Computational Science I

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Computational Science I

• Lecture 5
• CAAM 420, Fall 2004
• Instructor Tim Warburton

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Recall Integer Arithmetic

• We are able to perform integer based arithmetic
  with the int variable type

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Running The Arithmetic

• As before, we create a program, compile it, and
  run it

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float

• We can also create floating point variables which
  have approximately eight significant figures.
• We create these

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float cont

• By asking for at least 15 decimal places to be
  printed out we see that in fact those 19 decimal
  places
• were truncated at around the 8th or 9th decimal
  place (the rest is garbage)

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float arithmetic

• Again we can perform arithmetic with floats and
  can even use ints too, although the results may
  take a little effort to predict.

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float cont

• Running
• Explanations ?

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double

• When we need more precise answers (i.e. more than
  8 decimal places) we can use double type
  variables which can store up to about 16 decimal
  places.

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double cont

• When we run this we see
• i.e. we see some differences because dadb is not
  the same as fafb . This is because da!fa and
  db!fb
• ! from now on will stand for not equal

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Code Control In C

• Suppose I wish to sum up the numbers between 1
  and 10.
• I could write code like

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mysum

• So I run the code and it works

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Class Exercise F

• Write a piece of code which sums up the numbers
  between 1 and a million without using the well
  known formula.

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for loop

• C has a built in loop syntax.
• We can rewrite the mysum program as

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for loop

• The syntax of the for loop is
• for( (1) (2) (3) ) body
• In words
• initialize some variables (usually counters) to
  be used in the loop. This is done before the loop
  is entered.
• Completion test to see if the body of the for
  loop should be entered. If the test is true then
  the body of the loop is executed otherwise the
  for for loop is finished.
• the increment part of the for statement is
  executed after the body of the loop is executed
• we go back to (2)

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Step by Step

• We can go through this for loop step by step

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More Advanced Loop Tests

• The loop completion test can be quite complicated
• Here I compare iloop with iNterms so that I can
  add all the numbers between 1 and iNterms where
  iNterms is defined before the loop.

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Class Exercise G

• Write a routine to add all the odd numbers
  between 1 and 100
• Change the condition test to use a variable
  instead of 100.
• Compare your result with a math formula for this
  task (design it yourself).

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while loops

• We can also construct less rigid loops.
• A looser stucture is
• while(completion test is true)
• body

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The Sum Example Using while

• We initialize the iloop variable outside the
  while loop and increment it inside the while loop
  to achieve the same effect as the for loop.

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Using break

• We sometimes would like to break out of a for or
  while loop before the conditional test is made.

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Some Notes on mybreak.c

• Here I used a function call to cos() and referred
  to M_PI
• Believe it or not this is not part of the default
  C language.
• So at the top of the file I included math.h AND
  when I compiled I linked in libm.a because this
  includes the cos function

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What happens if we dont take care of cos()

• Suppose I do not include math.h
• The compiler complains that it has no idea what
  the cos function is or what the variable M_PI is
  and stops without completing the compile.

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cont

• Suppose I forget to link in (i.e. include lm on
  the compile line) but do remember to include
  math.h
• The compiler tells us it cant find the cos
  function definition.
• Thats why we have to tell the compiler to
  include libm.a by adding -lm

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For Next Time

• Read Chapter 3 of K R to reinforce todays
  class.
• Next time we will discuss memory pointers, memory
  allocation and structures.