qmckl/org/qmckl_distance.org

#+TITLE: Inter-particle distances
#+SETUPFILE: ../tools/theme.setup
#+INCLUDE: ../tools/lib.org

Functions for the computation of distances between particles.

* Headers                                                         :noexport:
  #+begin_src elisp :noexport :results none
(org-babel-lob-ingest "../tools/lib.org")
#+end_src

  #+begin_src c :comments link :tangle (eval c_test) :noweb yes
#include "qmckl.h"
#include "munit.h"
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
MunitResult test_<<filename()>>() {
  qmckl_context context;
  context = qmckl_context_create();

  #+end_src

* Squared distance

** ~qmckl_distance_sq~
   :PROPERTIES:
   :Name:     qmckl_distance_sq
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

 ~qmckl_distance_sq~ computes the matrix of the squared distances
   between all pairs of points in two sets, one point within each set:

   \[
   C_{ij} = \sum_{k=1}^3 (A_{k,i}-B_{k,j})^2
   \]

   #+NAME: qmckl_distance_sq_args
   | qmckl_context | context   | in  | Global state                                  |
   | char          | transa    | in  | Array ~A~ is ~'N'~: Normal, ~'T'~: Transposed |
   | char          | transb    | in  | Array ~B~ is ~'N'~: Normal, ~'T'~: Transposed |
   | int64_t       | m         | in  | Number of points in the first set             |
   | int64_t       | n         | in  | Number of points in the second set            |
   | double        | A[][lda]  | in  | Array containing the $m \times 3$ matrix $A$  |
   | int64_t       | lda       | in  | Leading dimension of array ~A~                |
   | double        | B[][ldb]  | in  | Array containing the $n \times 3$ matrix $B$  |
   | int64_t       | ldb       | in  | Leading dimension of array ~B~                |
   | double        | C[n][ldc] | out | Array containing the $m \times n$ matrix $C$  |
   | int64_t       | ldc       | in  | Leading dimension of array ~C~                |

*** Requirements

    - ~context~ is not ~QMCKL_NULL_CONTEXT~
    - ~m > 0~
    - ~n > 0~
    - ~lda >= 3~ if ~transa == 'N'~
    - ~lda >= m~ if ~transa == 'T'~
    - ~ldb >= 3~ if ~transb == 'N'~
    - ~ldb >= n~ if ~transb == 'T'~
    - ~ldc >= m~
    - ~A~ is allocated with at least $3 \times m \times 8$ bytes
    - ~B~ is allocated with at least $3 \times n \times 8$ bytes
    - ~C~ is allocated with at least $m \times n \times 8$ bytes

*** C header

    #+CALL: generate_c_header(table=qmckl_distance_sq_args,rettyp=get_value("CRetType"),fname=get_value("Name"))

    #+RESULTS:
    #+begin_src c :tangle (eval h_func) :comments org
    qmckl_exit_code qmckl_distance_sq (
          const qmckl_context context,
          const char transa,
          const char transb,
          const int64_t m,
          const int64_t n,
          const double* A,
          const int64_t lda,
          const double* B,
          const int64_t ldb,
          double* const C,
          const int64_t ldc );
    #+end_src

*** Source
    #+begin_src f90 :tangle (eval f)
integer function qmckl_distance_sq_f(context, transa, transb, m, n, &
     A, LDA, B, LDB, C, LDC) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  character  , intent(in)  :: transa, transb
  integer*8  , intent(in)  :: m, n
  integer*8  , intent(in)  :: lda
  real*8     , intent(in)  :: A(lda,*)
  integer*8  , intent(in)  :: ldb
  real*8     , intent(in)  :: B(ldb,*)
  integer*8  , intent(in)  :: ldc
  real*8     , intent(out) :: C(ldc,*)

  integer*8 :: i,j
  real*8    :: x, y, z
  integer   :: transab

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (m <= 0_8) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  if (n <= 0_8) then
     info = QMCKL_INVALID_ARG_5
     return
  endif

  if (transa == 'N' .or. transa == 'n') then
     transab = 0
  else if (transa == 'T' .or. transa == 't') then
     transab = 1
  else
     transab = -100
  endif

  if (transb == 'N' .or. transb == 'n') then
     continue
  else if (transa == 'T' .or. transa == 't') then
     transab = transab + 2
  else
     transab = -100
  endif

