examples/dotproduct/

# A dot product of two long vectors, banded across threads.
#
# THE ONE THIS FAMILY IS NAMED FOR. design.md Part 7.13's cost rule says the
# model pays off when "the message is small relative to the work it triggers —
# send a slice, get back a number". This program sends less than a slice and
# gets back a number: each thread is handed the INDEX of its band and builds
# its own two vectors from it, so nothing counted is shared and the reduction
# is one addition per thread.
#
# WHY THE VECTORS ARE COMPUTED AND NOT PASSED. A `[i64]` cannot cross into a
# thread — `crosses_the_boundary` refuses it inside a callback signature, and
# that refusal is what makes the whole thing safe rather than merely fast. So
# the elements are a function of the index, which is the shape every data
# parallel program in this corpus takes.

extern "hero_os.h"
    function hero_thread_spawn(body: (function(i64) -> i64), arg: i64) -> i64
    function hero_thread_join(handle: i64) -> i64

constant BANDS: i64
    6

constant PER_BAND: i64
    4000

# The two vectors, as functions of the position rather than as arrays. `left`
# counts up and `right` counts down, so the product is not a square and a
# transposition of the bands would be visible in the answer.
function left(at: i64) -> i64
    return at % 97 + 1

function right(at: i64) -> i64
    return 53 - at % 53

function band(index: i64) -> i64
    total: i64 @= 0
    at: i64 @= index * PER_BAND

    while at < index * PER_BAND + PER_BAND
        total @ total + left(at: at) * right(at: at)
        at @ at + 1

    return total

function together() -> i64
    handles: [i64] @= []
    i: i64 @= 0

    while i < BANDS
        handles @ handles.push(hero_thread_spawn(body: band, arg: i))
        i @ i + 1

    total: i64 @= 0

    for h in handles
        total @ total + hero_thread_join(handle: h)

    return total

function alone() -> i64
    total: i64 @= 0
    at: i64 @= 0

    while at < BANDS * PER_BAND
        total @ total + left(at: at) * right(at: at)
        at @ at + 1

    return total

function main()
    print("dot product over ", BANDS * PER_BAND, " terms: ", together())

test "the bands add up to the whole"
    assert together() == alone()

test "a band is a contiguous piece and they do not overlap"
    assert band(index: 0) + band(index: 1) + band(index: 2) + band(index: 3) + band(index: 4) + band(index: 5) == alone()

test "the two vectors are not the same vector"
    assert left(at: 3) != right(at: 3)