Improved API documentation and added documentation for level-2 and level-3 routines

2 files changed, 65 insertions, 50 deletions

diff --git a/scripts/generator/generator.py b/scripts/generator/generator.py
index 16a05564..7bb66749 100644
--- a/scripts/generator/generator.py
+++ b/scripts/generator/generator.py
@@ -59,6 +59,22 @@ TU = DataType("TU", "typename T, typename U", "T,U", ["T", "U", "T", "U"], "T")
 
 # ==================================================================================================
 
+# Different possibilities for requirements
+ald_m = "The value of `a_ld` must be at least `m`."
+ald_n = "The value of `a_ld` must be at least `n`."
+ald_k_one = "The value of `a_ld` must be at least `k + 1`."
+ald_kl_ku_one = "The value of `a_ld` must be at least `kl + ku + 1`."
+ald_transa_m_k = "When `transpose_a == Transpose::kNo`, then `a_ld` must be at least `m`, otherwise `a_ld` must be at least `k`."
+ald_trans_n_k = "When `transpose == Transpose::kNo`, then `a_ld` must be at least `n`, otherwise `a_ld` must be at least `k`."
+ald_side_m_n = "When `side = Side::kLeft` then `a_ld` must be at least `m`, otherwise `a_ld` must be at least `n`."
+bld_m = "The value of `b_ld` must be at least `m`."
+bld_transb_k_n = "When `transpose_b == Transpose::kNo`, then `b_ld` must be at least `k`, otherwise `b_ld` must be at least `n`."
+bld_trans_n_k = "When `transpose == Transpose::kNo`, then `b_ld` must be at least `n`, otherwise `b_ld` must be at least `k`."
+cld_m = "The value of `c_ld` must be at least `m`."
+cld_n = "The value of `c_ld` must be at least `n`."
+
+# ==================================================================================================
+
 # Populates a list of routines
 routines = [
 [ # Level 1: vector-vector
@@ -66,57 +82,57 @@ routines = [
   Routine(False, True,  "1", "rotmg", T, [S,D],            [], [], ["sy1"], ["sd1","sd2","sx1","sparam"], [], "", "Generate modified givens plane rotation", "", []),
   Routine(False, True,  "1", "rot",   T, [S,D],            ["n"], [], [], ["x","y"], ["cos","sin"], "", "Apply givens plane rotation", "", []),
   Routine(False, True,  "1", "rotm",  T, [S,D],            ["n"], [], [], ["x","y","sparam"], [], "", "Apply modified givens plane rotation", "", []),
-  Routine(True,  True,  "1", "swap",  T, [S,D,C,Z,H],      ["n"], [], [], ["x","y"], [], "", "Swap two vectors", "Interchanges the contents of vectors x and y.", []),
-  Routine(True,  True,  "1", "scal",  T, [S,D,C,Z,H],      ["n"], [], [], ["x"], ["alpha"], "", "Vector scaling", "Multiplies all elements of vector x by a scalar constant alpha.", []),
-  Routine(True,  True,  "1", "copy",  T, [S,D,C,Z,H],      ["n"], [], ["x"], ["y"], [], "", "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"], ["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", "Dot product of two vectors", "Multiplies the vectors x and y element-wise and accumulates the results. The sum is stored in the dot buffer.", []),
+  Routine(True,  True,  "1", "swap",  T, [S,D,C,Z,H],      ["n"], [], [], ["x","y"], [], "", "Swap two vectors", "Interchanges _n_ elements of vectors _x_ and _y_.", []),
+  Routine(True,  True,  "1", "scal",  T, [S,D,C,Z,H],      ["n"], [], [], ["x"], ["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"], [], "", "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"], ["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", "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", "Dot product of two complex vectors", "See the regular xDOT routine.", []),
   Routine(True,  True,  "1", "dotc",  T, [C,Z],            ["n"], [], ["x","y"], ["dot"], [], "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"], [], "2*n", "Euclidian norm of a vector", "Accumulates the square of each element 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", "Absolute sum of values in a vector", "Accumulates the absolute value of each element 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", "Sum of values in a vector (non-BLAS function)", "Accumulates the values of each element 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"], [], "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"], [], "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"], [], "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"], [], "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", "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", "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"], [], "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"], [], "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"], [], "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"], ["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.", []),
-  Routine(True,  True,  "2a", "gbmv",  T,  [S,D,C,Z,H], ["m","n","kl","ku"], ["layout","a_transpose"], ["a","x"], ["y"], ["alpha","beta"], "", "General banded matrix-vector multiplication", "Same operation as xGEMV, but matrix A is banded instead.", []),
-  Routine(True,  True,  "2a", "hemv",  T,  [C,Z],       ["n"], ["layout","triangle"], ["a","x"], ["y"], ["alpha","beta"], "", "Hermitian matrix-vector multiplication", "Same operation as xGEMV, but matrix A is an Hermitian matrix instead.", []),
-  Routine(True,  True,  "2a", "hbmv",  T,  [C,Z],       ["n","k"], ["layout","triangle"], ["a","x"], ["y"], ["alpha","beta"], "", "Hermitian banded matrix-vector multiplication", "Same operation as xGEMV, but matrix A is an Hermitian banded matrix instead.", []),
