My output is 20 random 1's, not between 10 and 1, can anyone explain why this is happening?
#include <iostream>
#include <ctime>
#include <cstdlib>
using namespace std;
int main()
{
srand((unsigned)time(0));
int random_integer;
int lowest=1, highest=10;
int range=(highest-lowest)+1;
for(int index=0; index<20; index++){
random_integer = lowest+int(range*rand()/(RAND_MAX + 1.0));
cout << random_integer << endl;
}
}
output:
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Because, on your platform, RAND_MAX == INT_MAX.
The expression range*rand() can never take on a value greater than INT_MAX. If the mathematical expression is greater than INT_MAX, then integer overflow reduces it to a number between INT_MIN and INT_MAX. Dividing that by RAND_MAX will always yield zero.
Try this expression:
random_integer = lowest+int(range*(rand()/(RAND_MAX + 1.0)))
It's much easier to use the <random> library correctly than rand (assuming you're familiar enough with C++ that the syntax doesn't throw you).
#include <random>
#include <iostream>
int main() {
std::random_device r;
std::seed_seq seed{r(), r(), r(), r(), r(), r(), r(), r()};
std::mt19937 eng(seed);
std::uniform_int_distribution<> dist(1, 10);
for(int i = 0; i < 20; ++i)
std::cout << dist(eng) << " ";
}
random_integer = (rand() % 10) + 1
That should give you a pseudo-random number between 1 & 10.
A somewhat late answer, but it should provide some additional
information if the quality of the generation is important. (Not all
applications need this—a slight bias is often not a problem.)
First, of course, the problem in the original code is the fact that
range * rand() has precedence over the following division, and is done
using integer arithmetic. Depending on RAND_MAX, this can easily
result in overflow, with implementation defined results; on all
implementations that I know, if it does result in overflow (because
RAND_MAX > INT_MAX / range, the actual results will almost certainly
be smaller than RAND_MAX + 1.0, and the division will result in a
value less than 1.0. There are several ways of avoiding this: the
simplest and most reliable is simply rand() % range + lowest.
Note that this supposes that rand() is of reasonable quality. Many
earlier implementations weren't, and I've seen at least one where
rand() % 6 + 1 to simulate a dice throw alternated odd and even. The
only correct solution here is to get a better implementation of
rand(); it has lead to people trying alternative solutions, such as
(range * (rand() / (RAND_MAX + 1.0))) + lowest. This masks the
problem, but it won't change a bad generator into a good one.
A second issue, if the quality of the generation is important, is
that when generating random integers, you're discretizing: if you're
simulating the throw of a die, for example, you have six possible
values, which you want to occur with equal probability. The random
generator will generate RAND_MAX + 1 different values, with equal
probability. If RAND_MAX + 1 is not a multiple of 6, there's no
possible way of distributing the values equaly amont the 6 desired
values. Imagine the simple case where RAND_MAX + 1 is 10. Using the
% method above, the values 1–4 are twice as likely as the the
values 5 and 6. If you use the more complicated formula 1 + int(6 *
(rand() / (RAND_MAX + 1.0))) (in the case where RAND_MAX + 1 == 10,
it turns out that 3 and 6 are only half as likely as the other values.
Mathematically, there's simply no way of distributing 10 different
values into 6 slots with an equal number of elements in each slot.
Of course, RAND_MAX will always be considerably larger than 10, and
the bias introduced will be considerably less; if the range is
significantly less than RAND_MAX, it could be acceptable. If it's
not, however, the usual procedure is something like:
int limit = (RAND_MAX + 1LL) - (RAND_MAX + 1LL) % range;
// 1LL will prevent overflow on most machines.
int result = rand();
while ( result >= limit ) {
result = rand();
}
return result % range + lowest;
(There are several ways of determining the values to throw out. This
happens to be the one I use, but I remember Andy Koenig using something
completely different—but which resulted in the same values being
thrown out in the end.)
Note that most of the time, you won't enter the loop; the worst case is
when range is (RAND_MAX + 1) / 2 + 1, in which case, you'll still
average just under one time through the loop.
Note that these comments only apply when you need a fixed number of
discrete results. For the (other) common case of generating a random
floating point number in the range of [0,1), rand() / (RAND_MAX +
1.0) is about as good as you're going to get.
Visual studio 2008 has no trouble with that program at all and happily generates a swathe of random numbers.
