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Func

Func Class

[class] Func

A CLOS class that represents a computation.

[Func] -> <Lower> -> [FastGraph] -> <Simplifier> -> [Completed]

Func is a syntax-sugar for generating lowered instructions defined in the caten/aasm package.

To properly lower the Func, You need to implement the following three methods:

  • lower: Lower the Func into a list of caten/air:node. This should return caten/air:graph.
  • forward: Create the type for the Tensor after computation. Be mindful of its lazy evaluation nature; do not perform the actual computation. ShapeTracker might help you. (use the st macro)
  • backward: Create the graph for backward of op given prev-grad. Return: (values input_1.grad input_2.grad ...).

[generic] lower

(lower op &rest nodes)

Lowers the Func into a list of caten/air:node. This should return caten/air:graph. - op[Func] Func to lower. - nodes[list] list of previous nodes (each position corresponds to the position of the variables in the Func).

[generic] forward

(forward op &rest tensors)

Create the type for the Tensor after computation. Be mindful of its lazy evaluation nature; do not perform the actual computation. Use the st macro to create a new tensor.

  • op[Func] Func to forward.
  • tensors[list] list of input tensors.

[generic] backward

(backward op &optional prev-grad)

Create the graph for backward of op given prev-grad. Return: (values input_1.grad input_2.grad ...). save-for-backward is determined automatically, so you do not have to consider about in-place operation.

  • op[Func] Func to backward.
  • prev-grad[Tensor] previous gradient tensor.

Differentiable Ops (built_in)

[function] !identity

(!identity tensor)

Equivalent to #'identity, but it is used to create a lazy computation node.

lisp
CATEN-USER> (proceed (!identity (make-tensor `(3 3) :initial-element 1.0)))
Result
Result
{Tensor[float32] :shape (3 3) :id STC92728
   ((1.0 1.0 1.0)
    (1.0 1.0 1.0)
    (1.0 1.0 1.0))
  :op #<PROCEEDNODE {10079FED63}>
  :requires-grad NIL
  :variables (STC92667)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !view

(!view base &rest subscripts)

Create a view node from the base tensor and subscripts.

We refer to VIEW as a node creating tensor whose buffers are shared with the base tensor, but shapes, strides, dtypes, offsets, or dtypes are different.

Subscripts has the following notation:

  • t keep using the base view.
  • fixnum refers to the specified element. e.g.: A[3]
  • (a b) slices in the range of [a, b)
  • (a b c) slices in the range of [a, b) with step c. c can be negative. In that case, b must be larger than a. For example: (10 0 -1) to reverse the elements in the axis.
  • (:~ n) to broadcast the axis, with the size of n

It is supported to compose mutliple views; the viewed tensors can be created from the viewed tensors.

lisp
CATEN-USER> (proceed (!contiguous (!view (ax+b `(10 10) 1 0) `(3 6) `(3 6))))
Result
Result
{Tensor[float32] :shape (3 3) :id STC93615
   ((33.0 34.0 35.0)
    (43.0 44.0 45.0)
    (53.0 54.0 55.0))
  :op #<PROCEEDNODE {1007C023F3}>
  :requires-grad NIL
  :variables (STC92932)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !permute

(!permute tensor &rest order)

Returns a tensor that is a permutation of the original tensor. The new tensor has the same data as the original tensor but with the dimensions permuted according to the order specified. order can be passed as a list or separated arguments. That is, both of (!permute x 0 1) or (!permute x (list 0 1)) are valid.

lisp
CATEN-USER> (proceed (!contiguous (!permute (ax+b `(10 10) 1 0) `(1 0))))
Result
Result
{Tensor[float32] :shape (10 10) :id STC93807
   ((0.0  10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0)
    (1.0  11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0)
    (2.0  12.0 22.0 32.0 42.0 52.0 62.0 72.0 82.0 92.0)
    (3.0  13.0 23.0 33.0 43.0 53.0 63.0 73.0 83.0 93.0)
    (4.0  14.0 24.0 34.0 44.0 54.0 64.0 74.0 84.0 94.0)
    (5.0  15.0 25.0 35.0 45.0 55.0 65.0 75.0 85.0 95.0)
    (6.0  16.0 26.0 36.0 46.0 56.0 66.0 76.0 86.0 96.0)
    (7.0  17.0 27.0 37.0 47.0 57.0 67.0 77.0 87.0 97.0)
    (8.0  18.0 28.0 38.0 48.0 58.0 68.0 78.0 88.0 98.0)
    (9.0  19.0 29.0 39.0 49.0 59.0 69.0 79.0 89.0 99.0))
  :op #<PROCEEDNODE {1007C663A3}>
  :requires-grad NIL
  :variables (TID93623)
  :tracker #<TRACKER :order={row(1 0)} :shape=(10 10) :contiguous-p=T>}

