So, I'm trying to create a random vector (think geometry, not an expandable array), and every time I call my random vector function I get the same x value, though y and z are different.
int main () {
srand ( (unsigned)time(NULL));
Vector<double> a;
a.randvec();
cout << a << endl;
return 0;
}
using the function
//random Vector
template <class T>
void Vector<T>::randvec()
{
const int min=-10, max=10;
int randx, randy, randz;
const int bucket_size = RAND_MAX/(max-min);
do randx = (rand()/bucket_size)+min;
while (randx <= min && randx >= max);
x = randx;
do randy = (rand()/bucket_size)+min;
while (randy <= min && randy >= max);
y = randy;
do randz = (rand()/bucket_size)+min;
while (randz <= min && randz >= max);
z = randz;
}
For some reason, randx will consistently return 8, whereas the other numbers seem to be following the (pseudo) randomness perfectly. However, if I put the call to define, say, randy before randx, randy will always return 8.
Why is my first random number always 8? Am I seeding incorrectly?
The issue is that the random number generator is being seeded with a values that are very close together - each run of the program only changes the return value of time() by a small amount - maybe 1 second, maybe even none! The rather poor standard random number generator then uses these similar seed values to generate apparently identical initial random numbers. Basically, you need a better initial seed generator than time() and a better random number generator than rand().
The actual looping algorithm used is I think lifted from Accelerated C++ and is intended to produce a better spread of numbers over the required range than say using the mod operator would. But it can't compensate for always being (effectively) given the same seed.
I don't see any problem with your srand(), and when I tried running extremely similar code, I did not repeatedly get the same number with the first rand(). However, I did notice another possible issue.
do randx = (rand()/bucket_size)+min;
while (randx <= min && randx >= max);
This line probably does not do what you intended. As long as min < max (and it always should be), it's impossible for randx to be both less than or equal to min and greater than or equal to max. Plus, you don't need to loop at all. Instead, you can get a value in between min and max using:
randx = rand() % (max - min) + min;
I had the same problem exactly. I fixed it by moving the srand() call so it was only called once in my program (previously I had been seeding it at the top of a function call).
Don't really understand the technicalities - but it was problem solved.
Also to mention, you can even get rid of that strange bucket_size variable and use the following method to generate numbers from a to b inclusively:
srand ((unsigned)time(NULL));
const int a = -1;
const int b = 1;
int x = rand() % ((b - a) + 1) + a;
int y = rand() % ((b - a) + 1) + a;
int z = rand() % ((b - a) + 1) + a;
A simple quickfix is to call rand a few times after seeding.
int main ()
{
srand ( (unsigned)time(NULL));
rand(); rand(); rand();
Vector<double> a;
a.randvec();
cout << a << endl;
return 0;
}
Just to explain better, the first call to rand() in four sequential runs of a test program gave the following output:
27592
27595
27598
27602
Notice how similar they are? For example, if you divide rand() by 100, you will get the same number 3 times in a row. Now take a look at the second result of rand() in four sequential runs:
11520
22268
248
10997
This looks much better, doesn't it? I really don't see any reason for the downvotes.
Your implementation, through integer division, ignores the smallest 4-5 bit of the random number. Since your RNG is seeded with the system time, the first value you get out of it will change only (on average) every 20 seconds.
This should work:
randx = (min) + (int) ((max - min) * rand() / (RAND_MAX + 1.0));
where
rand() / (RAND_MAX + 1.0)
is a random double value in [0, 1) and the rest is just shifting it around.
Not directly related to the code in this question, but I had same issue with using
srand ((unsigned)time(NULL)) and still having same sequence of values being returned from following calls to rand().
It turned out that srand needs to called on each thread you are using it on separately. I had a loading thread that was generating random content (that wasn't random cuz of the seed issue). I had just using srand in the main thread and not the loading thread. So added another srand ((unsigned)time(NULL)) to start of loading thread fixed this issue.