  if (transab < 0) then
     info = QMCKL_INVALID_ARG_1
     return
  endif

  if (iand(transab,1) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,1) == 1 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 2 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif


  select case (transab)

  case(0)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(1,j)
           y = A(2,i) - B(2,j)
           z = A(3,i) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(1)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(1,j)
           y = A(i,2) - B(2,j)
           z = A(i,3) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(2)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(j,1)
           y = A(2,i) - B(j,2)
           z = A(3,i) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  case(3)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(j,1)
           y = A(i,2) - B(j,2)
           z = A(i,3) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
     end do

  end select

end function qmckl_distance_sq_f
    #+end_src

*** Performance

    This function might be more efficient when ~A~ and ~B~ are
    transposed.

** C interface                                                     :noexport:

   #+CALL: generate_c_interface(table=qmckl_distance_sq_args,rettyp=get_value("FRetType"),fname=get_value("Name"))

   #+RESULTS:
   #+begin_src f90 :tangle (eval f) :comments org :exports none
   integer(c_int32_t) function qmckl_distance_sq &
       (context, transa, transb, m, n, A, lda, B, ldb, C, ldc) &
       bind(C) result(info)

     use, intrinsic :: iso_c_binding
     implicit none

     integer (c_int64_t) , intent(in)  , value :: context
     character           , intent(in)  , value :: transa
     character           , intent(in)  , value :: transb
     integer (c_int64_t) , intent(in)  , value :: m
     integer (c_int64_t) , intent(in)  , value :: n
     real    (c_double ) , intent(in)          :: A(lda,*)
     integer (c_int64_t) , intent(in)  , value :: lda
     real    (c_double ) , intent(in)          :: B(ldb,*)
     integer (c_int64_t) , intent(in)  , value :: ldb
     real    (c_double ) , intent(out)         :: C(ldc,n)
     integer (c_int64_t) , intent(in)  , value :: ldc

     integer(c_int32_t), external :: qmckl_distance_sq_f
     info = qmckl_distance_sq_f &
            (context, transa, transb, m, n, A, lda, B, ldb, C, ldc)

   end function qmckl_distance_sq
   #+end_src

   #+CALL: generate_f_interface(table=qmckl_distance_sq_args,rettyp=get_value("FRetType"),fname=get_value("Name"))

   #+RESULTS:
   #+begin_src f90 :tangle (eval fh_func) :comments org :exports none
   interface
     integer(c_int32_t) function qmckl_distance_sq &
         (context, transa, transb, m, n, A, lda, B, ldb, C, ldc) &
         bind(C)
       use, intrinsic :: iso_c_binding
       import
       implicit none

       integer (c_int64_t) , intent(in)  , value :: context
       character           , intent(in)  , value :: transa
       character           , intent(in)  , value :: transb
       integer (c_int64_t) , intent(in)  , value :: m
       integer (c_int64_t) , intent(in)  , value :: n
       real    (c_double ) , intent(in)          :: A(lda,*)
       integer (c_int64_t) , intent(in)  , value :: lda
       real    (c_double ) , intent(in)          :: B(ldb,*)
       integer (c_int64_t) , intent(in)  , value :: ldb
       real    (c_double ) , intent(out)         :: C(ldc,n)
       integer (c_int64_t) , intent(in)  , value :: ldc

     end function qmckl_distance_sq
   end interface
   #+end_src

*** Test                                                           :noexport:
    #+begin_src f90 :tangle (eval f_test)
integer(qmckl_exit_code) function test_qmckl_distance_sq(context) bind(C)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in), value :: context

  double precision, allocatable :: A(:,:), B(:,:), C(:,:)
  integer*8                     :: m, n, LDA, LDB, LDC
  double precision              :: x
  integer*8                     :: i,j

  m = 5
  n = 6
  LDA = m
  LDB = n
  LDC = 5

  allocate( A(LDA,m), B(LDB,n), C(LDC,n) )

  do j=1,m
     do i=1,m
        A(i,j) = -10.d0 + dble(i+j)
     end do
  end do
  do j=1,n
     do i=1,n
        B(i,j) = -1.d0 + dble(i*j)
     end do
  end do

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 'X', 't', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq == 0) return

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 't', 'X', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq == 0) return

