Why is the random number distribution in PHP extremely uneven?

When PHP generates a random number, if the range limit is too large, the generated random number is very large. Why? Test code: {code ...} result: {code ...} I have run this code for dozens of times. The result is the same. The random numbers generated are 10 ^ 17 or 10 ^ 18... when PHP generates a random number, if the range limit is too large, the generated random number is very large. Why?

Test code:

Result:

4821547998934728704809007189706617651215498198060923617286955922199861526528579259532523130060883225384794309263368261190596798971904359567904319576473657115882262343188483693958636641452032

I have run this code for dozens of times, and the results are the same. The random numbers generated are large numbers of the magnitude of 10 ^ 17 or 10 ^ 18 (on 64-bit systems, PHP_INT_MAX is 9223372036854775807, 9*10 ^ 18)

This applies to both rand and mt_rand. Before mt_rand () generates a random number, mt_srand () is executed. The official PHP manual says that since PHP 4.2, you do not need to manually execute t_srand.

As we all know, random numbers generated by computers are not real random numbers. PHP also officially said that they are pseudo-random numbers (pseudo-random). But why is it so powerful to PHP_INT_MAX?

Question added: If mt_rand () is directly called without parameters, the random number distribution is uneven, small (several hundred thousand) and (between 2 ^ 32 and 2 ^ 64) are not:

126193157812101522797775756971988855481179641824955196642306582590654301368501653301469521205

In addition, the random array I want is as follows:

Array( [31] => 301487779840 [57] => 10457165676412928 [32] => 2516742 [16] => 786840 [39] => 2142457578485972992 [81] => 16 [27] => 5472146880987136 [24] => 4979452 [6] => 24912932785618944 [48] => 930 [82] => 9223372036854775807)

Very large, very small, all have. I have been able to generate a random number with a slightly even distribution. I just want to ask why PHP's built-in random number function cannot do this.

Appendix: My improved mt_rand (0, PHP_INT_MAX)

--- Digress ---
@ Sha MIAO:

Therefore, using such a few broken data to say "uneven" is a great contempt for mathematics. I very much hope that the questioner can respect science and come up with arguments that can be interpreted according to statistics next time, rather than simply telling things in a superficial sense, so as to avoid common-sense jokes.

When talking about technical issues, everyone has an unfamiliar field. Even if they are skilled, they may be confused at the moment. I have been using PHP for many years and have answered many questions on this site. When I encountered this problem, it seems that it is not in line with my expectations. I tried to improve and think about it, and I couldn't figure it out. I just came to consult.

At the same time, I also made dozens of verifications myself, used Google and StackOverFlow, and found a way to get a more balanced random number of digits I wanted, it means that I have also made some efforts. Instead of posting answers to super-low-level questions, I have not come up with immature conclusions. [PHP engine is not doing well enough ].

Think of a story:

-What can I read with three dots? -I don't know. -Read lai again! -In this case, recognize the word half-what should I add to the three pieces of water? -Read qu! -Read fa, Oh, kiss-(thigh shot) Oh! Yes! Read fa! I know !!!

I think most people have had such experiences, maybe technically or in life.

Therefore, thank you for helping me answer your questions. Please do not be angry with me because I am not a high level and I am very impetuous at ordinary times, we have a rough understanding of probability on this issue. However, this posting is still very positive. It is too exaggerated to say "Break the problem" or "despise". For me, this is a good problem that has plagued me for a few days, I have no subjective willingness or skill to despise the mathematics and PHP engines.

Reply content:

When PHP generates a random number, if the range limit is too large, the generated random number is very large. Why?

Test code:

Result:

4821547998934728704809007189706617651215498198060923617286955922199861526528579259532523130060883225384794309263368261190596798971904359567904319576473657115882262343188483693958636641452032

I have run this code for dozens of times, and the results are the same. The random numbers generated are large numbers of the magnitude of 10 ^ 17 or 10 ^ 18 (on 64-bit systems, PHP_INT_MAX is 9223372036854775807, 9*10 ^ 18)

This applies to both rand and mt_rand. Before mt_rand () generates a random number, mt_srand () is executed. The official PHP manual says that since PHP 4.2, you do not need to manually execute t_srand.

As we all know, random numbers generated by computers are not real random numbers. PHP also officially said that they are pseudo-random numbers (pseudo-random). But why is it so powerful to PHP_INT_MAX?

Question added: If mt_rand () is directly called without parameters, the random number distribution is uneven, small (several hundred thousand) and (between 2 ^ 32 and 2 ^ 64) are not:

126193157812101522797775756971988855481179641824955196642306582590654301368501653301469521205

In addition, the random array I want is as follows:

Array( [31] => 301487779840 [57] => 10457165676412928 [32] => 2516742 [16] => 786840 [39] => 2142457578485972992 [81] => 16 [27] => 5472146880987136 [24] => 4979452 [6] => 24912932785618944 [48] => 930 [82] => 9223372036854775807)

Very large, very small, all have. I have been able to generate a random number with a slightly even distribution. I just want to ask why PHP's built-in random number function cannot do this.

Appendix: My improved mt_rand (0, PHP_INT_MAX)

--- Digress ---
@ Sha MIAO:

Therefore, using such a few broken data to say "uneven" is a great contempt for mathematics. I very much hope that the questioner can respect science and come up with arguments that can be interpreted according to statistics next time, rather than simply telling things in a superficial sense, so as to avoid common-sense jokes.

When talking about technical issues, everyone has an unfamiliar field. Even if they are skilled, they may be confused at the moment. I have been using PHP for many years and have answered many questions on this site. When I encountered this problem, it seems that it is not in line with my expectations. I tried to improve and think about it, and I couldn't figure it out. I just came to consult.

At the same time, I also made dozens of verifications myself, used Google and StackOverFlow, and found a way to get a more balanced random number of digits I wanted, it means that I have also made some efforts. Instead of posting answers to super-low-level questions, I have not come up with immature conclusions. [PHP engine is not doing well enough ].

Think of a story:

-What can I read with three dots? -I don't know. -Read lai again! -In this case, recognize the word half-what should I add to the three pieces of water? -Read qu! -Read fa, Oh, kiss-(thigh shot) Oh! Yes! Read fa! I know !!!

I think most people have had such experiences, maybe technically or in life.

Therefore, thank you for helping me answer your questions. Please do not be angry with me because I am not a high level and I am very impetuous at ordinary times, we have a rough understanding of probability on this issue. However, this posting is still very positive. It is too exaggerated to say "Break the problem" or "despise". For me, this is a good problem that has plagued me for a few days, I have no subjective willingness or skill to despise the mathematics and PHP engines.

Your range is a 19-digit integer (probably, don't go into it ). What you see is "very big", but it is "very long" and it is only 19 people.

But among all the non-negative integers of <10 ^ 19, the total number of 19 digits is(10^19-10^18) / 10^19 = 90%.

That is to say, if you want to follow the "different lengths" Distribution you expect, you can only achieve this if the probability is significantly skewed to the 10% side. This is ridiculous.

Statistics: statistics are called statistics only when the quantity is very large. To test the uniformity of the random function distribution, we should use the data size above 10 ^ 7 in experience to obtain that the error is acceptable within 5%.

Therefore, using such a few broken data to say "uneven" is a great contempt for mathematics. I very much hope that the questioner can respect science and come up with arguments that can be interpreted according to statistics next time, rather than simply telling things in a superficial sense, so as to avoid common-sense jokes.

First, your sample is indeed too small. Second, the random number in the program does seem to be a pseudo-random number. the random number is finally calculated by the algorithm, and the random number tends infinitely to be a pseudo-random number.