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33. Find a real number x in the range of the Marc-32 such that aCx)-(5 34. Show that fl(x)-x/(1 + ) with 181 2-34 under the assumptions made 35. Show that fl(ri)s + 8)i-l, where |&I e, if x is a floating-point machine nun 36. Show by examples that often f [fdry)| nix dy) for machine numbers x, y S) with 18a about the numbe o Computer Arithmetic large as possible. Can the bound 2-24 be attained by IS? Marc-32. in a computer that has unit roundoff e. This phenomenon is often described informally by saying machine multiplication is associative 37. Prove that if x and y are machine numbers in the Marc-32, and if Iyl l12-3, th 38. Suppose that x is a machine number in the range- 1. 1. Without using the Fortran 90 intrinsic procedures, write a program to compute the valuc of the machine precision e on your computer in both single and double precision. Is this the exact value or an approximation to it? Hint: Determine the smallest positive machin number of the form 2-k such that 1.0 + 1.0. 2. (Continuation) Repeat for the largest and smallest machine numbers. 3. Students are sometimes confused about the difference between the numbers tiny an epsilon. Explain the difference. Then design and execute a numerical computer periment to demonstrate the difference. 4. By repeated division by 2 and printing the results, you may observe that it seems that n real numbers smaller than the smallest machine number tiny are obtained. Explain why is not so and what is happening. 33. Find a real number x in the range of the Marc-32 such that aCx)-(5 34. Show that fl(x)-x/(1 + ) with 181 2-34 under the assumptions made 35. Show that fl(ri)s + 8)i-l, where |&I e, if x is a floating-point machine nun 36. Show by examples that often f [fdry)| nix dy) for machine numbers x, y S) with 18a about the numbe o Computer Arithmetic large as possible. Can the bound 2-24 be attained by IS? Marc-32. in a computer that has unit roundoff e. This phenomenon is often described informally by saying machine multiplication is associative 37. Prove that if x and y are machine numbers in the Marc-32, and if Iyl l12-3, th 38. Suppose that x is a machine number in the range- 1. 1. Without using the Fortran 90 intrinsic procedures, write a program to compute the valuc of the machine precision e on your computer in both single and double precision. Is this the exact value or an approximation to it? Hint: Determine the smallest positive machin number of the form 2-k such that 1.0 + 1.0. 2. (Continuation) Repeat for the largest and smallest machine numbers. 3. Students are sometimes confused about the difference between the numbers tiny an epsilon. Explain the difference. Then design and execute a numerical computer periment to demonstrate the difference. 4. By repeated division by 2 and printing the results, you may observe that it seems that n real numbers smaller than the smallest machine number tiny are obtained. Explain why is not so and what is happening
