Sets the proper sizes for the buffers for the Netlib CBLAS API

1 files changed, 81 insertions, 46 deletions

diff --git a/scripts/generator/generator.py b/scripts/generator/generator.py
index 4ba97ff8..99edf355 100755
--- a/scripts/generator/generator.py
+++ b/scripts/generator/generator.py
@@ -59,6 +59,41 @@ bld_trans_n_k = "When `transpose == Transpose::kNo`, then `b_ld` must be at leas
 cld_m = "The value of `c_ld` must be at least `m`."
 cld_n = "The value of `c_ld` must be at least `n`."
 
+
+# Helper functions to compute vector and matrix sizes
+def size_helper(condition, size_one, size_two, multiplier):
+    length = "(" + condition + ")" + " ? " + size_one + " * " + multiplier + " : " + size_two + " * " + multiplier
+    return length
+
+
+def layout_transpose_condition(prefix):
+    return "(layout == Layout::kColMajor && " + prefix + "_transpose != Transpose::kNo) || " +\
+           "(layout == Layout::kRowMajor && " + prefix + "_transpose == Transpose::kNo)"
+
+
+# Different possibilities for the vector and matrix sizes
+xn = "n * x_inc"
+xm = "m * x_inc"
+yn = "n * y_inc"
+ym = "m * y_inc"
+an = "n * a_ld"
+apn = "((n*(n+1)) / 2)"
+cn = "n * c_ld"
+xmn = size_helper("a_transpose != Transpose::kNo", "m", "n", "x_inc")
+ynm = size_helper("a_transpose != Transpose::kNo", "n", "m", "y_inc")
+amn = size_helper("layout == Layout::kRowMajor", "m", "n", "a_ld")
+amns = size_helper("side == Side::kLeft", "m", "n", "a_ld")
+amk = size_helper(layout_transpose_condition("a"), "m", "k", "a_ld")
+ank = size_helper(layout_transpose_condition("a"), "n", "k", "a_ld")
+ankab = size_helper(layout_transpose_condition("ab"), "n", "k", "a_ld")
+bkn = size_helper(layout_transpose_condition("b"), "k", "n", "b_ld")
+bnkab = size_helper(layout_transpose_condition("ab"), "n", "k", "b_ld")
+bmn = size_helper("layout == Layout::kRowMajor", "m", "n", "b_ld")
+bnma = size_helper(layout_transpose_condition("a"), "n", "m", "b_ld")
+cmn = size_helper("layout == Layout::kRowMajor", "m", "n", "c_ld")
+ammn = size_helper("layout == Layout::kRowMajor", "m", "((side == Side::kLeft) ? m : n)", "a_ld")
+bmnn = size_helper("layout == Layout::kRowMajor", "((side == Side::kLeft) ? m : n)", "n", "b_ld")
+
 # ==================================================================================================
 
 # Populates a list of routines
@@ -66,63 +101,63 @@ ROUTINES = [
 [  # Level 1: vector-vector
   Routine(False, True,  "1", "rotg",  T, [S,D],            [],                  [],                                                     [],         ["sa","sb","sc","ss"],        ["1","1","1","1"], [],       "",    "Generate givens plane rotation", "", []),
   Routine(False, True,  "1", "rotmg", T, [S,D],            [],                  [],                                                     ["sy1"],    ["sd1","sd2","sx1","sparam"], ["1","1","1","1","1"], [],   "",    "Generate modified givens plane rotation", "", []),
-  Routine(False, True,  "1", "rot",   T, [S,D],            ["n"],               [],                                                     [],         ["x","y"],                    ["n","n"], ["cos","sin"],    "",    "Apply givens plane rotation", "", []),
+  Routine(False, True,  "1", "rot",   T, [S,D],            ["n"],               [],                                                     [],         ["x","y"],                    ["n","n"],     ["cos","sin"],"",    "Apply givens plane rotation", "", []),
   Routine(False, True,  "1", "rotm",  T, [S,D],            ["n"],               [],                                                     [],         ["x","y","sparam"],           ["n","n","1"], [],           "",    "Apply modified givens plane rotation", "", []),
-  Routine(True,  True,  "1", "swap",  T, [S,D,C,Z,H],      ["n"],               [],                                                     [],         ["x","y"],                    ["n","n"], [],               "",    "Swap two vectors", "Interchanges _n_ elements of vectors _x_ and _y_.", []),
-  Routine(True,  True,  "1", "scal",  T, [S,D,C,Z,H],      ["n"],               [],                                                     [],         ["x"],                        ["n"], ["alpha"],            "",    "Vector scaling", "Multiplies _n_ elements of vector _x_ by a scalar constant _alpha_.", []),
-  Routine(True,  True,  "1", "copy",  T, [S,D,C,Z,H],      ["n"],               [],                                                     ["x"],      ["y"],                        ["n","n"], [],               "",    "Vector copy", "Copies the contents of vector _x_ into vector _y_.", []),
