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src/module/array [ Modules ]

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NAME

  Module array

USAGE

  use array

DESCRIPTION

  This module contains six functions which enable set manipulations knowing that
  a set of integers is represented with the digits of an integer. The six functions
  are : packb, unpackb, pminus, punion, countb and locateb

OUTPUT

  This module exports six functions:

  * packb -- to transform a set of integers into an integer (unique transformation)
  * unpackb -- to perform the inverse operation as packb do
  * pminus -- to subtract two sets
  * punion -- to add two sets
  * countb -- to count the number of element of the set
  * locateb -- to give the location of an element in a set

USES

  none

src/module/countb [ Functions ]

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NAME

  Function countb

USAGE

  integer = countb(bits)

DESCRIPTION

  This function computes the shape of the rank 1 integer 
  set given by unpackb(bits,dim)

INPUTS

  * bits -- an integer

SIDE EFFECTS

  No side effect (pure function)

RETURN VALUE

  an integer 

EXAMPLE

  i1 = packb( (/1,2,3/) )
  i2 = countb(i1)
  i2 is 3

src/module/locateb [ Functions ]

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NAME

  Function locateb

USAGE

  integer = locateb(i,bits)

DESCRIPTION

  The function locateb returns the location of the element i  
  in the set given by unpackb(bits,countb(bits)). 
  If i does not belong to bits, the function locateb 
  returns -1

INPUTS

  * i -- an integer, the element of a
  * bits -- an integer

SIDE EFFECTS

  No side effect (elemental)

RETURN VALUE

  It returns an integer, the location of i in the array a

EXAMPLE

  bits = packb( (/3,5,6,7/) )
  j = locateb(5,bits) --> j is equal to 2
  j = locateb(6,bits) --> j is equal to 3
  j = locateb(4,bits) --> j is equal to -1
  Note that if the set is not ordered, the packing
  orders it.
  Note also that this function has the attribute elemental
  that means that, the argument can be a set of integers:
  locateb( (/3,7/) , bits) will return (/1,4/)

src/module/packb [ Functions ]

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NAME

  Function packb

USAGE

  integer = packb(set)

DESCRIPTION

  This function transforms a set of integers into
  an integer, this integer is unique
 Apparently Fortran allows to use arrays
 for the second argument which saves us a loop.

 The elements in set have to be <= 31 which should
 not be a problem for realistic applications.

INPUTS

  * set -- a set of integer

SIDE EFFECTS

  No side effect (pure function)

RETURN VALUE

  an integer 

EXAMPLE

  i = packb( (/1,2,3/) ) 
  i is 14 which is in binary base 1110

src/module/pminus [ Functions ]

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NAME

  Function pminus

USAGE

  integer = pminus(bits1,bits2)

DESCRIPTION

  This function subtracts the set which is 
  represented by bits2 to the one that is 
  represented by bits1. If the two sets set1 and set2
  are defined by set1=unpackb(bits1,dim1)
  and set2=unpackb(bits2,dim2), then ib = pminus(bits1,bits2)
  gives an integer such that unpackb(ib,dim_ib) is the set
  of integers of shape dim1-dim2 (dim1 > dim2) which contains
  the elements of set1 which do not belong to set2
  Note that if dim1 < dim2, the result returns is pminus(bits2,bits1)
  If none of the elements of set2 belongs to set1, then 
  pminus(bits1,bits2) = bits1

INPUTS

  * bits1 -- an integer
  * bits2 -- an integer

SIDE EFFECTS

  No side effect (pure function)

RETURN VALUE

  an integer 

EXAMPLE

  i1 = packb( (/1,2,3/) ) 
  i2 = packb( (/2/) )
  i3 = pminus(i1,i2)
  unpackb(i3) is the set (/1,3/)

src/module/punion [ Functions ]

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NAME

  Function punion

USAGE

  integer = punion(bits1,bits2)

DESCRIPTION

  This function adds the set which is 
  represented by bits2 to the one that is 
  represented by bits1. If the two sets set1 and set2
  are defined by set1=unpackb(bits1,dim1)
  and set2=unpackb(bits2,dim2), then ib = punion(bits1,bits2)
  gives an integer such that unpackb(ib,dim_ib) is the set
  of integers of shape dim1+dim2 which contains
  the elements of set1 and those of set2
  Note that if some elements of set2 belong to set1, they do not
  appear twice

INPUTS

  * bits1 -- an integer
  * bits2 -- an integer

SIDE EFFECTS

  No side effect (pure function)

RETURN VALUE

  an integer 

EXAMPLE

  i1 = packb( (/1,3,4/) ) 
  i2 = packb( (/2/) )
  i3 = punion(i1,i2)
  unpackb(i3) is the set (/1,2,3,4/)

src/module/unpackb [ Functions ]

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NAME

  Function unpackb

USAGE

  integer_set = unpackb(bits,dim)

DESCRIPTION

  This function performs the inverse operation
  as packb does : from an integer, it reconstructs the
  set of integers

INPUTS

  * bits -- an integer
  * dim -- an integer, the dimension of the set obtained

SIDE EFFECTS

  No side effect (pure function)

RETURN VALUE

  an integer array of rank 1 and shape dim

EXAMPLE

  set = unpackb( 14 ) 
  set is (/1,2,3/) because the binary representation of 14 is 1110