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+# Parameterized Derived Types (PDTs)
+
+Derived types can be parameterized with type parameters. A type parameter is
+either a kind type parameter or a length type parameter. Both kind and length
+type parameters are of integer type.
+
+This document aims to give insights at the representation of PDTs in FIR and how
+PDTs related constructs and features are lowered to FIR.
+
+# Fortran standard
+
+Here is a list of the sections and constraints of the Fortran standard involved
+for parameterized derived types.
+
+- 7.2 Type parameters
+  - C701
+  - C702
+- 9.4.5: Type parameter inquiry
+- 9.7.1: ALLOCATE statement
+- 9.7.2: NULLIFY
+- 9.7.3: DEALLOCATE
+
+The constraints are implemented and tested in flang.
+
+### PDT with kind type parameter
+
+PDTs with kind type parameter are already implemented in flang. Since the kind
+type parameter shall be a constant expression, it can be determined at
+compile-time and is folded in the type itself. Kind type parameters also play
+a role in determining a specific type instance according to the Fortran
+standard.
+
+**Fortran**
+```fortran
+type t(k)
+  integer, kind :: k
+end type
+
+type(t(1)) :: tk1
+type(t(2)) :: tk2
+```
+
+In the example above, `tk1` and `tk2` have distinct types.
+
+Lowering makes the distinction between the two types by giving them different
+names `@_QFE.kp.t.1` and `@_QFE.kp.t.2`. More information about the unique names
+can be found here: `flang/docs/BijectiveInternalNameUniquing.md`
+
+### PDT with length type parameter
+
+Two PDTs with the same derived type and the same kind type parameters but
+different length type parameters are not distinct types. Unlike the kind type
+parameter, the length type parameters do not play a role in determining a
+specific type instance.
+PDTs with length type parameter can be seen as dependent types[1].
+
+In the example below, `tk1` and `tk2` have the same type but may have different
+layout in memory. They have different value for the length type parameter `l`.
+`tk1` and `tk2` are not convertible unlike `CHARACTER` types.
+Assigning `tk2` to `tk1` is not a valid program.
+
+**Fortran**
+```fortran
+type t(k,l)
+  integer, kind :: k
+  integer, len :: l
+end type
+
+type(t(1, i+1)) :: tk1
+type(t(1, i+2)) :: tk2
+
+! This is invalid
+tk2 = tk1
+```
+
+Components with length type parameters cannot be folded into the type at
+compile-time like the one with kind type parameters since their size is not
+known. There are multiple ways to implement length type parameters and here are
+two possibilities.
+
+1. Directly encapsulate the components in the derived type. This will be referred
+   as the "inlined" solution in the rest of the document. The size of the
+   descriptor will not be fixed and be computed at runtime. Size, offset need
+   to be computed at runtime as well.
+
+2. Use a level of indirection for the components outside of the descriptor. This
+   will be referred as the "outlined" solution in the rest of the document.
+   The descriptor size will then remain the same.
+
+These solutions have pros and cons and more details are given in the next few
+sections.
+
+#### Implementing PDT with inlined components
+
+In case of `len_type1`, the size, offset, etc. of `fld1` and `fld2` depend on
+the runtime values of `i` and `j` when the components are inlined into the
+derived type. At runtime, this information needs to be computed to be retrieved.
+While lowering the PDT, compiler generated functions can be created in order to
+compute this information. 
+
+Note: The type description tables generated by semantics and used throughout the
+runtime have component offsets as constants. Inlining component would require
+this representation to be extended.
+
+**Fortran**
+```fortran
+! PDT with one level of inlined components.
+type len_type1(i, j)
+  integer, len :: i, j
+  character(i+j) :: fld1
+  character(j-i+2) :: fld2
+end type
+```
+
+#### Implementing PDT with outlined components
+
+A level of indirection can be used and `fld1` and `fld2` are then outlined
+as shown in `len_type2`. _compiler_allocatable_ is here only to show which
+components have an indirection.
+
+**Fortran**
+```fortran
+! PDT with one level of indirection.
+type len_type2(i, j)
+  integer, len :: i, j
+  ! The two following components are not directly stored in the type but
+  ! allocatable components managed by the compiler. The
+  ! `compiler_managed_allocatable` is not a proper keyword but just added here
+  ! to have a better understanding.
+  character(i+j), compiler_managed_allocatable :: fld1 
+  character(j-i+2), compiler_managed_allocatable :: fld2
+end type
+```
+
+This solution has performance drawback because of the added indirections. It
+also has to deal with compiler managed allocation/deallocation of the components
+pointed by the indirections.
+
+These indirections are more problematic when we deal with array slice of derived
+types as it could require temporaries depending how the memory is allocated.
+
+The outlined solution is also problematic for unformatted I/O as the
+indirections need to be followed correctly when reading or writing records.
+
+#### Example of nested PDTs
+
+PDTs can be nested. Here are some example used later in the document.
+
+**Fortran**
+```fortran
+! PDT with second level of inlined components.
