Review
CS 100M: Lecture 3
February 1
Variable
Has a name and a value
Arithmetic Expression
A recipe involving variables,
functions, +, -, / , * , ^
Assignment Statements
< variable > = < arithmetic expression >
Built-In Functions
Trigonometric
Log, exponential
sine
cosine
tangent
inverse sine
inverse cosine
inverse tangent
sin
cos
tan
asin
acos
atan
Built-In Functions
exp
log
log10
log2
exponential
natural log
base-10 log
base-2 log
THINK RADIANS, NOT DEGREES
Built-In Functions
Useful functions for doing certain
computations with integers:
floor
ceiling
round
fix
mod
floor
p = floor(x)
p is assigned the largest integer less than
or equal to the value of x
floor(-3.5) has value -4
floor(3.5) has value 3
1
round
ceiling
q = round(x)
r = ceiling(x)
r is assigned the smallest integer greater
than or equal to the value of x.
ceiling(-3.5) has value -3
ceiling(3.5) has value 4
q is assigned the value of the closest
integer to the value of x
(In case of tie, round away from zero)
round(-3.5) has value -4
round(2.4) has value 2
fix
mod
q = fix(x)
q is assigned the value of the closest integer
to x that is between x and zero, i.e.,
round towards the origin.
round(3.7)
fix(3.7)
round(-3.7)
fix(-3.7)
has
has
has
has
value
value
value
value
If p and q are variables with whole number
values, then
r = mod(p,q)
assigns to r the value of the remainder when we
divide the value in p by the value in q.
4
3
-4
-3
p = 30;
q = 7;
r = mod(p,q)
% r has value 2
“Synonyms”
max, min, abs
Suppose x is initialized. Then
x
y
A
B
C
D
E
=
=
=
=
=
=
=
-3
2
max(x,y)
min(x,y)
abs(x)
max(abs(x),abs(y))
min(abs(x),abs(y))
%
%
%
%
%
A
B
C
D
E
gets
gets
gets
gets
gets
2
-3
3
3
2
A = sin(x); y = x+1; B = sin(y);
and
A = sin(x); B = sin(x+1);
assign the same values to A and B.
2
“Synonyms”
The command
Order of Operations
When in doubt, use parentheses:
fprintf(‘E = %20.15e’,abs(22/7 – pi))
produces the same output as
x = 22/7;
error = abs(x – pi);
fprintf(‘E = %20.15e’,error)
And
Q. When is a real number x in the
interval [L,R]?
A. If x is greater than or equal to L
and less than or equal to R.
Or
Q. When is a real number x not in the
interval [L,R]?
A. If x is less than L or greater than
R.
y = 1 / (a + b/c)*d + 1
is the same as
y = (1 /(a + (b/c)))*d + 1
The And Operation: &&
if x >= L && x <= R
fprintf(‘x is in [L,R]’)
else
fprintf(‘x is not in [L,R]’)
end
The Or Operation: ||
if x < L || x > R
fprintf(‘x is not in [L,R]’)
else
fprintf(‘x is in [L,R]’)
end
3
Boolean Expressions
• They involve comparisons.
• They have a value that can be thought of
as either True or False.
Examples:
2.Variable x has a positive integer value.
Is it divisible by 3 and 5? Yes if the
following is true:
mod(x,3) == 0 && (mod(x,5) == 0
1.Variables a, b, and c have positive real
values. Can we make a triangle with sides
that have those values? Yes if the following
is true:
(a < b+c) || (b < a+c) || (c < a+b)
3.Variable y has a positive integer value.
Does it name a non-leap year? Yes if the
following is true:
mod(y,4)~=0 ||
(mod(y,100)==0 && mod(y,400)~=0)
Rule: Y is an “ordinary” year if it is not divisible
by 4 or if it is a century year not divisible by
400.
4