[function] !t

(!t tensor)

Transposes the last two axes of the tensor

lisp
CATEN-USER> (proceed (!contiguous (!t (ax+b `(10 10) 1 0))))
Result
Result
{Tensor[float32] :shape (10 10) :id STC93999
   ((0.0  10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0)
    (1.0  11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0)
    (2.0  12.0 22.0 32.0 42.0 52.0 62.0 72.0 82.0 92.0)
    (3.0  13.0 23.0 33.0 43.0 53.0 63.0 73.0 83.0 93.0)
    (4.0  14.0 24.0 34.0 44.0 54.0 64.0 74.0 84.0 94.0)
    (5.0  15.0 25.0 35.0 45.0 55.0 65.0 75.0 85.0 95.0)
    (6.0  16.0 26.0 36.0 46.0 56.0 66.0 76.0 86.0 96.0)
    (7.0  17.0 27.0 37.0 47.0 57.0 67.0 77.0 87.0 97.0)
    (8.0  18.0 28.0 38.0 48.0 58.0 68.0 78.0 88.0 98.0)
    (9.0  19.0 29.0 39.0 49.0 59.0 69.0 79.0 89.0 99.0))
  :op #<PROCEEDNODE {1007CEA213}>
  :requires-grad NIL
  :variables (TID93815)
  :tracker #<TRACKER :order={row(1 0)} :shape=(10 10) :contiguous-p=T>}

[function] !transpose

(!transpose tensor &optional (dim0 1) (dim1 0))

Transposes the dim0 and dim1.

lisp
CATEN-USER> (proceed (!contiguous (!transpose (ax+b `(10 10) 1 0) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC94191
   ((0.0  10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0)
    (1.0  11.0 21.0 31.0 41.0 51.0 61.0 71.0 81.0 91.0)
    (2.0  12.0 22.0 32.0 42.0 52.0 62.0 72.0 82.0 92.0)
    (3.0  13.0 23.0 33.0 43.0 53.0 63.0 73.0 83.0 93.0)
    (4.0  14.0 24.0 34.0 44.0 54.0 64.0 74.0 84.0 94.0)
    (5.0  15.0 25.0 35.0 45.0 55.0 65.0 75.0 85.0 95.0)
    (6.0  16.0 26.0 36.0 46.0 56.0 66.0 76.0 86.0 96.0)
    (7.0  17.0 27.0 37.0 47.0 57.0 67.0 77.0 87.0 97.0)
    (8.0  18.0 28.0 38.0 48.0 58.0 68.0 78.0 88.0 98.0)
    (9.0  19.0 29.0 39.0 49.0 59.0 69.0 79.0 89.0 99.0))
  :op #<PROCEEDNODE {1007D4E113}>
  :requires-grad NIL
  :variables (TID94007)
  :tracker #<TRACKER :order={row(1 0)} :shape=(10 10) :contiguous-p=T>}

[function] !contiguous

(!contiguous x &key (force nil))

If the tensor is viewed, creates a copy of tensor with contiguous memory. Otherwise, returns the original tensor. If force is set to T, it always creates a copy.

lisp
CATEN-USER> (proceed (!contiguous (ax+b `(10 10) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC94291
   ((0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0)
    (10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0)
    (20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0)
    (30.0 31.0 32.0 33.0 34.0 35.0 36.0 37.0 38.0 39.0)
    (40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0)
    (50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0)
    (60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0)
    (70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0)
    (80.0 81.0 82.0 83.0 84.0 85.0 86.0 87.0 88.0 89.0)
    (90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 99.0))
  :op #<PROCEEDNODE {1007D91BE3}>
  :requires-grad NIL
  :variables (STC94198)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !copy

(!copy x)
Creates a copy of the tensor. In Caten, the in-place operations are automatically determined, so in general, you do not have to consider using it.

lisp
CATEN-USER> (proceed (!copy (ax+b `(10 10) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC94422
   ((0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0)
    (10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0)
    (20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0)
    (30.0 31.0 32.0 33.0 34.0 35.0 36.0 37.0 38.0 39.0)
    (40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0)
    (50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0)
    (60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0)
    (70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0)
    (80.0 81.0 82.0 83.0 84.0 85.0 86.0 87.0 88.0 89.0)
    (90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 99.0))
  :op #<PROCEEDNODE {1007DC1B63}>
  :requires-grad NIL
  :variables (STC94303)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !reshape

(!reshape x &rest shape)

Returns a same tensor but shape is changed. shape can be passed as a list or separated arguments. That is, both of (!reshape x '(1 2 3)) or (!reshape x 1 2 3) are valid.