+type len_type3(i, j)
+  integer, len :: i, j
+  character(2*j) :: name
+  type(len_type1(i*2, j+4)) :: field
+end type
+
+! PDT with second level of indirection
+type len_type4(i, j)
+  integer, len :: i, j
+  character(2*j), compiler_allocatable :: name
+  type(len_type2(i-1, 2**j)), compiler_allocatable :: field
+end type
+```
+
+#### Example with array slice
+
+Let's take an example with an array slice to see the advantages and
+disadvantages of the two solutions.
+
+For all derived types that do not have LEN type parameter (only have
+compile-time constants) a standard descriptor can be set with the correct offset
+and strides such that `array%field%fld2` can be encoded in the descriptor, is
+not contiguous, and does not require a copy. This is what is implemented in
+flang.
+
+**Fortran**
+```fortran
+! Declare arrays of PDTs
+type(len_type3(exp1,exp2)) :: pdt_inlined_array(exp3)
+type(len_type4(exp1,exp2)) :: pdt_outlined_array(exp3)
+
+! Passing/accessing a slice of PDTs array
+pdt_inlined_array%field%fld2
+```
+
+For a derived type with length type parameters inlined the expression
+`pdt_inlined_array%field%fld2` can be encoded in the standard descriptor because
+the components of `pdt_inlined_array` are inlined such that the array is laid
+out with all its subcomponents in a contiguous range of memory.
+
+For the `pdt_outlined_array` array, the implementation has to insert several
+level of indirections and therefore cannot be encoded in the standard
+descriptor.
+The different indirections levels break the property of the large contiguous
+block in memory if the allocation is done for each components. This would make
+the `pdt_outlined_array` a ragged array. The memory can also be allocated for
+components with length type parameters while allocating the base object (in this
+case the `pdt_outlined_array`).
+
+For each non-allocatable/non-pointer leaf automatic component of a PDT base
+entity (`pdt_outlined_array` here) or a base entity containing PDTs, the
+initialization will allocate a single block in memory for all the leaf
+components reachable in the base entity (`pdt_outlined_array(i)%field%fld1`).
+The size of this block will be `N * sizeof(leaf-component)` where `N` is the
+multiplication of the size of each part-ref from the base entity to the leaf
+component. The descriptor for each leaf component can then point to the correct
+location in the block `block[i*sizeof(leaf-component)]`.
+
+Outlining the components has the advantage that the size of the PDTs are
+compile-time constant as each field is encoded as a descriptor pointing to the
+data. It has a disadvantage to require non-standard descriptors and comes with
+additional runtime cost.
+
+With components inlining, the size of the PDTs are not compile-time constant.
+This solution has the advantage to not add a performance drawback with
+additional indirections but requires to compute the size of the descriptor
+at runtime.
+The size of the PDTs need to be computed at runtime. This is already the case
+for dynamic allocation sizes since it is possible for arrays to have dynamic
+shapes, etc.
+
+### Support of PDTs in other compilers
+
+1) Nested PDTs
+2) Array of PDTs
+3) Allocatable array of PDTs
+4) Pointer to array section
+5) Formatted I/O
+6) Unformatted I/O
+7) User-defined I/O
+8) FINAL subroutine
+9) ELEMENTAL FINAL subroutine
+
+| Compiler  |   1   |   2   |   3   |   4   |   5   |   6   |   7   |   8   |   9   |
+| --------- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- |
+| gfortran  | crash |   ok  | crash |   ok  |   ok  |   ok  |   no  |   no  |   no  |
+| nag       |   ok  |   ok  |   ok  | crash |   ok  |   ok  |   ok  |   no  |   no  |
+| nvfortran | crash |   ok  |   ok  |   ok  |   ok  |   ok  |   ok  |   ok  |   no  |
+| xlf       |   ok  |   ok  |   ok  |   ok  | wrong |   ok  | wrong |   no  |   no  |
+| ifort     |   ok  |   ok  |   ok  |   ok  |   ok  |   ok  |   ok  | crash | crash |
+
+_Legends of results in the table_
+```
+ok = compile + run + good result
+wrong = compile + run + wrong result
+crash = compiler crash or runtime crash
+no = doesn't compile with no crash
+```
+
+#### Field inlining in lowering
+
+A PDT with length type parameters has a list of 1 or more type parameters that
+are runtime values. These length type parameter values can be present in
+specification of other type parameters, array bounds expressions, etc.
+All these expressions are integer specifications expressions and can be
+evaluated at any given point with the length type parameters value of the PDT
+instance. This is possible because constraints C750 and C754 from Fortran 2018
+standard that restrict what can appear in the specification expression.
+
+_note: C750 and C754 are partially enforced in the semantic at the moment._
+
+These expressions can be lowered into small simple functions. For example,
+the offset of `fld1` in `len_type1` could be 0; its size would be computed as
+`sizeof(char) * (i+j)`. `size` can be lowered into a compiler generated
+function.
+
+**FIR**
+```c
+// Example of compiler generated functions to compute offsets, size, etc.