What I would be careful of is the /(RAND_MAX +1.0) as this will likely fall foul of integer problems and end up with a big fat zero.
Cast to double before dividing and then cast back to int afterwards
I suggest you replace rand()/(RAND_MAX + 1.0) with range*double(rand())/(RAND_MAX + 1.0)). Since my solution seems to give headaches ...
possible combinations of arguments:
range*rand() is an integer and overflows.
double(range*rand()) overflows before you convert it to double.
range*double(rand()) is not overflowing and yields expected results.
My original post had two braces but they did not change anything (results are the same).
(rand() % highest) + lowest + 1
Probably "10 * rand()" is smaller than "RAND_MAX + 1.0", so the value of your calculation is 0.
You are generating a random number (ie (range*rand()/(RAND_MAX + 1.0))) whose value is between -1 and 1 (]-1,1[) and then casting it to an integer. The integer value of such number is always 0 so you end up with the lower + 0
EDIT: added the formula to make my answer clearer
What about using a condition to check if the last number is the same as the current one? If the condition is met then generate another random number. This solution works but it will take more time though.
It is one of the simplest logics, got it from a blog. in this logic you can limit the random numbers with that given modulus(%) operator inside the for loop, its just a copy and paste from that blog, but any way check it out:
// random numbers generation in C++ using builtin functions
#include <iostream>
using namespace std;
#include <iomanip>
using std::setw;
#include <cstdlib> // contains function prototype for rand
int main()
{
// loop 20 times
for ( int counter = 1; counter <= 20; counter++ ) {
// pick random number from 1 to 6 and output it
cout << setw( 10 ) << ( 1 + rand() % 6 );
// if counter divisible by 5, begin new line of output
if ( counter % 5 == 0 )
cout << endl;
}
return 0; // indicates successful termination
} // end main
- See more at: http://www.programmingtunes.com/generation-of-random-numbers-c/#sthash.BTZoT5ot.dpuf
Related
I'm trying to make it so that rand_draw holds a random positive number between 0-8. But this code keeps giving negative numbers on some iterations. What's happening?
srand(time(0));
int draw_count = 8;
int rand_draw = (2 * rand()) % draw_count;
cout << rand_draw << endl;
According to cppreference, rand():
Returns a pseudo-random integral value between 0 and RAND_MAX (0 and RAND_MAX included).
The value of RAND_MAX is implementation defined, but may very well be the maximum value that can be represented in an int. By doubling the value you get from rand(), the result may overflow into a negative number. This is actually undefined behavior.
I see no reason to double the return value of rand(). You could correct this quite simply:
int rand_draw = rand() % (draw_count + 1);
This will give you random values between 0 and 8, as you specified.
But in modern C++, using the uniform_int_distribution from the C++ Standard Library is a much better way to go. Here's the example from the linked page, modified to show the range you specified:
#include <random>
#include <iostream>
int main()
{
std::random_device rd; //Will be used to obtain a seed for the random number engine
std::mt19937 gen(rd()); //Standard mersenne_twister_engine seeded with rd()
std::uniform_int_distribution<> distrib(0, 8);
for (int n=0; n<10; ++n)
//Use `distrib` to transform the random unsigned int generated by gen into an int in [0, 8]
std::cout << distrib(gen) << ' ';
std::cout << '\n';
}
rand() function will generates a random number in this range [0, RAND_MAX).
RAND_MAX is a large number.
More details are discussed in this link
When you use 2*rand(), basically you are shifting the generated number 1 bit to the left. If the generated number is large enough that its second bit from the left side is 1, then after shifting to the left you are generating a negative number.
Here is an example:
Let's assume the generated number in hexadecimal is 0x70000011.
The four most significant bits of this number are 0111, after shifting 1 bit to left, you can see the sign bit is changing.
then you try to use the % operation which results in negative number.
rand() % draw_count -> generates number [0, draw_count)
(rand() % draw_count) + draw_count -> generates number [draw_count, 2* draw_count)
rand() % (2draw_count) -> generates number [0, 2 draw_count)
I figured out a solution, given that I can only use the rand() function. I simply added an if-statement afterwards to check if it's even, and if so keep the variable set to rand_draw, and if not, increment by 1.
int rand_draw = rand() % draw_count;
if (rand_draw % 2 == 0)
{
rand_draw = rand_draw;
}
else
{
rand_draw += 1;
}
In this StackOverflow question:
Generating random integer from a range
the accepted answer suggests the following formula for generating a random integer in between given min and max, with min and max being included into the range:
output = min + (rand() % (int)(max - min + 1))
But it also says that
This is still slightly biased towards lower numbers ... It's also
possible to extend it so that it removes the bias.