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 'T', 't', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq /= 0) return

  test_qmckl_distance_sq = -1

  do j=1,n
     do i=1,m
        x =  (A(i,1)-B(j,1))**2 + &
             (A(i,2)-B(j,2))**2 + &
             (A(i,3)-B(j,3))**2
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 'n', 'T', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq /= 0) return

  test_qmckl_distance_sq = -1

  do j=1,n
     do i=1,m
        x =  (A(1,i)-B(j,1))**2 + &
             (A(2,i)-B(j,2))**2 + &
             (A(3,i)-B(j,3))**2
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 'T', 'n', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq /= 0) return

  test_qmckl_distance_sq = -1

  do j=1,n
     do i=1,m
        x =  (A(i,1)-B(1,j))**2 + &
             (A(i,2)-B(2,j))**2 + &
             (A(i,3)-B(3,j))**2
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_distance_sq = &
       qmckl_distance_sq(context, 'n', 'N', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_distance_sq /= 0) return

  test_qmckl_distance_sq = -1

  do j=1,n
     do i=1,m
        x =  (A(1,i)-B(1,j))**2 + &
             (A(2,i)-B(2,j))**2 + &
             (A(3,i)-B(3,j))**2
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_distance_sq = 0

  deallocate(A,B,C)
end function test_qmckl_distance_sq
    #+end_src

    #+begin_src c :comments link :tangle (eval c_test)
int test_qmckl_distance_sq(qmckl_context context);
munit_assert_int(0, ==, test_qmckl_distance_sq(context));
    #+end_src
* Distance

** ~qmckl_distance~
   :PROPERTIES:
   :Name:     qmckl_distance
   :CRetType: qmckl_exit_code
   :FRetType: qmckl_exit_code
   :END:

 ~qmckl_distance~ computes the matrix of the distances between all
   pairs of points in two sets, one point within each set:

   \[
   C_{ij} = \sqrt{\sum_{k=1}^3 (A_{k,i}-B_{k,j})^2}
   \]

   #+NAME: qmckl_distance_args
   | qmckl_context | context   | in  | Global state                                  |
   | char          | transa    | in  | Array ~A~ is ~'N'~: Normal, ~'T'~: Transposed |
   | char          | transb    | in  | Array ~B~ is ~'N'~: Normal, ~'T'~: Transposed |
   | int64_t       | m         | in  | Number of points in the first set             |
   | int64_t       | n         | in  | Number of points in the second set            |
   | double        | A[][lda]  | in  | Array containing the $m \times 3$ matrix $A$  |
   | int64_t       | lda       | in  | Leading dimension of array ~A~                |
   | double        | B[][ldb]  | in  | Array containing the $n \times 3$ matrix $B$  |
   | int64_t       | ldb       | in  | Leading dimension of array ~B~                |
   | double        | C[n][ldc] | out | Array containing the $m \times n$ matrix $C$  |
   | int64_t       | ldc       | in  | Leading dimension of array ~C~                |

*** Requirements

    - ~context~ is not ~QMCKL_NULL_CONTEXT~
    - ~m > 0~
    - ~n > 0~
    - ~lda >= 3~ if ~transa == 'N'~
    - ~lda >= m~ if ~transa == 'T'~
    - ~ldb >= 3~ if ~transb == 'N'~
    - ~ldb >= n~ if ~transb == 'T'~
    - ~ldc >= m~
    - ~A~ is allocated with at least $3 \times m \times 8$ bytes
    - ~B~ is allocated with at least $3 \times n \times 8$ bytes
    - ~C~ is allocated with at least $m \times n \times 8$ bytes

*** C header

    #+CALL: generate_c_header(table=qmckl_distance_args,rettyp=get_value("CRetType"),fname=get_value("Name"))

    #+RESULTS:
    #+begin_src c :tangle (eval h_func) :comments org
    qmckl_exit_code qmckl_distance (
          const qmckl_context context,
          const char transa,
          const char transb,
          const int64_t m,
          const int64_t n,
          const double* A,
          const int64_t lda,
          const double* B,
          const int64_t ldb,
          double* const C,
          const int64_t ldc );
    #+end_src

