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stdlib_intrinsics.fypp
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#:include "common.fypp"
#:set I_KINDS_TYPES = list(zip(INT_KINDS, INT_TYPES, INT_KINDS))
#:set R_KINDS_TYPES = list(zip(REAL_KINDS, REAL_TYPES, REAL_SUFFIX))
#:set C_KINDS_TYPES = list(zip(CMPLX_KINDS, CMPLX_TYPES, CMPLX_SUFFIX))
#:set RANKS = range(2, MAXRANK + 1)
module stdlib_intrinsics
!!Alternative implementations of some Fortran intrinsic functions offering either faster and/or more accurate evaluation.
!! ([Specification](../page/specs/stdlib_intrinsics.html))
use stdlib_kinds
use stdlib_linalg_state, only: linalg_state_type
implicit none
private
interface stdlib_sum
!! version: experimental
!!
!!### Summary
!! Sum elements of rank N arrays.
!! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_sum))
!!
!!### Description
!!
!! This interface provides standard conforming call for sum of elements of any rank.
!! The 1-D base implementation follows a chunked approach for optimizing performance and increasing accuracy.
!! The `N-D` interfaces calls upon the `(N-1)-D` implementation.
!! Supported data types include `real`, `complex` and `integer`.
!!
#:for k, t, s in I_KINDS_TYPES + R_KINDS_TYPES + C_KINDS_TYPES
pure module function stdlib_sum_1d_${s}$(a) result(s)
${t}$, intent(in) :: a(:)
${t}$ :: s
end function
pure module function stdlib_sum_1d_${s}$_mask(a,mask) result(s)
${t}$, intent(in) :: a(:)
logical, intent(in) :: mask(:)
${t}$ :: s
end function
#:for rank in RANKS
pure module function stdlib_sum_${rank}$d_${s}$( x, mask ) result( s )
${t}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask${ranksuffix(rank)}$
${t}$ :: s
end function
pure module function stdlib_sum_${rank}$d_dim_${s}$( x , dim, mask ) result( s )
${t}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in):: dim
logical, intent(in), optional :: mask${ranksuffix(rank)}$
${t}$ :: s${reduced_shape('x', rank, 'dim')}$
end function
#:endfor
#:endfor
end interface
public :: stdlib_sum
interface stdlib_sum_kahan
!! version: experimental
!!
!!### Summary
!! Sum elements of rank N arrays.
!! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_sum_kahan))
!!
!!### Description
!!
!! This interface provides standard conforming call for sum of elements of any rank.
!! The 1-D base implementation follows a chunked approach combined with a kahan kernel for optimizing performance and increasing accuracy.
!! The `N-D` interfaces calls upon the `(N-1)-D` implementation.
!! Supported data types include `real` and `complex`.
!!
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
pure module function stdlib_sum_kahan_1d_${s}$(a) result(s)
${t}$, intent(in) :: a(:)
${t}$ :: s
end function
pure module function stdlib_sum_kahan_1d_${s}$_mask(a,mask) result(s)
${t}$, intent(in) :: a(:)
logical, intent(in) :: mask(:)
${t}$ :: s
end function
#:for rank in RANKS
pure module function stdlib_sum_kahan_${rank}$d_${s}$( x, mask ) result( s )
${t}$, intent(in) :: x${ranksuffix(rank)}$
logical, intent(in), optional :: mask${ranksuffix(rank)}$
${t}$ :: s
end function
pure module function stdlib_sum_kahan_${rank}$d_dim_${s}$( x , dim, mask ) result( s )
${t}$, intent(in) :: x${ranksuffix(rank)}$
integer, intent(in):: dim
logical, intent(in), optional :: mask${ranksuffix(rank)}$
${t}$ :: s${reduced_shape('x', rank, 'dim')}$
end function
#:endfor
#:endfor
end interface
public :: stdlib_sum_kahan
interface stdlib_dot_product
!! version: experimental
!!
!!### Summary
!! dot_product of rank 1 arrays.
!! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_dot_product))
!!
!!### Description
!!
!! compute the dot_product of rank 1 arrays.
!! The 1-D base implementation follows a chunked approach for optimizing performance and increasing accuracy.
!! Supported data types include `real`, `complex` and `integer`.
!!
#:for k, t, s in I_KINDS_TYPES + R_KINDS_TYPES + C_KINDS_TYPES
pure module function stdlib_dot_product_${s}$(a,b) result(p)
${t}$, intent(in) :: a(:)
${t}$, intent(in) :: b(:)
${t}$ :: p
end function
#:endfor
end interface
public :: stdlib_dot_product
interface stdlib_dot_product_kahan
!! version: experimental
!!
!!### Summary
!! dot_product of rank 1 arrays.
!! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_dot_product_kahan))
!!
!!### Description
!!
!! compute the dot_product of rank 1 arrays.
!! The implementation follows a chunked approach combined with a kahan kernel for optimizing performance and increasing accuracy.
!! Supported data types include `real` and `complex`.
!!
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
pure module function stdlib_dot_product_kahan_${s}$(a,b) result(p)
${t}$, intent(in) :: a(:)
${t}$, intent(in) :: b(:)
${t}$ :: p
end function
#:endfor
end interface
public :: stdlib_dot_product_kahan
interface kahan_kernel
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
module procedure :: kahan_kernel_${s}$
module procedure :: kahan_kernel_m_${s}$
#:endfor
end interface
public :: kahan_kernel
interface stdlib_matmul
!! version: experimental
!!
!!### Summary
!! compute the matrix multiplication of more than two matrices with a single function call.
!! ([Specification](../page/specs/stdlib_intrinsics.html#stdlib_matmul))
!!
!!### Description
!!
!! matrix multiply more than two matrices with a single function call
!! the multiplication with the optimal parenthesization for efficiency of computation is done automatically
!! Supported data types are `real` and `complex`.
!!
!! Note: The matrices must be of compatible shapes to be multiplied
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
pure module function stdlib_matmul_pure_${s}$ (m1, m2, m3, m4, m5) result(r)
${t}$, intent(in) :: m1(:,:), m2(:,:)
${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
${t}$, allocatable :: r(:,:)
end function stdlib_matmul_pure_${s}$
module function stdlib_matmul_${s}$ (m1, m2, m3, m4, m5, err) result(r)
${t}$, intent(in) :: m1(:,:), m2(:,:)
${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
type(linalg_state_type), intent(out) :: err
${t}$, allocatable :: r(:,:)
end function stdlib_matmul_${s}$
#:endfor
end interface stdlib_matmul
public :: stdlib_matmul
! internal interface
interface stdlib_matmul_sub
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
pure module subroutine stdlib_matmul_sub_${s}$ (res, m1, m2, m3, m4, m5, err)
${t}$, intent(out), allocatable :: res(:,:)
${t}$, intent(in) :: m1(:,:), m2(:,:)
${t}$, intent(in), optional :: m3(:,:), m4(:,:), m5(:,:)
type(linalg_state_type), intent(out), optional :: err
end subroutine stdlib_matmul_sub_${s}$
#:endfor
end interface stdlib_matmul_sub
contains
#:for k, t, s in R_KINDS_TYPES + C_KINDS_TYPES
elemental subroutine kahan_kernel_${s}$(a,s,c)
${t}$, intent(in) :: a
${t}$, intent(inout) :: s
${t}$, intent(inout) :: c
${t}$ :: t, y
y = a - c
t = s + y
c = (t - s) - y
s = t
end subroutine
elemental subroutine kahan_kernel_m_${s}$(a,s,c,m)
${t}$, intent(in) :: a
${t}$, intent(inout) :: s
${t}$, intent(inout) :: c
logical, intent(in) :: m
${t}$ :: t, y
y = a - c
t = s + y
c = (t - s) - y
s = merge( s , t , m )
end subroutine
#:endfor
end module stdlib_intrinsics