But it doesn't explain why it's biased towards lower numbers or how to remove the bias. So, the question is: is this the most optimal approach to generation of a random integer within a (signed) range while not relying on anything fancy, just rand() function, and in case if it is optimal, how to remove the bias?
EDIT:
I've just tested the while-loop algorithm suggested by #Joey against floating-point extrapolation:
static const double s_invRandMax = 1.0/((double)RAND_MAX + 1.0);
return min + (int)(((double)(max + 1 - min))*rand()*s_invRandMax);
to see how much uniformly "balls" are "falling" into and are being distributed among a number of "buckets", one test for the floating-point extrapolation and another for the while-loop algorithm. But results turned out to be varying depending on the number of "balls" (and "buckets") so I couldn't easily pick a winner. The working code can be found at this Ideone page. For example, with 10 buckets and 100 balls the maximum deviation from the ideal probability among buckets is less for the floating-point extrapolation than for the while-loop algorithm (0.04 and 0.05 respectively) but with 1000 balls, the maximum deviation of the while-loop algorithm is lesser (0.024 and 0.011), and with 10000 balls, the floating-point extrapolation is again doing better (0.0034 and 0.0053), and so on without much of consistency. Thinking of the possibility that none of the algorithms consistently produces uniform distribution better than that of the other algorithm, makes me lean towards the floating-point extrapolation since it appears to perform faster than the while-loop algorithm. So is it fine to choose the floating-point extrapolation algorithm or my testings/conclusions are not completely correct?
The problem is that you're doing a modulo operation. This would be no problem if RAND_MAX would be evenly divisible by your modulus, but usually that is not the case. As a very contrived example, assume RAND_MAX to be 11 and your modulus to be 3. You'll get the following possible random numbers and the following resulting remainders:
0 1 2 3 4 5 6 7 8 9 10
0 1 2 0 1 2 0 1 2 0 1
As you can see, 0 and 1 are slightly more probable than 2.
One option to solve this is rejection sampling: By disallowing the numbers 9 and 10 above you can cause the resulting distribution to be uniform again. The tricky part is figuring out how to do so efficiently. A very nice example (one that took me two days to understand why it works) can be found in Java's java.util.Random.nextInt(int) method.
The reason why Java's algorithm is a little tricky is that they avoid slow operations like multiplication and division for the check. If you don't care too much you can also do it the naïve way:
int n = (int)(max - min + 1);
int remainder = RAND_MAX % n;
int x, output;
do {
x = rand();
output = x % n;
} while (x >= RAND_MAX - remainder);
return min + output;
EDIT: Corrected a fencepost error in above code, now it works as it should. I also created a little sample program (C#; taking a uniform PRNG for numbers between 0 and 15 and constructing a PRNG for numbers between 0 and 6 from it via various ways):
using System;
class Rand {
static Random r = new Random();
static int Rand16() {
return r.Next(16);
}
static int Rand7Naive() {
return Rand16() % 7;
}
static int Rand7Float() {
return (int)(Rand16() / 16.0 * 7);
}
// corrected
static int Rand7RejectionNaive() {
int n = 7, remainder = 16 % n, x, output;
do {
x = Rand16();
output = x % n;
} while (x >= 16 - remainder);
return output;
}
// adapted to fit the constraints of this example
static int Rand7RejectionJava() {
int n = 7, x, output;
do {
x = Rand16();
output = x % n;
} while (x - output + 6 > 15);
return output;
}
static void Test(Func<int> rand, string name) {
var buckets = new int[7];
for (int i = 0; i < 10000000; i++) buckets[rand()]++;
Console.WriteLine(name);
for (int i = 0; i < 7; i++) Console.WriteLine("{0}\t{1}", i, buckets[i]);
}
static void Main() {
Test(Rand7Naive, "Rand7Naive");
Test(Rand7Float, "Rand7Float");
Test(Rand7RejectionNaive, "Rand7RejectionNaive");
}
}
The result is as follows (pasted into Excel and added conditional coloring of cells so that differences are more apparent):
Now that I fixed my mistake in above rejection sampling it works as it should (before it would bias 0). As you can see, the float method isn't perfect at all, it just distributes the biased numbers differently.