Shape is a list of integers, symbols, or tensors.

If x is a viewed tensor, it creates a copy of the tensor with contiguous memory (but later JIT will try to eliminate this).

lisp
CATEN-USER> (proceed (!reshape (ax+b `(10 10) 1 0) `(5 20)))
Result
Result
{Tensor[float32] :shape (5 20) :id STC94620
   ((0.0  1.0  2.0  3.0  4.0  ~ 15.0 16.0 17.0 18.0 19.0)
    (20.0 21.0 22.0 23.0 24.0 ~ 35.0 36.0 37.0 38.0 39.0)
    (40.0 41.0 42.0 43.0 44.0 ~ 55.0 56.0 57.0 58.0 59.0)
    (60.0 61.0 62.0 63.0 64.0 ~ 75.0 76.0 77.0 78.0 79.0)
    (80.0 81.0 82.0 83.0 84.0 ~ 95.0 96.0 97.0 98.0 99.0))
  :op #<PROCEEDNODE {1007E2E4D3}>
  :requires-grad NIL
  :variables (TID94430)
  :tracker #<TRACKER :order={row(0 1)} :shape=(5 20) :contiguous-p=T>}

[function] !uprank

(!uprank x n)

Returns a tensor with one is inserted at the beginning of the shape of x for n times.

lisp
CATEN-USER> (proceed (!uprank (ax+b `(10 10) 1 0) 2))
Result
Result
{Tensor[float32] :shape (1 1 10 10) :id STC94884
   ((((0.0  1.0  2.0  3.0  4.0  5.0  6.0  7.0  8.0  9.0)
      (10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0)
      (20.0 21.0 22.0 23.0 24.0 25.0 26.0 27.0 28.0 29.0)
      (30.0 31.0 32.0 33.0 34.0 35.0 36.0 37.0 38.0 39.0)
      (40.0 41.0 42.0 43.0 44.0 45.0 46.0 47.0 48.0 49.0)
      (50.0 51.0 52.0 53.0 54.0 55.0 56.0 57.0 58.0 59.0)
      (60.0 61.0 62.0 63.0 64.0 65.0 66.0 67.0 68.0 69.0)
      (70.0 71.0 72.0 73.0 74.0 75.0 76.0 77.0 78.0 79.0)
      (80.0 81.0 82.0 83.0 84.0 85.0 86.0 87.0 88.0 89.0)
      (90.0 91.0 92.0 93.0 94.0 95.0 96.0 97.0 98.0 99.0))))
  :op #<PROCEEDNODE {1007ED8D23}>
  :requires-grad NIL
  :variables (TID94628)
  :tracker #<TRACKER :order={row(0 1 2 3)} :shape=(1 1 10 10) :contiguous-p=T>}

[function] !repeat

(!repeat x &rest repeats)

Returns a tensor with the shape of x broadcasted by repeats.

lisp
CATEN-USER> (proceed (!repeat (ax+b `(1 10) 1 0) 10 1))
Result
Result
{Tensor[float32] :shape (10 10) :id STC97422
   ((0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0)
    (0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0))
  :op #<PROCEEDNODE {10084C9463}>
  :requires-grad NIL
  :variables (VID95135)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10(0 10 1) 10(0 10 1)) :contiguous-p=NIL>}

[function] !expand

(!expand x &rest shape)

Returns a tensor that is expanded to the shape that is specified. Expand can also increase the number of dimensions that a tensor has.

lisp
CATEN-USER> (proceed (!expand (ax+b `(1 10) 1 0) `(10 10)))
Result
Result
{Tensor[float32] :shape (1 10) :id STC98058
   ((0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0))
  :op #<PROCEEDNODE {100860DAC3}>
  :requires-grad NIL
  :variables (VID97430)
  :tracker #<TRACKER :order={row(0 1)} :shape=(~1 10) :contiguous-p=T>}

[function] !move

(!move a b &key (reduce nil))

Moves the element of b into a, returning a. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!move (ax+b `(10 10) 0 0) (ax+b `(10 10) 0 2)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC98227
   ((2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0)
    (2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0))
  :op #<PROCEEDNODE {100864C8F3}>
  :requires-grad NIL
  :variables (STC98073)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !add

(!add a b &key (reduce nil))
;; or
(!+ &rest tensors)

