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# Random Number Generators....

I have a problem that I really don't understand at all. In my previous
post I could get started on my projects I just had a few problems with
syntax errors. This problem is something that I don't conceptually
understand very well. Here it is:

Î* â the ratio of the circumference of a circle to its diameter
â is one of the most common and important constants in mathematics.
It is an irrational number (a real number that cannot be expressed as
the ratio of two integers), but its value has been calculated to more
than a million decimal places using different formulas. (See, for
example, Petr Beckmann's A History of Î*, St. Martin's Press: New York,
1971) In this assignment you will estimate the value of Î* by
simulating randomly throwing darts at a target.

The figure at the left is a quarter circle of radius 1.0 inscribed in
a square of side 1.0 on the Cartesian plane. It can be show that area
of the dark blue quarter circle is Î*/4. If we were to randomly throw d
darts at the square, and c of them landed in the circle, we could
estimate the value of Î*/4 as c / d, so an approximation of Î* is 4* (
c / d ).

Your program should "throw" darts at the target by generating a
random coordinate pair (x, y) where x and y are floating point values
in the range [0.0, 1.0], which will represent the point the dart hit
the target. (You can generate numbers in this range with the expression
(double)rand()/RAND_MAX) .) This point will be inside the quarter
circle if:

sqrt( x2 + y2) <= 1.0

By maintaining counters for the number of darts landing in the
quarter circle and the the total number of darts thrown, the value of
Î* can be approximated. The larger the number of darts thrown, the
better the approximation will be.

Your program should use a function that, each time it is called,
generates a new random coordinate pair, determines if this pair
represents a point inside the quarter circle, and returns a 1 if it is,
and a 0 if it is not. Your program should run a simulation for a
user-specified number of dart throws, and then display the estimated
value of Î* and the percentage difference (percent error) between your
estimated value and the true value of Î*; if your estimated value is p,
then the percent error is (( p - Î*) / Î* ) * 100. (The actual value of
Î* to 15 significant figures is 3.14159265358979.)

__________________________________________________ _________________________

I do have some ideas about the variables that I need but I'm not sure
how to really implement the rand()/ RAND_MAX function... could someone
give a start in the right direction?

Feb 26 '06 #1
40 2730 [...]

Your program should "throw" darts at the target by generating a
random coordinate pair (x, y) where x and y are floating point values
in the range [0.0, 1.0], which will represent the point the dart hit
the target. (You can generate numbers in this range with the expression
(double)rand()/RAND_MAX) [...]

I do have some ideas about the variables that I need but I'm not sure
how to really implement the rand()/ RAND_MAX function... could someone
give a start in the right direction?

You do not need to implement the rand() function nor
define RAND_MAX; they are part of the Standard C library.
Just #include <stdlib.h> and start using them.

--
Eric Sosman
es*****@acm-dot-org.invalid
Feb 26 '06 #2
I do have some ideas about the variables that I need but I'm not sure
how to really implement the rand()/ RAND_MAX function... could someone
give a start in the right direction?

Both rand() and the associated constant RAND_MAX are part of the builtin C
API.

Uli

Feb 26 '06 #3
Your program should use a function that, each time it is called,
generates a new random coordinate pair, determines if this pair
represents a point inside the quarter circle, and returns a 1 if it is,
and a 0 if it is not.

Be careful with that. A -lot- of implementations use
linear congruential random number generators for rand(), and
there is a well known problem with those that if you use
consequative samples from the stream as (x,y) pairs and graph
the results, instead of filling a square evenly, you will get
a number of noticably seperated diagnonal lines.

There are various corrections that one can use to reduce this
problem, but the best correction is to use a much better random number
generator. One that is said to be fast and very good is the
Mersenne Twister,
http://www.math.sci.hiroshima-u.ac.j...at/MT/emt.html
--
All is vanity. -- Ecclesiastes
Feb 26 '06 #4

__________________________________________________ _________________________

I do have some ideas about the variables that I need but I'm not sure
how to really implement the rand()/ RAND_MAX function... could someone
give a start in the right direction?

rand() and RAND_MAX return integers. so rand()/RAND_MAX either 0 or 1.
Think for a moment about why that must be true.

So there must be a techinque you can do to ensure that you get a
floating point answer from that calculation.

