ITEC 120 2010fall ibarland

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lect05b
casting; %; syntax review

• Review: Order of precedence for boolean and other operators: Use parentheses, if it's at all ambiguous.
• Review: Order of precedence for arithmetic: you can assume everybody knows: first all multiplication/divisons (left-to-right), then all addition/subtractions (left-to-right). (Even so, parentheses can still add clarity.) Both quotient and remainder count as types of division.
• / can either mean “call the built-in function integer-division”, or “call the built-in function floating-point-division”, depending on context.
• Note that % and integer-division complement each other:
  For all ints p and q where q != 0, we have p == (p/q)*q + (p%q).
• Practice task: Write a function which computes a batting average -- the number of hits divided by the number of times at bat. (Don't worry about rounding, yet.) Follow all steps of the design recipe. (data analysis, signature/stub, javadoc, test cases, finish function).

• When you have two ints, and you want to do floating-point division on them, you have to convert them to doubles. If you have int literals like 4 and 3, you could write 4.0 / 3.0. But what if you had two int variables, like numHits and timesAtBat?

  The solution is that we must call a function to convert an int into a double. One sensibly-named function is Object120.intToDouble( int n ). What if we we didn't have Object120 to make life easy for us? Surely there is a built-in function to do so. It turns out, that's not the case¹. -- Java has a whole special syntax for calling this particular conversion function, called casting. You write (double) in front of the int expresion:

  ((double) numPizzas) / ((double) numPeople)

  Note that two outer sets of parentheses are for clarity. The parentheses around the word double are required.

  Casting is the only time you use the name of a type even though you aren't introducing a new name to the Java compiler. It is conceptually annoying that Java has a whole special syntax just for this small set² of conversion functions.

  Java calls these conversion functions for you all the time, behind your back. For instance, Math.sqrt(25) is silently re-written as Math.sqrt( (double) 25 ), since Math.sqrt's documentation shows it requires a double as input.

  Beware that casting can induce arithmetic errors (discussed yesterday).

• % is remainder; it is the complement to quotient. I always have to look up (or, type in) how % works with negative numbers.

(Optional) An application of %: public key cryptography

Web traffic is sent on postcards. How to securely communicate your credit-card number to amazon, without any pre-arrangement? “Inconceivable!”?

Amazon might say on their web page:

Our public key pubKey = 37. If you want to send us a secret message privMsg (a two-digit number), multiply your secret number by our public key, and tell us the last two digits (only) of the result: That is, tell us (privMsg * pubKey) % 100. (We can name this result pubMsg.)

Is announcing pubMsg secure, even if there are eavesdroppers? Let's try it! A volunteer: Choose your secret privMsg and write it down, without telling anybody. Compute pubMsg, and announce it. Can any of you eavesdroppers figure out the original message? (You want to just divide by 37, but how to do that in this world of mod-100 arithemetic?) The original privMsg was …

Note that this used no pre-arrangement between the sender and the receiver. This is called “public key cryptography”, since eavesdroppers know as much about breaking the code as the sender.

You could break this code, if you could divide by 37 mod 100. (Or more precisely: find the multiplicative inverse of 37, mod 100.) Project: read about the extended Euclidean algorithm for calculating muliplicative inverses. Break this code!

Although this particular scheme is easy to break with a bit of math knowledge (this Extended Euclidean algorithm), the example is to motivate how a public-key system is even conceivable.

Review

We have covered many topics over the last 4 weeks:

• types,
• syntax to call a function,
• syntax to declare a function (signature),
• comments (javadoc),
• test cases,
• converting arithmetic formulas into Java,
• return,
• local variables (initializing and declaring) to give a name to sub-computations so that you can use that sub-result later;
• if-else statements
• if-else-if statements
• arithmetic issues

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©2010, Ian Barland, Radford University Last modified 2010.Sep.29 (Wed)

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