-  Routine(True,  True,  "2a", "hpmv",  T,  [C,Z],       ["n"], ["layout","triangle"], ["ap","x"], ["y"], ["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"], ["alpha","beta"], "", "Symmetric matrix-vector multiplication", "Same operation as xGEMV, but matrix A is symmetric instead.", []),
-  Routine(True,  True,  "2a", "sbmv",  T,  [S,D,H],     ["n","k"], ["layout","triangle"], ["a","x"], ["y"], ["alpha","beta"], "", "Symmetric banded matrix-vector multiplication", "Same operation as xGEMV, but matrix A is symmetric and banded instead.", []),
-  Routine(True,  True,  "2a", "spmv",  T,  [S,D,H],     ["n"], ["layout","triangle"], ["ap","x"], ["y"], ["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", "Triangular matrix-vector multiplication", "Same operation as xGEMV, but matrix A is triangular instead.", []),
-  Routine(True,  True,  "2a", "tbmv",  T,  [S,D,C,Z,H], ["n","k"], ["layout","triangle","a_transpose","diagonal"], ["a"], ["x"], [], "n", "Triangular banded matrix-vector multiplication", "Same operation as xGEMV, but matrix A is triangular and banded instead.", []),
-  Routine(True,  True,  "2a", "tpmv",  T,  [S,D,C,Z,H], ["n"], ["layout","triangle","a_transpose","diagonal"], ["ap"], ["x"], [], "n", "Triangular packed matrix-vector multiplication", "Same operation as xGEMV, but matrix A is a triangular packed matrix instead and repreented as AP.", []),
+  Routine(True,  True,  "2a", "gemv",  T,  [S,D,C,Z,H], ["m","n"], ["layout","a_transpose"], ["a","x"], ["y"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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", "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", "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", "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"], [], "", "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"], [], "", "Solves a banded triangular system of equations", "", []),
+  Routine(False, True,  "2a", "tbsv",  T,  [S,D,C,Z],   ["n","k"], ["layout","triangle","a_transpose","diagonal"], ["a"], ["x"], [], "", "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"], [], "", "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"], ["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.", []),
-  Routine(True,  True,  "2b", "geru",  T,  [C,Z],       ["m","n"], ["layout"], ["x","y"], ["a"], ["alpha"], "", "General rank-1 complex matrix update", "Same operation as xGER, but with complex data-types.", []),
-  Routine(True,  True,  "2b", "gerc",  T,  [C,Z],       ["m","n"], ["layout"], ["x","y"], ["a"], ["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.", []),
-  Routine(True,  True,  "2b", "her",   Tc, [Css,Zdd],   ["n"], ["layout","triangle"], ["x"], ["a"], ["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.", []),
-  Routine(True,  True,  "2b", "hpr",   Tc, [Css,Zdd],   ["n"], ["layout","triangle"], ["x"], ["ap"], ["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"], ["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.", []),
-  Routine(True,  True,  "2b", "hpr2",  T,  [C,Z],       ["n"], ["layout","triangle"], ["x","y"], ["ap"], ["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"], ["alpha"], "", "Symmetric rank-1 matrix update", "Same operation as xHER, but matrix A is a symmetric matrix instead.", []),
-  Routine(True,  True,  "2b", "spr",   T,  [S,D,H],     ["n"], ["layout","triangle"], ["x"], ["ap"], ["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"], ["alpha"], "", "Symmetric rank-2 matrix update", "Same operation as xHER2, but matrix A is a symmetric matrix instead.", []),
-  Routine(True,  True,  "2b", "spr2",  T,  [S,D,H],     ["n"], ["layout","triangle"], ["x","y"], ["ap"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["alpha","beta"], "", "General matrix-matrix multiplication", "", []),
-  Routine(True,  True,  "3", "symm",  T,  [S,D,C,Z,H], ["m","n"], ["layout","side","triangle"], ["a","b"], ["c"], ["alpha","beta"], "", "Symmetric matrix-matrix multiplication", "", []),
-  Routine(True,  True,  "3", "hemm",  T,  [C,Z],       ["m","n"], ["layout","side","triangle"], ["a","b"], ["c"], ["alpha","beta"], "", "Hermitian matrix-matrix multiplication", "", []),
-  Routine(True,  True,  "3", "syrk",  T,  [S,D,C,Z,H], ["n","k"], ["layout","triangle","a_transpose"], ["a"], ["c"], ["alpha","beta"], "", "Rank-K update of a symmetric matrix", "", []),
-  Routine(True,  True,  "3", "herk",  Tc, [Css,Zdd],   ["n","k"], ["layout","triangle","a_transpose"], ["a"], ["c"], ["alpha","beta"], "", "Rank-K update of a hermitian matrix", "", []),
-  Routine(True,  True,  "3", "syr2k", T,  [S,D,C,Z,H], ["n","k"], ["layout","triangle","ab_transpose"], ["a","b"], ["c"], ["alpha","beta"], "", "Rank-2K update of a symmetric matrix", "", []),
-  Routine(True,  True,  "3", "her2k", TU, [Ccs,Zzd],   ["n","k"], ["layout","triangle","ab_transpose"], ["a","b"], ["c"], ["alpha","beta"], "", "Rank-2K update of a hermitian matrix", "", []),
-  Routine(True,  True,  "3", "trmm",  T,  [S,D,C,Z,H], ["m","n"], ["layout","side","triangle","a_transpose","diagonal"], ["a"], ["b"], ["alpha"], "", "Triangular matrix-matrix multiplication", "", []),
+  Routine(True,  True,  "3", "gemm",  T,  [S,D,C,Z,H], ["m","n","k"], ["layout","a_transpose","b_transpose"], ["a","b"], ["c"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["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"], ["alpha"], "", "Solves a triangular system of equations", "", []),
 ]]
 
