std/sum

1 export, from std/sum.vyrn.

The exact sum of an Array<Float64>, written in Vyrn. Adds m to the accumulator at the weight of exponent field e, negated when negative. m is a sum of up to 2048 values that share e: each is its fraction field, plus 2^52 when e is not 0.

Dependencies

The import graph shows the whole library.

Imports: nothing else in std/
Imported by: no other std module

sum fn

fn sum(xs: Array<Float64>) -> Float64

The true sum of xs, rounded once to the nearest Float64 with ties to even.

The result does not depend on the order of xs, on cancellation, or on an intermediate sum that would overflow: the largest finite value twice and its negation sum to the largest finite value. An infinity or a NaN follows IEEE: +inf + -inf is NaN, and a NaN anywhere makes the sum NaN. An exact zero is +0.0, and an empty array sums to 0.0. A loop that adds with + keeps sequential rounding.

An array of 512 values or more goes into slots by sign and exponent, with no rounding. Four tables of 4096 slots take every fourth value in turn, so a run of equal exponents does not wait on one slot. A slot moves into a 2304-bit accumulator before it can overflow. Shorter arrays go straight to the accumulator.

Tests

7 test blocks in std/sum.vyrn. CI runs all of them.

Test names

an exact sum survives cancellation
an intermediate overflow does not reach the result
an exact sum rounds once, ties to even
an exact sum counts subnormals and zeros
an exact sum follows IEEE for infinities and NaN
an exact sum does not depend on order
an exact sum carries across the slot blocks

Examples

No example program imports this module.