I suppose I could tell you it's a FAQ.....

You might want to print the value of RAND_MAX. Random number generators
start to show predictability when the number of numbers generated gets
"close to" the period of the pRNG. RAND_MAX isn't the period, but it
will give you a general idea how long the period is.

If RAND_MAX is 65535, you probably don't want to use more than 6000 or
so values from it in any simulation.

There are MANY things to learn about RNGs. Googling the topic will give
you more links than you might care to know.

Know that there is no software method that can produce "random numbers",
only a subset of an arbitrary, albeit ABSOLUTELY predictable sequence of
numbers. For MOST applications, the difference doesn't matter all that
much.

When it DOES matter, it becomes a hardware problem involving things like
mason or gamma ray detectors.

Feb 26 '06 #5
In article <-r********************@comcast.com>,
Charles Krug <cd****@aol.com> wrote:
Know that there is no software method that can produce "random numbers",
only a subset of an arbitrary, albeit ABSOLUTELY predictable sequence of
numbers. For MOST applications, the difference doesn't matter all that
much. When it DOES matter, it becomes a hardware problem involving things like
mason or gamma ray detectors.

Or Lava Lamps.

--
All is vanity. -- Ecclesiastes
Feb 26 '06 #6
Charles Krug wrote:
Know that there is no software method that can produce "random numbers",
only a subset of an arbitrary, albeit ABSOLUTELY predictable sequence of
numbers.

That is true, but some generators (by the way, that should be called
pseudo-random generators, because, indeed, we have no means of
expressing true randomness algorithmically, or that would be a giant
step forward!) are pretty good.

One of the best I have used came from one of the D. Knuth books. Simple
enough, yet incredibly efficient.

You can also try this: http://www.random.org/
It can help either generating random sequences for direct use, or for
comparing your own generator with good random sequences, using a
statistical tool such as: http://www.fourmilab.ch/random/

At any rate, I strongly suggest implementing the one Knuth suggests.
IIRC, it memorizes 55 past numbers to generate a new one (so that
should help you find the algorithm in question in "The Art of Computer
Programming".
Feb 26 '06 #7
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) writes:
Your program should use a function that, each time it is called,
generates a new random coordinate pair, determines if this pair
represents a point inside the quarter circle, and returns a 1 if it is,
and a 0 if it is not.

Be careful with that. A -lot- of implementations use
linear congruential random number generators for rand(), and
there is a well known problem with those that if you use
consequative samples from the stream as (x,y) pairs and graph
the results, instead of filling a square evenly, you will get
a number of noticably seperated diagnonal lines.

There are various corrections that one can use to reduce this
problem, but the best correction is to use a much better random number
generator. One that is said to be fast and very good is the
Mersenne Twister,
http://www.math.sci.hiroshima-u.ac.j...at/MT/emt.html

This is good advice for anyone doing real work with random numbers,
but I don't think it's something the OP should be worrying about. He
has a homework assignment to write a fairly elementary program that
uses random sampling to estimate the value of pi. For his purposes,
it's reasonable to assume that rand(), when used properly, yields
sufficiently random numbers. I suspect that any problems with
whatever random number generator he's using aren't going to show up in
the number of iterations he's going to be able to use (the method
converges very slowly).

The OP's major problem is how to write the program, not how to use a
random number generator, much less how to implement a high-quality
one.

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 26 '06 #8
I have a problem that I really don't understand at all. In my previous
post I could get started on my projects I just had a few problems with
syntax errors. This problem is something that I don't conceptually
understand very well. Here it is: [snip] Your program should use a function that, each time it is called,
generates a new random coordinate pair, determines if this pair
represents a point inside the quarter circle, and returns a 1 if it is,
and a 0 if it is not. Your program should run a simulation for a
user-specified number of dart throws, and then display the estimated
value of Ð and the percentage difference (percent error) between your
estimated value and the true value of Ð; if your estimated value is p,
then the percent error is (( p - Ð) / Ð ) * 100. (The actual value of
Ð to 15 significant figures is 3.14159265358979.)

Break the problem down into smaller parts. You're going to need
floating-point random numbers in the range 0.0 to 1.0. Write a
program that generates and displays one such number. Then add a loop
so it generates and displays a sequence of such numbers (say, 10 of
statements to display the values you're generating; visually examine
the output to be sure it makes sense (e.g., the number look more or
less random, they're in the proper range, etc.). As you get each part
of the program working, you can delete or comment out the printf
statements so the output isn't too cluttered.