Adds a and b. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!add (ax+b `(10 10) 1 0) (ax+b `(10 10) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC98397
   ((0.0   2.0   4.0   6.0   8.0   10.0  12.0  14.0  16.0  18.0)
    (20.0  22.0  24.0  26.0  28.0  30.0  32.0  34.0  36.0  38.0)
    (40.0  42.0  44.0  46.0  48.0  50.0  52.0  54.0  56.0  58.0)
    (60.0  62.0  64.0  66.0  68.0  70.0  72.0  74.0  76.0  78.0)
    (80.0  82.0  84.0  86.0  88.0  90.0  92.0  94.0  96.0  98.0)
    (100.0 102.0 104.0 106.0 108.0 110.0 112.0 114.0 116.0 118.0)
    (120.0 122.0 124.0 126.0 128.0 130.0 132.0 134.0 136.0 138.0)
    (140.0 142.0 144.0 146.0 148.0 150.0 152.0 154.0 156.0 158.0)
    (160.0 162.0 164.0 166.0 168.0 170.0 172.0 174.0 176.0 178.0)
    (180.0 182.0 184.0 186.0 188.0 190.0 192.0 194.0 196.0 198.0))
  :op #<PROCEEDNODE {100869A783}>
  :requires-grad NIL
  :variables (STC98242)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !sub

(!sub a b &key (reduce nil))
;; or
(!- &rest tensors)

Subtracts b from a. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!sub (ax+b `(10 10) 1 0) (ax+b `(10 10) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC98573
   ((0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0)
    (0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0))
  :op #<PROCEEDNODE {10086DC173}>
  :requires-grad NIL
  :variables (STC98413)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !mul

(!mul a b &key (reduce nil))
;; or
(!* &rest tensors)

Multiplies a and b. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!mul (ax+b `(10 10) 1 0) (ax+b `(10 10) 1 0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC98749
   ((0.0    1.0    4.0    9.0    16.0   25.0   36.0   49.0   64.0   81.0)
    (100.0  121.0  144.0  169.0  196.0  225.0  256.0  289.0  324.0  361.0)
    (400.0  441.0  484.0  529.0  576.0  625.0  676.0  729.0  784.0  841.0)
    (900.0  961.0  1024.0 1089.0 1156.0 1225.0 1296.0 1369.0 1444.0 1521.0)
    (1600.0 1681.0 1764.0 1849.0 1936.0 2025.0 2116.0 2209.0 2304.0 2401.0)
    (2500.0 2601.0 2704.0 2809.0 2916.0 3025.0 3136.0 3249.0 3364.0 3481.0)
    (3600.0 3721.0 3844.0 3969.0 4096.0 4225.0 4356.0 4489.0 4624.0 4761.0)
    (4900.0 5041.0 5184.0 5329.0 5476.0 5625.0 5776.0 5929.0 6084.0 6241.0)
    (6400.0 6561.0 6724.0 6889.0 7056.0 7225.0 7396.0 7569.0 7744.0 7921.0)
    (8100.0 8281.0 8464.0 8649.0 8836.0 9025.0 9216.0 9409.0 9604.0 9801.0))
  :op #<PROCEEDNODE {100872C583}>
  :requires-grad NIL
  :variables (STC98588)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !div

(!div a b &key (reduce nil))
;; or
(!/ &rest tensors)

Divides a by b. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!div (ax+b `(10 10) 1 1) (ax+b `(10 10) 1 1)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC98940
   ((1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (0.99999994 1.0        1.0        1.0        1.0        1.0        0.99999994 1.0        1.0        1.0)
    (1.0        1.0        1.0        1.0        0.99999994 1.0        1.0        1.0        1.0        1.0)
    (0.99999994 1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        0.99999994 0.99999994 1.0        1.0        1.0        1.0        1.0        1.0        1.0)
    (1.0        1.0        1.0        0.99999994 1.0        1.0        0.99999994 1.0        1.0        1.0))
  :op #<PROCEEDNODE {10087953E3}>
  :requires-grad NIL
  :variables (STC98765)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !idiv

(!idiv a b &key (reduce nil))

Assuming both of a and b are the integer, divides a by b and returns the integer part. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!idiv (ax+b `(10 10) 3 1 :dtype :uint32) (ax+b `(10 10) 0 2 :dtype :uint32)))
Result
Result
{Tensor[uint32] :shape (10 10) :id STC99105
   ((0   2   3   5   6   8   9   11  12  14)
    (15  17  18  20  21  23  24  26  27  29)
    (30  32  33  35  36  38  39  41  42  44)
    (45  47  48  50  51  53  54  56  57  59)
    (60  62  63  65  66  68  69  71  72  74)
    (75  77  78  80  81  83  84  86  87  89)
    (90  92  93  95  96  98  99  101 102 104)
    (105 107 108 110 111 113 114 116 117 119)
    (120 122 123 125 126 128 129 131 132 134)
    (135 137 138 140 141 143 144 146 147 149))
  :op #<PROCEEDNODE {1008821613}>
  :requires-grad NIL
  :variables (STC98955)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !maximum