+// This is just an example and actual implementation might have more functions.
+
+// name field offset.
+func.func @_len_type3.offset.name() -> index {
+  %0 = arith.constant 0 : index
+  return %0 : index
+}
+
+// size for `name`: sizeof(char) * (2 * i) + padding
+func.func @_len_type3.memsize.name(%i: index, %j: index) -> index {
+  %0 = arith.constant 2 : index
+  %1 = arith.constant 8 : index
+  %2 = arith.muli %0, %i : index
+  %3 = arith.muli %1, %2 : index
+  // padding not added here
+  return %3 : index
+}
+
+// `fld` field offset.
+func.func @_len_type3.offset.field(%i: index, %j: index) -> index {
+  %0 = call @_len_type3.offset.name() : () -> index
+  %1 = call @_len_type3.memsize.name(%i, %j) : (index, index) -> index
+  %2 = arith.addi %0, %1 : index
+  return %2 : index
+}
+
+// 1st type parameter used for field `fld`: i*2
+func.func @_len_type3.field.typeparam.1(%i : index, %j : index) -> index {
+  %0 = arith.constant 2 : index
+  %1 = arith.muli %0, %i : index
+  return %1 : index
+}
+
+// 2nd type parameter used for field `fld`: j+4
+func.func @_len_type3.field.typeparam.2(%i : index, %j : index) -> index {
+  %0 = arith.constant 4 : index
+  %1 = arith.addi %j, %0 : index
+  return %1 : index
+}
+
+// `fld1` offset in `len_type1`.
+func.func @_len_type1.offset.fld1() -> index {
+  %0 = arith.constant 0 : index
+  return %0 : index
+}
+
+// size for `fld1`.
+func.func @_len_type1.memsize.fld1(%i : index, %j : index) -> index {
+  %0 = arith.constant 8 : index
+  %1 = arith.addi %i, %j : index
+  %2 = arith.muli %0, %1 : index
+  return %2 : index
+}
+
+// `fld2` offset in `len_type1`.
+func.func @_len_type1.offset.fld2(%i : index, %j : index) -> index {
+  %0 = call @_len_type1.offset.fld1() : () -> index
+  %1 = call @_len_type1.memsize.fld1(%i, %j) : (index, index) -> index
+  %2 = arith.addi %0, %1 : index
+  return %2 : index
+}
+```
+
+Access a field
+```fortran
+pdt_inlined_array(1)%field%fld2
+```
+
+Example of offset computation in the PDTs.
+```c
+%0 = call @_len_type3.field.typeparam.1(%i, %j) : (index, index) -> index
+%1 = call @_len_type3.field.typeparam.2(%i, %j) : (index, index) -> index
+%2 = call @_len_type3.offset.fld(%i, %j) : (index, index) -> index
+%3 = call @_len_type1.offset.fld2(%0, %1) : (index, index) -> index
+%offset_of_1st_element = arith.addi %2, %3 : index
+// Use the value computed offset_of_1st_element
+```
+
+In the case where the length type parameters values `(i,j)` are compile-time
+constants then function inlining and constant folding will transform these
+dependent types into statically defined types with no runtime cost.
+
+**Fortran**
+```fortran
+type t(l)
+  integer, len :: l
+  integer :: i(l)
+end type
+
+type(t(n)), target :: a(10)
+integer, pointer :: p(:)
+p => a(:)%i(5)
+```
+
+When making a new descriptor like for pointer association, the `field_index`
+operation can take the length type parameters needed for size/offset
+computation.
+
+**FIR**
+```c
+%5 = fir.field_index i, !fir.type<_QMmod1Tt{l:i32,i:!fir.array<?xi32>}>(%n : i32)
+```
+
+### Length type parameter with expression
+
+The component of a PDT can be defined with expressions including the length
+type parameters.
+
+**Fortran**
+```fortran
+type t1(n, m)
+  integer, len :: n = 2
+  integer, len :: m = 4
+  real :: data(n*m)
+end type
+```
+
+The idea would be to replace the expression with an extra length type parameter
+with a compiler generated name and a default value of `n*m`. All instance of the
+expression would then reference the new name.
+
+**Fortran**
+```fortran
+type t1(n, m)
+  integer, len :: n = 2
+  integer, len :: m = 4
+  integer, len :: _t1_n_m = 8 ! hidden extra length type parameter
+  real :: data(_t1_n_m)
+end type
+```
+
+At any place where the a PDT is initialized, the lowering would make the
+evaluation and their values saved in the addendum and pointed to by the
+descriptor.
+
+### `ALLOCATE`/`DEALLOCATE` statements
+
+The allocation and deallocation of PDTs are delegated to the runtime.
+
+The corresponding function can be found in
+`flang/include/flang/Runtime/allocatable.h` and
+`flang/include/flang/Runtime/pointer.h` for pointer allocation.
+
+`ALLOCATE`
+
+The `ALLOCATE` statement is lowered to a sequence of function calls as shown in
+the example below.