Related
I've been trying to create a generalized Gradient Noise generator (which doesn't use the hash method to get gradients). The code is below:
class GradientNoise {
std::uint64_t m_seed;
std::uniform_int_distribution<std::uint8_t> distribution;
const std::array<glm::vec2, 4> vector_choice = {glm::vec2(1.0, 1.0), glm::vec2(-1.0, 1.0), glm::vec2(1.0, -1.0),
glm::vec2(-1.0, -1.0)};
public:
GradientNoise(uint64_t seed) {
m_seed = seed;
distribution = std::uniform_int_distribution<std::uint8_t>(0, 3);
}
// 0 -> 1
// just passes the value through, origionally was perlin noise activation
double nonLinearActivationFunction(double value) {
//return value * value * value * (value * (value * 6.0 - 15.0) + 10.0);
return value;
}
// 0 -> 1
//cosine interpolation
double interpolate(double a, double b, double t) {
double mu2 = (1 - cos(t * M_PI)) / 2;
return (a * (1 - mu2) + b * mu2);
}
double noise(double x, double y) {
std::mt19937_64 rng;
//first get the bottom left corner associated
// with these coordinates
int corner_x = std::floor(x);
int corner_y = std::floor(y);
// then get the respective distance from that corner
double dist_x = x - corner_x;
double dist_y = y - corner_y;
double corner_0_contrib; // bottom left
double corner_1_contrib; // top left
double corner_2_contrib; // top right
double corner_3_contrib; // bottom right
std::uint64_t s1 = ((std::uint64_t(corner_x) << 32) + std::uint64_t(corner_y) + m_seed);
std::uint64_t s2 = ((std::uint64_t(corner_x) << 32) + std::uint64_t(corner_y + 1) + m_seed);
std::uint64_t s3 = ((std::uint64_t(corner_x + 1) << 32) + std::uint64_t(corner_y + 1) + m_seed);
std::uint64_t s4 = ((std::uint64_t(corner_x + 1) << 32) + std::uint64_t(corner_y) + m_seed);
// each xy pair turns into distance vector from respective corner, corner zero is our starting corner (bottom
// left)
rng.seed(s1);
corner_0_contrib = glm::dot(vector_choice[distribution(rng)], {dist_x, dist_y});
rng.seed(s2);
corner_1_contrib = glm::dot(vector_choice[distribution(rng)], {dist_x, dist_y - 1});
rng.seed(s3);
corner_2_contrib = glm::dot(vector_choice[distribution(rng)], {dist_x - 1, dist_y - 1});
rng.seed(s4);
corner_3_contrib = glm::dot(vector_choice[distribution(rng)], {dist_x - 1, dist_y});
double u = nonLinearActivationFunction(dist_x);
double v = nonLinearActivationFunction(dist_y);
double x_bottom = interpolate(corner_0_contrib, corner_3_contrib, u);
double x_top = interpolate(corner_1_contrib, corner_2_contrib, u);
double total_xy = interpolate(x_bottom, x_top, v);
return total_xy;
}
};
I then generate an OpenGL texture to display with like this:
int width = 1024;
int height = 1024;
unsigned char *temp_texture = new unsigned char[width*height * 4];
double octaves[5] = {2,4,8,16,32};
for( int i = 0; i < height; i++){
for(int j = 0; j < width; j++){
double d_noise = 0;
d_noise += temp_1.noise(j/octaves[0], i/octaves[0]);
d_noise += temp_1.noise(j/octaves[1], i/octaves[1]);
d_noise += temp_1.noise(j/octaves[2], i/octaves[2]);
d_noise += temp_1.noise(j/octaves[3], i/octaves[3]);
d_noise += temp_1.noise(j/octaves[4], i/octaves[4]);
d_noise/=5;
uint8_t noise = static_cast<uint8_t>(((d_noise * 128.0) + 128.0));
temp_texture[j*4 + (i * width * 4) + 0] = (noise);
temp_texture[j*4 + (i * width * 4) + 1] = (noise);
temp_texture[j*4 + (i * width * 4) + 2] = (noise);
temp_texture[j*4 + (i * width * 4) + 3] = (255);
}
}
Which give good results:
But gprof is telling me that the Mersenne twister is taking up 62.4% of my time and growing with larger textures. Nothing else individual takes any where near as much time. While the Mersenne twister is fast after initialization, the fact that I initialize it every time I use it seems to make it pretty slow.
This initialization is 100% required for this to make sure that the same x and y generates the same gradient at each integer point (so you need either a hash function or seed the RNG each time).
