Electronics and Communication Engineering (ECE) Exam > Electronics and Communication Engineering (ECE) Videos > MIPS Assembly Programming Simplified > MIPS Tutorial 34 Recursive Factorial Program
MIPS Tutorial 34 Recursive Factorial Program Video Lecture | MIPS Assembly Programming Simplified - Electronics and Communication Engineering (ECE)
FAQs on MIPS Tutorial 34 Recursive Factorial Program Video Lecture - MIPS Assembly Programming Simplified - Electronics and Communication Engineering (ECE)
| 1. What is a recursive factorial program in MIPS? |  |
Ans. A recursive factorial program in MIPS is a program written in the MIPS assembly language that uses a recursive approach to calculate the factorial of a given number. It repeatedly calls itself with smaller values until it reaches the base case, which is usually when the input number becomes 1.
| 2. How does a recursive factorial program work in MIPS? | |
Ans. In a recursive factorial program in MIPS, the program first checks if the input number is equal to 1. If it is, the program returns 1 as the factorial of 1 is 1. If the input number is not equal to 1, the program calls itself with the input number decremented by 1 and multiplies the result with the input number. This process continues until the input number becomes 1, and then the program returns the final result.
| 3. What are the advantages of using recursion in a factorial program in MIPS? | |
Ans. Using recursion in a factorial program in MIPS has several advantages. Firstly, it allows for a more concise and elegant implementation of the factorial calculation logic. Secondly, recursion can handle larger input numbers as compared to iterative approaches, as it utilizes the stack to store intermediate results. Additionally, recursive solutions are often easier to understand and debug, making the code more maintainable.
| 4. Can a recursive factorial program in MIPS handle negative input numbers? | |
Ans. No, a recursive factorial program in MIPS cannot handle negative input numbers. The factorial operation is only defined for non-negative integers. If a negative number is provided as input, the program will not terminate and will result in an infinite recursive loop.
| 5. Are there any limitations or drawbacks of using recursion in a factorial program in MIPS? | |
Ans. Yes, there are some limitations and drawbacks of using recursion in a factorial program in MIPS. One limitation is that recursion can consume a significant amount of stack memory, especially for large input numbers. This can lead to stack overflow errors. Additionally, recursive solutions may not always be the most efficient approach, as they involve repeated function calls and can result in slower execution times compared to iterative solutions.
Text Transcript from Video
hello guys this is a male welcome back
and today we're going to continue our
discussion about factorial and about
recursion so you should be very excited
recursion is a very powerful technique
and it's very important that every
programmer has a very good foundation on
recursion and we are going to understand
recursion at a lower level today
we're going to understand recursion at
assembly level so very important topic
and let's begin so go to file new and
now go to file save as and I'm gonna
save it as recursion write recursion
tutorial you can give it any name you
want save then I do that data and I'm
gonna have some variables I global
variables in the first one it's gonna be
a message that I want to display to the
screen so it's gonna be prom message
datatype we start ask easy and it's
gonna say enter a number to find its
factorial now I want another message and
this message is going to be for the
result so it's gonna be resolved message
and the data type is going to be that
ASCII but not Z because I don't want to
display a long after after the prompt
this one is going to display a line
after the prompt so this one is going to
display a line after the message so I'm
gonna say the factorial of the number
yes and I also want to integers and one
is gonna be for the number I'm gonna
store the number from the user so the
number data type is going to be that
word and I'm gonna initialize it to 0
the second one is going to be a variable
for the answer and this is going to
store the answer that the function fine
factorial is going to return to
and now we can start coding the text
section remember that text is for all
the code in your program so I want to
declare my main function but I want to
make main to be global so so main can be
referenced from other files and then
main :
now the first thing that I want to do in
my main function or my main procedure is
that I want to actually read the value
from the user read the number so read
the number from the user and then I want
to display the message like this note
immediate Alice I'm to 0 comma 4 then
load address the sine is 0 from message
and then Sisco
so this is the code to display a message
to the screen and now I pass the message
to as an argument so the operating
system knows what what to print out and
then I tell the operating system to to
show the message and now I'm going to
read so loading media that assembly 0
comma 5 and then Sisco these right here
these two lines they're going to read
from the keyboard
they will not read an integer and it's
gonna the value that the user enters is
going to be stored in Dallas I'm v-0 so
I want to put that number in the low