+
+**Fortran**
+```fortran
+type t1(i)
+  integer, len :: i = 4
+  character(i) :: c
+end type
+
+type(t1), allocatable :: t
+type(t1), pointer :: p
+
+allocate(t1(2)::t)
+allocate(t1(2)::p)
+```
+
+**FIR**
+```c
+// For allocatable
+%5 = fir.call @_FortranAAllocatableInitDerived(%desc, %type) : (!fir.box<none>, ) -> ()
+// The AllocatableSetDerivedLength functions is called for each length type parameters.
+%6 = fir.call @_FortranAAllocatableSetDerivedLength(%desc, %pos, %value) : (!fir.box<none>, i32, i64) -> ()
+%7 = fir.call @_FortranAAllocatableAllocate(%3) : (!fir.box<none>) -> ()
+
+// For pointer
+%5 = fir.call @_FortranAPointerNullifyDerived(%desc, %type) : (!fir.box<none>, ) -> ()
+// The PointerSetDerivedLength functions is called for each length type parameters.
+%6 = fir.call @_FortranAPointerSetDerivedLength(%desc, %pos, %value) : (!fir.box<none>, i32, i64) -> ()
+%7 = fir.call @_FortranAPointerAllocate(%3) : (!fir.box<none>) -> ()
+```
+
+`DEALLOCATE`
+
+The `DEALLOCATE` statement is lowered to a runtime call to
+`AllocatableDeallocate` and `PointerDeallocate` for pointers.
+
+**Fortran**
+```fortran
+deallocate(pdt1)
+```
+
+**FIR** 
+```c
+// For allocatable
+%8 = fir.call @_FortranAAllocatableDeallocate(%desc1) : (!fir.box<none>) -> (i32)
+
+// For pointer
+%8 = fir.call @_FortranAPointerDeallocate(%desc1) : (!fir.box<none>) -> (i32)
+```
+
+### `NULLIFY`
+
+The `NULLIFY` statement is lowered to a call to the corresponding runtime
+function `PointerNullifyDerived` in `flang/include/flang/Runtime/pointer.h`.
+
+**Fortran**
+```fortran
+NULLIFY(p)
+```
+
+**FIR**
+```c
+%0 = fir.call @_FortranAPointerNullifyDerived(%desc, %type) : (!fir.box<none>, !fir.tdesc) -> ()
+```
+
+### Formatted I/O
+
+The I/O runtime internals are described in this file:
+`flang/docs/IORuntimeInternals.md`.
+
+When an I/O statement with a derived-type is encountered in lowering, the
+derived-type is emboxed in a descriptor if it is not already and a call to the
+runtime library is issued with the descriptor (as shown in the example below).
+The function is `_FortranAioOutputDescriptor`. The call make a call to
+`FormattedDerivedTypeIO` in `flang/runtime/descriptor-io.h` for derived-type.
+This function will need to be updated to support the chosen solution for PDTs.
+
+**Fortran**
+```fortran
+type t
+  integer, len :: l
+  integer :: i(l) = 42
+end type
+
+! ...
+
+subroutine print_pdt
+  type(t(10)) :: x
+  print*, x
+end subroutine
+```
+
+**FIR**
+```c
+func.func @_QMpdtPprint_pdt() {
+  %l = arith.constant = 10
+  %0 = fir.alloca !fir.type<_QMpdtTt{l:i32,i:!fir.array<?xi32>}> (%l : i32) {bindc_name = "x", uniq_name = "_QMpdt_initFlocalEx"}
+  %1 = fir.embox %0 : (!fir.ref<!fir.type<_QMpdtTt{l:i32,i:!fir.array<?xi32>}>>) (typeparams %l : i32) -> !fir.box<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<2xi32>}>> 
+  %2 = fir.address_of(@_QQcl.2E2F6669725F7064745F6578616D706C652E66393000) : !fir.ref<!fir.char<1,22>>
+  %c8_i32 = arith.constant 8 : i32
+  %3 = fir.convert %1 : (!fir.box<!fir.type<_QMpdtTt{l:i32,i:!fir.array<?xi32>}>>) -> !fir.box<none>
+  %4 = fir.convert %2 : (!fir.ref<!fir.char<1,22>>) -> !fir.ref<i8>
+  %5 = fir.call @_FortranAInitialize(%3, %4, %c8_i32) : (!fir.box<none>, !fir.ref<i8>, i32) -> none
+  %c-1_i32 = arith.constant -1 : i32
+  %6 = fir.address_of(@_QQcl.2E2F6669725F7064745F6578616D706C652E66393000) : !fir.ref<!fir.char<1,22>>
+  %7 = fir.convert %6 : (!fir.ref<!fir.char<1,22>>) -> !fir.ref<i8>
+  %c10_i32 = arith.constant 10 : i32
+  %8 = fir.call @_FortranAioBeginExternalListOutput(%c-1_i32, %7, %c10_i32) : (i32, !fir.ref<i8>, i32) -> !fir.ref<i8>
+  %9 = fir.embox %0 : (!fir.ref<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>) (typeparams %l : i32) -> !fir.box<!fir.type<_QMpdtTt{l:i32,i:!fir.array<?xi32>}>>
+  %10 = fir.convert %9 : (!fir.box<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>) -> !fir.box<none>
+  %11 = fir.call @_FortranAioOutputDescriptor(%8, %10) : (!fir.ref<i8>, !fir.box<none>) -> i1
+  %12 = fir.call @_FortranAioEndIoStatement(%8) : (!fir.ref<i8>) -> i32
+  return
+}
+```
+
+### Unformatted I/O
+
+The entry point in the runtime for unformatted I/O is similar than the one for
+formatted I/O. A call to `_FortranAioOutputDescriptor` with the correct
+descriptor is also issued by the lowering. For unformatted I/O, the runtime is
+calling `UnformattedDescriptorIO` from `flang/runtime/descriptor-io.h`.