-  Routine(True,  True,  "1", "axpy",  T, [S,D,C,Z,H],      ["n"],               [],                                                     ["x"],      ["y"],                        ["n","n"], ["alpha"],        "",    "Vector-times-constant plus vector", "Performs the operation _y = alpha * x + y_, in which _x_ and _y_ are vectors and _alpha_ is a scalar constant.", []),
+  Routine(True,  True,  "1", "swap",  T, [S,D,C,Z,H],      ["n"],               [],                                                     [],         ["x","y"],                    ["n","n"],     [],           "",    "Swap two vectors", "Interchanges _n_ elements of vectors _x_ and _y_.", []),
+  Routine(True,  True,  "1", "scal",  T, [S,D,C,Z,H],      ["n"],               [],                                                     [],         ["x"],                        ["n"],         ["alpha"],    "",    "Vector scaling", "Multiplies _n_ elements of vector _x_ by a scalar constant _alpha_.", []),
+  Routine(True,  True,  "1", "copy",  T, [S,D,C,Z,H],      ["n"],               [],                                                     ["x"],      ["y"],                        ["n","n"],     [],           "",    "Vector copy", "Copies the contents of vector _x_ into vector _y_.", []),
+  Routine(True,  True,  "1", "axpy",  T, [S,D,C,Z,H],      ["n"],               [],                                                     ["x"],      ["y"],                        ["n","n"],     ["alpha"],    "",    "Vector-times-constant plus vector", "Performs the operation _y = alpha * x + y_, in which _x_ and _y_ are vectors and _alpha_ is a scalar constant.", []),
   Routine(True,  True,  "1", "dot",   T, [S,D,H],          ["n"],               [],                                                     ["x","y"],  ["dot"],                      ["n","n","1"], [],           "n",   "Dot product of two vectors", "Multiplies _n_ elements of the vectors _x_ and _y_ element-wise and accumulates the results. The sum is stored in the _dot_ buffer.", []),
   Routine(True,  True,  "1", "dotu",  T, [C,Z],            ["n"],               [],                                                     ["x","y"],  ["dot"],                      ["n","n","1"], [],           "n",   "Dot product of two complex vectors", "See the regular xDOT routine.", []),
   Routine(True,  True,  "1", "dotc",  T, [C,Z],            ["n"],               [],                                                     ["x","y"],  ["dot"],                      ["n","n","1"], [],           "n",   "Dot product of two complex vectors, one conjugated", "See the regular xDOT routine.", []),
-  Routine(True,  True,  "1", "nrm2",  T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["nrm2"],                     ["n","1"], [],               "2*n", "Euclidian norm of a vector", "Accumulates the square of _n_ elements in the _x_ vector and takes the square root. The resulting L2 norm is stored in the _nrm2_ buffer.", []),
-  Routine(True,  True,  "1", "asum",  T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["asum"],                     ["n","1"], [],               "n",   "Absolute sum of values in a vector", "Accumulates the absolute value of _n_ elements in the _x_ vector. The results are stored in the _asum_ buffer.", []),
-  Routine(True,  False, "1", "sum",   T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["sum"],                      ["n","1"], [],               "n",   "Sum of values in a vector (non-BLAS function)", "Accumulates the values of _n_ elements in the _x_ vector. The results are stored in the _sum_ buffer. This routine is the non-absolute version of the xASUM BLAS routine.", []),
-  Routine(True,  True,  "1", "amax",  T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imax"],                     ["n","1"], [],               "2*n", "Index of absolute maximum value in a vector", "Finds the index of the maximum of the absolute values in the _x_ vector. The resulting integer index is stored in the _imax_ buffer.", []),
-  Routine(True,  False, "1", "max",   T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imax"],                     ["n","1"], [],               "2*n", "Index of maximum value in a vector (non-BLAS function)", "Finds the index of the maximum of the values in the _x_ vector. The resulting integer index is stored in the _imax_ buffer. This routine is the non-absolute version of the IxAMAX BLAS routine.", []),
-  Routine(True,  False, "1", "min",   T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imin"],                     ["n","1"], [],               "2*n", "Index of minimum value in a vector (non-BLAS function)", "Finds the index of the minimum of the values in the _x_ vector. The resulting integer index is stored in the _imin_ buffer. This routine is the non-absolute minimum version of the IxAMAX BLAS routine.", []),
