+Multiply by conversion factors instead of recomputing them:
+
+```csharp
+using Just.PreciseMath;
+
+DoubleDouble degrees = new(180.0);
+DoubleDouble radians = degrees * DoubleDouble.DegToRad;
+DoubleDouble convertedDegrees = radians * DoubleDouble.RadToDeg;
+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.
+
 ## Conversions and formatting
 
 - Explicit conversions support `double`, `float`, `int`, `long`, and `decimal`