COS 126: Spring 1997 Table of Powers

Due: Wed. 2/19, 11:59pm

In this assignment, you'll write three versions of a program to print the powers of a given integer. The display below shows the input and output of the program for three different integers: 3, 15, and 126. Slanted type identifies input.

% a.out
Enter a number:
3
3 ^ 0 = 1
3 ^ 1 = 3
3 ^ 2 = 9
3 ^ 3 = 27
3 ^ 4 = 81
3 ^ 5 = 243
3 ^ 6 = 729
3 ^ 7 = 2187
3 ^ 8 = 6561
3 ^ 9 = 19683
3 ^ 10 = 59049
3 ^ 11 = 177147
3 ^ 12 = 531441
3 ^ 13 = 1594323
3 ^ 14 = 4782969
3 ^ 15 = 14348907
3 ^ 16 = 43046721
3 ^ 17 = 129140163
3 ^ 18 = 387420489
3 ^ 19 = 1162261467

% a.out
Enter a number:
15
15 ^ 0 = 1
15 ^ 1 = 15
15 ^ 2 = 225
15 ^ 3 = 3375
15 ^ 4 = 50625
15 ^ 5 = 759375
15 ^ 6 = 11390625
15 ^ 7 = 170859375

% a.out
Enter a number:
126
126 ^ 0 = 1
126 ^ 1 = 126
126 ^ 2 = 15876
126 ^ 3 = 2000376
126 ^ 4 = 252047376

The purpose of this assignment is to familiarize yourself with the while and for loop statements in C and with the if-else selection statement, and to learn a bit about how the computer represents integers.

As illustrated above, your program should prompt for a number ("Enter a number:"), read an integer x (e.g., 3), and print a table of the powers of x. For this assignment, you can assume that x > 1.

Write and submit three versions of your program:

1. usewhile.c: A version that uses only while loops (and if-else statements, if you need them).
2. usefor.c: A version that uses only for loops.
3. usebreak.c: A version that uses either while or for loops and the break statement.

The break statement terminates the loop in which it appears prematurely. For example,

sum = 0;
for (i = 1; i <= n; i++) {
	sum = sum + i;
	if (sum > 100)
		break;
}

computes the sum of the first n integers, but quits early if that sum exceeds 100. Break statements should be used sparingly, because they can lead to unstructured code. But there a few loop idioms that are more clear with break statements, as you'll see in this assignment. For more information about break statements, see Dietel and Dietel, Sec. 4.9.

One question remains: How many powers should your program print? As the display above suggests, the answer is "As many as you can compute". You'll compute xⁱ by multiplying x by itself i times (there is a better algorithm, but discovering it is not necessary for this assignment). Computers can represent integers in only a limited range; the Sparc computers you're using can represent 2³² integers from -2³¹ to 2³¹-1, that is, from -2147483648 to 2147483647. So, it's possible that given two integers a and b, a*b is outside this range and thus too big. You should print all the powers of x that are less than or equal to 2147483647.

How can you test if an xⁱ is too big? Given a and b, you can't just write "if (a*b <= 2147483647) ..." because you can't compute a*b. You can avoid computing a*b by rearranging this conditional and testing if a <= 2147483647/b for any positive value of b. There are other approaches to this probem that also avoid computing a*b when it's too big.

Finally, it's best to use symbolic constants in your code instead of numbers like 2147483647, because the symbolic constants are self-documenting and help avoid platform dependencies. For example, 2147483647 is not the largest integer on Alpha computers. The standard symbolic constant INT_MAX is the largest integer. You can use INT_MAX by including limits.h in your program; that is, put the line

#include <limits.h>

at the beginning of your code.

Turn in all three versions of your program and your documentation with the command

/u/cs126/bin/submit 2 readme usewhile.c usefor.c usebreak.c