CODEWITHSUNDEEP
c++cprintfieee-754
Christopher J. Holland
Christopher J. Holland

Reputation: 61

printing the largest single-precision floating point number

I have come seeking knowledge.
I am trying to understand floating point numbers.
I am trying to figure out why, when I print the largest floating point number, it does not print correctly.

2-(2^-23)                          Exponent Bits
1.99999988079071044921875 * (1.7014118346046923173168730371588e+38) = 
    3.4028234663852885981170418348451e+38

This should be the largest single-precision floating point number:

340282346638528859811704183484510000000.0

So,

float i = 340282346638528859811704183484510000000.0;
printf(TEXT, "Float %.38f", i);
Output: 340282346638528860000000000000000000000.0

Obviously the number is being rounded up, so I am trying to figure out just exactly what is going on.

My questions are: The Wikipedia documentation states that 3.4028234663852885981170418348451e+38 is the largest number that can be represented in IEEE-754 fixed point.

Is the number stored in the floating point register = 0 11111111 11111111111111111111111 and it is just not being displayed incorrectly?

If I write printf(TEXT, "Float %.38f", FLT_MAX);, I get the same answer. Perhaps the computer I am using does not use IEEE-754?

I understand errors with calculations, but I don't understand why the number 340282346638528860000000000000000000000.0 is the largest floating point number that can be accurately represented.

Maybe the Mantissa * Exponent is causing calculation errors? If that is true, then 340282346638528860000000000000000000000.0 would be the largest number that can be faithfully represented without calculation errors. I guess that would make sense. Just need a blessing.

Thanks,

Upvotes: 3

Views: 1722

Answers (2)

chux
chux

Reputation: 153338

With float as binary32, the largest finite float is

340282346638528859811704183484516925440.0

printf("%.1f", FLT_MAX) is not obliged to print exactly to 38+ significant digits, so seeing output like the below is not unexpected.

340282346638528860000000000000000000000.0

printf() will print floating point accurately to DECIMAL_DIG significant digits. DECIMAL_DIG is at least 10. If more than DECIMAL_DIG significance is directed, a compliant printf() may round the result at some point. C11dr §7.21.6.1 6 goes into detail.

Upvotes: 4

Slava
Slava

Reputation: 44238

Looks like culprit is printf() (I guess because float is implicitly converted to double when passed to it):

#include <iostream>
#include <limits>

int main()
{
    std::cout.precision( 38 );
    std::cout << std::numeric_limits<float>::max() << std::endl;
}

Output is:

3.4028234663852885981170418348451692544e+38

Upvotes: 4

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