side is 0 2 I want to put it in my
global variable the number so I'm gonna
say store word dollar sign v-0 command
the number so now the value that the
user entered is stored in the variable
the number so now we can continue the
next step is to call the factorial
function
so in order to call it first we need the
value that the user entered as an
argument so we do love word load word
tell us I'm a zero comma the number and
jump and Link jump and Link to call the
function I haven't written the function
yet so I'm going to write it later after
I'm done with the main function so don't
worry for now we're just working with
the main function so jump and Link find
factorial and this is how we call
functions in MIPS and if you don't know
about this just go back to my previous
tutorial on functions and you will
understand how what I'm doing here
so after that I'm going to store word
the answer del x is 0 the answer so what
I'm doing what I'm doing here is that
I'm getting the value from 5 factorial
it's gonna be returned in these variable
V 0 remember that the 0 and V 1 those
registers they actually store the impact
convention they are used for return
values from functions so the factorial
of the number is going to be stored in
this 0 so I want to move it I want to
store it in the global variable the
answer so now we can continue the next
step is to display the results so what
we do is loading media the loss is 0
actually limit do it right here
loading million dollars on V 0 comma for
Laura tress that song is 0 comma result
message and Sysco so this is going to
display the
the factorial of the number is and now I
want to display the the factorial or I
want to display the result itself so to
display that result it's an integer so
we have to do it like this note a
million dollar sign this zero comma one
load word tell assign a zero comma the
answer and I want to say Cisco and
finally in my main function I want to
tell the operating system - that this is
the end of the program
norine meeting the last time V 0 comma
10 and Cisco wait yeah it's Cisco with
two L's so now we are done with the main
function now it's time to actually code
the factorial function so let's divide
is to make it clear make this little
division this comment and find factorial
function so we're going to say the
following
first of all let's declare the factorial
function global so that global find
factorial and then we're going to define
fine factorial so fine factorial so
remember that five factorial is
recursive and the first step that we
have to follow is to store the local
variables and also the return address to
the stack in the last tutorial I talked
to you about a stack so you should know
what I'm talking about if you watch the
last tutorial so we do
so on sign so we're going to do the
resign SP comment the resign SP comma 8
so now we have enough space for two for
two values it to be stored and now when
I say store word they'll assign our a
comma dollar sign SP and this has to be
important parenthesis and right here I'm
just storing the value of the return
address to the stack and then I want to
store the local variable to a stack so
in the second position of the stack
remember that the stack all these values
are going to be stored four bytes apart
so the first one the the return address
is going to be stored in location 0 in
the stack and this one is going to be
stored
starting at location 4 so it's gone it's
going to be 4 bytes apart because and we
make space this is like making room for
the two values that we store down here
so now we continue what we need to do
now is the base case in the base case
it's going to allow you to stop the
recursion so remember in factorial or
fine factorial the base case is when the
the argument is equal to zero in that
case we'll return one so let's say that
we want to return one loading media de
los Andes 0 comma 1 and then we say
branch if a close if the argument is
equal to 0 we're going to say if the
argument is equal to 0 then go to
factorial
done and factorial done it's going to be
a label that I'm going to make down I'm
gonna make it below so don't worry about
it
and I will continue
to the other step the recurse is that
the recursive step so move the
assignment Sirocco model Assange is zero
sub Villa sine is zero comma dollar sign
is zero comma one and jump and Link find
factorial and don't worry I'm about to
tell you what what I'm doing right now
so multiply notice I'm V zero comma L
sine is zero comma dollar sign V zero so
what I'm doing is the following in the
factorial function have the base case so
if the argument that I Palace is 0 then
return 1 and I return because I'm going
to go to this I'm going to go 2
factorial done when I go to factorial
done the recursion is going to rewind
it's going to go back all the functions
will be it will be popped off they're
gonna be going back to the color but if
the argument is not equal to 0 this is
not going to happen so what's going to
happen is that I'm gonna be subtracting
I'm gonna be subtracting 1 from the
argument so this is like when I say okay
I said the following find factorial of
the number minus 1 this is what I'm
doing here and then I'm calling the
factorial functions itself again fine
factorial again and this is recursion
and this line is where the magic happens
so the magic happens here yes
why what do I mean by that well what I
mean is that whenever the recursion is
rewinding they
is going to be executed when the