@@ -512,7 +528,6 @@ with open(filename, "w") as f:
 						f.write("* "+requirement+"\n")
 					f.write("\n")
 
-
 				# Routine footer
 				f.write("\n\n")
 
diff --git a/scripts/generator/routine.py b/scripts/generator/routine.py
index fe857ea8..00883776 100644
--- a/scripts/generator/routine.py
+++ b/scripts/generator/routine.py
@@ -58,9 +58,9 @@ def OptionToDoc(x):
 	    'a_transpose': "Transposing the input matrix A, either `Transpose::kNo` (111), `Transpose::kYes` (112), or `Transpose::kConjugate` (113) for a complex-conjugate transpose.",
 	    'b_transpose': "Transposing the input matrix B, either `Transpose::kNo` (111), `Transpose::kYes` (112), or `Transpose::kConjugate` (113) for a complex-conjugate transpose.",
 	    'ab_transpose': "Transposing the packed input matrix AP, either `Transpose::kNo` (111), `Transpose::kYes` (112), or `Transpose::kConjugate` (113) for a complex-conjugate transpose.",
-	    'side': "The horizontal position of the triangular matrix, either `Side::kLeft` (141) or `Side::kRight` (142).",
-	    'triangle': "The vertical position of the triangular matrix, either `Triangle::kUpper` (121) or `Triangle::kLower` (122).",
-	    'diagonal': "The property of the diagonal matrix, either `Diagonal::kNonUnit` (131) for a non-unit values on the diagonal or `Diagonal::kUnit` (132) for a unit values on the diagonal.",
+	    'side': "The position of the triangular matrix in the operation, either on the `Side::kLeft` (141) or `Side::kRight` (142).",
+	    'triangle': "The part of the array of the triangular matrix to be used, either `Triangle::kUpper` (121) or `Triangle::kLower` (122).",
+	    'diagonal': "The property of the diagonal matrix, either `Diagonal::kNonUnit` (131) for non-unit values on the diagonal or `Diagonal::kUnit` (132) for unit values on the diagonal.",
 	}[x]
 
 # ==================================================================================================
@@ -265,7 +265,7 @@ class Routine():
 			incld_description = "Leading dimension " if (name in self.BuffersMatrix()) else "Stride/increment "
 			a = ["`"+prefix+"cl_mem "+name+"_buffer`: OpenCL buffer to store the "+inout+" "+math_name+"."]
 			b = ["`const size_t "+name+"_offset`: The offset in elements from the start of the "+inout+" "+math_name+"."]
-			c = ["`const size_t "+name+"_"+self.Postfix(name)+"`: "+incld_description+"of the "+inout+" "+math_name+"."] if (name not in self.BuffersWithoutLdInc()) else []
+			c = ["`const size_t "+name+"_"+self.Postfix(name)+"`: "+incld_description+"of the "+inout+" "+math_name+". This value must be greater than 0."] if (name not in self.BuffersWithoutLdInc()) else []
 			return a+b+c
 		return []
 
@@ -366,7 +366,7 @@ class Routine():
 	# Retrieves the documentation of the sizes
 	def SizesDoc(self):
 		if self.sizes:
-			definitions = ["`const size_t "+s+"`: Integer size argument." for s in self.sizes]
+			definitions = ["`const size_t "+s+"`: Integer size argument. This value must be positive." for s in self.sizes]
 			return definitions
 		return []
 
@@ -416,7 +416,7 @@ class Routine():
 	# Retrieves the documentation of the options
 	def OptionsDoc(self):
 		if self.options:
-			definitions = ["`const "+OptionToCLBlast(o)+"`: "+OptionToDoc(o) for o in self.options]
+			definitions = ["`const "+OptionToCLBlast(o)+" "+o+"`: "+OptionToDoc(o) for o in self.options]
 			return definitions
 		return []
 
@@ -547,7 +547,7 @@ class Routine():
 
 	# Retrieves a list of routine requirements for documentation
 	def RequirementsDoc(self):
-		return []
+		return self.requirements
 
 	# ==============================================================================================