+  Routine(True,  True,  "1", "nrm2",  T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["nrm2"],                     ["n","1"],     [],           "2*n", "Euclidian norm of a vector", "Accumulates the square of _n_ elements in the _x_ vector and takes the square root. The resulting L2 norm is stored in the _nrm2_ buffer.", []),
+  Routine(True,  True,  "1", "asum",  T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["asum"],                     ["n","1"],     [],           "n",   "Absolute sum of values in a vector", "Accumulates the absolute value of _n_ elements in the _x_ vector. The results are stored in the _asum_ buffer.", []),
+  Routine(True,  False, "1", "sum",   T, [S,D,Sc,Dz,H],    ["n"],               [],                                                     ["x"],      ["sum"],                      ["n","1"],     [],           "n",   "Sum of values in a vector (non-BLAS function)", "Accumulates the values of _n_ elements in the _x_ vector. The results are stored in the _sum_ buffer. This routine is the non-absolute version of the xASUM BLAS routine.", []),
+  Routine(True,  True,  "1", "amax",  T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imax"],                     ["n","1"],     [],           "2*n", "Index of absolute maximum value in a vector", "Finds the index of the maximum of the absolute values in the _x_ vector. The resulting integer index is stored in the _imax_ buffer.", []),
+  Routine(True,  False, "1", "max",   T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imax"],                     ["n","1"],     [],           "2*n", "Index of maximum value in a vector (non-BLAS function)", "Finds the index of the maximum of the values in the _x_ vector. The resulting integer index is stored in the _imax_ buffer. This routine is the non-absolute version of the IxAMAX BLAS routine.", []),
+  Routine(True,  False, "1", "min",   T, [iS,iD,iC,iZ,iH], ["n"],               [],                                                     ["x"],      ["imin"],                     ["n","1"],     [],           "2*n", "Index of minimum value in a vector (non-BLAS function)", "Finds the index of the minimum of the values in the _x_ vector. The resulting integer index is stored in the _imin_ buffer. This routine is the non-absolute minimum version of the IxAMAX BLAS routine.", []),
 ],
 [  # Level 2: matrix-vector
-  Routine(True,  True,  "2a", "gemv",  T,  [S,D,C,Z,H],    ["m","n"],           ["layout","a_transpose"],                               ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "General matrix-vector multiplication", "Performs the operation _y = alpha * A * x + beta * y_, in which _x_ is an input vector, _y_ is an input and output vector, _A_ is an input matrix, and _alpha_ and _beta_ are scalars. The matrix _A_ can optionally be transposed before performing the operation.", [ald_m]),
-  Routine(True,  True,  "2a", "gbmv",  T,  [S,D,C,Z,H],    ["m","n","kl","ku"], ["layout","a_transpose"],                               ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "General banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is banded instead.", [ald_kl_ku_one]),
-  Routine(True,  True,  "2a", "hemv",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Hermitian matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian matrix instead.", [ald_n]),
-  Routine(True,  True,  "2a", "hbmv",  T,  [C,Z],          ["n","k"],           ["layout","triangle"],                                  ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Hermitian banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian banded matrix instead.", [ald_k_one]),
-  Routine(True,  True,  "2a", "hpmv",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["ap","x"], ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Hermitian packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
-  Routine(True,  True,  "2a", "symv",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Symmetric matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is symmetric instead.", [ald_n]),
-  Routine(True,  True,  "2a", "sbmv",  T,  [S,D,H],        ["n","k"],           ["layout","triangle"],                                  ["a","x"],  ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Symmetric banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is symmetric and banded instead.", [ald_k_one]),
-  Routine(True,  True,  "2a", "spmv",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["ap","x"], ["y"],                        ["n","n","n"], ["alpha","beta"], "",    "Symmetric packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
