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//! Implementation of Parallel Prefix Sum
use timely::progress::Timestamp;
use crate::{VecCollection, ExchangeData};
use crate::lattice::Lattice;
use crate::operators::*;
/// Extension trait for the prefix_sum method.
pub trait PrefixSum<'scope, T: Timestamp, K, D> {
/// Computes the prefix sum for each element in the collection.
///
/// The prefix sum is data-parallel, in the sense that the sums are computed independently for
/// each key of type `K`. For a single prefix sum this type can be `()`, but this permits the
/// more general accumulation of multiple independent sequences.
fn prefix_sum<F>(self, zero: D, combine: F) -> Self where F: Fn(&K,&D,&D)->D + 'static;
/// Determine the prefix sum at each element of `location`.
fn prefix_sum_at<F>(self, locations: VecCollection<'scope, T, (usize, K)>, zero: D, combine: F) -> Self where F: Fn(&K,&D,&D)->D + 'static;
}
impl<'scope, T, K, D> PrefixSum<'scope, T, K, D> for VecCollection<'scope, T, ((usize, K), D)>
where
T: Timestamp + Lattice,
K: ExchangeData + ::std::hash::Hash,
D: ExchangeData + ::std::hash::Hash,
{
fn prefix_sum<F>(self, zero: D, combine: F) -> Self where F: Fn(&K,&D,&D)->D + 'static {
self.clone().prefix_sum_at(self.map(|(x,_)| x), zero, combine)
}
fn prefix_sum_at<F>(self, locations: VecCollection<'scope, T, (usize, K)>, zero: D, combine: F) -> Self where F: Fn(&K,&D,&D)->D + 'static {
let combine1 = ::std::rc::Rc::new(combine);
let combine2 = combine1.clone();
let ranges = aggregate(self.clone(), move |k,x,y| (*combine1)(k,x,y));
broadcast(ranges, locations, zero, move |k,x,y| (*combine2)(k,x,y))
}
}
/// Accumulate data in `collection` into all powers-of-two intervals containing them.
pub fn aggregate<'scope, T, K, D, F>(collection: VecCollection<'scope, T, ((usize, K), D)>, combine: F) -> VecCollection<'scope, T, ((usize, usize, K), D)>
where
T: Timestamp + Lattice,
K: ExchangeData + ::std::hash::Hash,
D: ExchangeData + ::std::hash::Hash,
F: Fn(&K,&D,&D)->D + 'static,
{
// initial ranges are at each index, and with width 2^0.
let unit_ranges = collection.map(|((index, key), data)| ((index, 0, key), data));
unit_ranges
.clone()
.iterate(|scope, ranges| {
// Each available range, of size less than usize::max_value(), advertises itself as the range
// twice as large, aligned to integer multiples of its size. Each range, which may contain at
// most two elements, then summarizes itself using the `combine` function. Finally, we re-add
// the initial `unit_ranges` intervals, so that the set of ranges grows monotonically.
let unit_ranges = unit_ranges.enter(scope);
ranges
.filter(|&((_pos, log, _), _)| log < 64)
.map(|((pos, log, key), data)| ((pos >> 1, log + 1, key), (pos, data)))
.reduce(move |&(_pos, _log, ref key), input, output| {
let mut result = (input[0].0).1.clone();
if input.len() > 1 { result = combine(key, &result, &(input[1].0).1); }
output.push((result, 1));
})
.concat(unit_ranges)
})
}
/// Produces the accumulated values at each of the `usize` locations in `queries`.
pub fn broadcast<'scope, T, K, D, F>(
ranges: VecCollection<'scope, T, ((usize, usize, K), D)>,
queries: VecCollection<'scope, T, (usize, K)>,
zero: D,
combine: F) -> VecCollection<'scope, T, ((usize, K), D)>
where
T: Timestamp + Lattice + Ord + ::std::fmt::Debug,
K: ExchangeData + ::std::hash::Hash,
D: ExchangeData + ::std::hash::Hash,
F: Fn(&K,&D,&D)->D + 'static,
{
let zero0 = zero.clone();
let zero1 = zero.clone();
let zero2 = zero.clone();
// The `queries` collection may not line up with an existing element of `ranges`, and so we must
// track down the first range that matches. If it doesn't exist, we will need to produce a zero
// value. We could produce the full path from (0, key) to (idx, key), and aggregate any and all
// matches. This has the defect of being n log n rather than linear, as the root ranges will be
// replicated for each query.
//
// I think it works to have each (idx, key) propose each of the intervals it knows should be used
// to assemble its input. We then `distinct` these and intersect them with the offered `ranges`,
// essentially performing a semijoin. We then perform the unfolding, where we might need to use
// empty ranges if none exist in `ranges`.
// We extract desired ranges for each `idx` from its binary representation: each set bit requires
// the contribution of a range, and we call out each of these. This could produce a super-linear
// amount of data (multiple requests for the roots), but it will be compacted down in `distinct`.
// We could reduce the amount of data by producing the requests iteratively, with a distinct in
// the loop to pre-suppress duplicate requests. This comes at a complexity cost, though.
let requests =
queries
.clone()
.flat_map(|(idx, key)|
(0 .. 64)
.filter(move |i| (idx & (1usize << i)) != 0) // set bits require help.
.map(move |i| ((idx >> i) - 1, i, key.clone())) // width 2^i interval.
)
.distinct();
// Acquire each requested range.
let full_ranges =
ranges
.semijoin(requests.clone());
// Each requested range should exist, even if as a zero range, for correct reconstruction.
let zero_ranges =
full_ranges
.clone()
.map(move |((idx, log, key), _)| ((idx, log, key), zero0.clone()))
.negate()
.concat(requests.map(move |(idx, log, key)| ((idx, log, key), zero1.clone())));
// Merge occupied and empty ranges.
let used_ranges = full_ranges.concat(zero_ranges);
// Each key should initiate a value of `zero` at position `0`.
let init_states =
queries
.clone()
.map(move |(_, key)| ((0, key), zero2.clone()))
.distinct();
// Iteratively expand assigned values by joining existing ranges with current assignments.
init_states
.clone()
.iterate(|scope, states| {
let init_states = init_states.enter(scope);
used_ranges
.enter(scope)
.map(|((pos, log, key), data)| ((pos << log, key), (log, data)))
.join_map(states, move |&(pos, ref key), &(log, ref data), state|
((pos + (1 << log), key.clone()), combine(key, state, data)))
.concat(init_states)
.distinct()
})
.semijoin(queries)
}