recursion is unwinding this is not going
to be executed so what it's going to
happen is that the recursion is going to
be calling itself calling itself again
but but it will never get to this line
but when when the functions are
returning this line is going to be
executed and that's how we're going to
get the final answer but let's go to
this factorial done so the base case so
if if the argument is zero if the number
is zero then go to factorial done and
return one so let's call factorial done
factorial done so what we're going to do
here is the following we're going to say
load word the Messiaen are a coma
Thalassa SP so we're just restoring the
value of the return address from the
stack so now the return address is going
to be loaded from the stack from R and
away from random access memory and then
we're gonna say load word the design is
zero comma four little sighing SP so now
we are loading the value of the local
variable back to the register from the
stack so what we're doing is the
opposite from here here we are putting
the values to random access memory we're
putting the values to the stack and here
because the function is done what we are
doing is that we are getting the values
back from the stack so now what we do is
that we have to restore the stack itself
so we do I don't signed that as I have
to be the less I again speed comma eight
because here I subtracted eight from the
stack and remember we subtract from the
stack because the stack is screwing
downwards so if you don't know what I'm
talking about
watch my previous tutorial and see the
picture that I showed you the stack is
growing downward so that's why we have
to subtract from the stack so here
because we want to restore the stack we
add we add the same value 8 because we
have we subtracted 8 so we have to add 8
to put everything the way it was before
so now what we do is that we can go back
jump register the let's hang SP I mean
gel register design our a so this is
going to return from the function and
well we are done so now I'm going to
execute the program and after I execute
the program and I make sure that it's
working I'm gonna give you a final
explanation of how it works so you
understand how this program works so
save run assemble and execute it says
enter a number to find this factorial so
I want to find the factorial of the
number 4 I type 4 and then I press ENTER
the factorial of the number is 24 yes
the factorial of 4 is 24 because 4 times
3 is 12 times 2 is 24 yes in 24 times 1
is 24 so now let's do it again let me
clear and let me assemble and let me
execute enter a number to find this
factorial so I want to know the
factorial of 5 so I enter 5 press Enter
the factorial of the number is 120 Walla
we have built the factorial function
programmed the calculates factorial
using recursion so the program that I
showed you before in C++ we have
translated a program into nips assembly
and I will give
you a final walkthrough or how it works
so we have four variables two integers
one for the number that the user enters
and one for the answer and these are
just messages then we have the global
main function in the main function we
have we display the message we read that
we read an integer from the user and
then the number that the user entered we
store it in the variable the number then
we call the factorial function define
factorial function first we have to pass
the number as an argument then we call
the function and after the function
returns it's going to give you the value
it's going to give you the answer in the
register data scientist zero by
convention so we store that to the
global variable the answer in random
access memory and finally in the main
function we display the result message
then we display the number as you can
see the factorial of the number is 120
and finally we tell the operating system
to end the program loading media de los
ángeles 0 comma 10 and Sysco so the fine
factorial function is recursive it is
recursive because it is calling itself
final factorial it's going to go back to
fine factorial here so it's going to be
you can think of it as looping it's
gonna be going back back and forth back
and forth it's going to be it's gonna
call itself like a loop it's gonna be
calling itself until it finds the base
case the base case is when a 0 is equal
to 0 and when a 0 is equal to 0 it's
gonna stop the recursion so it's gonna
go to the factorial done which is right
here factorial done is just gonna load
all the values from the stack that we
saved previously right here and it's
going to restore the stack and then it's
gonna jump back it's gonna be jumping
back to their previous to the previous
address and
right here this is the base case but
until it has to be doing this before the
base case you will be doing this it's
gonna be subtracting one from the number
and it's gonna be calling fine factorial
it's gonna be calling it with the number
minus one and this line is going to
execute when the recursion is is
rewinding so these will not be executed
now it's going to execute when the
functions are being popped off the stack
and this is going to calculate the value
returned previously times the local
value and it's going to store it in this
zero so this is what the magic this is
where the magic happens this is going to
execute when the recursion is rewinding
so I know this is kind of confusing and
I was kind of fast this time I've been
trying to speed up a little bit but just