The problem occurs when the number of outputs from the random number generator (RAND_MAX+1) is not evenly divisible by the desired range (max-min+1). Since there will be a consistent mapping from a random number to an output, some outputs will be mapped to more random numbers than others. This is regardless of how the mapping is done - you can use modulo, division, conversion to floating point, whatever voodoo you can come up with, the basic problem remains.
The magnitude of the problem is very small, and undemanding applications can generally get away with ignoring it. The smaller the range and the larger RAND_MAX is, the less pronounced the effect will be.
I took your example program and tweaked it a bit. First I created a special version of rand that only has a range of 0-255, to better demonstrate the effect. I made a few tweaks to rangeRandomAlg2. Finally I changed the number of "balls" to 1000000 to improve the consistency. You can see the results here: http://ideone.com/4P4HY
Notice that the floating-point version produces two tightly grouped probabilities, near either 0.101 or 0.097, nothing in between. This is the bias in action.
I think calling this "Java's algorithm" is a bit misleading - I'm sure it's much older than Java.
int rangeRandomAlg2 (int min, int max)
{
int n = max - min + 1;
int remainder = RAND_MAX % n;
int x;
do
{
x = rand();
} while (x >= RAND_MAX - remainder);
return min + x % n;
}
It's easy to see why this algorithm produces a biased sample. Suppose your rand() function returns uniform integers from the set {0, 1, 2, 3, 4}. If I want to use this to generate a random bit 0 or 1, I would say rand() % 2. The set {0, 2, 4} gives me 0, and the set {1, 3} gives me 1 -- so clearly I sample 0 with 60% and 1 with 40% likelihood, not uniform at all!
To fix this you have to either make sure that your desired range divides the range of the random number generator, or otherwise discard the result whenever the random number generator returns a number that's larger than the largest possible multiple of the target range.
In the above example, the target range is 2, the largest multiple that fits into the random generation range is 4, so we discard any sample that is not in the set {0, 1, 2, 3} and roll again.
By far the easiest solution is std::uniform_int_distribution<int>(min, max).
You have touched on two points involving a random integer algorithm: Is it optimal, and is it unbiased?
Optimal
There are many ways to define an "optimal" algorithm. Here we look at "optimal" algorithms in terms of the number of random bits it uses on average. In this sense, rand is a poor method to use for randomly generated numbers because, among other problems with rand(), it need not necessarily produce random bits (because RAND_MAX is not exactly specified). Instead, we will assume we have a "true" random generator that can produce unbiased and independent random bits.
In 1976, D. E. Knuth and A. C. Yao showed that any algorithm that produces random integers with a given probability, using only random bits, can be represented as a binary tree, where random bits indicate which way to traverse the tree and each leaf (endpoint) corresponds to an outcome. (Knuth and Yao, "The complexity of nonuniform random number generation", in Algorithms and Complexity, 1976.) They also gave bounds on the number of bits a given algorithm will need on average for this task. In this case, an optimal algorithm to generate integers in [0, n) uniformly, will need at least log2(n) and at most log2(n) + 2 bits on average.
There are many examples of optimal algorithms in this sense. See the following answer of mine:
How to generate a random integer in the range [0,n] from a stream of random bits without wasting bits?
Unbiased
However, any optimal integer generator that is also unbiased will, in general, run forever in the worst case, as also shown by Knuth and Yao. Going back to the binary tree, each one of the n outcomes labels leaves in the binary tree so that each integer in [0, n) can occur with probability 1/n. But if 1/n has a non-terminating binary expansion (which will be the case if n is not a power of 2), this binary tree will necessarily either—
Have an "infinite" depth, or
include "rejection" leaves at the end of the tree,
And in either case, the algorithm won't run in constant time and will run forever in the worst case. (On the other hand, when n is a power of 2, the optimal binary tree will have a finite depth and no rejection nodes.)
