<project.out>.trafo

The file <project.out>.trafo contains the list of the transformation matrices used and their inverse matrices, plus a list of vectors indicating the indices that make up the basis of the transformation and linear combinations for each index bound by a loop that does not build a base vector for the transformation.

(See also the format of the <project.out>.qual file)

• Directory targout, File functionList.cc, Function functionList::loadAffineFunctions
  (only transformations)
• Directory targout, File transformations.cc, Function prepareVarTrafos
  (only usage vectors and linear combijnations)
• Directory dispo2, File trafomat.cc, Function load_trafos
  

Format:

  file               --> num_stat [<func_and_inv>] num_stat [<uvect_and_lincombs>]
                         (where <func_and_inv> and <uvect_and_lincombs> occur
                          num_stat times)
  func_and_inv       --> stat_ID 1 <func> <func>
                         (where the second occurrence of <func> corresponds to
                          the transformation matrix T, while the first one
                          corresponds to its inverse)
  func               --> n_vars n_pars n_rows <matrix>
  matrix             --> denom [entry]
  uvect_and_lincombs --> stat_ID <uvect> <all_lincombs>
  uvect              --> ulength [<is_used>]
                         (with is_used occurring ulength times and
                         the n-th occurrence being 1, iff the n-th outermost
                         loop built a base vector for the transformation)
  is_used            --> 1|0
  all_lincombs       --> nr_lincombs [<lincomb>]
                         (where <lincomb> occurs nr_lincombs times)
  lincomb            --> nr_coef lin_denom [coef]
                         (with coef occurring coef_nr times)

• num_stat is the number of statements in the target program
  
• stat_ID is the target statement number of a statement in the target program
  
• n_vars is the number of variables taken into account by an affine mapping
  
• n_pars is the number of parameters taken into account by an affine mapping
  
• n_rows is the number of rows of a matrix defining an affine mapping
  
• entry is the numerator part of a matrix entry
• CONSISTENCY CONDITIONS:
• the i-th column of the trafo matrix corresponds to the i-th outermost source loop surrounding the statement
• the i-th row of the trafo matrix corresponds to the i-th outermost, non-trivial target loop (the trivial, i.e., linearly dependent dimensions are dropped; thus, even in, e.g., synchronous programs, the first row might be a placement if the schedule of that statement is constantly 0)
• the name entry j of the i-th outermost loop is not necessarily equal to i, but gives the column (or row) number of the variable in coefficient vectors/matrices such as inequality systems describing the index set (since matrix entries are enumerated from 0, but names from 1, the column/row is j-1)
  
• denom is the denominator of a matrix
  
• ulength is the number of loops surrounding a statement in the transformed parse tree
• CONSISTENCY CONDITIONS:
• ulength is NOT always equal to the number of surrounding loops in the original parse tree
• ulength can be greater than the number of surrounding loops in the original parse tree, if dim(schedule) + dim(alloc) < dim(origISPC)
• the number of 1-entries in the used vector (is_used) is equal to the number of rows/columns in the trafo matrix for the statement that represent index variable dimensions
• ulength is always equal to the length of the loop quality vector
• nr_lincombs is the number of loops not building up a base vector for the transformation (i.e. the number of linear combinations)
• nr_coef is the number of coefficients of base vectors in a linear combination representing the dimension of a loop that did not build up a base vector for the transformation
• lin_denom is the denominator of a linear combination as described above
• coef (in its n-th occurrence) is the coefficient of the n-th base vector in a linear combination as described above
• the n-th entry in [ lincombs ] stands for the linear combination for the n-th not-0 entry in the used-vector
• the n-th coefficient stands for the n-th not-0 variable in the used-vector.
  The remaining coefficients stand for all parameters and the 1-constant.