Print largest single-precision floating point number
I was looking for 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 doesn't 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, so I'm trying to figure out what exactly is going on.
My questions: The Wikipedia documentation states that 3.4028234663852885981170418348451e+38
is the largest number that can be represented at the IEEE-754 fixed point.
Is the number stored in the floating point register = 0 11111111 11111111111111111111111
and it is not displayed correctly?
If I write printf(TEXT, "Float %.38f", FLT_MAX);
I get the same answer. Perhaps the computer I'm using isn't using IEEE-754?
I understand the calculation errors, but I don't understand why a number
340282346638528860000000000000000000000.0
is the largest floating point number that can be accurately represented.
Is the Mantissa * Expoment metric causing calculation errors? If so, it 340282346638528860000000000000000000000.0
will be the largest number that can be accurately represented without calculation errors. I think it would make sense. You just need a blessing.
Thank,
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It looks like the culprit printf()
(I think because it is float
implicitly converted to double
on passing it):
#include <iostream>
#include <limits>
int main()
{
std::cout.precision( 38 );
std::cout << std::numeric_limits<float>::max() << std::endl;
}
Output:
3.4028234663852885981170418348451692544e+38
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C float
as binary32 largest final float
is
340282346638528859811704183484516925440.0
printf("%.1f", FLT_MAX)
is not required to print exactly up to 38+ significant digits, so seeing output like the one below is not unexpected.
340282346638528860000000000000000000000.0
printf()
will accurately print floating point to DECIMAL_DIG
significant digits. DECIMAL_DIG
not less than 10. If more than is specified DECIMAL_DIG
, the compatible one printf()
can round the result at any time. C11dr §7.21.6.1 6 goes into detail.
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