Introduction to Floating-Point Data Types
In programming, float, double, and long double are fundamental data types used to represent fractional or real numbers such as 3.14 or -3276.789. These differ from integer and character types which represent whole numbers and individual characters, respectively. For a deeper understanding of integer types, see Understanding Integer Data Type: Size, Range, and Number Systems Explained.
Sizes and Precision Differences
- Float: Typically occupies 4 bytes of memory; follows the IEEE754 Single Precision standard.
- Double: Commonly uses 8 bytes; adheres to the IEEE754 Double Precision format.
- Long Double: Usually takes up 12 bytes or more; utilizes Extended Precision format.
The exact sizes may vary depending on the system architecture. To get a comprehensive view of how data sizes and modifiers affect types, refer to Comprehensive Guide to Integer Data Types and Modifiers in C Programming.
Fixed Point vs Floating Point Representation
Fixed Point
- Decimal point is fixed; for example, a 4-digit number with 2 digits for integer and 2 digits for fraction.
- Limited range (e.g., from -9.99 to +9.99) and precision.
- Cannot represent values like 0.00067 accurately without truncation.
Floating Point
- Decimal point 'floats' based on exponent, allowing a wider range.
- Uses a formula of the form (0.M) * base^exponent (base 10 in examples).
- Can represent very large or very small numbers more effectively.
- Preferred in modern computing for its versatility and range.
For foundational concepts on how data is represented in C, you may want to explore Understanding Data Representation in C Programming.
Why Multiple Floating-Point Types?
Using different data types allows trade-offs between memory use and precision:
- Float: Suitable for applications requiring less precision (up to ~7 decimal digits).
- Double: Offers higher precision (~16 decimal digits), common in scientific computations.
- Long Double: Provides even greater precision (~19 decimal digits), essential for highly sensitive calculations.
Practical Coding Examples
-
Printing values with different precision:
- Use
%fwith a precision specifier like.2or.16to control decimal places. - For double,
%lfis standard but%foften works. - For long double, use
%Lfto ensure correct output.
- Use
-
Precision observations:
- Float retains up to 7 digits accurately.
- Double maintains approximately 16 digits.
- Long double can represent about 19 digits accurately.
Common Pitfall: Integer Division
- Dividing two integers truncates fractional parts, e.g., 4/9 equals 0.
- Assigning integer division result to float or double still yields truncation.
- Correct approach: Use floating-point literals (e.g., 4.0/9.0) to get fractional results.
Understanding variable types and how operators work is key here; for more details, check out Understanding Variable Data Types and Operators in C++.
Summary
Understanding the characteristics of float, double, and long double helps programmers choose appropriate types based on precision and memory requirements. Also, awareness of fixed vs floating-point representations clarifies why floating-point types dominate modern computing. Proper use of format specifiers and data type literals ensures accurate numeric computations in code.
Today we are going to talk about two fundamental data types called float and double.
Our outline of this lecture would be- To study float, double, long double their sizes and the differences between them.
We are also going to have a brief introduction to fixed and floating point. We will also see some coding examples
to help you illustrate the concept of float, double and long double. Let's understand what float,
double and long double is used for. Like int data type is used to represent integer,
char data type is used to represent characters, Similarly float, double and long double are used in representing fractional
or real numbers. For example- 3.14, 0.678, -3276.789, 0.0000009999 etc.
These different data types are of different sizes as well. In my system, float takes 4 bytes of space.
Double takes 8 bytes of memory space. And long double takes 12 bytes of memory space. Size of these data types totally depend
on the system we are working on. For example- it is possible that size of these data types are same in
your PC or may be any two of them are same or may be all of them are different as in my computer.
There are several way to represent fractional numbers or you can say real numbers on computer.
And one of the most common representation in modern computers is IEEE754 Single Precision Floating Point representation.
Float data type follows IEEE754 Single Precision Floating Point number representation.
Double follows IEEE754 Double Precision Floating Point representation. And long double follows Extended Precision Floating Point.
We have two different representations for fractional numbers. One is Fixed point representation.
And the other one is Floating point representation. Let's see what do we mean by
Fixed and Floating points. Why floating point is used in modern computers
and fixed point isn't? What is the difference between fixed and floating point?
Fixed point representation is a natural representation of which we, the human beings are familiar with.