-  Routine(True,  True,  "2a", "trmv",  T,  [S,D,C,Z,H],    ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        ["n","n"], [],               "n",   "Triangular matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is triangular instead.", [ald_n]),
-  Routine(True,  True,  "2a", "tbmv",  T,  [S,D,C,Z,H],    ["n","k"],           ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        ["n","n"], [],               "n",   "Triangular banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is triangular and banded instead.", [ald_k_one]),
-  Routine(True,  True,  "2a", "tpmv",  T,  [S,D,C,Z,H],    ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["ap"],     ["x"],                        ["n","n"], [],               "n",   "Triangular packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is a triangular packed matrix instead and repreented as _AP_.", []),
-  Routine(False, True,  "2a", "trsv",  T,  [S,D,C,Z],      ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        ["n","n"], [],               "",    "Solves a triangular system of equations", "", []),
-  Routine(False, True,  "2a", "tbsv",  T,  [S,D,C,Z],      ["n","k"],           ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        ["n","n"], [],               "",    "Solves a banded triangular system of equations", "", [ald_k_one]),
-  Routine(False, True,  "2a", "tpsv",  T,  [S,D,C,Z],      ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["ap"],     ["x"],                        ["n","n"], [],               "",    "Solves a packed triangular system of equations", "", []),
+  Routine(True,  True,  "2a", "gemv",  T,  [S,D,C,Z,H],    ["m","n"],           ["layout","a_transpose"],                               ["a","x"],  ["y"],                        [amn,xmn,ynm], ["alpha","beta"], "",    "General matrix-vector multiplication", "Performs the operation _y = alpha * A * x + beta * y_, in which _x_ is an input vector, _y_ is an input and output vector, _A_ is an input matrix, and _alpha_ and _beta_ are scalars. The matrix _A_ can optionally be transposed before performing the operation.", [ald_m]),
+  Routine(True,  True,  "2a", "gbmv",  T,  [S,D,C,Z,H],    ["m","n","kl","ku"], ["layout","a_transpose"],                               ["a","x"],  ["y"],                        [amn,xmn,ynm], ["alpha","beta"], "",    "General banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is banded instead.", [ald_kl_ku_one]),
+  Routine(True,  True,  "2a", "hemv",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["a","x"],  ["y"],                        [an,xn,yn],    ["alpha","beta"], "",    "Hermitian matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian matrix instead.", [ald_n]),
+  Routine(True,  True,  "2a", "hbmv",  T,  [C,Z],          ["n","k"],           ["layout","triangle"],                                  ["a","x"],  ["y"],                        [an,xn,yn],    ["alpha","beta"], "",    "Hermitian banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian banded matrix instead.", [ald_k_one]),
+  Routine(True,  True,  "2a", "hpmv",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["ap","x"], ["y"],                        [apn,xn,yn],   ["alpha","beta"], "",    "Hermitian packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2a", "symv",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["a","x"],  ["y"],                        [an,xn,yn],    ["alpha","beta"], "",    "Symmetric matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is symmetric instead.", [ald_n]),
+  Routine(True,  True,  "2a", "sbmv",  T,  [S,D,H],        ["n","k"],           ["layout","triangle"],                                  ["a","x"],  ["y"],                        [an,xn,yn],    ["alpha","beta"], "",    "Symmetric banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is symmetric and banded instead.", [ald_k_one]),
+  Routine(True,  True,  "2a", "spmv",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["ap","x"], ["y"],                        [apn,xn,yn],   ["alpha","beta"], "",    "Symmetric packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2a", "trmv",  T,  [S,D,C,Z,H],    ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        [an,xn],       [],               "n",   "Triangular matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is triangular instead.", [ald_n]),
+  Routine(True,  True,  "2a", "tbmv",  T,  [S,D,C,Z,H],    ["n","k"],           ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        [an,xn],       [],               "n",   "Triangular banded matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is triangular and banded instead.", [ald_k_one]),
