Representation of arrays in memory

F-style transformation of non-contiguous to contiguous layout

For a F-style non-contiguous layout with shape, (d₀, d₁, …, d_N−1), the value associated with (n₀, n₁, …, n_N−1) is located in the contiguous layout with index = n^F.

$expression for index in contiguous layout mapped from index in F-style non-contiguous layout$

such that, if j > i−1

$products of d sub j is 1 if start index is greater than final index$

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Examples illustrating transformation to contiguous layout in F-style

Eg.1: Location of element in x with index (1, 2, 1)

For a F-style non-contiguous layout with shape, (d₀ = 2, d₁ = 4, d₂ = 3) the value in (n₀ = 1, n₁ = 2, n₂ = 1) of the non-contiguous layout is located in the contiguous layout with index n^F given by,

$index in contiguous layout for (1, 2, 1) index in F-style non-contiguous layout is equal to 13$

index in F-style non-contiguous layout into respective mapped index in contiguous layout

Eg.2: Location of element in x with index (1, 1, 1)

For a F-style non-contiguous layout with shape, (d₀ = 2, d₁ = 4, d₂ = 3) the value in (n₀ = 1, n₁ = 1, n₂ = 1) of the non-contiguous layout is located in the contiguous layout with index n^Fgiven by,

$index in contiguous layout for (1, 1, 1) index in F-style non-contiguous layout is equal to 11$

To move from the element with index (1, 2, 1) in the array x to the element at (1, 1, 1), two elements within the array must be jumped.

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