And for general n, there is no way to "fix" this worst case time complexity without introducing bias. For instance, modulo reductions (including the min + (rand() % (int)(max - min + 1)) in your question) are equivalent to a binary tree in which rejection leaves are replaced with labeled outcomes — but since there are more possible outcomes than rejection leaves, only some of the outcomes can take the place of the rejection leaves, introducing bias. The same kind of binary tree — and the same kind of bias — results if you stop rejecting after a set number of iterations. (However, this bias may be negligible depending on the application. There are also security aspects to random integer generation, which are too complicated to discuss in this answer.)
Without loss of generality, the problem of generating random integers on [a, b] can be reduced to the problem of generating random integers on [0, s). The state of the art for generating random integers on a bounded range from a uniform PRNG is represented by the following recent publication:
Daniel Lemire,"Fast Random Integer Generation in an Interval." ACM Trans. Model. Comput. Simul. 29, 1, Article 3 (January 2019) (ArXiv draft)
Lemire shows that his algorithm provides unbiased results, and motivated by the growing popularity of very fast high-quality PRNGs such as Melissa O'Neill's PCG generators, shows how to the results can be computed fast, avoiding slow division operations almost all of the time.
An exemplary ISO-C implementation of his algorithm is shown in randint() below. Here I demonstrate it in conjunction with George Marsaglia's older KISS64 PRNG. For performance reasons, the required 64×64→128 bit unsigned multiplication is typically best implemented via machine-specific intrinsics or inline assembly that map directly to appropriate hardware instructions.
#include <stdio.h>
#include <stdlib.h>
#include <stdint.h>
/* PRNG state */
typedef struct Prng_T *Prng_T;
/* Returns uniformly distributed integers in [0, 2**64-1] */
uint64_t random64 (Prng_T);
/* Multiplies two 64-bit factors into a 128-bit product */
void umul64wide (uint64_t, uint64_t, uint64_t *, uint64_t *);
/* Generate in bias-free manner a random integer in [0, s) with Lemire's fast
algorithm that uses integer division only rarely. s must be in [0, 2**64-1].
Daniel Lemire, "Fast Random Integer Generation in an Interval," ACM Trans.
Model. Comput. Simul. 29, 1, Article 3 (January 2019)
*/
uint64_t randint (Prng_T prng, uint64_t s)
{
uint64_t x, h, l, t;
x = random64 (prng);
umul64wide (x, s, &h, &l);
if (l < s) {
t = (0 - s) % s;
while (l < t) {
x = random64 (prng);
umul64wide (x, s, &h, &l);
}
}
return h;
}
#define X86_INLINE_ASM (0)
/* Multiply two 64-bit unsigned integers into a 128 bit unsined product. Return
the least significant 64 bist of the product to the location pointed to by
lo, and the most signfiicant 64 bits of the product to the location pointed
to by hi.
*/
void umul64wide (uint64_t a, uint64_t b, uint64_t *hi, uint64_t *lo)
{
#if X86_INLINE_ASM
uint64_t l, h;
__asm__ (
"movq %2, %%rax;\n\t" // rax = a
"mulq %3;\n\t" // rdx:rax = a * b
"movq %%rax, %0;\n\t" // l = (a * b)<31:0>
"movq %%rdx, %1;\n\t" // h = (a * b)<63:32>
: "=r"(l), "=r"(h)
: "r"(a), "r"(b)
: "%rax", "%rdx");
*lo = l;
*hi = h;
#else // X86_INLINE_ASM
uint64_t a_lo = (uint64_t)(uint32_t)a;
uint64_t a_hi = a >> 32;
uint64_t b_lo = (uint64_t)(uint32_t)b;
uint64_t b_hi = b >> 32;
uint64_t p0 = a_lo * b_lo;
uint64_t p1 = a_lo * b_hi;
uint64_t p2 = a_hi * b_lo;
uint64_t p3 = a_hi * b_hi;
uint32_t cy = (uint32_t)(((p0 >> 32) + (uint32_t)p1 + (uint32_t)p2) >> 32);
*lo = p0 + (p1 << 32) + (p2 << 32);
*hi = p3 + (p1 >> 32) + (p2 >> 32) + cy;
#endif // X86_INLINE_ASM
}
/* George Marsaglia's KISS64 generator, posted to comp.lang.c on 28 Feb 2009
https://groups.google.com/forum/#!original/comp.lang.c/qFv18ql_WlU/IK8KGZZFJx4J
*/
struct Prng_T {
uint64_t x, c, y, z, t;
};
struct Prng_T kiss64 = {1234567890987654321ULL, 123456123456123456ULL,
362436362436362436ULL, 1066149217761810ULL, 0ULL};
/* KISS64 state equations */
#define MWC64 (kiss64->t = (kiss64->x << 58) + kiss64->c, \
kiss64->c = (kiss64->x >> 6), kiss64->x += kiss64->t, \
kiss64->c += (kiss64->x < kiss64->t), kiss64->x)
#define XSH64 (kiss64->y ^= (kiss64->y << 13), kiss64->y ^= (kiss64->y >> 17), \
kiss64->y ^= (kiss64->y << 43))
#define CNG64 (kiss64->z = 6906969069ULL * kiss64->z + 1234567ULL)
#define KISS64 (MWC64 + XSH64 + CNG64)
uint64_t random64 (Prng_T kiss64)
{
return KISS64;
}
int main (void)
{
int i;
Prng_T state = &kiss64;
for (i = 0; i < 1000; i++) {
printf ("%llu\n", randint (state, 10));
}
return EXIT_SUCCESS;
}
If you really want to get a perfect generator assuming rand() function that you have is perfect, you need to apply the method explained bellow.
