specs and examples

Author: jalvesz

doc/specs/stdlib_intrinsics.md

@@ -15,7 +15,7 @@ The `stdlib_intrinsics` module provides replacements for some of the well known
 
 #### Description
 
-The `fsum` function can replace the intrinsic `sum` for 1D `real` or `complex` arrays. It follows a chunked implementation which maximaxes vectorization potential as well as reducing the round-off error.
+The `fsum` function can replace the intrinsic `sum` 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 summing large arrays, for repetitive summation of smaller arrays consider the classical `sum`.
 
 #### Syntax
 
@@ -32,7 +32,7 @@ Pure function.
 #### Argument(s)
 
 `x`: 1D array of either `real` or `complex` type. This argument is `intent(in)`.
-`mask`: 1D array of `logical` values. This argument is `intent(in)`.
+`mask` (optional): 1D array of `logical` values. This argument is `intent(in)`.
 
 #### Output value or Result value
 
@@ -43,3 +43,116 @@ The output is a scalar of `type` and `kind` same as to that of `x`.
 ```fortran
 {!example/math/example_intrinsics_sum.f90!}
 ```
+
+<!-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -->
+### `fsum_kahan` function
+
+#### Description
+
+The `fsum_kahan` function can replace the intrinsic `sum` for 1D `real` or `complex` arrays. It follows a chunked implementation which maximizes vectorization potential, complemented by an `elemental` kernel based on the [kahan summation](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) strategy to reduce the round-off error:
+
+```fortran
+elemental subroutine vkahan_<kind>(a,s,c)
+    type(<kind>), intent(in) :: a
+    type(<kind>), intent(inout) :: s
+    type(<kind>), intent(inout) :: c
+    type(<kind>) :: t, y
+    y = a - c
+    t = s + y
+    c = (t - s) - y
+    s = t
+end subroutine
+```
+
+#### Syntax
+
+`res = ` [[stdlib_intrinsics(module):fsum_kahan(interface)]] ` (x [,mask] )`
+
+#### Status
+
+Experimental
+
+#### Class
+
+Pure function.
+
+#### Argument(s)
+
+`x`: 1D array of either `real` or `complex` type. This argument is `intent(in)`.
+`mask` (optional): 1D array of `logical` values. This argument is `intent(in)`.
+
+#### Output value or Result value
+
+The output is a scalar of `type` and `kind` same as to that of `x`.
+
+#### Example
+
+```fortran
+{!example/math/example_intrinsics_sum.f90!}
+```
+
+<!-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -->
+### `fprod` function
+
+#### Description
+
+The `fprod` 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`.
+
+#### Syntax
+
+`res = ` [[stdlib_intrinsics(module):fprod(interface)]] ` (x, y)`
+
+#### Status
+
+Experimental
+
+#### Class
+
+Pure function.
+
+#### Argument(s)
+
+`x`: 1D array of either `real` or `complex` type. This argument is `intent(in)`.
+`y`: 1D array of the same type and kind as `x`. This argument is `intent(in)`.
+
+#### Output value or Result value
+
+The output is a scalar of `type` and `kind` same as to that of `x` and `y`.
+
+#### Example
+
+```fortran
+{!example/math/example_intrinsics_dot_duct.f90!}
+```
+
+<!-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -->
+### `fprod_kahan` function
+
+#### Description
+
+The `fprod_kahan` function can replace the intrinsic `dot_product` for 1D `real` or `complex` arrays. It follows a chunked implementation which maximizes vectorization potential , complemented by the same `elemental` kernel based on the [kahan summation](https://en.wikipedia.org/wiki/Kahan_summation_algorithm) used for `fsum` to reduce the round-off error.
+
+#### Syntax
+
+`res = ` [[stdlib_intrinsics(module):fprod_kahan(interface)]] ` (x, y)`
+
+#### Status
+
+Experimental
+
+#### Class
+
+Pure function.
+
+#### Argument(s)
+
+`x`: 1D array of either `real` or `complex` type. This argument is `intent(in)`.
+`y`: 1D array of the same type and kind as `x`. This argument is `intent(in)`.
+
+#### Output value or Result value
+
+The output is a scalar of `type` and `kind` same as to that of `x` and `y`.
+
+```fortran
+{!example/math/example_intrinsics_dot_duct.f90!}
+```

example/CMakeLists.txt

@@ -13,6 +13,7 @@ add_subdirectory(constants)
 add_subdirectory(error)
 add_subdirectory(hashmaps)
 add_subdirectory(hash_procedures)
+add_subdirectory(intrinsics)
 add_subdirectory(io)
 add_subdirectory(linalg)
 add_subdirectory(logger)

example/intrinsics/CMakeLists.txt

@@ -0,0 +1,2 @@
+ADD_EXAMPLE(sum)
+ADD_EXAMPLE(dot_product)

example/intrinsics/example_dot_product.f90

@@ -0,0 +1,18 @@
+program example_dot_product
+    use stdlib_kinds, only: sp
+    use stdlib_intrinsics, only: fprod, fprod_kahan
+    implicit none
+
+    real(sp), allocatable :: x(:), y(:)
+    real(sp) :: total_prod(3)
+
+    allocate( x(1000), y(1000) )
+    call random_number(x)
+    call random_number(y)
+
+    total_prod(1) = dot_product(x,y) !> compiler intrinsic
+    total_prod(2) = fprod(x,y)       !> chunked summation over inner product
+    total_prod(3) = fprod_kahan(x,y) !> chunked kahan summation over inner product
+    print *, total_prod(1:3)
+    
+end program example_dot_product

example/intrinsics/example_sum.f90

@@ -0,0 +1,17 @@
+program example_sum
+    use stdlib_kinds, only: sp
+    use stdlib_intrinsics, only: fsum, fsum_kahan
+    implicit none
+
+    real(sp), allocatable :: x(:)
+    real(sp) :: total_sum(3)
+
+    allocate( x(1000) )
+    call random_number(x)
+
+    total_sum(1) = sum(x)       !> compiler intrinsic
+    total_sum(2) = fsum(x)      !> chunked summation
+    total_sum(3) = fsum_kahan(x)!> chunked kahan summation
+    print *, total_sum(1:3)
+    
+end program example_sum