birt code 39

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9.35 Use these formulas to implement the hyperbolic sine and hyperbolic cosine functions recursively: sinh2x = 2sinhxcoshx cosh2x = 1 + 2(sinhx)2 sin x x + x 3/6 cos x 1 + x 2/2 Compare your results with the corresponding values of the Math.sinh() and Math.cosh() methods. 9.36 Use these trigonometric formulas to implement the tangent function recursively: tan2 = 2tan /(1 tan2 ) tan x x + x 3/3 Compare your results with the corresponding values of the Math.tan() method. 9.37 Implement a recursive function that evaluates a polynomial a0 + a1 x + a2 x2 + + a3 x3, where the n+1 coefficients ai are passed to the function in an array along with the degree n.

A page fault causes a trap to the operating system, and the operating system must handle the page fault by: 1 2 3 4 5 6 Locating the required page of code or data from the process image Finding an unused memory frame Copying the required code or data to the frame Adding a mapping of the new frame to the process s page table Setting the valid bit in the new page table entry to valid Restarting the instruction which faulted.

(a) In polar form, the given frequency transfer function is 1 1 q j tan 1 ! A j! q 2 1 1 ! j tan ! =1 1 ! 2 Hence, and tan 1 ! 1 Mdb 20 log jA j! j 20 log q 10 log 1 ! 2 1 ! 2 (8.5) (8.6)

9.1 The basis of a recursive function is its starting point in its definition and its final step when it is being called recursively; it is what stops the recursion. The recursive part of a recursive function is the assignment that includes the function on the right side of the assignment operator, causing the function to call itself; it is what produces the repetition. For example, in the factorial function, the basis is n! = 1 if n = 0, and the recursive part is n! = n (n 1) if n > 0. The call factorial(10) will generate 10 recursive calls. The call f(6) to the Fibonacci function will generate 14 + 8 = 22 recursive calls because it calls f(5) and f(4), which generate 14 and 8 recursive calls, respectively. A recursive solution is often easier to understand than its equivalent iterative solution. But recursion usually runs more slowly than iteration. Direct recursion is where a function calls itself. Indirect recursion is where a group of functions call each other.

(b) If values of (8.5) and (8.6) are calculated and plotted for various values of !, then a Bode plot is generated. This is done in Fig. 8-2, where ! is given in terms of time constants rather than, say, hertz. This particular system is called a lag network because its phase angle is negative for all !.

The processing of a page fault can also be more complex, as when all memory is allocated, and some previously allocated page mapping must be replaced. Also, because of the wait for disk I/O in reading the process image into memory, it s likely that another process will be scheduled while the disk I/O completes.

9.2 9.3 9.4 9.5

Mdb T (s) = A(s) =

9.1 A recursive function that returns the sum of the first n squares:

1 +1

Virtual Memory Problems and Solutions It s fine that each process has a page table mapping its logical address space to physical memory However, there are additional problems to solve in real systems, in order to make virtual memory systems work well First, every reference to memory first requires a reference to the page table, which is also in memory Right away, even when there is no page fault, using a page table cuts the speed of access to memory by a factor of 2 A solution to this problem is to use an associative memory called a translation lookaside buffer (TLB) An associative memory is a small, expensive, magic piece of hardware that can perform a whole set of comparisons (usually 64 or fewer) at once As a process is executing, the TLB, which is part of the MMU, maintains the recently accessed page table entries.

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A recursive function that returns the sum of the first n powers of a base b:

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double sum(double b, int n) { if (n == 0) { return 1; // basis } return 1 + b*sum(b,n-1); // recursion }

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