This chapter attempts to cover some of the common issues encountered
when writing 16-bit code to run under MS-DOS
or
Windows 3.x
. It covers how to link programs to produce
.EXE
or .COM
files, how to write
.SYS
device drivers, and how to interface assembly language
code with 16-bit C compilers and with Borland Pascal.
.EXE
FilesAny large program written under DOS needs to be built as a
.EXE
file: only .EXE
files have the necessary
internal structure required to span more than one 64K segment. Windows
programs, also, have to be built as .EXE
files, since Windows
does not support the .COM
format.
In general, you generate .EXE
files by using the
obj
output format to produce one or more .obj
files, and then linking them together using a linker. However, NASM also
supports the direct generation of simple DOS .EXE
files using
the bin
output format (by using DB
and
DW
to construct the .EXE
file header), and a
macro package is supplied to do this. Thanks to Yann Guidon for
contributing the code for this.
NASM may also support .EXE
natively as another output
format in future releases.
obj
Format To Generate .EXE
FilesThis section describes the usual method of generating .EXE
files by linking .OBJ
files together.
Most 16-bit programming language packages come with a suitable linker;
if you have none of these, there is a free linker called VAL, available in
LZH
archive format from
x2ftp.oulu.fi
.
An LZH archiver can be found at
ftp.simtel.net
.
There is another `free' linker (though this one doesn't come with sources)
called FREELINK, available from
www.pcorner.com
.
A third, djlink
, written by DJ Delorie, is available at
www.delorie.com
.
A fourth linker, ALINK
, written by Anthony A.J. Williams, is
available at
alink.sourceforge.net
.
When linking several .OBJ
files into a .EXE
file, you should ensure that exactly one of them has a start point defined
(using the ..start
special symbol defined by the
obj
format: see section
8.4.6). If no module defines a start point, the linker will not know
what value to give the entry-point field in the output file header; if more
than one defines a start point, the linker will not know which
value to use.
An example of a NASM source file which can be assembled to a
.OBJ
file and linked on its own to a .EXE
is
given here. It demonstrates the basic principles of defining a stack,
initialising the segment registers, and declaring a start point. This file
is also provided in the test
subdirectory of the NASM
archives, under the name objexe.asm
.
segment code ..start: mov ax,data mov ds,ax mov ax,stack mov ss,ax mov sp,stacktop
This initial piece of code sets up DS
to point to the data
segment, and initializes SS
and SP
to point to
the top of the provided stack. Notice that interrupts are implicitly
disabled for one instruction after a move into SS
, precisely
for this situation, so that there's no chance of an interrupt occurring
between the loads of SS
and SP
and not having a
stack to execute on.
Note also that the special symbol ..start
is defined at the
beginning of this code, which means that will be the entry point into the
resulting executable file.
mov dx,hello mov ah,9 int 0x21
The above is the main program: load DS:DX
with a pointer to
the greeting message (hello
is implicitly relative to the
segment data
, which was loaded into DS
in the
setup code, so the full pointer is valid), and call the DOS print-string
function.
mov ax,0x4c00 int 0x21
This terminates the program using another DOS system call.
segment data hello: db 'hello, world', 13, 10, '$'
The data segment contains the string we want to display.
segment stack stack resb 64 stacktop:
The above code declares a stack segment containing 64 bytes of
uninitialized stack space, and points stacktop
at the top of
it. The directive segment stack stack
defines a segment
called stack
, and also of type
STACK
. The latter is not necessary to the correct running of
the program, but linkers are likely to issue warnings or errors if your
program has no segment of type STACK
.
The above file, when assembled into a .OBJ
file, will link
on its own to a valid .EXE
file, which when run will print
`hello, world' and then exit.
bin
Format To Generate .EXE
FilesThe .EXE
file format is simple enough that it's possible to
build a .EXE
file by writing a pure-binary program and
sticking a 32-byte header on the front. This header is simple enough that
it can be generated using DB
and DW
commands by
NASM itself, so that you can use the bin
output format to
directly generate .EXE
files.
Included in the NASM archives, in the misc
subdirectory, is
a file exebin.mac
of macros. It defines three macros:
EXE_begin
, EXE_stack
and EXE_end
.
