Function fixed_exp

fn fixed_exp<T>(x: &T) -> Option<T>
where
    T: FixedPointNumber + Copy + PartialOrd + FixedPointInfo,
    T::Inner: From<u8> + Shr<u32, Output = T::Inner> + TryInto<i128> + Copy,

Computes e^x for a fixed-point number using argument reduction and a Taylor series expansion.

Algorithm

Splits x = n + r where n is the integer part and |r| <= 0.5:

exp(x) = exp(n) * exp(r)

exp(r) is computed via Taylor series (fast for small |r|). exp(n) is computed by raising e ~= 2.718281828459045235 to integer power n via binary exponentiation (fixed_powi).

e is approximated as 2_718_281_828_459_045_235 / 10^18, giving 18 significant figures - matching the full precision of FixedU128 and over-specified but harmless for the other three types.

Domain

Defined for all fixed-point values, but:

• Large positive x overflows the fixed-point range - returns None.
• Large negative x underflows to zero - returns Some(0). Threshold: x < -(DECIMAL_PLACES * 10).

Arguments

• x - The fixed-point exponent value.

Returns

• Some(exp(x)) on success
• Some(0) when x is below the underflow threshold
• None on overflow, or if internal arithmetic fails

Examples

let x = FixedU64::saturating_from_integer(1);
let result = fixed_exp(&x).unwrap();
// result ~= 2.718281828