PHP: While Loops II

Derek Bridge

Department of Computer Science,
University College Cork

PHP: While Loops II

Aims:

• to recognise a classic use of a while-loop for unbounded repetition

Comparing floating-point numbers

• It is not possible to store all real numbers exactly using floating-point representation, which uses a finite number of bits
• E.g. in decimal 1/3 = 0.33333…
• E.g. the decimal number 0.1 becomes an infinitely recurring number in binary (see this FAQ or this guide)
• The floating-point representation will introduce a small truncation error
• One consequence is our programs' results may be off slightly: how to analyse, and minimise, these errors is the subject of modules on numerical analysis
• Another consequence is, when using floats, you should never expect one value you calculate to exactly equal another
• Class exercise: What do you think the output will be:
  if ( sqrt(2) * sqrt(2) == 2 )
{
    echo 'Yes';
}

Computing square roots, again

• In the previous lecture, we computed the square root of a non-negative integer by counting the number of successive odd numbers we needed to subtract to reach zero
• In this lecture, we take another approach to computing square roots: by repeatedly 'guessing'
• So we use the following form. The second text field will be explained in the lecture:

  <form action="root.php" method="get">
      <input type="text" name="number" />
      <input type="text" name="epsilon" />
      <input type="submit" />
  </form>

  In the rest of the lecture we'll write root.php

Repeated 'guessing'

• We'll keep two numbers, $lo and $hi
• Initially, $lo will 0 and $hi will be the number the user supplies and $guess will be the number the user supplies
• If $guess is 'good enough', we will stop
• If not,
  • if $guess was too big, our next guess can lie halfway between $lo and $guess
  • if $guess was too small, our next guess can lie halfway between $guess and $hi
• Class exercise: Why will we use a while-loop for this, rather than a for-loop?