+  Routine(True,  True,  "2a", "tpmv",  T,  [S,D,C,Z,H],    ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["ap"],     ["x"],                        [apn,xn],      [],               "n",   "Triangular packed matrix-vector multiplication", "Same operation as xGEMV, but matrix _A_ is a triangular packed matrix instead and repreented as _AP_.", []),
+  Routine(False, True,  "2a", "trsv",  T,  [S,D,C,Z],      ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        [an,xn],       [],               "",    "Solves a triangular system of equations", "", []),
+  Routine(False, True,  "2a", "tbsv",  T,  [S,D,C,Z],      ["n","k"],           ["layout","triangle","a_transpose","diagonal"],         ["a"],      ["x"],                        [an,xn],       [],               "",    "Solves a banded triangular system of equations", "", [ald_k_one]),
+  Routine(False, True,  "2a", "tpsv",  T,  [S,D,C,Z],      ["n"],               ["layout","triangle","a_transpose","diagonal"],         ["ap"],     ["x"],                        [apn,xn],      [],               "",    "Solves a packed triangular system of equations", "", []),
   # Level 2: matrix update
-  Routine(True,  True,  "2b", "ger",   T,  [S,D,H],        ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        ["n","n","n"], ["alpha"],        "",    "General rank-1 matrix update", "Performs the operation _A = alpha * x * y^T + A_, in which _x_ is an input vector, _y^T_ is the transpose of the input vector _y_, _A_ is the matrix to be updated, and _alpha_ is a scalar value.", [ald_m]),
-  Routine(True,  True,  "2b", "geru",  T,  [C,Z],          ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        ["n","n","n"], ["alpha"],        "",    "General rank-1 complex matrix update", "Same operation as xGER, but with complex data-types.", [ald_m]),
-  Routine(True,  True,  "2b", "gerc",  T,  [C,Z],          ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        ["n","n","n"], ["alpha"],        "",    "General rank-1 complex conjugated matrix update", "Same operation as xGERU, but the update is done based on the complex conjugate of the input vectors.", [ald_m]),
-  Routine(True,  True,  "2b", "her",   Tc, [Css,Zdd],      ["n"],               ["layout","triangle"],                                  ["x"],      ["a"],                        ["n","n"], ["alpha"],        "",    "Hermitian rank-1 matrix update", "Performs the operation _A = alpha * x * x^T + A_, in which x is an input vector, x^T is the transpose of this vector, _A_ is the triangular Hermetian matrix to be updated, and alpha is a scalar value.", [ald_n]),
-  Routine(True,  True,  "2b", "hpr",   Tc, [Css,Zdd],      ["n"],               ["layout","triangle"],                                  ["x"],      ["ap"],                       ["n","n"], ["alpha"],        "",    "Hermitian packed rank-1 matrix update", "Same operation as xHER, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
-  Routine(True,  True,  "2b", "her2",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["x","y"],  ["a"],                        ["n","n","n"], ["alpha"],        "",    "Hermitian rank-2 matrix update", "Performs the operation _A = alpha * x * y^T + conj(alpha) * y * x^T + A_, in which _x_ is an input vector and _x^T_ its transpose, _y_ is an input vector and _y^T_ its transpose, _A_ is the triangular Hermetian matrix to be updated, _alpha_ is a scalar value and _conj(alpha)_ its complex conjugate.", [ald_n]),
-  Routine(True,  True,  "2b", "hpr2",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["x","y"],  ["ap"],                       ["n","n","n"], ["alpha"],        "",    "Hermitian packed rank-2 matrix update", "Same operation as xHER2, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
-  Routine(True,  True,  "2b", "syr",   T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x"],      ["a"],                        ["n","n"], ["alpha"],        "",    "Symmetric rank-1 matrix update", "Same operation as xHER, but matrix A is a symmetric matrix instead.", [ald_n]),
-  Routine(True,  True,  "2b", "spr",   T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x"],      ["ap"],                       ["n","n"], ["alpha"],        "",    "Symmetric packed rank-1 matrix update", "Same operation as xSPR, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
-  Routine(True,  True,  "2b", "syr2",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x","y"],  ["a"],                        ["n","n","n"], ["alpha"],        "",    "Symmetric rank-2 matrix update", "Same operation as xHER2, but matrix _A_ is a symmetric matrix instead.", [ald_n]),