To produce a .EXE
file using this method, you should start
by using %include
to load the exebin.mac
macro
package into your source file. You should then issue the
EXE_begin
macro call (which takes no arguments) to generate
the file header data. Then write code as normal for the bin
format – you can use all three standard sections .text
,
.data
and .bss
. At the end of the file you should
call the EXE_end
macro (again, no arguments), which defines
some symbols to mark section sizes, and these symbols are referred to in
the header code generated by EXE_begin
.
In this model, the code you end up writing starts at 0x100
,
just like a .COM
file – in fact, if you strip off the
32-byte header from the resulting .EXE
file, you will have a
valid .COM
program. All the segment bases are the same, so you
are limited to a 64K program, again just like a .COM
file.
Note that an ORG
directive is issued by the
EXE_begin
macro, so you should not explicitly issue one of
your own.
You can't directly refer to your segment base value, unfortunately,
since this would require a relocation in the header, and things would get a
lot more complicated. So you should get your segment base by copying it out
of CS
instead.
On entry to your .EXE
file, SS:SP
are already
set up to point to the top of a 2Kb stack. You can adjust the default stack
size of 2Kb by calling the EXE_stack
macro. For example, to
change the stack size of your program to 64 bytes, you would call
EXE_stack 64
.
A sample program which generates a .EXE
file in this way is
given in the test
subdirectory of the NASM archive, as
binexe.asm
.
.COM
FilesWhile large DOS programs must be written as .EXE
files,
small ones are often better written as .COM
files.
.COM
files are pure binary, and therefore most easily produced
using the bin
output format.
bin
Format To Generate .COM
Files.COM
files expect to be loaded at offset 100h
into their segment (though the segment may change). Execution then begins
at 100h
, i.e. right at the start of the program. So to write a
.COM
program, you would create a source file looking like
org 100h section .text start: ; put your code here section .data ; put data items here section .bss ; put uninitialized data here
The bin
format puts the .text
section first in
the file, so you can declare data or BSS items before beginning to write
code if you want to and the code will still end up at the front of the file
where it belongs.
The BSS (uninitialized data) section does not take up space in the
.COM
file itself: instead, addresses of BSS items are resolved
to point at space beyond the end of the file, on the grounds that this will
be free memory when the program is run. Therefore you should not rely on
your BSS being initialized to all zeros when you run.
To assemble the above program, you should use a command line like
nasm myprog.asm -fbin -o myprog.com
The bin
format would produce a file called
myprog
if no explicit output file name were specified, so you
have to override it and give the desired file name.
obj
Format To Generate .COM
FilesIf you are writing a .COM
program as more than one module,
you may wish to assemble several .OBJ
files and link them
together into a .COM
program. You can do this, provided you
have a linker capable of outputting .COM
files directly (TLINK
does this), or alternatively a converter program such as
EXE2BIN
to transform the .EXE
file output from
the linker into a .COM
file.
If you do this, you need to take care of several things:
The first object file containing code should start its code segment with
a line like RESB 100h
. This is to ensure that the code begins
at offset 100h
relative to the beginning of the code segment,
so that the linker or converter program does not have to adjust address
references within the file when generating the .COM
file.
Other assemblers use an ORG
directive for this purpose, but
ORG
in NASM is a format-specific directive to the
bin
output format, and does not mean the same thing as it does
in MASM-compatible assemblers.
You don't need to define a stack segment.
All your segments should be in the same group, so that every time your
code or data references a symbol offset, all offsets are relative to the
same segment base. This is because, when a .COM
file is
loaded, all the segment registers contain the same value.
.SYS
FilesMS-DOS device drivers – .SYS
files – are pure
binary files, similar to .COM
files, except that they start at
origin zero rather than 100h
. Therefore, if you are writing a
device driver using the bin
format, you do not need the
ORG
directive, since the default origin for bin
is zero. Similarly, if you are using obj
, you do not need the
RESB 100h
at the start of your code segment.
.SYS
files start with a header structure, containing
pointers to the various routines inside the driver which do the work. This
structure should be defined at the start of the code segment, even though
it is not actually code.
For more information on the format of .SYS
files, and the
data which has to go in the header structure, a list of books is given in
the Frequently Asked Questions list for the newsgroup
comp.os.msdos.programmer
.
This section covers the basics of writing assembly routines that call,
or are called from, C programs. To do this, you would typically write an
assembly module as a .OBJ
file, and link it with your C
modules to produce a mixed-language program.