Section 13 of the comp.lang.C FAQ, <http://www.c-faq.com/>, has some
good information on generating random numbers. Don't worry too much
almost certainly isn't good enough for cryptography, but it's fine for

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 26 '06 #9
Thanks for all the help from everyone. I'm working on the solution now

Feb 26 '06 #10
I have not written any code yet, I'm still trying to get my head around
this problem.
Here are my ideas so far:

My only input from the user will be how many darts they choose to
throw. This will be an int.

Once I get this value I need to generate coordinate pairs from their
value of darts. Say they choose 500 darts.

What I need then is two variables to hold the coordinate pairs. Say x
and y. So, x will get 500 and y will get 500.

So I will loop 500 times.

Now I need to count the number of 'hits' in the range of sqrt(x^2 +
y^2)<= 1.00

I can use a simple IF statement for this counter.

I think this is the right track

Feb 27 '06 #11
Ok, I have a question. How do I generate a specific number of random
numbers?

For instance if I needed 500 random numbers how do I 'put' these 500
numbers into the Random Number Generator?

Feb 27 '06 #12

Ok, I have a question. How do I generate a specific number of random
numbers?

For instance if I needed 500 random numbers how do I 'put' these 500
numbers into the Random Number Generator?

Uh, you don't put numbers INTO the generator, you take them out.

Call the rand() function 1000 times (for each of the 500 x & y
values you need) and save the returned values. Each time
you call it, you'll get back a new random number.

Feb 27 '06 #13
could you give me an example of some sample code ?

Feb 27 '06 #14
Ok, I have a question. How do I generate a specific number of random
numbers?

For instance if I needed 500 random numbers how do I 'put' these 500
numbers into the Random Number Generator?

questions.)

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 27 '06 #15
could you give me an example of some sample code ?

/*
randtest.c
*/

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int main()
{
float r;
int i;

srand((unsigned int)time((time_t *)NULL));

for (i=0; i<500; ++i) {
r[i] = rand() / (RAND_MAX + 1.);
r[i] = rand() / (RAND_MAX + 1.);
}
printf("\n\n");
for (i=0; i<500; ++i) {
printf("%f %f\n", r[i],r[i]);
}
return 0;
}

Feb 27 '06 #16
"me********@aol.com" <me********@aol.com> writes:
could you give me an example of some sample code ?

/*
randtest.c
*/

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int main()
{
float r;
int i;

srand((unsigned int)time((time_t *)NULL));

[snip]

Both casts are unnecessary. As long as the prototypes for srand() and
time() are visible (which they are since you have the proper #include
directives), the conversions will be done implicitly. Just use:

srand(time(NULL));

(You do sometimes need an explicit cast when you're calling a function
with a variable number of parameters, such as printf.)

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 27 '06 #17
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote:
In article <-r********************@comcast.com>,
Charles Krug <cd****@aol.com> wrote:
Know that there is no software method that can produce "random numbers",
only a subset of an arbitrary, albeit ABSOLUTELY predictable sequence of
numbers. For MOST applications, the difference doesn't matter all that
much.

When it DOES matter, it becomes a hardware problem involving things like
mason or gamma ray detectors.

Or Lava Lamps.

Or tea. Or even ATS; it is the only known purpose for which that
substance is useful.

Richard
Feb 27 '06 #18
I have not written any code yet, I'm still trying to get my head around
this problem.
Here are my ideas so far:

My only input from the user will be how many darts they choose to
throw. This will be an int.
Make this a function.
Once I get this value I need to generate coordinate pairs from their
value of darts. Say they choose 500 darts.

What I need then is two variables to hold the coordinate pairs. Say x
and y. So, x will get 500 and y will get 500.
Hmmm? You already have the 500 from the previous function. No need to
save it again (twice) in x or y.
So I will loop 500 times.

Now I need to count the number of 'hits' in the range of sqrt(x^2 +
y^2)<= 1.00

I can use a simple IF statement for this counter.

I think this is the right track

Define the functions used in main() below and, hopefully, you'll have a
working program.
Don't forget to #include other necessary headers; maybe test if the user
requested 0 (zero) throws.