-  Routine(True,  True,  "2b", "spr2",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x","y"],  ["ap"],                       ["n","n","n"], ["alpha"],        "",    "Symmetric packed rank-2 matrix update", "Same operation as xSPR2, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2b", "ger",   T,  [S,D,H],        ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        [xm,yn,amn],   ["alpha"],        "",    "General rank-1 matrix update", "Performs the operation _A = alpha * x * y^T + A_, in which _x_ is an input vector, _y^T_ is the transpose of the input vector _y_, _A_ is the matrix to be updated, and _alpha_ is a scalar value.", [ald_m]),
+  Routine(True,  True,  "2b", "geru",  T,  [C,Z],          ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        [xm,yn,amn],   ["alpha"],        "",    "General rank-1 complex matrix update", "Same operation as xGER, but with complex data-types.", [ald_m]),
+  Routine(True,  True,  "2b", "gerc",  T,  [C,Z],          ["m","n"],           ["layout"],                                             ["x","y"],  ["a"],                        [xm,yn,amn],   ["alpha"],        "",    "General rank-1 complex conjugated matrix update", "Same operation as xGERU, but the update is done based on the complex conjugate of the input vectors.", [ald_m]),
+  Routine(True,  True,  "2b", "her",   Tc, [Css,Zdd],      ["n"],               ["layout","triangle"],                                  ["x"],      ["a"],                        [xn,an],       ["alpha"],        "",    "Hermitian rank-1 matrix update", "Performs the operation _A = alpha * x * x^T + A_, in which x is an input vector, x^T is the transpose of this vector, _A_ is the triangular Hermetian matrix to be updated, and alpha is a scalar value.", [ald_n]),
+  Routine(True,  True,  "2b", "hpr",   Tc, [Css,Zdd],      ["n"],               ["layout","triangle"],                                  ["x"],      ["ap"],                       [xn,apn],      ["alpha"],        "",    "Hermitian packed rank-1 matrix update", "Same operation as xHER, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2b", "her2",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["x","y"],  ["a"],                        [xn,yn,an],    ["alpha"],        "",    "Hermitian rank-2 matrix update", "Performs the operation _A = alpha * x * y^T + conj(alpha) * y * x^T + A_, in which _x_ is an input vector and _x^T_ its transpose, _y_ is an input vector and _y^T_ its transpose, _A_ is the triangular Hermetian matrix to be updated, _alpha_ is a scalar value and _conj(alpha)_ its complex conjugate.", [ald_n]),
+  Routine(True,  True,  "2b", "hpr2",  T,  [C,Z],          ["n"],               ["layout","triangle"],                                  ["x","y"],  ["ap"],                       [xn,yn,apn],   ["alpha"],        "",    "Hermitian packed rank-2 matrix update", "Same operation as xHER2, but matrix _A_ is an Hermitian packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2b", "syr",   T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x"],      ["a"],                        [xn,an],       ["alpha"],        "",    "Symmetric rank-1 matrix update", "Same operation as xHER, but matrix A is a symmetric matrix instead.", [ald_n]),
+  Routine(True,  True,  "2b", "spr",   T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x"],      ["ap"],                       [xn,apn],      ["alpha"],        "",    "Symmetric packed rank-1 matrix update", "Same operation as xSPR, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
+  Routine(True,  True,  "2b", "syr2",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x","y"],  ["a"],                        [xn,yn,an],    ["alpha"],        "",    "Symmetric rank-2 matrix update", "Same operation as xHER2, but matrix _A_ is a symmetric matrix instead.", [ald_n]),
+  Routine(True,  True,  "2b", "spr2",  T,  [S,D,H],        ["n"],               ["layout","triangle"],                                  ["x","y"],  ["ap"],                       [xn,yn,apn],   ["alpha"],        "",    "Symmetric packed rank-2 matrix update", "Same operation as xSPR2, but matrix _A_ is a symmetric packed matrix instead and represented as _AP_.", []),
 ],
 [  # Level 3: matrix-matrix
-  Routine(True,  True,  "3", "gemm",  T,  [S,D,C,Z,H],     ["m","n","k"],        ["layout","a_transpose","b_transpose"],                ["a","b"],  ["c"],                        ["n","n","n"], ["alpha","beta"], "",    "General matrix-matrix multiplication", "Performs the matrix product _C = alpha * A * B + beta * C_, in which _A_ (_m_ by _k_) and _B_ (_k_ by _n_) are two general rectangular input matrices, _C_ (_m_ by _n_) is the matrix to be updated, and _alpha_ and _beta_ are scalar values. The matrices _A_ and/or _B_ can optionally be transposed before performing the operation.", [ald_transa_m_k, bld_transb_k_n, cld_m]),
