float512

float512 is the maximum-precision float in Rux. It is a Rux extension beyond IEEE 754, but follows the same structural rules (sign, biased exponent, significand) and round-to-nearest behaviour. Special values (Inf, -Inf, NaN) are supported, and division by zero produces Inf or NaN rather than a fatal error. It is always software-emulated — expect large slowdowns versus float64, so it is not recommended for hot paths.

Literals

float512 has no literal suffix, so an explicit type annotation is required:

let ext: float512 = 1.0;       // explicit annotation
let big: float512 = 1.3e308;   // scientific notation

Unsuffixed floating-point literals otherwise default to float64. See Literals for the full grammar.

Typical Use Cases

• Specialized research
• Long-running simulations where error accumulation must be tightly bounded

Arithmetic

let a: float512 = 10.0;
let b: float512 = 3.0;

let sum  = a + b;   // 13.0
let quot = a / b;   // 3.333…
let rem  = a % b;   // 1.0

Both operands must share the same type; mixed-width expressions require an explicit cast. Arithmetic rounds to nearest (ties to even), unary negation (-x) flips the sign, and results that exceed the range overflow to Inf. Subtracting nearly equal values loses significant digits (catastrophic cancellation) — reorder the computation when accuracy matters.

Division by zero never fails: it yields signed infinity, and 0.0 / 0.0 yields NaN. Inf and NaN then propagate — Inf - Inf and Inf * 0.0 are both NaN.

let p =  1.0 / 0.0;  //  Inf
let n = -1.0 / 0.0;  // -Inf
let u =  0.0 / 0.0;  //  NaN

Comparison

Both operands must have the same type; comparing a different float width, or a float with an integer, is a compile-time error — cast explicitly first.

NaN is unordered: every comparison involving it returns false, including NaN == NaN. Detect it with IsNan, never ==. For the same reason, avoid == between computed results and compare within a tolerance instead:

let x = 0.1 + 0.2;
let close = Abs(x - 0.3) < 1.0e-140;  // not  x == 0.3

Conversion

Rux implicitly widens to any larger float type, so no precision is lost. float512 is the widest float, so there is no wider type to widen into. Narrowing to a smaller float must be explicit and rounds to nearest (ties to even).

let x: float512 = 1.5;
let narrow = x as float64;   // narrowing — explicit cast

Float-to-integer conversions are always explicit and truncate toward zero; casting NaN or Inf to an integer raises a fatal error in debug builds.

let whole = x as int32;      // 1   truncates toward zero

See Also

• float64 — the default double-precision float
• float256 — the next precision down