This question already has answers here:
Is floating point math broken?
(31 answers)
Closed 4 years ago.
I'm a Little confused about some numbers in C-Code. I have the following piece of Code
int k;
float a = 0.04f;
for (k=0; k*a < 0.12; k++) {
* do something *
}
in this case, what is the type of "0.12" ? double ? float ? it has never been declared anywhere. Anyways, in my program the Loop above is excuted 4 times, even though 3*0.04=0.12 < 0.12 is not true. Once I Exchange 0.12 with 0.12F (because I am globally restricted to float precision in all of the program), the Loop is now executed 3 times. I do not understand why, and what is happening here. Are there any proper Guidelines on how to write such statements to not get unexpected issues?
Another related issue is the following: in the Definition of variables, say
float b = 1/180 * 3.14159265359;
what exactly "is" "1" in this case ? and "180" ? Integers ? Are they converted to float numbers ? Is it okay to write it like that ? Or should it be "1.0f/180.0f*3.14159265359f;"
Last part of the question,
if i have a fuction
void testfunction(float a)
which does some things.
if I call the fuction with testfunction(40.0/6.0), how is that Division handled ? It seems that its calculated with double precision and then converted to a float. Why ?
That was a Long question, I hope someone can help me understand it.
...numbers that are not stored in a variable
They are called "constants".
Any unsuffixed floating point constant has type double.
Quoting C11, chapter §6.4.4.2
An unsuffixed floating constant has type double. If suffixed by the letter f or F, it has
type float. If suffixed by the letter l or L, it has type long double.
For Integer constants, the type will depend on the value.
Quoting C11, chapter §6.4.4.1,
The type of an integer constant is the first of the corresponding list in which its value can
be represented. [..]
and for unsuffixed decimal number, the list is
int
long int
long long int
Regarding the mathematical operation accuracy of floating point numbers, see this post
"0.12" is a constant, and yes, without a trailing f or F, it will be interpreted as a double.
That number can not be expressed exactly as a binary fraction. When you compare k * a, the result is a float because both operands are floats. The result is slightly less than 0.12, but when you compare against a double, it gets padded out with zeros to the required size, which increases the discrepancy. When you use a float constant, the result is not padded (cast), and by good luck, comes out exactly equal to the binary representation of "0.12f". This would likely not be the case for a more complicated operation.
if we use a fractional number for eg, like 3.4 it's default type if double. You should explicitly specify it like 3.4f if you want it to consider as single precision (float).
if you call the following function
int fun()
{
float a= 1.2f;
double b = 1.2;
return (a==b);
}
this will always return zero (false).because before making comparison the float type is converted to double (lower type to higher type) , At this time sometimes it can't reproduce exact 1.2, a slight variations in value can be happen after 6th position from decimal point. You can check the difference by the following print statement
printf("double: %0.9f \n float: %0.9f\n",1.2,1.2f);
It results ike
double: 1.200000000
float: 1.200000481
Related
This question already has answers here:
C integer division and floor
(4 answers)
Closed 7 years ago.
#include <stdio.h>
int main(void)
{
float c =8/5;
printf("The Result: %f", c);
return 0;
}
The answer is 1.000000. Why isn't it 1.600000?
C is interpreting your 8/5 input as integers. With integers, C truncates it down to 1.
Change your code to 8.0/5.0. That way it knows you're working with real numbers, and it will store the result you're looking for.
The expression
8/5
is an all int expression. So, it evaluates to (int )1
The automatic conversion to float happens in the assignment.
If you convert to float before the divide, you will get the answer you seek:
(float )8/5
or just
8.0/5
When you don't specify what data types you use (for example, in your code you use the integer constants 8 and 5) C uses the smallest reasonable type. In your case, it assigned 8 and 5 the integer type, and because both operands to the division expression were integers, C produced an integer result. Integers don't have decimal points or fractional parts, so C truncates the result. This throws away the remainder of the division operation leaving you with 1 instead of 1.6.
Notice this happens even though you store the result in a float. This is because the expression is evaluated using integer types, then the result is stored as is.
There are at least two ways to fix this:
Cast the part of the expression to a double type or other type that can store fractional parts:
Here 8 is cast to the double type, so C will perform float division with the operands. Note that if you cast (8 / 5), integer division will be performed before the cast.
foo = (double) 8 / 5
Use a double as one of the operands:
foo = 8.0/5
This question already has answers here:
strange output in comparison of float with float literal
(8 answers)
Closed 9 years ago.