(!maximum a b &key (reduce nil))
Returns the maximum of a and b. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!maximum (rand `(3 3)) (randn `(3 3))))
Result
Result
{Tensor[float32] :shape (3 3) :id STC122925
   ((0.7591348 0.646458  0.6929876)
    (1.7865713 0.9344596 0.0257933)
    (0.0458906 1.0599645 0.803172))
  :op #<PROCEEDNODE {1004C51DB3}>
  :requires-grad NIL
  :variables (STC122834)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !minimum

(!minimum a b &key (reduce nil))
Returns the minimum of a and b. If reduce is T, it will reduce the result. (Broadcast)

lisp
CATEN-USER> (proceed (!minimum (rand `(3 3)) (randn `(3 3))))
Result
Result
{Tensor[float32] :shape (3 3) :id STC123033
   ((-1.0500464   0.1391572    0.79089206)
    (-0.48569393  -1.0057052   0.64497745)
    (0.22257398   -1.3091459   -0.027061272))
  :op #<PROCEEDNODE {1004E187E3}>
  :requires-grad NIL
  :variables (STC122941)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !gcd

(!gcd a b &key (reduce nil))
Returns the greatest common divisor of a and b. If reduce is T, it will reduce the result. (Broadcast)

a, b are expected to be integer scalars. (dedicated to the view computation)

lisp
CATEN-USER> (ctx:with-contextvar (:jit 0) (proceed (!gcd (iconst 8) (iconst 4))))
Result
Result
{Tensor[int64] :shape NIL :id STC123055
  4
  :op #<PROCEEDNODE {1006A660E3}>
  :requires-grad NIL
  :variables (STC123036)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[function] !lcm

(!lcm a b)
Returns the least common multiple of a and b.

a, b are expected to be integer scalars.

lisp
CATEN-USER> (ctx:with-contextvar (:jit 0) (proceed (!lcm (iconst 8) (iconst 4))))
Result
Result
{Tensor[int64] :shape NIL :id STC123118
  8
  :op #<PROCEEDNODE {1006C86DE3}>
  :requires-grad NIL
  :variables (STC123061)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[function] !exp

(!exp x)

Computes (exp x).

lisp
CATEN-USER> (proceed (!exp (ax+b `(10 10) 0.01 0.0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC123232
   ((1.0       1.0100502 1.0202013 1.0304545 1.0408108 1.0512711 1.0618366 1.0725082 1.0832871 1.0941743)
    (1.105171  1.116278  1.1274968 1.1388284 1.1502738 1.1618342 1.1735109 1.1853049 1.1972173 1.2092496)
    (1.2214028 1.2336781 1.2460767 1.2586    1.2712492 1.2840254 1.2969301 1.3099644 1.3231298 1.3364275)
    (1.3498588 1.3634251 1.3771278 1.3909681 1.4049476 1.4190675 1.4333293 1.4477346 1.4622846 1.4769808)
    (1.4918246 1.5068177 1.5219616 1.5372574 1.5527072 1.5683122 1.5840739 1.5999942 1.6160744 1.6323161)
    (1.6487212 1.6652912 1.6820276 1.6989322 1.7160068 1.733253  1.7506725 1.768267  1.7860384 1.8039883)
    (1.8221188 1.8404315 1.8589281 1.8776106 1.8964808 1.9155407 1.9347923 1.9542372 1.9738777 1.9937155)
    (2.0137527 2.033991  2.054433  2.0750806 2.0959353 2.1169999 2.138276  2.1597662 2.181472  2.2033963)
    (2.2255409 2.2479079 2.2704997 2.2933185 2.316367  2.3396468 2.3631606 2.386911  2.4108996 2.4351294)
    (2.4596028 2.4843223 2.5092902 2.5345092 2.5599813 2.5857096 2.6116965 2.6379445 2.664456  2.691234))
  :op #<PROCEEDNODE {1006E315B3}>
  :requires-grad NIL
  :variables (STC123126)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !log

(!log x)

Computes (log x).