*** Source
    #+begin_src f90 :tangle (eval f)
integer function qmckl_distance_f(context, transa, transb, m, n, &
     A, LDA, B, LDB, C, LDC) &
     result(info)
  use qmckl
  implicit none
  integer(qmckl_context)  , intent(in)  :: context
  character  , intent(in)  :: transa, transb
  integer*8  , intent(in)  :: m, n
  integer*8  , intent(in)  :: lda
  real*8     , intent(in)  :: A(lda,*)
  integer*8  , intent(in)  :: ldb
  real*8     , intent(in)  :: B(ldb,*)
  integer*8  , intent(in)  :: ldc
  real*8     , intent(out) :: C(ldc,*)

  integer*8 :: i,j
  real*8    :: x, y, z
  integer   :: transab

  info = QMCKL_SUCCESS

  if (context == QMCKL_NULL_CONTEXT) then
     info = QMCKL_INVALID_CONTEXT
     return
  endif

  if (m <= 0_8) then
     info = QMCKL_INVALID_ARG_4
     return
  endif

  if (n <= 0_8) then
     info = QMCKL_INVALID_ARG_5
     return
  endif

  if (transa == 'N' .or. transa == 'n') then
     transab = 0
  else if (transa == 'T' .or. transa == 't') then
     transab = 1
  else
     transab = -100
  endif

  if (transb == 'N' .or. transb == 'n') then
     continue
  else if (transa == 'T' .or. transa == 't') then
     transab = transab + 2
  else
     transab = -100
  endif

  if (transab < 0) then
     info = QMCKL_INVALID_ARG_1
     return
  endif

  if (iand(transab,1) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,1) == 1 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 0 .and. LDA < 3) then
     info = QMCKL_INVALID_ARG_7
     return
  endif

  if (iand(transab,2) == 2 .and. LDA < m) then
     info = QMCKL_INVALID_ARG_7
     return
  endif


  select case (transab)

  case(0)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(1,j)
           y = A(2,i) - B(2,j)
           z = A(3,i) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
        C(:,j) = dsqrt(C(:,j))
     end do

  case(1)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(1,j)
           y = A(i,2) - B(2,j)
           z = A(i,3) - B(3,j)
           C(i,j) = x*x + y*y + z*z
        end do
        C(:,j) = dsqrt(C(:,j))
     end do

  case(2)

     do j=1,n
        do i=1,m
           x = A(1,i) - B(j,1)
           y = A(2,i) - B(j,2)
           z = A(3,i) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
        C(:,j) = dsqrt(C(:,j))
     end do

  case(3)

     do j=1,n
        do i=1,m
           x = A(i,1) - B(j,1)
           y = A(i,2) - B(j,2)
           z = A(i,3) - B(j,3)
           C(i,j) = x*x + y*y + z*z
        end do
        C(:,j) = dsqrt(C(:,j))
     end do

  end select

end function qmckl_distance_f
    #+end_src

*** Performance

    This function might be more efficient when ~A~ and ~B~ are
    transposed.

** C interface                                                     :noexport:

   #+CALL: generate_c_interface(table=qmckl_distance_args,rettyp=get_value("FRetType"),fname=get_value("Name"))

   #+RESULTS:
   #+begin_src f90 :tangle (eval f) :comments org :exports none
   integer(c_int32_t) function qmckl_distance &
       (context, transa, transb, m, n, A, lda, B, ldb, C, ldc) &
       bind(C) result(info)

     use, intrinsic :: iso_c_binding
     implicit none

     integer (c_int64_t) , intent(in)  , value :: context
     character           , intent(in)  , value :: transa
     character           , intent(in)  , value :: transb
     integer (c_int64_t) , intent(in)  , value :: m
     integer (c_int64_t) , intent(in)  , value :: n
     real    (c_double ) , intent(in)          :: A(lda,*)
     integer (c_int64_t) , intent(in)  , value :: lda
     real    (c_double ) , intent(in)          :: B(ldb,*)
     integer (c_int64_t) , intent(in)  , value :: ldb
     real    (c_double ) , intent(out)         :: C(ldc,n)
     integer (c_int64_t) , intent(in)  , value :: ldc

     integer(c_int32_t), external :: qmckl_distance_f
     info = qmckl_distance_f &
            (context, transa, transb, m, n, A, lda, B, ldb, C, ldc)

   end function qmckl_distance
   #+end_src

   #+CALL: generate_f_interface(table=qmckl_distance_args,rettyp=get_value("FRetType"),fname=get_value("Name"))