#include <stdio.h>

int main(void) {
int i, inside = 0;
int throws = get_user_number();

for (i = 0; i < throws; ++i) {
double x = get_random_double(0, 1);
double y = get_random_double(0, 1);
if (distance_to_origin(x, y) <= 1) {
++inside;
}
}
printf("Out of %d throws, %d were inside the quarter circle.\n",
throws, inside);
return 0;
}

--
Feb 27 '06 #19

Keith Thompson wrote:
"me********@aol.com" <me********@aol.com> writes:
could you give me an example of some sample code ?

/*
randtest.c
*/

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int main()
{
float r;
int i;

srand((unsigned int)time((time_t *)NULL));

[snip]

Both casts are unnecessary. As long as the prototypes for srand() and
time() are visible (which they are since you have the proper #include
directives), the conversions will be done implicitly. Just use:

srand(time(NULL));

(You do sometimes need an explicit cast when you're calling a function
with a variable number of parameters, such as printf.)

Ok, thanks for pointing that out.

BTW, I copied it from the FAQ (some of us _do_ actually look
at the FAQ first).

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

Feb 27 '06 #20
"me********@aol.com" <me********@aol.com> writes:
Keith Thompson wrote:
"me********@aol.com" <me********@aol.com> writes: [...]
> srand((unsigned int)time((time_t *)NULL));

[snip]

Both casts are unnecessary. As long as the prototypes for srand() and
time() are visible (which they are since you have the proper #include
directives), the conversions will be done implicitly. Just use:

srand(time(NULL));

(You do sometimes need an explicit cast when you're calling a function
with a variable number of parameters, such as printf.)

Ok, thanks for pointing that out.

BTW, I copied it from the FAQ (some of us _do_ actually look
at the FAQ first).

I've just sent a note to Steve Summit.

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 27 '06 #21
Keith Thompson wrote:
"me********@aol.com" <me********@aol.com> writes:
could you give me an example of some sample code ?

/*
randtest.c
*/

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

int main()
{
float r;
int i;

srand((unsigned int)time((time_t *)NULL));

[snip]

Both casts are unnecessary. As long as the prototypes for srand() and
time() are visible (which they are since you have the proper #include
directives), the conversions will be done implicitly. Just use:

srand(time(NULL));

(You do sometimes need an explicit cast when you're calling a function
with a variable number of parameters, such as printf.)

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

Here is the code that I've written thus far
#include <stdio.h>
#include<math.h>
#include<stdlib.h>

int randG();

int main()
{
int numDarts;
int hits=0;
int k;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", numDarts);

for(k=0;k<=numDarts;++k);
{
randG();
}
system("pause");
return 0;
}

randG()

{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

return 1;

else

return 0;

}

Feb 27 '06 #22
Here is the code that I've written thus far
Your code gave me a lot of warnings when I tried to compile it.
I suggest you turn up your compiler warning level and deal with warnings
as if they were errors (and therefore the code doesn't compile)

<OT>
for my compiler (gcc) I do

"gcc -W -Wall -Werror -std=c89 -pedantic source.c"
</OT>
#include <stdio.h>
#include<math.h>
#include<stdlib.h>
#include <time.h> /* for time() */
int randG();

int main()
{
int numDarts;
int hits=0;
int k;

srand(time(NULL));

printf("Enter The number of darts");
fflush(stdout); /* make sure printf output is done before
reaching the scanf() call */
scanf("%d", numDarts);
scanf("%d", &numDarts);
^
for(k=0;k<=numDarts;++k);
{
randG();
}
No matter what the value of numDarts is, randG() will execute exactly
once.
I think you don't want the last semicolon on the for() line.

Also randG() by itself will execute the function, return 0 or 1, and
promptly ignore that 0 or 1. You may want to do something with the
return value of randG() (maybe adding it to `hits').

