Mathematical Operators

1
Mathematical Operators
Lect06

• So far we have seen the rudimentary mathematical
  operators
• add
• subtract -
• multiply
• divide /

2
Assignment and Addition

• int a, b, c //define variables
• a1 //make assignments
• b2 // to a and b
• cab //assign the sum
• // of a and b to c

3
Subtraction

• Similarly subtraction
• float a, b, c //define variables
• a1.0 //make assignments
• b2.0 // to a and b
• ca-b //assign the
• // difference of
• // a and b to c

4
Multiplication and Division

• int a, b, c //define variables
• a1 //make assignments
• b2 // to a, b and c
• c4
• cc/(ab) //assign the answer to c

5
Mixed Type Arithmetic

• int a
• float b
• a5
• b2.0
• aa/b
• aa/b is 5/2 ? quotient 2 and remainder 1
• a is assigned the value 2

6
BEWARE!

• int a, b
• float c
• a5
• b2
• ca/b
• a/b is carried out as integer arithmetic
• c is assigned the value 2.0

7
Typing in Operations

• int a, b
• float c
• a5
• b2
• c((float) a)/((float) b)
• c is assigned the value 2.5
• a and b are said to be cast as floats

8
Modulus Operator -

• int a, b
• a5
• b2
• aab
• a is assigned the value of the remainder, 1

9
Precedence

• / left to right
• - left to right
• right to left
• xyz (yz) x
• wx/yz (x/y) w z
• (wx)/(yz)
• x/yz (x/y)z
• x/(yz)

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Assignment

• In-line assignment
• int i
• i3
• Assignment during compilation
• int i3
• Multiple common assignment
• int a, b, c
• abc8 // is right to left

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Mathematical Functions

• There is a set of standard mathematical functions
  available with the inclusion of the header file
  math.h
• sine x double sin(double x)
• cosine x double cos(double x)
• tangent x double tan(double x)
• plus the inverse functions
• tan-1 double atan(double) etc.
• Note x is in radians.

12
More Mathematical Functions

• loge x double log(double x)
• log10 x double log10(double x)
• exponential (ex) double exp(double x)
• square root x double sqrt(double x)
• power (xy) double pow(double x, double y)

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Example

• Length of a line on a graph

y
x2, y2
Length
?(x2-x1)2(y2-y1)2
x1, y1
x
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Program for Length of Line

• include ltstdio.hgt
• include ltmath.hgt
• int main()
• float dx, dy, length
• float x11.0, x210.0, y15.0, y220.0
• dxx2-x1 dyy2-y1
• lengthsqrt(pow(dx,2.0)pow(dy,2.0))
• printf("Length is f\n", length)
• system("PAUSE") return 0
• Length is 17.492855

Lect0601.c
15
Animation

• Problem definition
• A programmer of a computer game wants to
  calculate the position of the spokes on a wheel
  after the wheel has turned 30 degrees.

30
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Input-Output Description
Starting diagram
Rotated diagram
Rotation angle
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Gather Information

• 1 - The circle of the wheel is the same at all
  angles of rotation.
• 2 - The rotation is about the centre of the
  wheel.
• 3 - The straight lines of the spokes remain
  straight lines after the rotation.
• 4 - We need to calculate the end points of the
  spokes and then draw straight lines between them.

18
Rotation of Spokes

• End of spoke at (x, y) moves to (x, y)

45
y
(x, y)
30
(x, y)
15
x
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Equations

• Length of spoke from centre of rotation L
• L?(x2y2)
• xL cos(15), yL sin(15)
• Conversion of 15 to radians
• there are 2? radians in 360 or
• 1 2?/360 ?/180 radians
• 15 15?/180 15.0 3.14159/180.0

20
Program

• include ltmath.hgt
• .
• float length, x, y, xdash, ydash
• .
• .
• lengthsqrt(xxyy)
• xdashlengthcos(15.03.14159/180.0)
• ydashlengthsin(15.03.14159/180.0)

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Other Spoke Ends

• Similarly we can calculate the other ends of the
  two spokes given the different starting values of
  the end points.

y
30
(x, y)
(x, y)
45
105
x
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Starting Ending Values
(9.6, 2.6)
(-2.6, 9.6)
(2.6, -9.6)
(-9.6, -2.6)
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Symbolic Constants

• Sometimes we wish to use the same constant at
  different places in a program. We can just place
  the number in the different places or we can
  define a name which we can use repeatedly.
• One change at the top of the program changes the
  value everywhere.
• Constants usually are in uppercase.

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define

• include ltstdio.hgt
• include ltmath.hgt
• define PI 3.14159
• define DEGREETORADS PI/180.0
• .
• .
• xdashlengthcos(15.0DEGREETORADS)
• ydashlengthsin(15.0DEGREETORADS)

Lect0602.c
25
Random Numbers

• Random numbers occur when we throw a die
• the numbers 1 to 6 appear randomly
• in a fair die, we expect the numbers to have
  equal chance of appearing Uniformly distributed.
• Randomness occurs in physical phenomena
• static on radio, TV or phone signals can be
  expressed as a random signal.

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int rand(void)

• The rand function returns a random integer in the
  range 0 to RAND_MAX (32767).
• rand and RAND_MAX are defined in stdlib.h.
• Each call generates a new random integer
• printf("Random numbers d, d\n", rand(), rand())

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Pseudo-Random

• The sequence from rand is not truely random, it
  is pseudo-random.
• To set the start point in the sequence we can
  use srand
• void srand(unsigned int)
• the unsigned int is the seed value for the start
  of the sequence.

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Reducing the Sequence Length

• To get the numbers 1 to 6 on a die we can use
• int die
• dierand()61
• rand()6 produces a number in the range 0 to 5,
  then add 1.
• For a number in the range 0 to 1
• float p
• p ((float) rand()/RAND_MAX)

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Uses of Random Numbers

• Die throwing and card shuffling for games.
• Simulation add noise to a signal to test noise
  removal algorithms.
• Monte Carlo analysis
• random arrival times
• production variations
• reliability.