C compilers have the convention that the names of all global symbols
(functions or data) they define are formed by prefixing an underscore to
the name as it appears in the C program. So, for example, the function a C
programmer thinks of as printf
appears to an assembly language
programmer as _printf
. This means that in your assembly
programs, you can define symbols without a leading underscore, and not have
to worry about name clashes with C symbols.
If you find the underscores inconvenient, you can define macros to
replace the GLOBAL
and EXTERN
directives as
follows:
%macro cglobal 1 global _%1 %define %1 _%1 %endmacro %macro cextern 1 extern _%1 %define %1 _%1 %endmacro
(These forms of the macros only take one argument at a time; a
%rep
construct could solve this.)
If you then declare an external like this:
cextern printf
then the macro will expand it as
extern _printf %define printf _printf
Thereafter, you can reference printf
as if it was a symbol,
and the preprocessor will put the leading underscore on where necessary.
The cglobal
macro works similarly. You must use
cglobal
before defining the symbol in question, but you would
have had to do that anyway if you used GLOBAL
.
Also see section 2.1.28.
NASM contains no mechanism to support the various C memory models directly; you have to keep track yourself of which one you are writing for. This means you have to keep track of the following things:
In models using a single code segment (tiny, small and compact),
functions are near. This means that function pointers, when stored in data
segments or pushed on the stack as function arguments, are 16 bits long and
contain only an offset field (the CS
register never changes
its value, and always gives the segment part of the full function address),
and that functions are called using ordinary near CALL
instructions and return using RETN
(which, in NASM, is
synonymous with RET
anyway). This means both that you should
write your own routines to return with RETN
, and that you
should call external C routines with near CALL
instructions.
In models using more than one code segment (medium, large and huge),
functions are far. This means that function pointers are 32 bits long
(consisting of a 16-bit offset followed by a 16-bit segment), and that
functions are called using CALL FAR
(or
CALL seg:offset
) and return using RETF
. Again,
you should therefore write your own routines to return with
RETF
and use CALL FAR
to call external routines.
In models using a single data segment (tiny, small and medium), data
pointers are 16 bits long, containing only an offset field (the
DS
register doesn't change its value, and always gives the
segment part of the full data item address).
In models using more than one data segment (compact, large and huge),
data pointers are 32 bits long, consisting of a 16-bit offset followed by a
16-bit segment. You should still be careful not to modify DS
in your routines without restoring it afterwards, but ES
is
free for you to use to access the contents of 32-bit data pointers you are
passed.
The huge memory model allows single data items to exceed 64K in size. In all other memory models, you can access the whole of a data item just by doing arithmetic on the offset field of the pointer you are given, whether a segment field is present or not; in huge model, you have to be more careful of your pointer arithmetic.
In most memory models, there is a default data segment, whose
segment address is kept in DS
throughout the program. This
data segment is typically the same segment as the stack, kept in
SS
, so that functions' local variables (which are stored on
the stack) and global data items can both be accessed easily without
changing DS
. Particularly large data items are typically
stored in other segments. However, some memory models (though not the
standard ones, usually) allow the assumption that SS
and
DS
hold the same value to be removed. Be careful about
functions' local variables in this latter case.
In models with a single code segment, the segment is called
_TEXT
, so your code segment must also go by this name in order
to be linked into the same place as the main code segment. In models with a
single data segment, or with a default data segment, it is called
_DATA
.
The C calling convention in 16-bit programs is as follows. In the following description, the words caller and callee are used to denote the function doing the calling and the function which gets called.
The caller pushes the function's parameters on the stack, one after another, in reverse order (right to left, so that the first argument specified to the function is pushed last).
The caller then executes a CALL
instruction to pass control
to the callee. This CALL
is either near or far depending on
the memory model.
The callee receives control, and typically (although this is not
actually necessary, in functions which do not need to access their
parameters) starts by saving the value of SP
in
BP
so as to be able to use BP
as a base pointer
to find its parameters on the stack. However, the caller was probably doing
this too, so part of the calling convention states that BP
must be preserved by any C function. Hence the callee, if it is going to
set up BP
as a frame pointer, must push the previous
value first.
The callee may then access its parameters relative to BP
.