Please explain the output for different cases
#include<stdio.h>
int main()
{
float a=5.9; //a=0.9
if (a==5.9)
printf("Equal");
else if (a<5.9)
printf("Less than");
else
printf("Greater than");
return 0;
}
When a is 5.9 the output is "Greater than", when a is 0.9 the output is "Less than". Why?
In C, the literal “5.9” has type double and is converted by common compilers to 5.9000000000000003552713678800500929355621337890625, because they use binary IEEE-754 floating point, and that number is the value representable as a double that is closest to 5.9. Your code initializes a float with that value. That requires converting a double to a float, and the result is 5.900000095367431640625, because that is the float value that is closest to the double value. Obviously, the latter is greater than the former, which is why your output is “Greater than”.
With .9, the literal “.9” is converted to the double 0.90000000000000002220446049250313080847263336181640625. Then that double is converted to the float 0.89999997615814208984375, which is obviously less than the double.
Your variable is a float but the constant is a double. Since that value can't be stored precisely ti will be stored differently as a float and as a double. If you use the same data types you'll get the desired results
http://codepad.org/1q5mwFGd
http://codepad.org/Q4lOQnG8
Floating point numbers are inherently imprecise. For a quick introduction, you can read up a bit here. http://floating-point-gui.de/errors/comparison/
For some suggestions on effective comparison strategies, see this post. What is the most effective way for float and double comparison?
This is because internally, the floating point numbers are stored in binary form and 5.9 can't be represented exactly as 5.9. Have a look at the following similar question and answer: Why does a C floating-point type modify the actual input of 125.1 to 125.099998 on output?
When comparing floating-point numbers it is best to avoid '=='.
This because some values cannot be correctly stored without some loss of precision.
So it is better to say:
if( fabs(a-5.9) < .0001 ) {
// 'EQUAL' or at least near enough!
}
I know this takes more to compute, but it will behave the way you expect.
Due to decimal binary conversion, 0.9 represented as a summation of powers of 2^-1:
0.9 - (0.5 + 0.25 + 0.125) = 0.025
But 0.025 is not an exact power of 2^-1. So you need to represent both numbers in the comparison with the same precision. Since float and double have different precision they compare not equal.
This question already has answers here:
Using %f to print an integer variable
(6 answers)
Closed 3 years ago.
May be this is a simple question but I am not sure about how float variables are stored in memory and why it is behaving in this way, can someone please explain about the following behavior.
#include<stdio.h>
int main ()
{
int a = 9/5;
printf("%f\n", a);
return 0;
}
Output:
0.000000
I have looked at some information on how float variables are stored in memory, it has stuff about mantissa, exponent and sign. But I am not getting how to relate that here.
int a = 9/5;
performs integer division and ignores the remainder, so a is set to 1. Attempting to print that using %f gives undefined behavior, but by chance you got 0.000000 out of it.
Do
double a = 9./5.;
instead, or print with %d if integer division was the desired behavior. (float would also work, but a will be promoted to double when passed to printf, so there's no reason not to use double.)
It is an Undefined Behaviour.
You are using float format specifier (%f) to print an int (a). You should use %d to see correct output.
It is an undefined behaviour in C. Use %d format specifier instead of %f.
Does printf() depend on order of format specifiers? gives you detailed answer.
Here's a brief analysis of your code:
int a = 9/5; // 9/5 = 1.8, but since you are doing integer division and storing the value in an integer it will store 1.
printf("%f\n", a);//Using incorrect format specifiers with respect to datatypes, will cause undefined behavior
printf("%d\n",a);//This should print 1. And correct.
Or if you want the float:
instead of int use float :
float a=9.0f/5;//This will store 1.800000f
//float a=9/5 will store 1.000000 not, 1.8 because of integer divison
printf("%f\n",a); //This will print 1.800000
Also do read this: http://en.wikipedia.org/wiki/IEEE_754-2008 on how floating points work.
Clarification about integer division:
C99:
6.5.5 Multiplicative operators
6 When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded.88) If the quotient a/b is representable, the expression (a/b)*b + a%b shall equal a
88) This is often called ‘‘truncation toward zero’’.
Just assuming that your division should result in a fraction in normal math won't magically make it a float.
int a = 9/5;
You need to use
float a = 9.0/5;
First you need the right data type i.e. float (or better yet double for higher precision) to store a float.
Secondly, if you are dividing two integers i.e. 9 and 5, it will simply follow integer division i.e. only store the integer part of division and discard the rest. To avoid that i have added .0 after 9. This would force compiler to implicitly covert into float and do the division.
