How is that both float and double can store same number of decimal points in C?

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This is the code. (C)

C++

float f  = 3.1415926535897932384626433832795;
double d = 3.1415926535897932384626433832795;
	
printf("float  = %.20f \n", f);
printf("double = %.20f \n", d);

According to wikipedia article, double has 2x precision than float. But the output I get is this.

float  = 3.14159274101257320000
double = 3.14159265358979310000

There isn't a big difference between float and double except the double has rounded the last digit.

How is this possible if float has only a 7 digits precision ?

What I have tried:

C++

float f  = 3.1415926535897932384626433832795;
double d = 3.1415926535897932384626433832795;
	
printf("float  = %.20f \n", f);
printf("double = %.20f \n", d);

Posted 29-Jul-18 4:59am

Mark

Updated 29-Jul-18 23:23pm

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4 solutions

Solution 1

c++ - What is the difference between float and double? - Stack Overflow[^]

Posted 29-Jul-18 5:12am

Richard MacCutchan

Comments

Mark 29-Jul-18 11:38am

I have read it and it doesn't answer my question. Even the answer in that question says float has ~7 digits and double has ~16 digits. But in the code given above both float and double turned out to have 16 digits.

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Jochen Arndt · Accepted Answer · 2018-07-29T23:24:00

You have specified that 20 digits after the decimal point should be printed. And so they are. But that does not mean that these digits are correct and meaningful.

You have also noticed that the last four digits are zeroes. That is because a double has that precision and the additional digits are set to zero by the printf() function.

The reason that both printed values have these 16 digits is sourced by the fact that the printf() function only supports double values as floating point arguments and passed float arguments are converted to double behind the scenes. The compiler is processing it as:

printf("float  = %.20f \n", (double)f);

The resulting values printed with appropriate resolution are:

input  = 3.1415926535897932384626433832795
double = 3.14159265358979311
float  = 3.141592741

As you can see the float differs from the input at the 8th digit and the double at the 17th digit.

Gerry Schmitz · Accepted Answer · 2018-07-29T06:00:00

Solution 2

How is this possible if float has only a 7 digits precision ?

According to wikipedia article, double has 2x precision than float. But the output I get is this.

float = 3.14159274101257320000
double = 3.14159265358979310000

(It still only has "7 digits of precision").

Posted 29-Jul-18 6:00am

Gerry Schmitz

Comments

Mark 29-Jul-18 12:18pm

Oh I didn't see that. But where did those wrong numbers came from ? Shouldn't they be 00000 after 7th position in float?

[no name] 29-Jul-18 16:16pm

They are only "wrong" if you use them :)

You "asked" for 20; the displayed result is "calculated".

Check out the "decimal" type: 28-29 significant digits.

Patrice T · Accepted Answer · 2018-07-29T06:37:00

Solution 3

Quote:
But where did those wrong numbers came from ? Shouldn't they be 00000 after 7th position in float?

That is because the values are stored internally as sub-powers of 2 and the value is not exact.
See: Pi and e In Binary - Exploring Binary[^]

Posted 29-Jul-18 6:37am

Patrice T

How is that both float and double can store same number of decimal points in C?

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How is that both float and double can store same number of decimal points in C?

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