The word at [BP]
holds the previous value of BP
as it was pushed; the next word, at [BP+2]
, holds the offset
part of the return address, pushed implicitly by CALL
. In a
small-model (near) function, the parameters start after that, at
[BP+4]
; in a large-model (far) function, the segment part of
the return address lives at [BP+4]
, and the parameters begin
at [BP+6]
. The leftmost parameter of the function, since it
was pushed last, is accessible at this offset from BP
; the
others follow, at successively greater offsets. Thus, in a function such as
printf
which takes a variable number of parameters, the
pushing of the parameters in reverse order means that the function knows
where to find its first parameter, which tells it the number and type of
the remaining ones.
The callee may also wish to decrease SP
further, so as to
allocate space on the stack for local variables, which will then be
accessible at negative offsets from BP
.
The callee, if it wishes to return a value to the caller, should leave
the value in AL
, AX
or DX:AX
depending on the size of the value. Floating-point results are sometimes
(depending on the compiler) returned in ST0
.
Once the callee has finished processing, it restores SP
from BP
if it had allocated local stack space, then pops the
previous value of BP
, and returns via RETN
or
RETF
depending on memory model.
When the caller regains control from the callee, the function parameters
are still on the stack, so it typically adds an immediate constant to
SP
to remove them (instead of executing a number of slow
POP
instructions). Thus, if a function is accidentally called
with the wrong number of parameters due to a prototype mismatch, the stack
will still be returned to a sensible state since the caller, which
knows how many parameters it pushed, does the removing.
It is instructive to compare this calling convention with that for
Pascal programs (described in section 9.5.1).
Pascal has a simpler convention, since no functions have variable numbers
of parameters. Therefore the callee knows how many parameters it should
have been passed, and is able to deallocate them from the stack itself by
passing an immediate argument to the RET
or RETF
instruction, so the caller does not have to do it. Also, the parameters are
pushed in left-to-right order, not right-to-left, which means that a
compiler can give better guarantees about sequence points without
performance suffering.
Thus, you would define a function in C style in the following way. The following example is for small model:
global _myfunc _myfunc: push bp mov bp,sp sub sp,0x40 ; 64 bytes of local stack space mov bx,[bp+4] ; first parameter to function ; some more code mov sp,bp ; undo "sub sp,0x40" above pop bp ret
For a large-model function, you would replace RET
by
RETF
, and look for the first parameter at [BP+6]
instead of [BP+4]
. Of course, if one of the parameters is a
pointer, then the offsets of subsequent parameters will change
depending on the memory model as well: far pointers take up four bytes on
the stack when passed as a parameter, whereas near pointers take up two.
At the other end of the process, to call a C function from your assembly code, you would do something like this:
extern _printf ; and then, further down... push word [myint] ; one of my integer variables push word mystring ; pointer into my data segment call _printf add sp,byte 4 ; `byte' saves space ; then those data items... segment _DATA myint dw 1234 mystring db 'This number -> %d <- should be 1234',10,0
This piece of code is the small-model assembly equivalent of the C code
int myint = 1234; printf("This number -> %d <- should be 1234\n", myint);
In large model, the function-call code might look more like this. In
this example, it is assumed that DS
already holds the segment
base of the segment _DATA
. If not, you would have to
initialize it first.
push word [myint] push word seg mystring ; Now push the segment, and... push word mystring ; ... offset of "mystring" call far _printf add sp,byte 6
The integer value still takes up one word on the stack, since large
model does not affect the size of the int
data type. The first
argument (pushed last) to printf
, however, is a data pointer,
and therefore has to contain a segment and offset part. The segment should
be stored second in memory, and therefore must be pushed first. (Of course,
PUSH DS
would have been a shorter instruction than
PUSH WORD SEG mystring
, if DS
was set up as the
above example assumed.) Then the actual call becomes a far call, since
functions expect far calls in large model; and SP
has to be
increased by 6 rather than 4 afterwards to make up for the extra word of
parameters.
