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fix documentation
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doc/specs/stdlib_intrinsics.md

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@@ -15,7 +15,7 @@ The `stdlib_intrinsics` module provides replacements for some of the well known
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#### Description
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The `stdlib_sum` function can replace the intrinsic `sum` for `real` or `complex` arrays. It follows a chunked implementation which maximizes vectorization potential as well as reducing the round-off error. This procedure is recommended when summing large arrays, for repetitive summation of smaller arrays consider the classical `sum`.
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The `stdlib_sum` function can replace the intrinsic `sum` for `real`, `complex` or `integer` arrays. It follows a chunked implementation which maximizes vectorization potential as well as reducing the round-off error. This procedure is recommended when summing large arrays, for repetitive summation of smaller arrays consider the classical `sum`.
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#### Syntax
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#### Description
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The `stdlib_sum_kahan` function can replace the intrinsic `sum` for `real`, `complex` or `integer` arrays. It follows a chunked implementation which maximizes vectorization potential complemented by an `elemental` kernel based on the [kahan summation](https://doi.org/10.1145%2F363707.363723) strategy to reduce the round-off error:
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The `stdlib_sum_kahan` function can replace the intrinsic `sum` for `real` or `complex` arrays. It follows a chunked implementation which maximizes vectorization potential complemented by an `elemental` kernel based on the [kahan summation](https://doi.org/10.1145%2F363707.363723) strategy to reduce the round-off error:
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```fortran
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elemental subroutine kahan_kernel_<kind>(a,s,c)
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#### Argument(s)
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`x`: 1D array of either `real`, `complex` or `integer` type. This argument is `intent(in)`.
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`x`: 1D array of either `real` or `complex` type. This argument is `intent(in)`.
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`dim` (optional): scalar of type `integer` with a value in the range from 1 to n, where n equals the rank of `x`.
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#### Description
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The `stdlib_dot_product` function can replace the intrinsic `dot_product` for 1D `real` or `complex` arrays. It follows a chunked implementation which maximizes vectorization potential as well as reducing the round-off error. This procedure is recommended when crunching large arrays, for repetitive products of smaller arrays consider the classical `dot_product`.
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The `stdlib_dot_product` function can replace the intrinsic `dot_product` for 1D `real`, `complex` or `integer` arrays. It follows a chunked implementation which maximizes vectorization potential as well as reducing the round-off error. This procedure is recommended when crunching large arrays, for repetitive products of smaller arrays consider the classical `dot_product`.
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#### Syntax
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src/stdlib_intrinsics.fypp

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!! This interface provides standard conforming call for sum of elements of any rank.
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!! The 1-D base implementation follows a chunked approach combined with a kahan kernel for optimizing performance and increasing accuracy.
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!! The `N-D` interfaces calls upon the `(N-1)-D` implementation.
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!! Supported data types include `real`, `complex` and `integer`.
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!! Supported data types include `real` and `complex`.
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!!
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#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
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pure module function stdlib_sum_kahan_1d_${s}$(a) result(s)
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!!
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!! compute the dot_product of rank 1 arrays.
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!! The implementation follows a chunked approach combined with a kahan kernel for optimizing performance and increasing accuracy.
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!! Supported data types include `real`, `complex` and `integer`.
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!! Supported data types include `real` and `complex`.
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!!
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#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
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pure module function stdlib_dot_product_kahan_${s}$(a,b) result(p)

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