Transcript Random numbers in C++

Random numbers in
C++
Nobody knows what’s next...
Deterministic machines
That means that computers do the same
predictable thing every time you give them
the same instructions
 we WANT this – we don't want random
happenings - most of the time
 when would you NOT want this?

 games
of reality – traffic flows, nuclear
explosions, star formation
 Cryptography!
 simulations
What is "random"?
A “real” random number is generated by a
real world event like an atom decaying or
not in a certain time
 Hard to do that in a computer
 Best we can do with a deterministic
machine is make “pseudorandom”
numbers
 They are “good enough”

“good enough”?
A “good” random number is one that is
distributed evenly in its range
 If you were rolling a die, you want
numbers from 1 to 6 to be equally likely to
show up
 This is over the “long run”, not each
individual trial

Lots of research
Lots has been done on random numbers
 Trying to get faster algorithms
 With larger cycles – all algorithms will
eventually start repeating but the best
ones not before a few million numbers at
least
 Very heavy statistics and mathematics in
the latest algorithms

A simple one – “mid square”
Take a number to start with (the “seed”)
 Square it
 Take the “middle” of it – trim off some
digits at front and end
 That’s the random number
 Repeat the process by feeding the number
just generated back in as the starting
number next time
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An example
12345 squared = 152399025
 chop it off and get 23990
 23990 squared = 575520100
 chop it off and get 55201
 55201 squared = 3047150401
 chop it off and get 47150
 And so on
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Properties of an RNG

Give the algorithm a DIFFERENT seed to
start with and what comes out?

Give the algorithm the SAME seed to start
with and what comes out?
Syntax
Include the cstdlib library to get the
functions
 Use srand(seed); to set the initial seed
(seed must be an integer)
 Use rand() to get the next random number
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 returns
an integer between 0 and
RAND_MAX

Call srand ONCE per program, call rand
many times
Seeds to start with
srand(23); will always give you the same
sequence of random numbers – good
when testing!
 Asking the user for a number and then
using it as the seed - works but is a bit
aggravating to the user
 Using the time function is most flexible
(see example on web page)
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rand() and RAND_MAX
rand() returns a integer between 0 and
RAND_MAX (a constant defined in cstdlib)
 What if you need an integer number
between 1 and 6? rand() % 6 + 1
 What if you need a number between 0 and
1 (i.e, a fraction) ? rand() / RAND_MAX
(but watch your TYPE here!)
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