try to write this program yourself and
try to understand the logic and you will
you will understand that if you spend
time studying the program this is just
like scratching the surface so there's a
lot more about recursion probably in the
future tutorials I'm going to give you
more examples of recursion recursion
becomes very useful when you're when you
are using when you are doing algorithms
especially binary trees and there are
many recursive algorithms that they are
recursive by nature so in this case
factorial final factorial is just an
example because it's simple but actually
you you could have done using loops and
it's a lot more efficient so final
factorial is not a very efficient
implementation using recursion but
it's good just to learn it so thank you
for watching I know it's been a while I
haven't posted any videos recently
because I've been very busy with my
algorithms course and many of the
courses I'm taking thank you very much
don't forget to subscribe
and yes they tuned because I will post
more videos in the future especially
about arrays and data structures in
mames and eventually we're going to go
to the next level and probably start
working with x86 and more so thank you
very much see you next time
and today we're going to continue our
discussion about factorial and about
recursion so you should be very excited
recursion is a very powerful technique
and it's very important that every
programmer has a very good foundation on
recursion and we are going to understand
recursion at a lower level today
we're going to understand recursion at
assembly level so very important topic
and let's begin so go to file new and
now go to file save as and I'm gonna
save it as recursion write recursion
tutorial you can give it any name you
want save then I do that data and I'm
gonna have some variables I global
variables in the first one it's gonna be
a message that I want to display to the
screen so it's gonna be prom message
datatype we start ask easy and it's
gonna say enter a number to find its
factorial now I want another message and
this message is going to be for the
result so it's gonna be resolved message
and the data type is going to be that
ASCII but not Z because I don't want to
display a long after after the prompt
this one is going to display a line
after the prompt so this one is going to
display a line after the message so I'm
gonna say the factorial of the number
yes and I also want to integers and one
is gonna be for the number I'm gonna
store the number from the user so the
number data type is going to be that
word and I'm gonna initialize it to 0
the second one is going to be a variable
for the answer and this is going to
store the answer that the function fine
factorial is going to return to
and now we can start coding the text
section remember that text is for all
the code in your program so I want to
declare my main function but I want to
make main to be global so so main can be
referenced from other files and then
main :
now the first thing that I want to do in
my main function or my main procedure is
that I want to actually read the value
from the user read the number so read
the number from the user and then I want
to display the message like this note
immediate Alice I'm to 0 comma 4 then
load address the sine is 0 from message
and then Sisco
so this is the code to display a message
to the screen and now I pass the message
to as an argument so the operating
system knows what what to print out and
then I tell the operating system to to
show the message and now I'm going to
read so loading media that assembly 0
comma 5 and then Sisco these right here
these two lines they're going to read
from the keyboard
they will not read an integer and it's
gonna the value that the user enters is
going to be stored in Dallas I'm v-0 so
I want to put that number in the low
side is 0 2 I want to put it in my
global variable the number so I'm gonna
say store word dollar sign v-0 command
the number so now the value that the
user entered is stored in the variable
the number so now we can continue the
next step is to call the factorial
function
so in order to call it first we need the
value that the user entered as an
argument so we do love word load word
tell us I'm a zero comma the number and
jump and Link jump and Link to call the
function I haven't written the function
yet so I'm going to write it later after
I'm done with the main function so don't
worry for now we're just working with
the main function so jump and Link find
factorial and this is how we call
functions in MIPS and if you don't know
about this just go back to my previous
tutorial on functions and you will
understand how what I'm doing here
so after that I'm going to store word
the answer del x is 0 the answer so what
I'm doing what I'm doing here is that
I'm getting the value from 5 factorial
it's gonna be returned in these variable
V 0 remember that the 0 and V 1 those
registers they actually store the impact
convention they are used for return
values from functions so the factorial
of the number is going to be stored in
this 0 so I want to move it I want to
store it in the global variable the
answer so now we can continue the next
step is to display the results so what
we do is loading media the loss is 0
actually limit do it right here
loading million dollars on V 0 comma for
Laura tress that song is 0 comma result
message and Sysco so this is going to
display the