Regarding your mentioning of why it is printing 0, it is already mentioned that trying %f on integer is undefined behavior. Technically, a float is 4 bytes containing 3 byte number and 1 byte exponent and these are combined to generate the resultant value.
This question already has answers here:
Closed 10 years ago.
Possible Duplicate:
print the float value in integer in C language
I am trying out a rather simple code like this:
float a = 1.5;
printf("%d",a);
It prints out 0. However, for other values, like 1.4,1.21, etc, it is printing out a garbage value. Not only for 1.5, for 1.25, 1.5, 1.75, 1.3125 (in other words, decimal numbers which can be perfectly converted into binary form), it is printing 0. What is the reason behind this? I found a similar post here, and the first answer looks like an awesome answer, but I couldn't discern it. Can any body explain why is this happening? What has endian-ness got to do with t?
you're not casting the float, printf is just interpreting it as an integer which is why you're getting seemingly garbage values.
Edit:
Check this example C code, which shows how a double is stored in memory:
int main()
{
double a = 1.5;
unsigned char *p = &a;
int i;
for (i=0; i<sizeof(double); i++) {
printf("%.2x", *(p+i));
}
printf("\n");
return 0;
}
If you run that with 1.5 it prints
000000000000f83f
If you try it with 1.41 it prints
b81e85eb51b8f63f
So when printf interprets 1.5 as an int, it prints zero because the 4 LSBs are zeros and some other value when trying with 1.41.
That being said, it is an undefined behaviour and you should avoid it plus you won't always get the same result it depends on the machine and how the arguments are passed.
Note: the bytes are reversed because this is compiled on a little indian machine which means the least significant byte comes first.
You don't take care about argument promotions. Because printf is a variadic function, the arguments are promoted:
C11 (n1570), § 6.5.2.2 Function calls
arguments that have type float are promoted to double.
So printf tries to interpret your double variable as an integer type. It leads to an undefined behavior. Just add a cast:
double a = 1.5;
printf("%d", (int)a);
Mismatch of arguments in printf is undefined beahivour
either typecast a or use %f
use this way
printf("%d",(int)a);
or
printf("%f",a);
d stands for : decimal. so, nevertheless a is float/double/integer/char,.... when you use : "%d", C will print that number by decimal. So, if a is integer type (integer, long), no problem. If a is char : because char is a type of integer, so, C will print value of char in ASCII.
But, the problem appears, when a is float type (float/double), just because if a is float type, C will have special way to read this, but not by decimal way. So, you will have strange result.
Why has this strange result ?
I just give a short explanation : in computer, real number is presented by two part: exponent and a mantissa. If you say : this is a real number, C will know which is exponent, which is mantissa. But, because you say : hey, this is integer. no difference between exponent part and mantissa part -> strange result.
If you want understand exactly, how can know which integer will it print (and of course, you can guess that). You can visit this link : represent FLOAT number in memory in C
If you don't want to have this trange result, you can cast int to float, so, it will print the integer part of float number.
float a = 1.5;
printf("%d",(int)a);
Hope this help :)
Both are mathematical values, however the float does have more precision. Is that the only reason for the error - the difference in precision? Or is there another potential (and more serious) problem?
It's because the set of integer values does not equal the set of float values for the 'int' and 'float' types. For example, the float value 0.5 has no equal in the integer set and the integer value 4519245367 might not exist in the set of values a float can store. So, the checker flags this as an issue to be checked by the programmer.
Because it probably isn't a very good idea. Not all floats can be truncated to ints; not all ints can be converted to floats.
When doing the comparison, the integer value will get "promoted" to a floating point value. At that point you are doing a exact equality comparison between two floating point numbers, which is almost always a bad thing.
You should generally have some sort of "epsilon ball", or range of acceptable values, and you do the comparison if the two vaues are close enough to each other to be considered equal. You need a function roughly like this:
int double_equals(double a, double b, double epsilon)
{
return ( a > ( b - epsilon ) && a < ( b + epsilon ) );
}
If your application doesn't have an obvious choice of epsilon, then use DBL_EPSILON.
Because floats can't store an exact int value, so if you have two variables, int i and float f, even if you assign "i = f;", the comparison "if (i == f)" probably won't return true.
Assuming signed integers and IEEE floating point format, the magnitudes of integers that can be represented are:
short -> 15 bits
float -> 23 bits
long -> 31 bits
double -> 52 bits
Therefore a float can represent any short and a double can represent any long.
If you need to get around this (you have a legitimate reason and are happy none of the issues mentioned in the other answers are an issue for you) then just cast from one type to another.