-  Routine(True,  True,  "3", "symm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle"],                          ["a","b"],  ["c"],                        ["n","n","n"], ["alpha","beta"], "",    "Symmetric matrix-matrix multiplication", "Same operation as xGEMM, but _A_ is symmetric instead. In case of `side == kLeft`, _A_ is a symmetric _m_ by _m_ matrix and _C = alpha * A * B + beta * C_ is performed. Otherwise, in case of `side == kRight`, _A_ is a symmtric _n_ by _n_ matrix and _C = alpha * B * A + beta * C_ is performed.", [ald_side_m_n, bld_m, cld_m]),
-  Routine(True,  True,  "3", "hemm",  T,  [C,Z],           ["m","n"],            ["layout","side","triangle"],                          ["a","b"],  ["c"],                        ["n","n","n"], ["alpha","beta"], "",    "Hermitian matrix-matrix multiplication", "Same operation as xSYMM, but _A_ is an Hermitian matrix instead.", [ald_side_m_n, bld_m, cld_m]),
-  Routine(True,  True,  "3", "syrk",  T,  [S,D,C,Z,H],     ["n","k"],            ["layout","triangle","a_transpose"],                   ["a"],      ["c"],                        ["n","n"], ["alpha","beta"], "",    "Rank-K update of a symmetric matrix", "Performs the matrix product _C = alpha * A * A^T + beta * C_ or _C = alpha * A^T * A + beta * C_, in which _A_ is a general matrix and _A^T_ is its transpose, _C_ (_n_ by _n_) is the symmetric matrix to be updated, and _alpha_ and _beta_ are scalar values.", [ald_trans_n_k, cld_m]),
-  Routine(True,  True,  "3", "herk",  Tc, [Css,Zdd],       ["n","k"],            ["layout","triangle","a_transpose"],                   ["a"],      ["c"],                        ["n","n"], ["alpha","beta"], "",    "Rank-K update of a hermitian matrix", "Same operation as xSYRK, but _C_ is an Hermitian matrix instead.", [ald_trans_n_k, cld_m]),
-  Routine(True,  True,  "3", "syr2k", T,  [S,D,C,Z,H],     ["n","k"],            ["layout","triangle","ab_transpose"],                  ["a","b"],  ["c"],                        ["n","n","n"], ["alpha","beta"], "",    "Rank-2K update of a symmetric matrix", "Performs the matrix product _C = alpha * A * B^T + alpha * B * A^T + beta * C_ or _C = alpha * A^T * B + alpha * B^T * A + beta * C_, in which _A_ and _B_ are general matrices and _A^T_ and _B^T_ are their transposed versions, _C_ (_n_ by _n_) is the symmetric matrix to be updated, and _alpha_ and _beta_ are scalar values.", [ald_trans_n_k, bld_trans_n_k, cld_n]),
-  Routine(True,  True,  "3", "her2k", TU, [Ccs,Zzd],       ["n","k"],            ["layout","triangle","ab_transpose"],                  ["a","b"],  ["c"],                        ["n","n","n"], ["alpha","beta"], "",    "Rank-2K update of a hermitian matrix", "Same operation as xSYR2K, but _C_ is an Hermitian matrix instead.", [ald_trans_n_k, bld_trans_n_k, cld_n]),
-  Routine(True,  True,  "3", "trmm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle","a_transpose","diagonal"], ["a"],      ["b"],                        ["n","n"], ["alpha"],        "",    "Triangular matrix-matrix multiplication", "Performs the matrix product _B = alpha * A * B_ or _B = alpha * B * A_, in which _A_ is a unit or non-unit triangular matrix, _B_ (_m_ by _n_) is the general matrix to be updated, and _alpha_ is a scalar value.", [ald_side_m_n, bld_m]),
-  Routine(False, True,  "3", "trsm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle","a_transpose","diagonal"], ["a"],      ["b"],                        ["n","n"], ["alpha"],        "",    "Solves a triangular system of equations", "", []),
+  Routine(True,  True,  "3", "gemm",  T,  [S,D,C,Z,H],     ["m","n","k"],        ["layout","a_transpose","b_transpose"],                ["a","b"],  ["c"],                        [amk,bkn,cmn],   ["alpha","beta"], "",    "General matrix-matrix multiplication", "Performs the matrix product _C = alpha * A * B + beta * C_, in which _A_ (_m_ by _k_) and _B_ (_k_ by _n_) are two general rectangular input matrices, _C_ (_m_ by _n_) is the matrix to be updated, and _alpha_ and _beta_ are scalar values. The matrices _A_ and/or _B_ can optionally be transposed before performing the operation.", [ald_transa_m_k, bld_transb_k_n, cld_m]),