the factorial of the number is and now I
want to display the the factorial or I
want to display the result itself so to
display that result it's an integer so
we have to do it like this note a
million dollar sign this zero comma one
load word tell assign a zero comma the
answer and I want to say Cisco and
finally in my main function I want to
tell the operating system - that this is
the end of the program
norine meeting the last time V 0 comma
10 and Cisco wait yeah it's Cisco with
two L's so now we are done with the main
function now it's time to actually code
the factorial function so let's divide
is to make it clear make this little
division this comment and find factorial
function so we're going to say the
following
first of all let's declare the factorial
function global so that global find
factorial and then we're going to define
fine factorial so fine factorial so
remember that five factorial is
recursive and the first step that we
have to follow is to store the local
variables and also the return address to
the stack in the last tutorial I talked
to you about a stack so you should know
what I'm talking about if you watch the
last tutorial so we do
so on sign so we're going to do the
resign SP comment the resign SP comma 8
so now we have enough space for two for
two values it to be stored and now when
I say store word they'll assign our a
comma dollar sign SP and this has to be
important parenthesis and right here I'm
just storing the value of the return
address to the stack and then I want to
store the local variable to a stack so
in the second position of the stack
remember that the stack all these values
are going to be stored four bytes apart
so the first one the the return address
is going to be stored in location 0 in
the stack and this one is going to be
stored
starting at location 4 so it's gone it's
going to be 4 bytes apart because and we
make space this is like making room for
the two values that we store down here
so now we continue what we need to do
now is the base case in the base case
it's going to allow you to stop the
recursion so remember in factorial or
fine factorial the base case is when the
the argument is equal to zero in that
case we'll return one so let's say that
we want to return one loading media de
los Andes 0 comma 1 and then we say
branch if a close if the argument is
equal to 0 we're going to say if the
argument is equal to 0 then go to
factorial
done and factorial done it's going to be
a label that I'm going to make down I'm
gonna make it below so don't worry about
it
and I will continue
to the other step the recurse is that
the recursive step so move the
assignment Sirocco model Assange is zero
sub Villa sine is zero comma dollar sign
is zero comma one and jump and Link find
factorial and don't worry I'm about to
tell you what what I'm doing right now
so multiply notice I'm V zero comma L
sine is zero comma dollar sign V zero so
what I'm doing is the following in the
factorial function have the base case so
if the argument that I Palace is 0 then
return 1 and I return because I'm going
to go to this I'm going to go 2
factorial done when I go to factorial
done the recursion is going to rewind
it's going to go back all the functions
will be it will be popped off they're
gonna be going back to the color but if
the argument is not equal to 0 this is
not going to happen so what's going to
happen is that I'm gonna be subtracting
I'm gonna be subtracting 1 from the
argument so this is like when I say okay
I said the following find factorial of
the number minus 1 this is what I'm
doing here and then I'm calling the
factorial functions itself again fine
factorial again and this is recursion
and this line is where the magic happens
so the magic happens here yes
why what do I mean by that well what I
mean is that whenever the recursion is
rewinding they
is going to be executed when the
recursion is unwinding this is not going
to be executed so what it's going to
happen is that the recursion is going to
be calling itself calling itself again
but but it will never get to this line
but when when the functions are
returning this line is going to be
executed and that's how we're going to
get the final answer but let's go to
this factorial done so the base case so
if if the argument is zero if the number
is zero then go to factorial done and
return one so let's call factorial done
factorial done so what we're going to do
here is the following we're going to say
load word the Messiaen are a coma
Thalassa SP so we're just restoring the
value of the return address from the
stack so now the return address is going
to be loaded from the stack from R and
away from random access memory and then
we're gonna say load word the design is
zero comma four little sighing SP so now
we are loading the value of the local
variable back to the register from the
stack so what we're doing is the
opposite from here here we are putting
the values to random access memory we're
putting the values to the stack and here
because the function is done what we are
doing is that we are getting the values
back from the stack so now what we do is
that we have to restore the stack itself
so we do I don't signed that as I have
to be the less I again speed comma eight
because here I subtracted eight from the
stack and remember we subtract from the
stack because the stack is screwing
downwards so if you don't know what I'm
talking about
watch my previous tutorial and see the
