tensors: optimize matrix operations.
tensors: Add benchmarking file tensors: Add addition and multiplication tests for benchmarking tensors: inlined slicing to improve metrics. tensors: fix help-lint warnings. tensors: restore newer matmul tensors: add fixnum declaration. tensors: away with you, unsafe! tensors: transpose added to benchmarks tensors: optimize matmul to be within an order of magnitude of np. tensors: remove type declaration. tensors: optimize matmul.fix-linux
Nandeeka Nayak
John Benediktsson
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ec58d39bb2
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a7722b0804
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! Copyright (C) 2019 HMC Clinic.
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! See http://factorcode.org/license.txt for BSD license.
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USING: arrays io kernel locals math prettyprint tensors tools.time ;
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IN: tensors.benchmark
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<PRIVATE
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:: add-tensors ( trials elems -- time )
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! Create the arrays to be added
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elems 1array naturals dup
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! Benchmark!
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[ trials [ 2dup t+ drop ] times ] benchmark
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! Normalize
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trials / >float
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nip nip ;
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:: matmul-tensors ( trials elems -- time )
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! Create the arrays to be multiplied
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elems elems 2array naturals dup
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! Benchmark!
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[ trials [ 2dup matmul drop ] times ] benchmark
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! Normalize
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trials / >float
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nip nip ;
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:: transpose-tensor ( trials elems -- time )
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! Create the array to be transposed
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elems elems 2array naturals
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! benchmark
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[ trials [ dup transpose drop ] times ] benchmark
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! Normalize
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trials / >float
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nip ;
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PRIVATE>
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: run-benchmarks ( -- )
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"Benchmarking the tensors vocabulary" print
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"Add two 100 element tensors" print
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1000000 100 add-tensors .
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"Add two 100,000 element tensors" print
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10000 100000 add-tensors .
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"Multiply two 10x10 matrices" print
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100000 10 matmul-tensors .
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"Multiply two 100x100 matrices" print
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1000 100 matmul-tensors .
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"Transpose a 10x10 matrix" print
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10000 10 transpose-tensor .
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"Transpose a 100x100 matrix" print
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10 100 transpose-tensor . ;
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@ -1,9 +1,12 @@
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! Copyright (C) 2019 HMC Clinic.
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! See http://factorcode.org/license.txt for BSD license.
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USING: accessors alien.c-types alien.data arrays
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concurrency.combinators grouping kernel locals math.functions
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math.ranges math.statistics math multi-methods quotations sequences
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sequences.private specialized-arrays tensors.tensor-slice typed ;
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sequences.extras sequences.private specialized-arrays
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tensors.tensor-slice typed ;
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QUALIFIED-WITH: alien.c-types c
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SPECIALIZED-ARRAY: c:float
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IN: tensors
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@ -47,7 +50,7 @@ PRIVATE>
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! Construct a one-dimensional tensor with values start, start+step,
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! ..., stop (inclusive)
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: arange ( a b step -- tensor )
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<range> [ length 1array ] keep >float-array <tensor> ;
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<range> [ length >fixnum 1array ] keep >float-array <tensor> ;
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! Construct a tensors with vec { 0 1 2 ... } and reshape to the desired shape
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: naturals ( shape -- tensor )
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@ -148,20 +151,24 @@ METHOD: t% { number tensor } swap [ swap mod ] curry t-uop ;
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! Perform matrix multiplication muliplying an
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! mxn matrix with a nxp matrix
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TYPED:: 2d-matmul ( vec1: slice vec2: slice res: slice n: number p: number -- )
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TYPED:: 2d-matmul ( vec1: float-array start1: fixnum
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vec2: float-array start2: fixnum
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res: float-array start3: fixnum
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m: fixnum n: fixnum p: fixnum -- )
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! For each element in the range, we want to compute the dot product of the
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! corresponding row and column
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res
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[ >fixnum
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! Get the row
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[ [ vec1 n ] dip p row ]
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! Get the column
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! [ p mod vec2 swap p every ] bi
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[ p mod f p vec2 <step-slice> ] bi
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! Take the dot product
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[ * ] [ + ] 2map-reduce
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]
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map! drop ;
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m [ :> i
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p [ :> j
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0.0 ! This is the sum
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n [ :> k
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! Add to the sum
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i n * k + start1 + vec1 nth-unsafe
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k p * j + start2 + vec2 nth-unsafe
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* +
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] each-integer