To get at the contents of C variables, or to declare variables which C
can access, you need only declare the names as GLOBAL
or
EXTERN
. (Again, the names require leading underscores, as
stated in section 9.4.1.) Thus, a C variable
declared as int i
can be accessed from assembler as
extern _i mov ax,[_i]
And to declare your own integer variable which C programs can access as
extern int j
, you do this (making sure you are assembling in
the _DATA
segment, if necessary):
global _j _j dw 0
To access a C array, you need to know the size of the components of the
array. For example, int
variables are two bytes long, so if a
C program declares an array as int a[10]
, you can access
a[3]
by coding mov ax,[_a+6]
. (The byte offset 6
is obtained by multiplying the desired array index, 3, by the size of the
array element, 2.) The sizes of the C base types in 16-bit compilers are: 1
for char
, 2 for short
and int
, 4 for
long
and float
, and 8 for double
.
To access a C data structure, you need to know the offset from the base
of the structure to the field you are interested in. You can either do this
by converting the C structure definition into a NASM structure definition
(using STRUC
), or by calculating the one offset and using just
that.
To do either of these, you should read your C compiler's manual to find
out how it organizes data structures. NASM gives no special alignment to
structure members in its own STRUC
macro, so you have to
specify alignment yourself if the C compiler generates it. Typically, you
might find that a structure like
struct { char c; int i; } foo;
might be four bytes long rather than three, since the int
field would be aligned to a two-byte boundary. However, this sort of
feature tends to be a configurable option in the C compiler, either using
command-line options or #pragma
lines, so you have to find out
how your own compiler does it.
c16.mac
: Helper Macros for the 16-bit C InterfaceIncluded in the NASM archives, in the misc
directory, is a
file c16.mac
of macros. It defines three macros:
proc
, arg
and endproc
. These are
intended to be used for C-style procedure definitions, and they automate a
lot of the work involved in keeping track of the calling convention.
(An alternative, TASM compatible form of arg
is also now
built into NASM's preprocessor. See
section 4.10 for details.)
An example of an assembly function using the macro set is given here:
proc _nearproc %$i arg %$j arg mov ax,[bp + %$i] mov bx,[bp + %$j] add ax,[bx] endproc
This defines _nearproc
to be a procedure taking two
arguments, the first (i
) an integer and the second
(j
) a pointer to an integer. It returns i + *j
.
Note that the arg
macro has an EQU
as the
first line of its expansion, and since the label before the macro call gets
prepended to the first line of the expanded macro, the EQU
works, defining %$i
to be an offset from BP
. A
context-local variable is used, local to the context pushed by the
proc
macro and popped by the endproc
macro, so
that the same argument name can be used in later procedures. Of course, you
don't have to do that.
The macro set produces code for near functions (tiny, small and
compact-model code) by default. You can have it generate far functions
(medium, large and huge-model code) by means of coding
%define FARCODE
. This changes the kind of return instruction
generated by endproc
, and also changes the starting point for
the argument offsets. The macro set contains no intrinsic dependency on
whether data pointers are far or not.
arg
can take an optional parameter, giving the size of the
argument. If no size is given, 2 is assumed, since it is likely that many
function parameters will be of type int
.
The large-model equivalent of the above function would look like this:
%define FARCODE proc _farproc %$i arg %$j arg 4 mov ax,[bp + %$i] mov bx,[bp + %$j] mov es,[bp + %$j + 2] add ax,[bx] endproc
This makes use of the argument to the arg
macro to define a
parameter of size 4, because j
is now a far pointer. When we
load from j
, we must load a segment and an offset.
Interfacing to Borland Pascal programs is similar in concept to interfacing to 16-bit C programs. The differences are:
The leading underscore required for interfacing to C programs is not required for Pascal.
The memory model is always large: functions are far, data pointers are
far, and no data item can be more than 64K long. (Actually, some functions
are near, but only those functions that are local to a Pascal unit and
never called from outside it. All assembly functions that Pascal calls, and
all Pascal functions that assembly routines are able to call, are far.)
However, all static data declared in a Pascal program goes into the default
data segment, which is the one whose segment address will be in
DS
when control is passed to your assembly code. The only
things that do not live in the default data segment are local variables
(they live in the stack segment) and dynamically allocated variables. All
data pointers, however, are far.
The function calling convention is different – described below.
Some data types, such as strings, are stored differently.
There are restrictions on the segment names you are allowed to use – Borland Pascal will ignore code or data declared in a segment it doesn't like the name of. The restrictions are described below.
The 16-bit Pascal calling convention is as follows. In the following description, the words caller and callee are used to denote the function doing the calling and the function which gets called.
The caller pushes the function's parameters on the stack, one after another, in normal order (left to right, so that the first argument specified to the function is pushed first).