Are you going to print something to let you know the number of hits your
program achieved?
system("pause");
return 0;
}

randG()
int randG()
{

[snip randG() implementation]

--
Feb 28 '06 #23
Here is the code that I've written thus far
#include <stdio.h>
#include<math.h>
#include<stdlib.h>
Don't you need to include <time.h>?
int randG();

int main()
{
int numDarts;
int hits=0;
int k;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", numDarts);
You mean: scanf("%d", &numDarts);
Maybe you should check for invalid user input later on and handle it
appropriately.
for(k=0;k<=numDarts;++k);
That semicolon is very harmful.
You are throwing numDarts+1 here, that will not make any difference,
remember that later though.
{
randG();
More stuff will be here in the future, maybe:

if (randG()) hits++;
}
system("pause");
That is a pretty system specific.
return 0;
}

randG()

Why not: int randG()?
{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.
return 1;

else

return 0;

}

Feb 28 '06 #24

stathis gotsis wrote:
Here is the code that I've written thus far
#include <stdio.h>
#include<math.h>
#include<stdlib.h>
Don't you need to include <time.h>?
int randG();

int main()
{
int numDarts;
int hits=0;
int k;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", numDarts);

You mean: scanf("%d", &numDarts);
Maybe you should check for invalid user input later on and handle it
appropriately.
for(k=0;k<=numDarts;++k);

That semicolon is very harmful.
You are throwing numDarts+1 here, that will not make any difference,
remember that later though.
{
randG();

More stuff will be here in the future, maybe:

if (randG()) hits++;
}
system("pause");

That is a pretty system specific.
return 0;
}

randG()

Why not: int randG()?
{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.

How?
return 1;

else

return 0;

}

Feb 28 '06 #25
On 2006-02-27, Richard Bos <rl*@hoekstra-uitgeverij.nl> wrote:
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote:
In article <-r********************@comcast.com>,
Charles Krug <cd****@aol.com> wrote:
>Know that there is no software method that can produce "random numbers",
>only a subset of an arbitrary, albeit ABSOLUTELY predictable sequence of
>numbers. For MOST applications, the difference doesn't matter all that
>much.

>When it DOES matter, it becomes a hardware problem involving things like
>mason or gamma ray detectors.

Or Lava Lamps.

Or tea. Or even ATS; it is the only known purpose for which that
substance is useful.

Or a device that extracts the whole of the Universe from a piece of
fairycake and then tells you "You are HERE"...

Feb 28 '06 #26
stathis gotsis wrote:
Here is the code that I've written thus far
#include <stdio.h>
#include<math.h>
#include<stdlib.h>

Don't you need to include <time.h>?
int randG();

int main()
{
int numDarts;
int hits=0;
int k;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", numDarts);

You mean: scanf("%d", &numDarts);
Maybe you should check for invalid user input later on and handle it
appropriately.
for(k=0;k<=numDarts;++k);

That semicolon is very harmful.
You are throwing numDarts+1 here, that will not make any difference,
remember that later though.
{
randG();

More stuff will be here in the future, maybe:

if (randG()) hits++;
}
system("pause");

That is a pretty system specific.
return 0;
}

randG()

Why not: int randG()?
{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.
return 1;

else

return 0;

}
Here is my updated code. I'm not trying to get any quck answers, I really want to learn this stuff. There are some things that I just don't have enough experiece with, and this is one of them

#include <stdio.h>
#include<math.h>
#include<stdlib.h>
#include<time.h>

int randG();

int main()
{
int numDarts;
int hits=0;
int k;
double pi;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", &numDarts);

for(k=0;k<=numDarts;++k);
{
hits = randG();
printf("%d\n",hits);
}

system("pause");
return 0;
}

randG()

{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

return 1;

else

return 0;

}

Feb 28 '06 #27
"me********@aol.com" <me********@aol.com> wrote:
stathis gotsis wrote:
{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.

How?

If a non-negative real number is smaller than or equal to 1.0, how large
must the square of that number be?

Richard
Feb 28 '06 #28
Here is my updated code. I'm not trying to get any quck answers, I really want to learn this stuff. There are some things that I just don't have
enough experiece with, and this is one of them

#include <stdio.h>
#include<math.h>
#include<stdlib.h>
#include<time.h>

int randG();

int main()
{
int numDarts;
int hits=0;
int k;
double pi;

srand(time(NULL));

printf("Enter The number of darts");
scanf("%d", &numDarts);

for(k=0;k<=numDarts;++k);
{
hits = randG();
If you do it this way, hits will be set to 0 or 1. You need to count the
number of hits, maybe this way:

if (randG()) hits++;
printf("%d\n",hits);
That prints 0 or 1. It would be a nicer test if you printed the number of
hits after the above loop has ended.
}

system("pause");
return 0;
}

randG()