   #+RESULTS:
   #+begin_src f90 :tangle (eval fh_func) :comments org :exports none
   interface
     integer(c_int32_t) function qmckl_distance &
         (context, transa, transb, m, n, A, lda, B, ldb, C, ldc) &
         bind(C)
       use, intrinsic :: iso_c_binding
       import
       implicit none

       integer (c_int64_t) , intent(in)  , value :: context
       character           , intent(in)  , value :: transa
       character           , intent(in)  , value :: transb
       integer (c_int64_t) , intent(in)  , value :: m
       integer (c_int64_t) , intent(in)  , value :: n
       real    (c_double ) , intent(in)          :: A(lda,*)
       integer (c_int64_t) , intent(in)  , value :: lda
       real    (c_double ) , intent(in)          :: B(ldb,*)
       integer (c_int64_t) , intent(in)  , value :: ldb
       real    (c_double ) , intent(out)         :: C(ldc,n)
       integer (c_int64_t) , intent(in)  , value :: ldc

     end function qmckl_distance
   end interface
   #+end_src

*** Test                                                           :noexport:
    #+begin_src f90 :tangle (eval f_test)
integer(qmckl_exit_code) function test_qmckl_dist(context) bind(C)
  use qmckl
  implicit none
  integer(qmckl_context), intent(in), value :: context

  double precision, allocatable :: A(:,:), B(:,:), C(:,:)
  integer*8                     :: m, n, LDA, LDB, LDC
  double precision              :: x
  integer*8                     :: i,j

  m = 5
  n = 6
  LDA = m
  LDB = n
  LDC = 5

  allocate( A(LDA,m), B(LDB,n), C(LDC,n) )

  do j=1,m
     do i=1,m
        A(i,j) = -10.d0 + dble(i+j)
     end do
  end do
  do j=1,n
     do i=1,n
        B(i,j) = -1.d0 + dble(i*j)
     end do
  end do

  test_qmckl_dist = &
       qmckl_distance(context, 'X', 't', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist == 0) return

  test_qmckl_dist = &
       qmckl_distance(context, 't', 'X', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist == 0) return

  test_qmckl_dist = &
       qmckl_distance(context, 'T', 't', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist /= 0) return

  test_qmckl_dist = -1

  do j=1,n
     do i=1,m
        x =  dsqrt((A(i,1)-B(j,1))**2 + &
                   (A(i,2)-B(j,2))**2 + &
                   (A(i,3)-B(j,3))**2)
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_dist = &
       qmckl_distance(context, 'n', 'T', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist /= 0) return

  test_qmckl_dist = -1

  do j=1,n
     do i=1,m
        x = dsqrt((A(1,i)-B(j,1))**2 + &
                  (A(2,i)-B(j,2))**2 + &
                  (A(3,i)-B(j,3))**2)
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_dist = &
       qmckl_distance(context, 'T', 'n', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist /= 0) return

  test_qmckl_dist = -1

  do j=1,n
     do i=1,m
        x =  dsqrt((A(i,1)-B(1,j))**2 + &
                   (A(i,2)-B(2,j))**2 + &
                   (A(i,3)-B(3,j))**2)
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_dist = &
       qmckl_distance(context, 'n', 'N', m, n, A, LDA, B, LDB, C, LDC)

  if (test_qmckl_dist /= 0) return

  test_qmckl_dist = -1

  do j=1,n
     do i=1,m
        x = dsqrt((A(1,i)-B(1,j))**2 + &
                  (A(2,i)-B(2,j))**2 + &
                  (A(3,i)-B(3,j))**2)
        if ( dabs(1.d0 - C(i,j)/x) > 1.d-14 ) return
     end do
  end do

  test_qmckl_dist = 0

  deallocate(A,B,C)
end function test_qmckl_dist
    #+end_src

    #+begin_src c :comments link :tangle (eval c_test)
int test_qmckl_dist(qmckl_context context);
munit_assert_int(0, ==, test_qmckl_dist(context));
    #+end_src
* End of files                                                     :noexport:

   #+begin_src c :comments link :tangle (eval c_test)
  if (qmckl_context_destroy(context) != QMCKL_SUCCESS)
    return QMCKL_FAILURE;
  return MUNIT_OK;
}

   #+end_src


# -*- mode: org -*-
# vim: syntax=c