How to calculate the largest real number in IEEE double and single precision representation.

How do you calculate (in your own way) the largest real number in IEEE double and single precision representations wihtout using realmax('single') and realmax('double')? thank you!

[Matt Kindig]

Wikipedia gives a pretty good overview of how to do so in its article:

http://en.wikipedia.org/wiki/IEEE-754#Formats

I happened to have been reading this article just today.

[James Tursa]

Using just floating point operations? Or allowing for bit manipulation and type casting?

Answer 1

[Jan]

Using the bit-patterns defined e.g. here http://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html and a typecast should be sufficient. Because IEEE754 is a convention, there is nothing wrong with using the bit-patterns defined in this convention directly.

[EDITED] What about pow2(2 - eps, 1023)? Does this reply the correct answer?

[José-Luis]

It should give the correct answer since that is the formula invoked by realmax. Without using eps:

 pow2(1 + (1 - 2^-52),1023) == realmax

Or even without pow2:

 (1 + (1 - 2^-52))*2^1023 == realmax

Speedwise it might not be optimal but William seemed reluctant to use built-in functions.

[Jan]

@Jose-Luis: Thanks for explaining this. I do not have access to Matlab currently, otherwise I had taken a look into edit realmax.