We follow the same principle when we write fractional numbers like for example: -3.33 by fixing the decimal point between
3 and 33. Let's say suppose we are available with 4 places,
to enter the fractional numbers. Suppose first place is fixed for sign, second place is fixed for integer,
and the last two places are fixed for fraction part. The minimum value possible with such a
representation would be -9.99. and the maximum value that would be possible is +9.99
Isn't it? You can represent any real number between -9.99 to +9.99
but up to two decimal places after the decimal point. This means we wont be able to
represent numbers like -7.9765 or 0.00067 or 99.99999 and so on. We can but you have to
truncate some digits at the end. means if you want to represent -7.9765 then you would be only
able to represent -7.97. 65 is truncated and removed. This is called reducing the precision.
Floating point representation on the other hand is quite unnatural way of representing real numbers.
It requires formula to represent real numbers. For example- suppose again we have only 4 places to enter the digits.
First place is fixed for sign, next two places are fixed for exponent and the last place is fixed for mantissa
or you can say significant. Now the formula to represent the real numbers would be
(0.M) * Base to the power of Exponent. Here Base is 10 Because in our example we are
representing the decimal numbers therefore, the base needs be 10. Exponent is +9
the first place of the exponent is fixed for sign and the next place for the integer.
M represents the Mantissa part. Here in our example, this is 9. If you want to represent the minimum value,
then this is -0.9 * 10 to the power +9. Here 9 is our Mantissa, +9 represents the exponent
and this negative sign is this sign over here. And the maximum value would be +0.9 * 10 to the power +9
As you can see here, there is a huge difference between fixed point and floating point.
Fixed point would be able to represent very least range of fractional values, while on the other hand,
floating point representation using equal number of places, would be able to represent
much larger range of values. Isn't that so? Here, you can shift the decimal point
and thus allowing more numbers to be represented easily. That is why it is called floating point
because the decimal point is not fixed. For example- Instead of 0.9 if you want to represent 9.0
you would be able to do that by reducing the exponent to 1 and make it +8.
-0.9 * 10 raised to the power +9 is very small value as compared to -9.99.
+0.9 * 10 raised to the power +9 is very large value as compared to +9.99 This is the reason why floating point
is preferred over fixed point. This is the brief introduction to fixed and floating points
This topic is a part of computer organization and architecture and explaining any further details
regarding this topic is out of the scope of this lecture. Let's see why we have 3 different data types?
Is it not sufficient to have only one data type like integer and character? What is the need of having
3 different data types? Let's not talk much about this. and Let the code speaks it out.
Before explaining the code what i have written over here, It is better to execute the code first.
Let's build and run. As size of float is 4 bytes in my computer, therefore in the first line,
4 is printed. Size of double is 8 bytes, therefore 8 is printed.
Size of long double is 12 bytes therefore 12 is printed on to the screen. In this first line, I have declared
a variable of float type and assigned it a value which is famously known as PIE.
Value of PIE is 3.1415926535897932 and so on. It is going on continuously without even repetition of the digits.
That is why it is called irrational number. To the second variable, I assigned the same value.
To the third variable also I assigned the same value bur extended it by adding random digits at the end.
We can print the contents of the float variable by using %f over here. Here, .16 means
that after the decimal point I need to print digits 16 places long. Like if I want to print only
2 integers, after the decimal point then I will put 2 instead of 16. And let's see the output.
Here, you can see after the decimal point only 2 values are getting printed. That is what it means.
If I change this to 16, again the, this is what it prints. It will print up to 16 decimal values.
Similarly we can print the contents of double variable using %f again. The actual format specifier
for double is %lf. This is l and this is f. But some compilers won't accept it.
Therefore %f will also work. And to print long double, we need to put format specifier
as L and f. Putting L is important because l is for double and L is for long double.
Now let's understand the major difference between float, double and long double by seeing the output.
If you observe it carefully, before this 2 everything is as it is
what we have assigned in to this variable. That is 3.141592 Here also it is 3.141592
But here after 2 it is 6535 and here it it 7410 and everything after that is changed.
Isn't that so? This is because float would be able to represent fractional values
precisely up to 7 digits starting from the first place itself. If you count this out this is 1 2 3 4 5 6 7.
Up to this point it will print everything as it is as it is mentioned over here. But after that, everything is getting changed.
Double as a variable would be print fractional values precisely up to 16 digits.