+This function will need to be updated to support the chosen solution for PDTs.
+
+### Default component initialization of local variables
+
+Default initializers for components with length type parameters need to be
+processed as the derived type instance is created.
+The length parameters block must also be created and attached to the addendum.
+See _New f18addendum_ section for more information.
+
+### Assignment
+
+As mentioned in 10.2.1.2 (8), for an assignment, each length type parameter of
+the variable shall have the same value as the corresponding type parameter
+unless the lhs is allocatable.
+
+**Fortran**
+```fortran
+type t(l)
+  integer, len :: l
+  integer :: i(l)
+end type
+
+! ...
+
+type(t(10)) :: a, b
+type(t(20)) :: c
+type(t(:)), allocatable :: d
+a = b ! Legal assignment
+c = b ! Illegal assignment because `c` does not have the same length type 
+      ! parameter value than `b`.
+d = c ! Legal because `d` is allocatable
+```
+
+A simple intrinsic assignment without allocatable or pointer follows the same
+path than the traditional derived-type (addressing of component is different)
+since the length type parameter values are identical and do not need to be
+copied or reallocated. The length type parameters values are retrieved when
+copying the data.
+
+Assignment of PDTs with allocatable or pointer components are done with the help
+of the runtime. A call to `_FortranAAssign` is done with the lhs and rhs
+descriptors. The length type parameters are available in the descriptors.
+
+For allocatable PDTs, if the rhs side has different length type parameters than
+the lhs, it is deallocated first and allocated with the rhs length type
+parameters information (F'2018 10.2.1.3(3)). There is code in the runtime to
+handle this already. It will need to be updated for the new f18addendum.
+
+### Finalization
+
+A final subroutine is called for a PDT if the subroutine has the same kind type
+parameters and rank as the entity to be finalized. The final subroutine is
+called with the entity as the actual argument.
+If there is an elemental final subroutine whose dummy argument has the same kind
+type parameters as the entity to be finalized, or a final subroutine whose dummy
+argument is assumed-rank with the same kind type parameters as the entity to be
+finalized, the subroutine is called with the entity as the actual argument.
+Otherwise, no subroutine is called.
+
+**Example from the F2018 standard**
+```fortran
+module m
+
+  type t(k)
+    integer, kind :: k
+    real(k), pointer :: vector(:) => NULL()
+  contains
+    final :: finalize_t1s, finalize_t1v, finalize_t2e
+  end type
+
+contains
+  
+  subroutine finalize_t1s(x)
+    type(t(kind(0.0))) x
+    if (associated(x%vector)) deallocate(x%vector)
+  END subroutine
+  
+  subroutine finalize_t1v(x)
+    type(t(kind(0.0))) x(:)
+    do i = lbound(x,1), ubound(x,1)
+      if (associated(x(i)%vector)) deallocate(x(i)%vector)
+    end do
+  end subroutine
+
+  elemental subroutine finalize_t2e(x)
+    type(t(kind(0.0d0))), intent(inout) :: x
+    if (associated(x%vector)) deallocate(x%vector)
+  end subroutine
+end module
+
+subroutine example(n)
+use m
+
+type(t(kind(0.0))) a, b(10), c(n,2)
+type(t(kind(0.0d0))) d(n,n)
+...
+! Returning from this subroutine will effectively do
+!    call finalize_t1s(a)
+!    call finalize_t1v(b)
+!    call finalize_t2e(d)
+! No final subroutine will be called for variable C because the user
+! omitted to define a suitable specific procedure for it.
+end subroutine
+```
+
+### Type parameter inquiry
+
+Type parameter inquiry is used to get the value of a type parameter in a PDT.
+
+**Fortran**
+```fortran
+module t
+type t1(i, j)
+  integer, len :: i = 4
+  integer, len :: j = 2
+  character(i*j) :: c
+end type
+end
+
+program main
+use t
+type(t1(2, 2)) :: ti
+print*, ti%c%len
+print*, ti%i
+print*, ti%j
+end
+
+! Should print:
+! 4
+! 2
+! 2
+```
+
+These values are present in the `f18Addendum` and can be retrieved from it with
+the correct index. If the length type parameter for a field is an expression,
+a compiler generated function is used to computed its value.