{
double x;
double y;

x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;

if((sqrt(x*x + y*y)<=1.0))
For a real number a>=0, a<=b <=> a^2<=b^2. You can use that to omit the
sqrt().
return 1;

else

return 0;

}

Maybe you should consider the comments made in previous posts as well.
Feb 28 '06 #29

Richard Bos wrote:
"me********@aol.com" <me********@aol.com> wrote:
stathis gotsis wrote:
> {
> double x;
> double y;
>
> x = (double)rand()/RAND_MAX;
> y = (double)rand()/RAND_MAX;
>
> if((sqrt(x*x + y*y)<=1.0))
>

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.
How?

If a non-negative real number is smaller than or equal to 1.0, how large
must the square of that number be?

Oh, I get it.
x = 0.9
If the x coordinate is less than 1, its square is less than 1.
y = 0.9
And if the y coordinate is less than 1, its square is less than 1.

So if the squares of both are less than 1, then the distance
from the origin is less than 1.
print math.sqrt(x**2 + y**2)

1.27279220614

Uh, what went wrong?

Richard

Feb 28 '06 #30
On 2006-02-28, me********@aol.com <me********@aol.com> wrote:

Richard Bos wrote:
"me********@aol.com" <me********@aol.com> wrote:
> stathis gotsis wrote:
> > "RadiationX" <he*********@gmail.com> wrote in message
> > > {
> > > double x;
> > > double y;
> > >
> > > x = (double)rand()/RAND_MAX;
> > > y = (double)rand()/RAND_MAX;
> > >
> > > if((sqrt(x*x + y*y)<=1.0))
> > >
> >
> > That sqrt() is not absolutely needed there, if you choose to discard it you
> > can get rid of <math.h> too.
>
> How?
If a non-negative real number is smaller than or equal to 1.0, how large
must the square of that number be?

Oh, I get it.
x = 0.9
If the x coordinate is less than 1, its square is less than 1.

True.
y = 0.9
And if the y coordinate is less than 1, its square is less than 1.

True.
So if the squares of both are less than 1, then the distance
from the origin is less than 1.
False.
print math.sqrt(x**2 + y**2)

1.27279220614

Uh, what went wrong?

The distance from the origin is 1.27. Hint: the distance from the origin
being less than one is determined by being inside the unit _circle_, not
the unit square.
Feb 28 '06 #31

Jordan Abel wrote:
On 2006-02-28, me********@aol.com <me********@aol.com> wrote:

Richard Bos wrote:
"me********@aol.com" <me********@aol.com> wrote:

> stathis gotsis wrote:
> > "RadiationX" <he*********@gmail.com> wrote in message
> > > {
> > > double x;
> > > double y;
> > >
> > > x = (double)rand()/RAND_MAX;
> > > y = (double)rand()/RAND_MAX;
> > >
> > > if((sqrt(x*x + y*y)<=1.0))
> > >
> >
> > That sqrt() is not absolutely needed there, if you choose to discard it you
> > can get rid of <math.h> too.
>
> How?

If a non-negative real number is smaller than or equal to 1.0, how large
must the square of that number be?

Oh, I get it.
> x = 0.9

If the x coordinate is less than 1, its square is less than 1.

True.
> y = 0.9

And if the y coordinate is less than 1, its square is less than 1.

True.
So if the squares of both are less than 1, then the distance
from the origin is less than 1.

False.
> print math.sqrt(x**2 + y**2)

1.27279220614

Uh, what went wrong?

The distance from the origin is 1.27. Hint: the distance from the origin
being less than one is determined by being inside the unit _circle_, not
the unit square.

Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt. The stuff about
how big the square of a number <1 must be doesn't cut it.

Feb 28 '06 #32
me********@aol.com <me********@aol.com> wrote:
> Richard Bos wrote:
>> > > > if((sqrt(x*x + y*y)<=1.0)) >> > > That sqrt() is not absolutely needed there, if you choose to discard it you
>> > > can get rid of <math.h> too.
Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt. The stuff about
how big the square of a number <1 must be doesn't cut it.

He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".