We will create a random number, r, from 0 to max-min=b-1, which is then easy to move to the range that you want, just take r+min
We will create a random number where b < RAND_MAX, but the procedure can be easily adopted to have a random number for any base
PROCEDURE:
Take a random number r in its original RAND_MAX size without any truncation
Display this number in base b
Take first m=floor(log_b(RAND_MAX)) digits of this number for m random numbers from 0 to b-1
Shift each by min (i.e. r+min) to get them into the range (min,max) as you wanted
Since log_b(RAND_MAX) is not necessarily an integer, the last digit in the representation is wasted.
The original approach of just using mod (%) is mistaken exactly by
(log_b(RAND_MAX) - floor(log_b(RAND_MAX)))/ceil(log_b(RAND_MAX))
which you might agree is not that much, but if you insist on being precise, that is the procedure.
I have a problem with the small game that I made.
#include "stdafx.h"
#include <iostream>
#include <cstdlib>
#include <ctime>
using namespace std;
int main()
{
int span = 100;
srand(time(0));
int TheNumber = static_cast<double> (rand()) /RAND_MAX * (span -1) +1;
cout << "You need to guess the number between 1 and " << span << endl;
int mynumber;
int numberofAttempts = 0;
do {
cout << ++numberofAttempts <<" Attempt: ";
cin >> mynumber;
if (mynumber > TheNumber)
cout <<"Lower!" << endl;
else if (mynumber < TheNumber)
cout <<"Higher!" << endl;
} while (mynumber != TheNumber);
cout << "SUCESS!!!" << endl;
return 0;
}
The game is supposed to generate a random number between 0-100 and you are supposed to guess it. After running this code 15-20times the same numbers generated some even 8 times (the number 2 in my case).
I know that there is no absolute random number and that it uses some math formula or something to get one.I know that using srand(time(0)) makes it dependent on the current time. But how would I make it "more" random, since I don't want the stuff to happen that I mentioned above.
First time I ran it the result was 11, after running it again (after guessing the right number) , it was still 11, even though the time changed.
[ADDITION1]
If you DO truly wish to look into better random number generation, then this is a good algorithm to begin with:
http://en.wikipedia.org/wiki/Mersenne_twister
Remember though that any "Computer Generated" (i.e. mathematically generated) random number is ONLY pseudo-random. Pseudo-random means that while the outputs from the algorithm look to have normal distribution, they are truly deterministic if one knows the input seed. True random numbers are completely non-deterministic.
[ORIGINAL]
Try simply one of the following lines:
rand() % (span + 1); // This will give 0 - 100
rand() % span; // this will give 0 - 99
rand() % span + 1; // This will give 1 - 100
Instead of:
(rand()) /RAND_MAX * (span -1) +1
Also, don't cast the result of that to a double, then place into an int.
Look here also:
http://www.cplusplus.com/reference/clibrary/cstdlib/rand/
In Response to the comment!!!
If you use:
rand() / (span + 1);
then in order to get values between 0 and 100, then the output values from rand would indeed have to be between 0 and (100 * 100), and this nature would have to be guaranteed. This is because of simple division. A value of 1 will essentially pop out when rand() produces a 101 - 201, a 2 will pop out of the division when the rand() outputs a value of 202 - 302, etc...