Here you can see, up to this point everything is as it is. But after this, this is 2 and here it is 1.
And that is the major difference. And long double up to 19 digits. Up to this point there are 17 digits.
After that this is 18 19 Up to this point everything is printed correctly but after that everything is changed.
As you can see over here, there is 456 and here it is 359. Of course the precision depends on the
size of these data types. Therefore, if you want less precision, then you can use float
or if you want more accurate fractional numbers then you can use double or long double. Many scientific applications are
sensitive to precision. Therefore, they will use double or long double. Some applications require precision
up to 2 3 or 4 decimal places. Then using float would be a better choice. That will save you a lot of space.
Now here is one more thing that I would like to talk about Again I will run the code first and then go step by step.
Here, I have divided 4 with 9. As we know this thing, that when 4 is divided by 9,
you get 0.44 as the answer. Isn't that so? We know, that the result of this expression
is stored inside this variable. Therefore, when we try to print it we would get our result.
But here in this case, 4 divided by 9 gives me the result as 0. This is because, here we are performing
division between two integers and storing the result in integer variable. And if you try to print this value,
it will truncate the rest of the part after the decimal point. Because integers won't be able to represent
the fractional numbers. And whatever is there after the decimal point is simply truncated.
Due to this reason, we won't be able to represent 0.44 as 44 is simply truncated
after the decimal point. Now, suppose I store the result into this float variable
and try to print it. Thinking that may be this time I will get the right answer.
But here, as you can see, I will again get a wrong answer. There is 0.00 instead of 0.44.
The reason behind that is Here we are performing the division between two integer values.
Therefore, again the result is getting truncated. Whatever is there after the decimal
point is getting truncated. Due to this reason, if we try to print this value, it will only print
this thing. 44 is totally lost. Because of this .2 , we would be able to print up to 2 decimal points
but because there in nothing inside that therefore, it will just print 00. Now the only change we need to make
in order to get the correct answer is changing these integer values to fractional values.
That is by making them 4.0 and 9.0. Placing .0 after 4 and 9 make these these integer values, double values.
By default they are double constants. And if you want to make them float you just have to place
f at the suffix. If you try to print this value then it will give you, your desired
result which is 0.44 OK friends, this is it for now.
See you in the next lecture. Bye.
The primary differences lie in memory size and precision. Float typically uses 4 bytes and offers about 7 decimal digits of precision, double uses 8 bytes with approximately 16 digits of precision, and long double usually takes 12 bytes or more, providing about 19 digits of precision. Choosing among them depends on the precision needs and memory constraints of your application.
Fixed-point representation uses a fixed position for the decimal, limiting its range and precision (e.g., numbers like 0.00067 may be truncated). Floating-point 'floats' the decimal point by using an exponent, allowing it to handle a much wider range of values and fractional parts effectively. Therefore, floating-point types are preferred for most real number computations in modern programming.
Dividing two integers in C performs integer division, which truncates any fractional part (e.g., 4/9 results in 0). Even if assigned to a float or double variable, the fractional data is lost. To get accurate fractional results, at least one operand must be a floating-point literal (e.g., 4.0/9.0), ensuring floating-point division is performed.
Use format specifiers in printf to control precision: for float and double, '%f' works, with '%lf' standard for double (though '%f' is widely accepted). Use a precision modifier like '%.2f' for 2 decimal places or '%.16f' for more precision. For long double, use '%Lf' to correctly print the value. This ensures numeric outputs match the desired decimal precision.
Yes. While float is commonly 4 bytes and double 8 bytes per IEEE754 standards, long double size can vary (often 12 bytes or more) depending on system architecture and compiler. It's important to check your development environment's specifications when exact size and precision matter for your application.
Choose float when memory is limited and approximate precision (~7 digits) suffices, such as in graphics or simple calculations. Double is preferred for general scientific computations requiring higher precision (~16 digits). Long double is suitable for highly sensitive calculations needing maximum precision (~19 digits), keeping in mind potential performance and compatibility trade-offs.
The truncation occurs because integer division happens before assignment, and integer division discards any fractional part. For example, 4/9 computes to 0 as an integer division, so assigning it to a float results in 0.0. To prevent this, use floating-point operands like 4.0/9.0 to ensure floating-point division happens, preserving the fraction in the result.
Heads up!
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