Static Methodswift-numerics 1.0.3RealModule

    sum(large:small:)

    The sum a + b represented as an implicit sum head + tail.

    AugmentedArithmetic.swift:90
    static func sum<T>(large a: T, small b: T) -> (head: T, tail: T) where T : Real
    Mangled symbol
    s10RealModule9AugmentedO3sum5large5smallx4head_x4tailtx_xtAA0A0RzlFZ What are these?
    FNV24 hash
    4930T

    Parameters

    a

    The summand with larger magnitude.

    b

    The summand with smaller magnitude.

    head is the correctly rounded value of a + b. tail is the error from that computation rounded to the closest representable value.

    Unlike Augmented.product(a, b), the rounding error of a sum can never underflow. However, it may not be exactly representable when a and b differ widely in magnitude.

    This operation is sometimes called “fastTwoSum”.

    Preconditions:

    • large.magnitude must not be smaller than small.magnitude. They may be equal, or one or both may be NaN. This precondition is only enforced in debug builds.

    Edge Cases:

    • head is always the IEEE 754 sum a + b.

    • If head is not finite, tail is unspecified and should not be interpreted as having any meaning (it may be NaN or infinity).

    Postconditions:

    • If head is normal, then abs(tail) < head.ulp. Assuming IEEE 754 default rounding, abs(tail) <= head.ulp/2.