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#1
April 16th, 2003, 11:21 PM
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[c] bigger numbers?

i'm messing round with a poisson random distribution formula and it loops through using the loop number in the equation. one part of it is a factorial like in mathematics 4! which means 1 X 2 X 3 X 4 = 24. by the time i've got to the 13th loop the result (it's the loop number that gets factorialised) exceeds an unsigned long. how can i continue to loop while getting and being able to use the correct factorial result. how can i get bigger numbers basically? possible?

#2
April 16th, 2003, 11:52 PM
 MJEggertson
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Factorials get really big, really fast. You probably want to avoid integers all together and use floating point types, like a double.

#3
April 17th, 2003, 12:18 AM
 Scorpions4ever
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Try using the GMP library http://www.swox.com/gmp/

#4
April 18th, 2003, 11:18 AM
 Jason Doucette
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double has a max range of 1.7E+308, which is enough to compute 170! = 7.2574E+306, so I would use this. If your compiler supports long double, you can compute much larger numbers.

#5
April 18th, 2003, 02:03 PM
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yup, it's getting to the 169th loop now, then it goes to infinity. the factorial number is 307 digits long at that point! that's with a double. my compiler isn't having long double. double's long enough. never realised there was so much difference between double and int (i knew there was some, but not 280+ digits worth)

so there's no need to use a library to extend it. thanks.

does anyone know anything about poisson curves? the results from it are lop sided.
Code:
```m = 10  (average number of random occurrences per interval)
Probability of occurrences in intervals :
------------------------------------------------------------------
0: 0.000045   0.00%    < probability of no occurance
1: 0.000454   0.05%
2: 0.002270   0.23%
3: 0.007567   0.76%
4: 0.018917   1.89%
5: 0.037833   3.78%
6: 0.063055   6.31%
7: 0.090079   9.01%
8: 0.112599   11.26%
9: 0.125110   12.51%
10: 0.125110   12.51%    <<<<
11: 0.113736   11.37%
12: 0.094780   9.48%
13: 0.072908   7.29%
14: 0.052077   5.21%
15: 0.034718   3.47%
16: 0.021699   2.17%
17: 0.012764   1.28%
18: 0.007091   0.71%
19: 0.003732   0.37%
20: 0.001866   0.19%
21: 0.000889   0.09%
22: 0.000404   0.04%
23: 0.000176   0.02%
24: 0.000073   0.01%
25: 0.000029   0.00%```

you'd expect, seeing as the input number is 10, that 10 would be at the height of the curve and it'd be fairly symetrical either side of 10. but it isn't. should it be like that, or is it my code do you think? (i'm guessing it's my code)

#6
April 18th, 2003, 02:16 PM
 Jason Doucette
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Quote:
 Originally posted by balance never realised there was so much difference between double and int (i knew there was some, but not 280+ digits worth)
A double takes 8 bytes of memory. A long int also takes 8 bytes of memory. 8 bytes of memory can contain exactly 2^(8*8) = 2^64 = 18,446,744,073,709,551,616 different possibilities. Therefore, double does not have 280+ digits worth of more information. In fact, since several combinations of 64 bits in a double mean the same floating point number, a long int can actually store more different combinations of numbers than a double.

The true difference in the way they use the 64 bits to store a number is the fact that a double has bits reserved for storing an exponent. So, it can store a number like 1.234E+89. However, since it can only store about 15 or 16 decimal digits of accuracy, you can try to store 1.2345678901234567890E+89, but only 1.23456789012345E+89 is actually stored. Here's a detailed article explaining exactly how they are stored.

#7
April 18th, 2003, 02:24 PM
 MJEggertson
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I don't know too much about Poisson statistics, beyone how it relates to sampling noise at low numbers of count events. One of the main point of Poisson statistics is that the curve is not symmetric as you get to lower number of occurrences. It only becomes symmetric as m gets very large, to the point where the error introduced in the sampling of m becomes irrelevant (when m >> sqrt(m)).

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