lisp
CATEN-USER> (proceed (!log (ax+b `(10 10) 0.01 0.001)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC123344
   ((-6.9077554   -4.50986     -3.8632329   -3.4737678   -3.1941833   -2.97593     -2.7968814   -2.6450753   -2.5133061   -2.396896)
    (-2.2926347   -2.198225    -2.1119647   -2.032558    -1.9589953   -1.8904755   -1.8263509   -1.7660917   -1.7092583   -1.6554819)
    (-1.6044505   -1.555897    -1.5095925   -1.4653376   -1.4229584   -1.3823024   -1.343235    -1.3056365   -1.2694006   -1.2344321)
    (-1.2006451   -1.1679624   -1.1363143   -1.105637    -1.0758728   -1.046969    -1.0188774   -0.99155325  -0.964956    -0.93904775)
    (-0.9137939   -0.8891622   -0.8651225   -0.84164727  -0.81871045  -0.796288    -0.7743574   -0.7528972   -0.73188806  -0.7113112)
    (-0.6911492   -0.6713857   -0.6520053   -0.63299334  -0.6143361   -0.59602046  -0.5780344   -0.5603661   -0.5430046   -0.52593935)
    (-0.5091604   -0.49265832  -0.47642422  -0.46044946  -0.44472587  -0.42924568  -0.41400146  -0.39898625  -0.38419297  -0.36961547)
    (-0.35524744  -0.3410829   -0.3271162   -0.3133419   -0.29975465  -0.28634965  -0.27312195  -0.26006696  -0.24718018  -0.23445737)
    (-0.22189441  -0.20948724  -0.19723219  -0.18512551  -0.17316367  -0.1613432   -0.14966084  -0.1381133   -0.12669767  -0.11541088)
    (-0.10425006  -0.093212426 -0.082295306 -0.07149601  -0.060812157 -0.050241243 -0.039780907 -0.029428856 -0.019182874 -0.009040808))
  :op #<PROCEEDNODE {1006E7F3F3}>
  :requires-grad NIL
  :variables (STC123240)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !sqrt

(!sqrt x)
Computes (sqrt x).

lisp
CATEN-USER> (proceed (!sqrt (ax+b `(10 10) 0.01 0.0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC123625
   ((0.0        0.1        0.14142135 0.17320508 0.2        0.2236068  0.24494897 0.26457512 0.2828427  0.29999998)
    (0.31622776 0.33166248 0.34641016 0.3605551  0.37416574 0.38729832 0.4        0.41231057 0.42426407 0.4358899)
    (0.4472136  0.45825756 0.4690416  0.47958314 0.48989794 0.5        0.50990194 0.51961523 0.52915025 0.53851646)
    (0.5477225  0.55677646 0.5656854  0.5744563  0.5830952  0.591608   0.59999996 0.60827625 0.61644137 0.6244998)
    (0.6324555  0.64031243 0.64807403 0.65574384 0.66332495 0.67082036 0.67823297 0.6855655  0.6928203  0.7)
    (0.70710677 0.71414286 0.7211102  0.72801095 0.7348469  0.7416199  0.7483315  0.7549834  0.7615773  0.76811457)
    (0.77459663 0.781025   0.7874008  0.7937254  0.8        0.8062258  0.8124038  0.81853527 0.82462114 0.83066237)
    (0.83666    0.84261495 0.84852815 0.85440034 0.86023253 0.8660254  0.8717798  0.8774964  0.8831761  0.8888194)
    (0.8944272  0.9        0.9055385  0.91104335 0.9165151  0.92195445 0.92736185 0.9327379  0.9380832  0.9433981)
    (0.94868326 0.9539392  0.9591663  0.96436507 0.96953595 0.9746794  0.9797959  0.98488575 0.98994946 0.9949874))
  :op #<PROCEEDNODE {1006F38613}>
  :requires-grad NIL
  :variables (STC123352)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !neg

(!neg tensor)
!neg computes the negative value of the tensor.

lisp
CATEN-USER> (proceed (!neg (ax+b `(10 10) 0.01 0.0)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC123729
   ((-0.0         -0.01        -0.02        -0.03        -0.04        -0.049999997 -0.06        -0.07        -0.08        -0.089999996)
    (-0.099999994 -0.11        -0.12        -0.13        -0.14        -0.14999999  -0.16        -0.17        -0.17999999  -0.19)
    (-0.19999999  -0.21        -0.22        -0.22999999  -0.24        -0.25        -0.26        -0.26999998  -0.28        -0.29)
    (-0.29999998  -0.31        -0.32        -0.32999998  -0.34        -0.35        -0.35999998  -0.37        -0.38        -0.39)
    (-0.39999998  -0.41        -0.42        -0.42999998  -0.44        -0.45        -0.45999998  -0.47        -0.48        -0.48999998)
    (-0.5         -0.51        -0.52        -0.53        -0.53999996  -0.55        -0.56        -0.57        -0.58        -0.59)
    (-0.59999996  -0.61        -0.62        -0.63        -0.64        -0.65        -0.65999997  -0.66999996  -0.68        -0.69)
    (-0.7         -0.71        -0.71999997  -0.72999996  -0.74        -0.75        -0.76        -0.77        -0.78        -0.78999996)
    (-0.79999995  -0.81        -0.82        -0.83        -0.84        -0.84999996  -0.85999995  -0.87        -0.88        -0.89)
    (-0.9         -0.90999997  -0.91999996  -0.93        -0.94        -0.95        -0.96        -0.96999997  -0.97999996  -0.98999995))
  :op #<PROCEEDNODE {1006F67C13}>
  :requires-grad NIL
  :variables (STC123633)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !recip

