{-# LANGUAGE NoImplicitPrelude #-} -- | This module provides destination arrays -- -- == What are destination arrays? What are they good for? -- -- Destination arrays are write-only arrays that are only allocated once, -- thereby avoiding your reliance on GHC's fusion mechanisms to remove -- unneccessary allocations. -- -- The current status-quo for computations that have a write-only array -- threaded along is to rely on fusion. While the optimizations in say, -- `Data.Vector` are quite good at ensuring GHC fuses, they aren't -- foolproof and can sometimes break by simple refactorings. -- -- Avoiding extra allocations of a write-only array is easy in C, with -- something the functional programming world calls destination passing style, -- or DPS for short. -- -- Here is a C function that manipulates an array written in DPS style; it -- takes in the destiniation array @res@ and writes to it: -- -- @ -- // ((a + b) * c) for vectors a,b and scalar c -- void apbxc(int size, int *a, int *b, int c, int *res){ -- for (int i=0; i<size;++i){res[i]=a[i]+b[i];} -- mult(size, c, res); -- } -- -- void mult(int size, int scalar, int* vec){ -- for (int i=0; i<size; ++i){vec[i] *= scalar;} -- } -- @ -- -- == Example: Stencil computation -- -- One possible use of destination arrays could be the stencil computation -- typically called -- [jacobi](https://en.wikipedia.org/wiki/Iterative_Stencil_Loops#Example:_2D_Jacobi_iteration). -- Here we show one time step of this computation in a single dimension: -- -- @ -- jacobi1d :: Int -> Vector Double -> Vector Double -- jacobi1d n oldA = case stepArr n oldA of -- newB -> stepArr n newB -- -- -- @jacobi1d N A[N] B[N] = (new_A[N], new_B[N])@. -- stepArr :: Int -> Vector Double -> Vector Double -- stepArr n oldArr = alloc n $ \newArr -> fillArr newArr oldArr 1 -- where -- fillArr :: DArray Double %1-> Vector Double -> Int -> () -- fillArr newA oldA ix -- | ix == (n-1) = newA & -- fill (0.33 * ((oldA ! (ix-1)) + (oldA ! ix) + (oldA ! (ix+1)))) -- | True = split 1 newA & \(fst, rest) -> -- fill (0.33 * ((oldA ! (ix-1)) + (oldA ! ix) + (oldA ! (ix+1)))) fst & -- \() -> fillArr rest oldA (ix+1) -- @ -- -- We can be sure that @stepArr@ only allocates one array. In certain -- variations and implementations of the jacobi kernel or similar dense array -- computations, ensuring one allocation with @Data.Vector@'s fusion oriented -- implementation may not be trivial. -- -- For reference, the C equivalent of this code is the following: -- -- @ -- static void jacobi_1d_time_step(int n, int *A, int *B){ -- int t, i; -- for (i = 1; i < _PB_N - 1; i++) -- B[i] = 0.33333 * (A[i-1] + A[i] + A[i + 1]); -- for (i = 1; i < _PB_N - 1; i++) -- A[i] = 0.33333 * (B[i-1] + B[i] + B[i + 1]); -- } -- @ -- -- This example is taken from the -- [polybench test-suite](https://web.cse.ohio-state.edu/~pouchet.2/software/polybench/) -- of dense array codes. -- -- == Aside: Why do we need linear types? -- -- Linear types avoids ambiguous writes to the destination array. -- For example, this function could never be linear and hence we avoid -- ambiguity: -- -- @ -- nonLinearUse :: DArray Int -> () -- nonLinearUse arr = case (replicate 3 arr, replicate 4 arr) of -- ((),()) -> () -- @ -- -- Furthermore, this API is safely implemented by mutating an underlying array -- which is good for performance. The API is safe because linear types -- enforce the fact that each reference to an underlying mutable array -- (and there can be more than one by using @split@) is -- linearly threaded through functions and at the end consumed by one of our -- write functions. -- -- Lastly, linear types are used to ensure that each cell in the destination -- array is written to exactly once. This is because the only way to create and -- use a destination array is via -- -- @ -- alloc :: Int -> (DArray a %1-> ()) %1-> Vector a -- @ -- -- and the only way to really consume a @DArray@ is via our API -- which requires you to completely fill the array. module Data.Array.Destination ( -- * The Data Type DArray, -- * Create and use a @DArray@ alloc, size, -- * Ways to write to a @DArray@ replicate, split, mirror, fromFunction, fill, dropEmpty, ) where import Data.Array.Destination.Internal