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i p * j + start3 + res set-nth-unsafe
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] each-integer
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] each-integer ;
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PRIVATE>
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@ -176,70 +183,52 @@ TYPED:: matmul ( tensor1: tensor tensor2: tensor -- tensor3: tensor )
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tensor1 shape>> unclip-last-slice :> n
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unclip-last-slice :> m :> top-shape
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tensor2 shape>> last :> p
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top-shape product :> rest
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top-shape product :> top-prod
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! Now create the new tensor with { 0 ... m*p-1 } repeating
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top-shape { m p } append naturals m p * t% :> tensor3
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! Create the shape of the resulting tensor
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top-shape { m p } append
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! Now create the new float array to store the underlying result
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dup product c:float (c-array) :> vec3
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! Now update the tensor3 to contain the multiplied matricies
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rest [0,b)
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[
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top-prod [
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:> i
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! First make vec1
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m n * i * dup m n * + tensor1 vec>> <slice>
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! Now make vec2
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n p * i * dup n p * + tensor2 vec>> <slice>
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! Now make the resulting vector
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m p * i * dup m p * + tensor3 vec>> <slice>
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! Push n and p and multiply the clices
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n p 2d-matmul
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0
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] map drop
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tensor3 ;
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! Compute vec1 and start1
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tensor1 vec>> m n * i *
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! Compute vec2 and start2
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tensor2 vec>> n p * i *
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! Compute the result
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vec3 m p * i *
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! Push m, n, and p and multiply the arrays
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m n p 2d-matmul
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] each-integer
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vec3 <tensor> ;
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<PRIVATE
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! helper for transpose: gets the turns a shape into a list of things
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! helper for transpose: turns a shape into a list of things
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! by which to multiply indices to get a full index
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: ind-mults ( shape -- seq )
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rest-slice <reversed> cum-product { 1 } prepend ;
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<reversed> 1 swap [ swap [ * ] keep ] map nip ;
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! helper for transpose: given shape, flat index, & mults for the shape, gives nd index
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:: trans-index ( ind shape mults -- seq )
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! what we use to divide things
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shape reverse :> S
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! accumulator
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V{ } clone
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! loop thru elements & indices of S (mod by elment m)
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S [| m i |
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! we divide by the product of the 1st n elements of S
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S i head-slice product :> div
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! do not mod on the last index
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i S length 1 - = not :> mod?
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! multiply accumulator by mults & sum
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dup mults [ * ] 2map sum
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! subtract from ind & divide
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ind swap - div /
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! mod if necessary
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mod? [ m mod ] [ ] if
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! append to accumulator
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[ dup ] dip swap push
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] each-index
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reverse ;
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: transpose-index ( i shape -- seq )
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<reversed> [ /mod ] map reverse nip ;
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PRIVATE>
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! Transpose an n-dimensional tensor
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! Transpose an n-dimensional tensor by flipping the axes
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TYPED:: transpose ( tensor: tensor -- tensor': tensor )
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! new shape
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tensor shape>> reverse :> newshape
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! what we multiply by to get indices in the old tensor
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tensor shape>> ind-mults :> old-mults
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! what we multiply to get indices in new tensor
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newshape ind-mults :> mults
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! new tensor of correct shape
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newshape naturals dup vec>>
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[ ! go thru each index
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tensor shape>> :> old-shape
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tensor vec>> :> vec
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old-shape reverse :> new-shape
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! check that the size is fine
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new-shape product vec length assert=
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old-shape ind-mults reverse :> mults
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! loop through new tensor
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new-shape dup product <iota> [
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! find index in original tensor
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newshape mults trans-index old-mults [ * ] 2map sum >fixnum
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old-shape mults [ [ /mod ] dip * ] 2map-sum nip
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! get that index in original tensor
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tensor vec>> nth
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] map! >>vec ;
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vec nth-unsafe
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] float-array{ } map-as <tensor> ;
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