Increment

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Increment Decrement OperatorsRounding Errors
ECOR 1606 - Problem Solving and Computers
Carleton University Department of Systems and
Computer Engineering
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Increment and Decrement Operators

• Example

int main() int a 5 a a--

• equivalent to a a 1
• increases the value of the variable a by 1

• equivalent to a a - 1
• decreases the value of the variable a by 1

• Most commonly used in for loops

int main() int i for (i 0 i lt 10
i) // do something 10 times

• Only use with integer variables.

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Postfix Increment

• Can be used in expressions
• e.g. assignment statements
• e.g. function calls
• These are examples of "postfix-increment"
• the value is used, then the variable is
  incremented

int a 5, b b a
value of variable a (e.g. 5) is copied to b, then
a is incremented (e.g. to 6).
int a 5 funct(a)
value of variable a (e.g. 5) is passed to
function funct( ), then a is incremented (e.g. to
6).
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Prefix Increment

• Alternative "prefix-increment"
• increment the variable, then use its value
• put before the variable name
• e.g. assignment statements
• e.g. function calls

int a 5, b b a
the variable a is incremented, then the new value
of a (e.g. 6) is copied to b.
the variable a is incremented, then the new value
of a (e.g. 6) is passed to function funct( ).
int a 5 funct(a)
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Postfix and Prefix Decrement

• Can also use postfix- and prefix-decrement
• e.g.

int a 5, b b a--
int a 5, b b --a
produces
produces
b 5 a 4
b 4 a 4
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Floating-point Number Representation Error

• Consider the fraction 1/3. In decimal, it is
  represented as
• 0.333333333333333333333333333333333333333
• This number can not be exactly represented with
  finite precision (a finite number of places after
  the decimal point).
• If we were only allowed, for example, six places
  after the decimal point, the closest we could
  come to representing 1/3 is
• 0.333333
• Suppose our computer stores real numbers up to
  only 6 decimal places, and we run the following
  program fragment

double x, y x 1.0 / 3.0 y x
3.0 if (y 1.0) // do
something
x 0.333333 y 0.999999 y ! 1.0
true or false?
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Floating-point Number Representation Error

• Another example

double x for (x 0.0 x ! 1.0 x
1.0 / 3.0) cout ltlt "x " ltlt x ltlt
endl
what happens?
x 0.000000
x 0.333333
x 0.666666
x 0.999999
x 1.333332
x 1.666665
etc. Infinite loop!
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Floating-point Number Representation Error

• Computers actually store floating-point numbers
  in binary, so even non-repeating decimal numbers
  may require infinite precision in binary
• e.g., The closest that a type double variable can
  come to representing the decimal number 0.1 is
• 0.1000000000000000055513312
• As a result, you should never make exact
  comparisons between floating-point numbers, but
  make approximate comparisons.

16 zeros
if (angle 90.0) // this is a right
angle
if (fabs(angle - 90.0) lt 1e-6) // this is
a right angle
Bad You'll never get equality
Good You can get arbitrarily close to a right
angle
89.999999 lt angle lt 90.000001