In this case, you may be able to get away with it at 100 * 100 is only 10000, and there are definitely integers larger than this in the 32 bit space, but in general doing a divide will not allow you to take advantage utilizing the full number space provided!!!
There are a number of problems with rand(). You've run into one of them, which is that the first several values aren't "random". If you must use rand(), it is always a good idea to discard the first four or results from rand().
srand (time(0));
rand();
rand();
rand();
rand();
Another problem with rand() is that the low order bits are notoriously non-random, even after the above hack. On some systems, the lowest order bit alternates 0,1,0,1,0,1,... It's always better to use the high order bits such as by using the quotient rather than the remainder.
Other problems: Non-randomness (most implementations of rand() fails a number of tests of randomness) and short cycle. With all these problems, the best advice is to use anything but rand().
First, rand() / RAND_MAX does not give a number between 0 and 1, it returns 0. This is because RAND_MAX fits 0 times in the result of rand(). Both are integers, so with integer division it does not return a floating point number.
Second, RAND_MAX may well be the same size as an INT. Multiplying RAND_MAX with anything will then give an overflow.
So the following code makes 0 < r < 1
r = ((double) rand() / (RAND_MAX))
Why does having r = ((double) rand() / (RAND_MAX + 1)) make -1 < r < 0?
Shouldn't adding one to RAND_MAX make 1 < r < 2?
Edit: I was getting a warning: integer overflow in expression
on that line, so that might be the problem. I just did cout << r << endl and it definitely gives me values between -1 and 0
This is entirely implementation specific, but it appears that in the C++ environment you're working in, RAND_MAX is equal to INT_MAX.
Because of this, RAND_MAX + 1 exhibits undefined (overflow) behavior, and becomes INT_MIN. While your initial statement was dividing (random # between 0 and INT_MAX)/(INT_MAX) and generating a value 0 <= r < 1, now it's dividing (random # between 0 and INT_MAX)/(INT_MIN), generating a value -1 < r <= 0
In order to generate a random number 1 <= r < 2, you would want
r = ((double) rand() / (RAND_MAX)) + 1
rand() / double(RAND_MAX) generates a floating-point random number between 0 (inclusive) and 1 (inclusive), but it's not a good way for the following reasons (because RAND_MAX is usually 32767):
The number of different random numbers that can be generated is too small: 32768. If you need more different random numbers, you need a different way (a code example is given below)
The generated numbers are too coarse-grained: you can get 1/32768, 2/32768, 3/32768, but never anything in between.
Limited states of random number generator engine: after generating RAND_MAX random numbers, implementations usually start to repeat the same sequence of random numbers.
Due to the above limitations of rand(), a better choice for generation of random numbers between 0 (inclusive) and 1 (exclusive) would be the following snippet (similar to the example at http://en.cppreference.com/w/cpp/numeric/random/uniform_real_distribution ):
#include <iostream>
#include <random>
#include <chrono>
int main()
{
std::mt19937_64 rng;
// initialize the random number generator with time-dependent seed
uint64_t timeSeed = std::chrono::high_resolution_clock::now().time_since_epoch().count();
std::seed_seq ss{uint32_t(timeSeed & 0xffffffff), uint32_t(timeSeed>>32)};
rng.seed(ss);
// initialize a uniform distribution between 0 and 1
std::uniform_real_distribution<double> unif(0, 1);
// ready to generate random numbers
const int nSimulations = 10;
for (int i = 0; i < nSimulations; i++)
{
double currentRandomNumber = unif(rng);
std::cout << currentRandomNumber << std::endl;
}
return 0;
}
This is easy to modify to generate random numbers between 1 (inclusive) and 2 (exclusive) by replacing unif(0, 1) with unif(1, 2).
No, because RAND_MAX is typically expanded to MAX_INT. So adding one (apparently) puts it at MIN_INT (although it should be undefined behavior as I'm told), hence the reversal of sign.
To get what you want you will need to move the +1 outside the computation:
r = ((double) rand() / (RAND_MAX)) + 1;
It doesn't. It makes 0 <= r < 1, but your original is 0 <= r <= 1.
Note that this can lead to undefined behavior if RAND_MAX + 1 overflows.