+The length type parameters are indexed in declaration order; i.e., 0 is the
+first length type parameter in the deepest base type.
+
+### PDTs and polymorphism
+
+In some cases with polymorphic entities, it is necessary to copy the length
+type parameters from a descriptor to another. With the current design this is
+not possible since the descriptor cannot be reallocated and the addendum is
+allocated with a fixed number of length type parameters.
+
+**Fortran**
+```fortran
+! The example below illustrates a case where the number of length type
+! parameters are different and need to be copied to an existing descriptor
+! addendum.
+module m1
+type t1
+  integer :: i
+end type
+
+! This type could be defined in another compilation unit.
+type, extends(t1) :: t2(l1, l2)
+  integer, len :: l1, l2
+end type
+
+contains
+
+subroutine reallocate(x)
+  class(t1), allocatable :: x
+  allocate(t2(l1=1, l2=2):: x)
+end subroutine
+
+end module
+
+program p
+  use m1
+
+  class(t1), allocatable :: x
+
+  call reallocate(x)
+  ! The new length type parameters need to be propagated at this point.
+
+  ! rest of code using `x`
+end program
+```
+
+The proposed solution is to add indirection in the `f18Addendum` and store the
+length type parameters in a separate block instead of directly in the addendum.
+At the moment the storage for the length type parameters is allocated once as
+a `std::int64_t` array.
+
+**New f18Addendum**
+```cpp
+{*derivedType_, *lenParamValues_}
+```
+
+Adding the indirection in the descriptor's addendum requires to manage the
+lifetime of the block holding the length type parameter values.
+
+Here are some thoughts of how to manage it:
+- For allocatables, the space for the LEN parameters can be allocated as part of
+  the same malloc as the payload data.
+- For automatics, same thing, if we implement automatics as allocatables.
+- For monomorphic local variables, the LEN parameters would be in a little array
+  on the stack. Or we could treat any variable or component with LEN parameters
+  as being automatic even when it's monomorphic.
+- For pointers and dummy arguments, we can just copy the pointer in the addendum
+  from the target to the pointer or dummy descriptor.
+- For dynamically allocated descriptors, the LEN parameter values could just
+  follow the addendum in the same malloc.
+
+The addendum of an array sections/sub-objects would point to the same block than
+the base object.
+
+In some special cases, a descriptor needs to be passed between the caller and
+the callee. This includes array of PDTs and derived-type with PDT components.
+The example describe one of the corner case where the length type parameter
+would be lost if the descriptor is not passed.
+
+### Example that require a descriptor
+
+Because of the length type parameters store in the addendum, it is required in
+some case to pass the PDT with a descriptor to preserve the length type
+parameters information. The example below illustrates such a case.
+
+**Fortran**
+```fortran
+module m
+type t
+ integer :: i
+end type
+
+type, extends(t) :: t2(l)
+  integer, len :: l
+  real :: x(l)
+end type
+
+type base
+  type(t2(20)) :: pdt_component
+end type
+
+class(t), pointer :: p(:)
+
+contains
+
+subroutine foo(x, n)
+  integer :: n
+  type(base), target :: x(n)
+  ! Without descriptor, the actual argument is a zero-sized array. The length
+  ! type parameters of `x(n)%pdt_component` are not propagated from the caller.
+
+  ! A descriptor local to this function is created to pass the array section
+  ! in bar. 
+  call bar(x%pdt_component)
+end subroutine
+
+subroutine bar(x)
+  type(t2(*)), target :: x(:)
+  p => x
+end subroutine
+
+subroutine test()
+  type(base), target :: x(100)
+  call foo(x(1:-1:1), 0)
+  select type (p)
+   type is (t2(*))
+    ! This type parameters of x(1:60:3) in foo must still live here
+    print *, p%l
+   class default
+     print *, "something else"
+  end select
+end subroutine
+end module
+
+  use m
+  call test()
+end
+```
+
+Because of the use case described above, PDTs, array of PDTs or derived-type
+with PDT components will be passed by descriptor.
+
+## FIR operations with length type parameters
+
+Couple of operations have length type parameters as operands already in their
+design. For some operations, length type parameters are likely needed with
+the two proposed solution. Some other operation like the array operations, the
+operands are not needed when dealing with a descriptor since the length type
+parameters are in it.
+
+The operations will be updated if needed during the implementation of the
+chosen solution.
+
+#### `fir.alloca`
+
+This primitive operation is used to allocate an object on the stack. When
+allocating a PDT, the length type parameters are passed to the
+operation so its size can be computed accordingly.
+
+**FIR**
+```c
+%i = arith.constant 10 : i32
+%0 = fir.alloca !fir.type<_QMmod1Tpdt{i:i32,data:!fir.array<?xf32>}> (%i : i32)
+// %i is the ssa value of the length type parameter
+```
+
+#### `fir.allocmem`
+
+This operation is used to create a heap memory reference suitable for storing a
+value of the given type. When creating a PDT, the length type parameters are
+passed so the size can be computed accordingly.
