Problem 28
Consider the following simple program inspired by Chapter 1.4.3: a = 1/947.0*947 b = 1 if a != b: print ’Wrong result!’ Try to run this example! One should never compare two floating-point objects directly using \(==\) or \(!=\) because round-off errors quickly make two identical mathematical values different on a computer. A better result is to test if \(|a-b|\) is sufficiently small, i.e., if \(a\) and \(b\) are "close enough" to be considered equal. Modify the test according to this idea. Thereafter, read the documentation of the function float_eq from SciTools: scitools numpyutils .float_eq (see page 80 for how to bring up the documentation of a module or a function in a module). Use this function to check whether two real numbers are equal within a tolerance. Name of program file: compare_float.py. 0
Problem 29
The function time in the module time returns the number of seconds since a particular date (called the Epoch, which is January 1 , 1970 on many types of computers). Python programs can therefore use time.time() to mimic a stop watch. Another function, time.sleep(n) causes the program to "sleep" n seconds and is handy to insert a pause. Use this information to explain what the following code does: import time t0 = time.time() while time.time() - t0 < 10: print ’....I like while loops!’ time.sleep(2) print ’Oh, no - the loop is over.’ How many times is the print statement inside the loop executed? Now, copy the code segment and change < with > in the loop condition. Explain what happens now. Name of program: time_while.py.
Problem 30
Type in the following program in a file and check carefully that you have exactly the same spaces: C = -60; dC = 2 while C <= 60: F = (9.0/5)*C + 32 print C, F C = C + dC Run the program. What is the first problem? Correct that error. What is the next problem? What is the cause of that problem? (See Exercise \(2.12\) for how to stop a hanging program.) The lesson learned from this exercise is that one has to be very careful with indentation in Python programs! Other computer languages usually enclose blocks belonging to loops in curly braces, parentheses, or BEGIN-END marks. Python's convention with using solely indentation contributes to visually attractive, easy-to-read code, at the cost of requiring a pedantic attitude to blanks from the programmer.
Problem 31
Go through the code below by hand, statement by statement, and calculate the numbers that will be printed. n = 3 for i in range(-1, n): if i != 0: print i for i in range(1, 13, 2*n): for j in range(n): print i, j for i in range(1, n+1): for j in range(i): if j: print i, j for i in range(1, 13, 2*n): for j in range(0, i, 2): for k in range(2, j, 1): b = i > j > k if b: print i, j, k You may use a debugger, see Appendix F.1, to step through the code to see what happens.
Problem 33
Study the following interactive session and explain in detail what happens in each pass of the loop, and use this explanation to understand the output. >>> numbers = range(10) >>> print numbers [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] >>> for n in numbers: ... i = len(numbers)/2 ... del numbers[i] ... print ’n=%d, del %d’ % (n,i), numbers ... n=0, del 5 [0, 1, 2, 3, 4, 6, 7, 8, 9] n=1, del 4 [0, 1, 2, 3, 6, 7, 8, 9] n=2, del 4 [0, 1, 2, 3, 7, 8, 9] n=3, del 3 [0, 1, 2, 7, 8, 9] n=8, del 3 [0, 1, 2, 8, 9] The message in this exercise is to never modify a list that is used in \(a\) for loop. Modification is indeed technically possible, as we show above, but you really need to know what you are dingo - to avoid getting frustrated by strange program behavior. \(\diamond\)