If sqrt(x*x+y*y) < c then by squaring both sides,
sqrt(x*x+y*y)*sqrt(x*x+y*y) < c*c so
x*x+y*y < c*c

but when c is 1.0 then c*c is also 1.0 so the test in the code
in question could be:

if ((x*x + y*y) <= 1.0)

Thus the sqrt() was indeed not absolutely needed there and could be
--
Programming is what happens while you're busy making other plans.
Feb 28 '06 #33
me********@aol.com wrote:

stathis gotsis wrote:
>
> if((sqrt(x*x + y*y)<=1.0))

That sqrt() is not absolutely needed there, if you choose to discard it you
can get rid of <math.h> too.

How?

sqrt(FOOBAR) <= 1.0

but 1.0 == sqrt(1.0), so that can written that as

sqrt(FOOBAR) <= sqrt(1.0)

and, as all the numbers are positive, the "sqrt()" can be safely removed

FOOBAR <= 1.0

to get an equivalent condition.

--
Feb 28 '06 #34
On 2006-02-28, me********@aol.com <me********@aol.com> wrote:

Jordan Abel wrote:
On 2006-02-28, me********@aol.com <me********@aol.com> wrote:
>
> Richard Bos wrote:
>> "me********@aol.com" <me********@aol.com> wrote:
>>
>> > stathis gotsis wrote:
>> > > "RadiationX" <he*********@gmail.com> wrote in message
>> > > > {
>> > > > double x;
>> > > > double y;
>> > > >
>> > > > x = (double)rand()/RAND_MAX;
>> > > > y = (double)rand()/RAND_MAX;
>> > > >
>> > > > if((sqrt(x*x + y*y)<=1.0))
>> > > >
>> > >
>> > > That sqrt() is not absolutely needed there, if you choose to discard it you
>> > > can get rid of <math.h> too.
>> >
>> > How?
>>
>> If a non-negative real number is smaller than or equal to 1.0, how large
>> must the square of that number be?
>
> Oh, I get it.
>
>>>> x = 0.9
>
> If the x coordinate is less than 1, its square is less than 1.

True.
>>>> y = 0.9
>
> And if the y coordinate is less than 1, its square is less than 1.

True.
> So if the squares of both are less than 1, then the distance
> from the origin is less than 1.

False.
>
>>>> print math.sqrt(x**2 + y**2)
> 1.27279220614
>
> Uh, what went wrong?

The distance from the origin is 1.27. Hint: the distance from the origin
being less than one is determined by being inside the unit _circle_, not
the unit square.

Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt. The stuff about
how big the square of a number <1 must be doesn't cut it.

But you're not looking at the square of X and the square of Y - you're
looking at the square of the distance, which is the sum of those two
squares.
Feb 28 '06 #35

Walter Roberson wrote:
me********@aol.com <me********@aol.com> wrote:
> Richard Bos wrote:
>> > > > if((sqrt(x*x + y*y)<=1.0))> > > That sqrt() is not absolutely needed there, if you choose to discard it you
>> > > can get rid of <math.h> too.
Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt. The stuff about
how big the square of a number <1 must be doesn't cut it.

He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".

If sqrt(x*x+y*y) < c then by squaring both sides,
sqrt(x*x+y*y)*sqrt(x*x+y*y) < c*c so
x*x+y*y < c*c

but when c is 1.0 then c*c is also 1.0 so the test in the code
in question could be:

if ((x*x + y*y) <= 1.0)

Thus the sqrt() was indeed not absolutely needed there and could be

Ok, I see it.

Another fine example of the kind of thinking that makes space shuttles
explode.
--
Programming is what happens while you're busy making other plans.

Feb 28 '06 #36
"me********@aol.com" <me********@aol.com> writes:
Walter Roberson wrote:

[...]
He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".

If sqrt(x*x+y*y) < c then by squaring both sides,
sqrt(x*x+y*y)*sqrt(x*x+y*y) < c*c so
x*x+y*y < c*c

but when c is 1.0 then c*c is also 1.0 so the test in the code
in question could be:

if ((x*x + y*y) <= 1.0)

Thus the sqrt() was indeed not absolutely needed there and could be

Ok, I see it.

Another fine example of the kind of thinking that makes space shuttles
explode.

Huh???

