Thread: IEEE floating point arithmetic

Estimate the largest real number x such that 1 - exp(-2x^2) = 0 on a machine using
the IEEE standard for binary double precision floating point arithmetic. (Hint: a Maclaurin series
might be useful.)

What would be this number? Obviously, zero is a solution to the expression, but there must be a positive root somewhere. If not, then it should be zero + eps/2. How do you think you use the Maclaurin series?

Originally Posted by PvtBillPilgrim

Estimate the largest real number x such that 1 - exp(-2x^2) = 0 on a machine using
the IEEE standard for binary double precision floating point arithmetic. (Hint: a Maclaurin series
might be useful.)

What would be this number? Obviously, zero is a solution to the expression, but there must be a positive root somewhere. If not, then it should be zero + eps/2. How do you think you use the Maclaurin series?

You want the largest such that:



to IEEE double pressicion. Well this is a small value so we may as well write (this where the Maclaurin series comes in):



to IEEE double prescission, so:



or

CB