picture that I showed you the stack is
growing downward so that's why we have
to subtract from the stack so here
because we want to restore the stack we
add we add the same value 8 because we
have we subtracted 8 so we have to add 8
to put everything the way it was before
so now what we do is that we can go back
jump register the let's hang SP I mean
gel register design our a so this is
going to return from the function and
well we are done so now I'm going to
execute the program and after I execute
the program and I make sure that it's
working I'm gonna give you a final
explanation of how it works so you
understand how this program works so
save run assemble and execute it says
enter a number to find this factorial so
I want to find the factorial of the
number 4 I type 4 and then I press ENTER
the factorial of the number is 24 yes
the factorial of 4 is 24 because 4 times
3 is 12 times 2 is 24 yes in 24 times 1
is 24 so now let's do it again let me
clear and let me assemble and let me
execute enter a number to find this
factorial so I want to know the
factorial of 5 so I enter 5 press Enter
the factorial of the number is 120 Walla
we have built the factorial function
programmed the calculates factorial
using recursion so the program that I
showed you before in C++ we have
translated a program into nips assembly
and I will give
you a final walkthrough or how it works
so we have four variables two integers
one for the number that the user enters
and one for the answer and these are
just messages then we have the global
main function in the main function we
have we display the message we read that
we read an integer from the user and
then the number that the user entered we
store it in the variable the number then
we call the factorial function define
factorial function first we have to pass
the number as an argument then we call
the function and after the function
returns it's going to give you the value
it's going to give you the answer in the
register data scientist zero by
convention so we store that to the
global variable the answer in random
access memory and finally in the main
function we display the result message
then we display the number as you can
see the factorial of the number is 120
and finally we tell the operating system
to end the program loading media de los
ángeles 0 comma 10 and Sysco so the fine
factorial function is recursive it is
recursive because it is calling itself
final factorial it's going to go back to
fine factorial here so it's going to be
you can think of it as looping it's
gonna be going back back and forth back
and forth it's going to be it's gonna
call itself like a loop it's gonna be
calling itself until it finds the base
case the base case is when a 0 is equal
to 0 and when a 0 is equal to 0 it's
gonna stop the recursion so it's gonna
go to the factorial done which is right
here factorial done is just gonna load
all the values from the stack that we
saved previously right here and it's
going to restore the stack and then it's
gonna jump back it's gonna be jumping
back to their previous to the previous
address and
right here this is the base case but
until it has to be doing this before the
base case you will be doing this it's
gonna be subtracting one from the number
and it's gonna be calling fine factorial
it's gonna be calling it with the number
minus one and this line is going to
execute when the recursion is is
rewinding so these will not be executed
now it's going to execute when the
functions are being popped off the stack
and this is going to calculate the value
returned previously times the local
value and it's going to store it in this
zero so this is what the magic this is
where the magic happens this is going to
execute when the recursion is rewinding
so I know this is kind of confusing and
I was kind of fast this time I've been
trying to speed up a little bit but just
try to write this program yourself and
try to understand the logic and you will
you will understand that if you spend
time studying the program this is just
like scratching the surface so there's a
lot more about recursion probably in the
future tutorials I'm going to give you
more examples of recursion recursion
becomes very useful when you're when you
are using when you are doing algorithms
especially binary trees and there are
many recursive algorithms that they are
recursive by nature so in this case
factorial final factorial is just an
example because it's simple but actually
you you could have done using loops and
it's a lot more efficient so final
factorial is not a very efficient
implementation using recursion but
it's good just to learn it so thank you
for watching I know it's been a while I
haven't posted any videos recently
because I've been very busy with my
algorithms course and many of the
courses I'm taking thank you very much
don't forget to subscribe
and yes they tuned because I will post
more videos in the future especially
about arrays and data structures in
mames and eventually we're going to go
to the next level and probably start
working with x86 and more so thank you
very much see you next time
About this Video
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Nov 21, 2024 Last updated |
Video Description: MIPS Tutorial 34 Recursive Factorial Program for Electronics and Communication Engineering (ECE) 2024 is part of MIPS Assembly Programming Simplified preparation.
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