(!recip tensor)
!recip computes the reciprocal of the tensor.

lisp
CATEN-USER> (proceed (!recip (ax+b `(10 10) 0.01 0.1)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC123841
   ((10.0       9.090909   8.333333   7.692308   7.142857   6.6666665  6.25       5.882353   5.5555553  5.263158)
    (5.0000005  4.7619047  4.5454545  4.3478265  4.1666665  4.0        3.846154   3.7037036  3.5714285  3.448276)
    (3.3333335  3.2258065  3.125      3.0303032  2.9411764  2.857143   2.777778   2.702703   2.631579   2.5641026)
    (2.5000002  2.4390244  2.3809524  2.3255816  2.2727273  2.2222223  2.1739132  2.1276596  2.0833335  2.0408163)
    (2.0000002  1.9607843  1.923077   1.8867925  1.8518518  1.8181818  1.7857143  1.754386   1.724138   1.6949153)
    (1.6666666  1.6393442  1.6129032  1.5873016  1.5625     1.5384614  1.5151515  1.4925373  1.4705882  1.4492754)
    (1.4285715  1.4084506  1.3888888  1.369863   1.3513514  1.3333334  1.3157895  1.2987013  1.2820512  1.2658228)
    (1.25       1.2345679  1.2195122  1.2048193  1.1904762  1.1764705  1.1627907  1.1494253  1.1363636  1.1235955)
    (1.1111112  1.098901   1.0869565  1.0752689  1.0638298  1.0526316  1.0416667  1.0309278  1.0204082  1.010101)
    (1.0        0.990099   0.98039216 0.97087383 0.9615385  0.952381   0.9433963  0.9345795  0.92592597 0.91743124))
  :op #<PROCEEDNODE {1006FB38E3}>
  :requires-grad NIL
  :variables (STC123737)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !signum

(!signum x)

Returns the sign of the tensor. If the tensor is positive, it returns 1. If the tensor is negative, it returns -1. If the tensor is zero, it returns 0.

lisp
CATEN-USER> (proceed (!signum (ax+b `(10 10) 0.02 -0.1)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC126939
   ((-1.0 -1.0 -1.0 -1.0 -1.0 -1.0 1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0)
    (1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0  1.0))
  :op #<PROCEEDNODE {1007793F13}>
  :requires-grad NIL
  :variables (STC124441)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !abs

(!abs x)

Returns the absolute value of the tensor.

lisp
CATEN-USER> (proceed (!abs (ax+b `(10 10) 0.02 -0.1)))
Result
Result
{Tensor[float32] :shape (10 10) :id STC130042
   ((0.1         0.08        0.060000002 0.040000003 0.020000003 7.450581e-9 0.019999996 0.04        0.059999995 0.07999999)
    (0.09999999  0.12        0.13999999  0.16        0.18        0.19999999  0.22        0.24000001  0.26        0.28)
    (0.29999998  0.32        0.34        0.35999998  0.38        0.4         0.42        0.43999997  0.46        0.48)
    (0.49999997  0.52        0.53999996  0.55999994  0.58        0.59999996  0.61999995  0.64        0.65999997  0.67999995)
    (0.6999999   0.71999997  0.73999995  0.75999993  0.78        0.79999995  0.81999993  0.84        0.85999995  0.87999994)
    (0.9         0.91999996  0.93999994  0.9599999   0.9799999   1.0         1.02        1.04        1.06        1.0799999)
    (1.0999999   1.12        1.14        1.16        1.18        1.1999999   1.2199999   1.2399999   1.26        1.28)
    (1.3         1.3199999   1.3399999   1.3599999   1.38        1.4         1.42        1.4399999   1.4599999   1.4799999)
    (1.4999999   1.52        1.54        1.56        1.5799999   1.5999999   1.6199999   1.64        1.66        1.68)
    (1.6999999   1.7199999   1.7399999   1.76        1.78        1.8         1.8199999   1.8399999   1.8599999   1.8799999))
  :op #<PROCEEDNODE {1007EE9E43}>
  :requires-grad NIL
  :variables (STC127540)
  :tracker #<TRACKER :order={row(0 1)} :shape=(10 10) :contiguous-p=T>}

