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Math Help - IEEE floating point arithmetic

  1. #1
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    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?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by PvtBillPilgrim View Post
    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 x such that:

    \exp(-2x^2)=1

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

    -2x^2=0

    to IEEE double prescission, so:

    2 x^2<\text{eps}

    or x<\sqrt{\frac{\text{eps}}{2}}

    CB
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