+
+**FIR**
+```c
+%i = arith.constant 10 : i32
+%0 = fir.alloca !fir.type<_QMmod1Tpdt{i:i32,data:!fir.array<?xf32>}> (%i : i32)
+// ...
+fir.freemem %0 : !fir.type<_QMmod1Tpdt{i:i32,data:!fir.array<?xf32>}>
+```
+
+#### `fir.embox`
+
+The `fir.embox` operation create a boxed reference value. In the case of PDTs
+the length type parameters can be passed as well to the operation.
+
+**Fortran**
+```fortran
+subroutine local()
+  type(t(2)) :: x ! simple local PDT
+  ! ...
+end subroutine
+```
+
+**FIR**
+```c
+func.func @_QMpdt_initPlocal() {
+  %c2_i32 = arith.constant 2 : i32
+  %0 = fir.alloca !fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}> (%c2 : i32)
+       {bindc_name = "x", uniq_name = "_QMpdt_initFlocalEx"}
+  // The fir.embox operation is responsible to place the provided length type
+  // parameters in the descriptor addendum so they are available to the runtime
+  // call later.
+  %1 = fir.embox %0 : (!fir.ref<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>) (typeparams %c2 : i32)
+       -> !fir.box<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>
+  %2 = fir.address_of(@_QQcl.2E2F6669725F7064745F6578616D706C652E66393000) : !fir.ref<!fir.char<1,22>>
+  %c8_i32 = arith.constant 8 : i32
+  %3 = fir.convert %1 : (!fir.box<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>) -> !fir.box<none>
+  %4 = fir.convert %2 : (!fir.ref<!fir.char<1,22>>) -> !fir.ref<i8>
+  %5 = fir.call @_FortranAInitialize(%3, %4, %c8_i32) : (!fir.box<none>, !fir.ref<i8>, i32) -> none
+  return
+}
+```
+
+#### `fir.field_index`
+
+The `fir.field_index` operation is used to generate a field offset value from
+a field identifier in a derived-type. The operation takes length type parameter
+values with a PDT so it can compute a correct offset.
+
+**FIR**
+```c
+%l = arith.constant 10 : i32
+%1 = fir.field_index i, !fir.type<_QMpdt_initTt{l:i32,i:i32}> (%l : i32)
+%2 = fir.coordinate_of %ref, %1 : (!fir.type<_QMpdt_initTt{l:i32,i:i32}>, !fir.field) -> !fir.ref<i32>
+%3 = fir.load %2 : !fir.ref<i32>
+return %3
+```
+
+#### `fir.len_param_index`
+
+This operation is used to get the length type parameter offset in from a PDT.
+
+**FIR**
+```c
+func.func @_QPpdt_len_value(%arg0: !fir.box<!fir.type<t1{l:i32,!fir.array<?xi32>}>>) -> i32 {
+  %0 = fir.len_param_index l, !fir.box<!fir.type<t1{l:i32,!fir.array<?xi32>}>>
+  %1 = fir.coordinate_of %arg0, %0 : (!fir.box<!fir.type<t1{l:i32,!fir.array<?xi32>}>>, !fir.len) -> !fir.ref<i32>
+  %2 = fir.load %1 : !fir.ref<i32>
+  return %2 : i32
+}
+```
+
+#### `fir.save_result`
+
+Save the result of a function returning an array, box, or record type value into
+a memory location given the shape and LEN parameters of the result. Length type
+parameters is passed if the PDT is not boxed.
+
+**FIR**
+```c
+func.func @return_pdt(%buffer: !fir.ref<!fir.type<t2(l1:i32,l2:i32){x:f32}>>) {
+  %l1 = arith.constant 3 : i32
+  %l2 = arith.constant 5 : i32
+  %res = fir.call @foo() : () -> !fir.type<t2(l1:i32,l2:i32){x:f32}>
+  fir.save_result %res to %buffer typeparams %l1, %l2 : !fir.type<t2(l1:i32,l2:i32){x:f32}>, !fir.ref<!fir.type<t2(l1:i32,l2:i32){x:f32}>>, i32, i32
+  return
+}
+```
+
+#### `fir.array_*` operations
+
+The current design of the different `fir.array_*` operations include length type
+parameters operands. This is designed to use PDT without descriptor directly in
+FIR.
+
+**FIR**
+```c
+// Operation used with a boxed PDT does not need the length type parameters as
+// they are directly retrieved from the box.
+%0 = fir.array_coor %boxed_pdt, %i, %j  (fir.box<fir.array<?x?xfir.type<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>>>, index, index) -> !fir.ref<fir.type<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>>
+
+// In case the PDT would not be boxed, the length type parameters are needed to
+// compute the correct addressing.
+%0 = fir.array_coor %pdt_base, %i, %j typeparams %l  (fir.ref<fir.array<?x?xfir.type<!fir.type<_QMpdt_initTt{l:i32,i:!fir.array<?xi32>}>>>>, index, index, index) -> !fir.ref<fir.type<PDT>>
+```
+
+---
+
+## Implementation choice
+
+While both solutions have pros and cons, we want to implement the outlined
+solution.