[function] !>

(!> x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!> (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC131460
   ((0 0 0)
    (1 0 1)
    (0 1 0))
  :op #<PROCEEDNODE {100842C343}>
  :requires-grad NIL
  :variables (STC130255)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !<

(!< x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!< (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC132870
   ((0 1 1)
    (0 0 0)
    (0 0 0))
  :op #<PROCEEDNODE {10088FA6E3}>
  :requires-grad NIL
  :variables (STC131673)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !>=

(!>= x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!>= (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC134294
   ((1 1 1)
    (0 1 1)
    (1 1 0))
  :op #<PROCEEDNODE {1008D270D3}>
  :requires-grad NIL
  :variables (STC133083)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !<=

(!<= x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!<= (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC135710
   ((0 0 1)
    (0 1 0)
    (1 1 0))
  :op #<PROCEEDNODE {1009273D23}>
  :requires-grad NIL
  :variables (STC134507)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !eq

(!EQ x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!eq (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC137122
   ((0 0 0)
    (0 0 0)
    (0 0 0))
  :op #<PROCEEDNODE {100397C4C3}>
  :requires-grad NIL
  :variables (STC135923)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !neq

(!NEQ x y)

Compares x and y element-wise and returns the result as a boolean tensor.

lisp
CATEN-USER> (proceed (!where (!neq (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC138532
   ((1 1 1)
    (1 1 1)
    (1 1 1))
  :op #<PROCEEDNODE {1003E326E3}>
  :requires-grad NIL
  :variables (STC137335)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !and

(!AND x y)

Computes the logical/bitwise and of the tensor.

lisp
CATEN-USER> (proceed (!and (iconst 5) (iconst 3)))
Result
Result
{Tensor[int64] :shape NIL :id STC138550
  1
  :op #<PROCEEDNODE {1003E49AC3}>
  :requires-grad NIL
  :variables (STC138535)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[function] !xor

(!XOR x y)

Computes the logical/bitwise xor of the tensor.

lisp
CATEN-USER> (proceed (!xor (iconst 5) (iconst 3)))
Result
Result
{Tensor[int64] :shape NIL :id STC138568
  6
  :op #<PROCEEDNODE {1003E51443}>
  :requires-grad NIL
  :variables (STC138553)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[function] !or

(!OR x y)

Computes the logical/bitwise or of the tensor.

lisp
CATEN-USER> (proceed (!or (iconst 5) (iconst 3)))
Result
Result
{Tensor[int64] :shape NIL :id STC138586
  7
  :op #<PROCEEDNODE {1003E68503}>
  :requires-grad NIL
  :variables (STC138571)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[function] !where

(!where condition x y)

Selects elements from x or y based on the condition. If the condition is true, it selects the element from x, otherwise from y.

lisp
CATEN-USER> (proceed (!where (!eq (rand `(3 3)) (randn `(3 3))) (iconst 1) (iconst 0)))
Result
Result
{Tensor[int64] :shape (3 3) :id STC139998
   ((0 0 0)
    (0 0 0)
    (0 0 0))
  :op #<PROCEEDNODE {1004D06873}>
  :requires-grad NIL
  :variables (STC138799)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}

[function] !const

(!const tensor value)
Creates a constant tensor with the specified value from the tensor.

lisp
CATEN-USER> (proceed (!const (make-tensor `(3 3)) 1.0))
Result
Result
{Tensor[float32] :shape NIL :id STC140013
  1.0
  :op #<PROCEEDNODE {1004D2BA73}>
  :requires-grad NIL
  :variables (SID140003)
  :tracker #<TRACKER :order={rowNIL} :shape=() :contiguous-p=T>}

[generic] !index-components

(!index-components object)

Returns the index components of the tensor. object can be either of tensor or list.

lisp
CATEN-USER> (proceed (!index-components (make-tensor `(3 3))))
Result
Result
{Tensor[float32] :shape (3 3) :id STC140096
   ((0.0 1.0 2.0)
    (3.0 4.0 5.0)
    (6.0 7.0 8.0))
  :op #<PROCEEDNODE {1004D34C63}>
  :requires-grad NIL
  :variables (STC140018)
  :tracker #<TRACKER :order={row(0 1)} :shape=(3 3) :contiguous-p=T>}
lisp
CATEN-USER> (proceed (!index-components `(1 3)))
Result
Result
{Tensor[float32] :shape (1 3) :id STC140179
   ((0.0 1.0 2.0))
  :op #<PROCEEDNODE {1004D4DD83}>
  :requires-grad NIL
  :variables (STC140101)
  :tracker #<TRACKER :order={row(0 1)} :shape=(1 3) :contiguous-p=T>}