+  Routine(True,  True,  "3", "symm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle"],                          ["a","b"],  ["c"],                        [ammn,bmnn,cmn], ["alpha","beta"], "",    "Symmetric matrix-matrix multiplication", "Same operation as xGEMM, but _A_ is symmetric instead. In case of `side == kLeft`, _A_ is a symmetric _m_ by _m_ matrix and _C = alpha * A * B + beta * C_ is performed. Otherwise, in case of `side == kRight`, _A_ is a symmtric _n_ by _n_ matrix and _C = alpha * B * A + beta * C_ is performed.", [ald_side_m_n, bld_m, cld_m]),
+  Routine(True,  True,  "3", "hemm",  T,  [C,Z],           ["m","n"],            ["layout","side","triangle"],                          ["a","b"],  ["c"],                        [ammn,bmnn,cmn], ["alpha","beta"], "",    "Hermitian matrix-matrix multiplication", "Same operation as xSYMM, but _A_ is an Hermitian matrix instead.", [ald_side_m_n, bld_m, cld_m]),
+  Routine(True,  True,  "3", "syrk",  T,  [S,D,C,Z,H],     ["n","k"],            ["layout","triangle","a_transpose"],                   ["a"],      ["c"],                        [ank,cn],        ["alpha","beta"], "",    "Rank-K update of a symmetric matrix", "Performs the matrix product _C = alpha * A * A^T + beta * C_ or _C = alpha * A^T * A + beta * C_, in which _A_ is a general matrix and _A^T_ is its transpose, _C_ (_n_ by _n_) is the symmetric matrix to be updated, and _alpha_ and _beta_ are scalar values.", [ald_trans_n_k, cld_m]),
+  Routine(True,  True,  "3", "herk",  Tc, [Css,Zdd],       ["n","k"],            ["layout","triangle","a_transpose"],                   ["a"],      ["c"],                        [ank,cn],        ["alpha","beta"], "",    "Rank-K update of a hermitian matrix", "Same operation as xSYRK, but _C_ is an Hermitian matrix instead.", [ald_trans_n_k, cld_m]),
+  Routine(True,  True,  "3", "syr2k", T,  [S,D,C,Z,H],     ["n","k"],            ["layout","triangle","ab_transpose"],                  ["a","b"],  ["c"],                        [ankab,bnkab,cn],["alpha","beta"], "",    "Rank-2K update of a symmetric matrix", "Performs the matrix product _C = alpha * A * B^T + alpha * B * A^T + beta * C_ or _C = alpha * A^T * B + alpha * B^T * A + beta * C_, in which _A_ and _B_ are general matrices and _A^T_ and _B^T_ are their transposed versions, _C_ (_n_ by _n_) is the symmetric matrix to be updated, and _alpha_ and _beta_ are scalar values.", [ald_trans_n_k, bld_trans_n_k, cld_n]),
+  Routine(True,  True,  "3", "her2k", TU, [Ccs,Zzd],       ["n","k"],            ["layout","triangle","ab_transpose"],                  ["a","b"],  ["c"],                        [ankab,bnkab,cn],["alpha","beta"], "",    "Rank-2K update of a hermitian matrix", "Same operation as xSYR2K, but _C_ is an Hermitian matrix instead.", [ald_trans_n_k, bld_trans_n_k, cld_n]),
+  Routine(True,  True,  "3", "trmm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle","a_transpose","diagonal"], ["a"],      ["b"],                        [amns,bmn],      ["alpha"],        "",    "Triangular matrix-matrix multiplication", "Performs the matrix product _B = alpha * A * B_ or _B = alpha * B * A_, in which _A_ is a unit or non-unit triangular matrix, _B_ (_m_ by _n_) is the general matrix to be updated, and _alpha_ is a scalar value.", [ald_side_m_n, bld_m]),
+  Routine(False, True,  "3", "trsm",  T,  [S,D,C,Z,H],     ["m","n"],            ["layout","side","triangle","a_transpose","diagonal"], ["a"],      ["b"],                        [amns,bmn],      ["alpha"],        "",    "Solves a triangular system of equations", "", []),
 ],
 [  # Level X: extra routines (not part of BLAS)
-  Routine(True,  True,  "x", "omatcopy", T, [S,D,C,Z,H],   ["m","n"],            ["layout","a_transpose"],                              ["a"],      ["b"],                        ["n","n"], ["alpha"],        "",    "Scaling and out-place transpose/copy (non-BLAS function)", "Performs scaling and out-of-place transposition/copying of matrices according to _B = alpha*op(A)_, in which _A_ is an input matrix (_m_ rows by _n_ columns), _B_ an output matrix, and _alpha_ a scalar value. The operation _op_ can be a normal matrix copy, a transposition or a conjugate transposition.", [ald_m, bld_n]),
+  Routine(True,  True,  "x", "omatcopy", T, [S,D,C,Z,H],   ["m","n"],            ["layout","a_transpose"],                              ["a"],      ["b"],                        [amn,bnma],      ["alpha"],        "",    "Scaling and out-place transpose/copy (non-BLAS function)", "Performs scaling and out-of-place transposition/copying of matrices according to _B = alpha*op(A)_, in which _A_ is an input matrix (_m_ rows by _n_ columns), _B_ an output matrix, and _alpha_ a scalar value. The operation _op_ can be a normal matrix copy, a transposition or a conjugate transposition.", [ald_m, bld_n]),
 ]]