+- The runtime was implemented with this solution in mind.
+- The size of the descriptor does not need to be computed at runtime.
+
+---
+
+# Testing
+
+- Lowering part is tested with LIT tests in tree
+- PDTs involved a lot of runtime information so executable
+  tests will be useful for full testing.
+
+---
+
+# Current TODOs
+Current list of TODOs in lowering:
+- `flang/lib/Lower/Allocatable.cpp:461` not yet implement: derived type length parameters in allocate
+- `flang/lib/Lower/Allocatable.cpp:645` not yet implement: deferred length type parameters
+- `flang/lib/Lower/Bridge.cpp:454` not yet implemented: get length parameters from derived type BoxValue
+- `flang/lib/Lower/ConvertExpr.cpp:341` not yet implemented: copy derived type with length parameters
+- `flang/lib/Lower/ConvertExpr.cpp:993` not yet implemented: component with length parameters in structure constructor
+- `flang/lib/Lower/ConvertExpr.cpp:1063` not yet implemented: component with length parameters in structure constructor
+- `flang/lib/Lower/ConvertExpr.cpp:1146` not yet implemented: type parameter inquiry
+- `flang/lib/Lower/ConvertExpr.cpp:2424` not yet implemented: creating temporary for derived type with length parameters
+- `flang/lib/Lower/ConvertExpr.cpp:3742` not yet implemented: gather rhs LEN parameters in assignment to allocatable
+- `flang/lib/Lower/ConvertExpr.cpp:4725` not yet implemented: derived type array expression temp with LEN parameters
+- `flang/lib/Lower/ConvertExpr.cpp:6400` not yet implemented: PDT size
+- `flang/lib/Lower/ConvertExpr.cpp:6419` not yet implemented: PDT offset
+- `flang/lib/Lower/ConvertExpr.cpp:6679` not yet implemented: array expr type parameter inquiry
+- `flang/lib/Lower/ConvertExpr.cpp:7135` not yet implemented: need to adjust type parameter(s) to reflect the final component
+- `flang/lib/Lower/ConvertType.cpp:334` not yet implemented: parameterized derived types
+- `flang/lib/Lower/ConvertType.cpp:370` not yet implemented: derived type length parameters
+- `flang/lib/Lower/ConvertVariable.cpp:169` not yet implemented: initial-data-target with derived type length parameters
+- `flang/lib/Lower/ConvertVariable.cpp:197` not yet implemented: initial-data-target with derived type length parameters
+- `flang/lib/Lower/VectorSubscripts.cpp:121` not yet implemented: threading length parameters in field index op
+- `flang/lib/Optimizer/Builder/BoxValue.cpp:60` not yet implemented: box value is missing type parameters
+- `flang/lib/Optimizer/Builder/BoxValue.cpp:67` not yet implemented: mutable box value is missing type parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:688` not yet implemented: read fir.box with length parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:746` not yet implemented: generate code to get LEN type parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:779` not yet implemented: derived type with type parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:905` not yet implemented: allocatable and pointer components non deferred length parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:917` not yet implemented: array component shape depending on length parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:924` not yet implemented: get character component length from length type parameters
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:934` not yet implemented: lower component ref that is a derived type with length parameter
+- `flang/lib/Optimizer/Builder/FIRBuilder.cpp:956` not yet implemented: get length parameters from derived type BoxValue
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:70` not yet implemented: updating mutablebox of derived type with length parameters
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:168` not yet implemented: read allocatable or pointer derived type LEN parameters
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:310` not yet implemented: update allocatable derived type length parameters
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:505` not yet implemented: pointer assignment to derived with length parameters
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:597` not yet implemented: pointer assignment to derived with length parameters
+- `flang/lib/Optimizer/Builder/MutableBox.cpp:740` not yet implemented: reallocation of derived type entities with length parameters
+
+
+Current list of TODOs in code generation:
+
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:1034` not yet implemented: fir.allocmem codegen of derived type with length parameters
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:1581` not yet implemented: generate call to calculate size of PDT
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:1708` not yet implemented: fir.embox codegen of derived with length parameters
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:1749` not yet implemented: reboxing descriptor of derived type with length parameters
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:2229` not yet implemented: derived type with type parameters
+- `flang/lib/Optimizer/CodeGen/CodeGen.cpp:2256` not yet implemented: compute size of derived type with type parameters
+- `flang/lib/Optimizer/CodeGen/TypeConverter.h:257` not yet implemented: extended descriptor derived with length parameters
+
+Current list of TODOs in optimizations:
+
+- `flang/lib/Optimizer/Transforms/ArrayValueCopy.cpp:1007` not yet implemented: unhandled dynamic type parameters
+
+---
+
+Resources:
+- [0] Fortran standard
+- [1] https://en.wikipedia.org/wiki/Dependent_type