The caller then executes a far CALL
instruction to pass
control to the callee.
The callee receives control, and typically (although this is not
actually necessary, in functions which do not need to access their
parameters) starts by saving the value of SP
in
BP
so as to be able to use BP
as a base pointer
to find its parameters on the stack. However, the caller was probably doing
this too, so part of the calling convention states that BP
must be preserved by any function. Hence the callee, if it is going to set
up BP
as a frame pointer, must push the previous value first.
The callee may then access its parameters relative to BP
.
The word at [BP]
holds the previous value of BP
as it was pushed. The next word, at [BP+2]
, holds the offset
part of the return address, and the next one at [BP+4]
the
segment part. The parameters begin at [BP+6]
. The rightmost
parameter of the function, since it was pushed last, is accessible at this
offset from BP
; the others follow, at successively greater
offsets.
The callee may also wish to decrease SP
further, so as to
allocate space on the stack for local variables, which will then be
accessible at negative offsets from BP
.
The callee, if it wishes to return a value to the caller, should leave
the value in AL
, AX
or DX:AX
depending on the size of the value. Floating-point results are returned in
ST0
. Results of type Real
(Borland's own custom
floating-point data type, not handled directly by the FPU) are returned in
DX:BX:AX
. To return a result of type String
, the
caller pushes a pointer to a temporary string before pushing the
parameters, and the callee places the returned string value at that
location. The pointer is not a parameter, and should not be removed from
the stack by the RETF
instruction.
Once the callee has finished processing, it restores SP
from BP
if it had allocated local stack space, then pops the
previous value of BP
, and returns via RETF
. It
uses the form of RETF
with an immediate parameter, giving the
number of bytes taken up by the parameters on the stack. This causes the
parameters to be removed from the stack as a side effect of the return
instruction.
When the caller regains control from the callee, the function parameters have already been removed from the stack, so it needs to do nothing further.
Thus, you would define a function in Pascal style, taking two
Integer
–type parameters, in the following way:
global myfunc myfunc: push bp mov bp,sp sub sp,0x40 ; 64 bytes of local stack space mov bx,[bp+8] ; first parameter to function mov bx,[bp+6] ; second parameter to function ; some more code mov sp,bp ; undo "sub sp,0x40" above pop bp retf 4 ; total size of params is 4
At the other end of the process, to call a Pascal function from your assembly code, you would do something like this:
extern SomeFunc ; and then, further down... push word seg mystring ; Now push the segment, and... push word mystring ; ... offset of "mystring" push word [myint] ; one of my variables call far SomeFunc
This is equivalent to the Pascal code
procedure SomeFunc(String: PChar; Int: Integer); SomeFunc(@mystring, myint);
Since Borland Pascal's internal unit file format is completely different
from OBJ
, it only makes a very sketchy job of actually reading
and understanding the various information contained in a real
OBJ
file when it links that in. Therefore an object file
intended to be linked to a Pascal program must obey a number of
restrictions:
Procedures and functions must be in a segment whose name is either
CODE
, CSEG
, or something ending in
_TEXT
.
initialized data must be in a segment whose name is either
CONST
or something ending in _DATA
.
Uninitialized data must be in a segment whose name is either
DATA
, DSEG
, or something ending in
_BSS
.
Any other segments in the object file are completely ignored.
GROUP
directives and segment attributes are also ignored.
c16.mac
With Pascal ProgramsThe c16.mac
macro package, described in
section 9.4.5, can also be used to simplify
writing functions to be called from Pascal programs, if you code
%define PASCAL
. This definition ensures that functions are far
(it implies FARCODE
), and also causes procedure return
instructions to be generated with an operand.
Defining PASCAL
does not change the code which calculates
the argument offsets; you must declare your function's arguments in reverse
order. For example:
%define PASCAL proc _pascalproc %$j arg 4 %$i arg mov ax,[bp + %$i] mov bx,[bp + %$j] mov es,[bp + %$j + 2] add ax,[bx] endproc
This defines the same routine, conceptually, as the example in
section 9.4.5: it defines a function taking
two arguments, an integer and a pointer to an integer, which returns the
sum of the integer and the contents of the pointer. The only difference
between this code and the large-model C version is that PASCAL
is defined instead of FARCODE
, and that the arguments are
declared in reverse order.