The test
if (x*x + y*y <= 1.0)
is mathematically and practically equivalent to
if (sqrt(x*x + y*y) <= 1.0)
and likely to be substantially more efficient. We don't need to
compute the distance; we only care whether the distance is less than
or equal to 1.0, and we can easily determine that from the square of
the distance, which is easier to compute.

optimization? If so, what?

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.
Feb 28 '06 #37

Keith Thompson wrote:
"me********@aol.com" <me********@aol.com> writes:
Walter Roberson wrote: [...]
He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".

If sqrt(x*x+y*y) < c then by squaring both sides,
sqrt(x*x+y*y)*sqrt(x*x+y*y) < c*c so
x*x+y*y < c*c

but when c is 1.0 then c*c is also 1.0 so the test in the code
in question could be:

if ((x*x + y*y) <= 1.0)

Thus the sqrt() was indeed not absolutely needed there and could be

Ok, I see it.

Another fine example of the kind of thinking that makes space shuttles
explode.

Huh???

The test
if (x*x + y*y <= 1.0)
is mathematically and practically equivalent to
if (sqrt(x*x + y*y) <= 1.0)
and likely to be substantially more efficient. We don't need to
compute the distance; we only care whether the distance is less than
or equal to 1.0, and we can easily determine that from the square of
the distance, which is easier to compute.

optimization? If so, what?

Never mind. I've re-thought it.

--
Keith Thompson (The_Other_Keith) ks***@mib.org <http://www.ghoti.net/~kst>
San Diego Supercomputer Center <*> <http://users.sdsc.edu/~kst>
We must do something. This is something. Therefore, we must do this.

Mar 1 '06 #38
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote:
me********@aol.com <me********@aol.com> wrote:
> Richard Bos wrote:
>> > > > if((sqrt(x*x + y*y)<=1.0))> > > That sqrt() is not absolutely needed there, if you choose to discard it you
>> > > can get rid of <math.h> too.
Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt.

You're not determining the exact distance, you're only trying to
discover whether it's smaller than a certain number. And since the
square root function is strictly ascending...
The stuff about how big the square of a number <1 must be doesn't cut it.

Do the actual math on the actual functions, not on an incoherent jumble
of words.
He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".

Actually, I didn't. stathis gotsis wrote that. All I did was agree, and
point out why.

Richard
Mar 2 '06 #39

Richard Bos wrote:
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote:
me********@aol.com <me********@aol.com> wrote:
> > Richard Bos wrote:
> >> > > > if((sqrt(x*x + y*y)<=1.0))
> >> > > That sqrt() is not absolutely needed there, if you choose to discard it you
> >> > > can get rid of <math.h> too.

Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt.
You're not determining the exact distance, you're only trying to
discover whether it's smaller than a certain number.

Yeah, it's already been cleared up.
And since the
square root function is strictly ascending...
The stuff about how big the square of a number <1 must be doesn't cut it.

Do the actual math on the actual functions, not on an incoherent jumble
of words.

I DID do the actual math. But because you were not clear,
I went down the wrong path and got nonsensical results.
And since I believed that I understood what I think you said,
it did not occur to me that what I heard was not what you
meant.
He didn't say that you could determine distances without using sqrt().
He said "that sqrt() is not absolutely needed there".
Actually, I didn't. stathis gotsis wrote that. All I did was agree, and
point out why.

The issue is settled as far as I'm concerned.

Richard

Mar 2 '06 #40
"Richard Bos" <rl*@hoekstra-uitgeverij.nl> wrote in message
news:44****************@news.xs4all.nl...
ro******@ibd.nrc-cnrc.gc.ca (Walter Roberson) wrote:
me********@aol.com <me********@aol.com> wrote:
> > Richard Bos wrote:
> >> > > > if((sqrt(x*x + y*y)<=1.0))

> >> > > That sqrt() is not absolutely needed there, if you choose to discard it you> >> > > can get rid of <math.h> too.

Yeah, _I_ know that. I'm waiting to hear Richards Bos' explanation
of how to determine distance without using sqrt.

You're not determining the exact distance, you're only trying to
discover whether it's smaller than a certain number. And since the
square root function is strictly ascending...

Or that since both root and 1 are non-negative numbers... But this way we
implicitly use the fact that x^2 is strictly ascending for x>=0.
Mar 3 '06 #41

This thread has been closed and replies have been disabled. Please start a new discussion.

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