This is the right way:
double randd() {
return (double)rand() / ((double)RAND_MAX + 1);
}
or
double randd() {
return (double)rand() / (RAND_MAX + 1.0);
}
My guess is that RAND_MAX is equal to INT_MAX and so you're overflowing it to a negative.
Just do this:
r = ((double) rand() / (RAND_MAX)) + 1;
Or even better, use C++11's random number generators.
this->value = rand() % (this->max + 1);
Seems to work fine between 0 and 1++.
I created a test application that generates 10k random numbers in a range from 0 to 250 000. Then I calculated MAX and min values and noticed that the MAX value is always around 32k...
Do you have any idea how to extend the possible range? I need a range with MAX value around 250 000!
This is according to the definition of rand(), see:
http://cplusplus.com/reference/clibrary/cstdlib/rand/
http://cplusplus.com/reference/clibrary/cstdlib/RAND_MAX/
If you need larger random numbers, you can use an external library (for example http://www.boost.org/doc/libs/1_49_0/doc/html/boost_random.html) or calculate large random numbers out of multiple small random numbers by yourself.
But pay attention to the distribution you want to get. If you just sum up the small random numbers, the result will not be equally distributed.
If you just scale one small random number by a constant factor, there will be gaps between the possible values.
Taking the product of random numbers also doesn't work.
A possible solution is the following:
1) Take two random numbers a,b
2) Calculate a*(RAND_MAX+1)+b
So you get equally distributed random values up to (RAND_MAX+1)^2-1
Presumably, you also want an equal distribution over this extended
range. About the only way you can effectively do this is to generate a
sequence of smaller numbers, and scale them as if you were working in a
different base. For example, for 250000, you might 4 random numbers
in the range [0,10) and one in range [0,25), along the lines:
int
random250000()
{
return randomInt(10) + 10 * randomInt(10)
+ 100 * randomInt(10) + 1000 * randomInt(10)
+ 10000 * randomInt(25);
}
For this to work, your random number generator must be good; many
implementations of rand() aren't (or at least weren't—I've not
verified the situation recently). You'll also want to eliminate the
bias you get when you map RAND_MAX + 1 different values into 10 or
25 different values. Unless RAND_MAX + 1 is an exact multiple of
10 and 25 (e.g. is an exact multiple of 50), you'll need something
like:
int
randomInt( int upperLimit )
{
int const limit = (RAND_MAX + 1) - (RAND_MAX + 1) % upperLimit;
int result = rand();
while ( result >= limit ) {
result = rand();
return result % upperLimit;
}
(Attention when doing this: there are some machines where RAND_MAX + 1
will overflow; if portability is an issue, you'll need to take
additional precautions.)
All of this, of course, supposes a good quality generator, which is far
from a given.
You can just manipulate your number bitwise by generating smaller random numbers.
For instance, if you need a 32-bit random number:
int32 x = 0;
for (int i = 0; i < 4; ++i) { // 4 == 32/8
int8 tmp = 8bit_random_number_generator();
x <<= 8*i; x |= tmp;
}
If you don't need good randomness in your numbers, you can just use rand() & 0xff for the 8-bit random number generator. Otherwise, something better will be necessary.
Are you using short ints? If so, you will see 32,767 as your max number because anything larger will overflow the short int.
Scale your numbers up by N / RAND_MAX, where N is your desired maximum. If the numbers fit, you can do something like this:
unsigned long long int r = rand() * N / RAND_MAX;
Obviously if the initial part overflows you can't do this, but with N = 250000 you should be fine. RAND_MAX is 32K on many popular platforms.
More generally, to get a random number uniformly in the interval [A, B], use:
A + rand() * (B - A) / RAND_MAX;
Of course you should probably use the proper C++-style <random> library; search this site for many similar questions explaining how to use it.
Edit: In the hope of preventing an escalation of comments, here's yet another copy/paste of the Proper C++ solution for truly uniform distribution on an interval [A, B]:
#include <random>
typedef std::mt19937 rng_type;
typedef unsigned long int int_type; // anything you like
std::uniform_int_distribution<int_type> udist(A, B);
rng_type rng;
int main()
{
// seed rng first:
rng_type::result_type const seedval = get_seed();
rng.seed(seedval);
int_type random_number = udist(rng);
// use random_number
}
Don't forget to seend the RNG! If you store the seed value, you can replay the same random sequence later on.