I attempted to change the PRNG to both the linear congruential generator and Xorshiftplus, and while both ran orders of magnitude faster, they gave odd results:
LCG (one time, then running 5 times before using)
Xorshiftplus
After one iteration
After 10,000 iterations.
I've tried:
Running the generator several times before utilizing output, this results in slow execution or simply different artifacts.
Using the output of two consecutive runs after initial seed to seed the PRNG again and use the value after wards. No difference in result.
What is happening? What can i do to get faster results that are of the same quality as the mersenne twister?
OK BIG UPDATE:
I don't know why this works, I know it has something to do with the prime number utilized, but after messing around a bit, it appears that the following works:
Step 1, incorporate the x and y values as seeds separately (and incorporate some other offset value or additional seed value with them, this number should be a prime/non trivial factor)
Step 2, Use those two seed results into seeding the generator again back into the function (so like geza said, the seeds made were bad)
Step 3, when getting the result, instead of using modulo number of items (4) trying to get, or & 3, modulo the result by a prime number first then apply & 3. I'm not sure if the prime being a mersenne prime matters or not.
Here is the result with prime = 257 and xorshiftplus being used! (note I used 2048 by 2048 for this one, the others were 256 by 256)
LCG is known to be inadequate for your purpose.
Xorshift128+'s results are bad, because it needs good seeding. And providing good seeding defeats the whole purpose of using it. I don't recommend this.
However, I recommend using an integer hash. For example, one from Bob's page.
Here's a result of the first hash of that page, it looks OK to me, and it is fast (I think it is much faster than Mersenne Twister):
Here's the code I've written to generate this:
#include <cmath>
#include <stdio.h>
unsigned int hash(unsigned int a) {
a = (a ^ 61) ^ (a >> 16);
a = a + (a << 3);
a = a ^ (a >> 4);
a = a * 0x27d4eb2d;
a = a ^ (a >> 15);
return a;
}
unsigned int ivalue(int x, int y) {
return hash(y<<16|x)&0xff;
}
float smooth(float x) {
return 6*x*x*x*x*x - 15*x*x*x*x + 10*x*x*x;
}
float value(float x, float y) {
int ix = floor(x);
int iy = floor(y);
float fx = smooth(x-ix);
float fy = smooth(y-iy);
int v00 = ivalue(iy+0, ix+0);
int v01 = ivalue(iy+0, ix+1);
int v10 = ivalue(iy+1, ix+0);
int v11 = ivalue(iy+1, ix+1);
float v0 = v00*(1-fx) + v01*fx;
float v1 = v10*(1-fx) + v11*fx;
return v0*(1-fy) + v1*fy;
}
unsigned char pic[1024*1024];
int main() {
for (int y=0; y<1024; y++) {
for (int x=0; x<1024; x++) {
float v = 0;
for (int o=0; o<=9; o++) {
v += value(x/64.0f*(1<<o), y/64.0f*(1<<o))/(1<<o);
}
int r = rint(v*0.5f);
pic[y*1024+x] = r;
}
}
FILE *f = fopen("x.pnm", "wb");
fprintf(f, "P5\n1024 1024\n255\n");
fwrite(pic, 1, 1024*1024, f);
fclose(f);
}
If you want to understand, how a hash function work (or better yet, which properties a good hash have), check out Bob's page, for example this.
You (unknowingly?) implemented a visualization of PRNG non-random patterns. That looks very cool!
Except Mersenne Twister, all your tested PRNGs do not seem fit for your purpose. As I have not done further tests myself, I can only suggest to try out and measure further PRNGs.
The randomness of LCGs are known to be sensitive to the choice of their parameters. In particular, the period of a LCG is relative to the m parameter - at most it will be m (your prime factor) & for many values it can be less.
Similarly, the careful parameters selection is required to get a long period from Xorshift PRNGs.
You've noted that some PRNGs give good procedural generation results while other do not. In order to isolate the cause, I would factor out the proc gen stuff & examine the PRNG output directly. An easy way to visualize the data is to build a grey scale image where each pixel value is a (possibly scaled) random value. For image based stuff, I find this to be an easy way to find stuff that may lead to visual artifacts. Any artifacts you see with this are likely to cause issues with your proc gen output.
Another option is to try something like the Diehard tests. If the aforementioned image test failed to reveal any problems, I might use this just to be sure my PRNG techniques were trustworthy.
Note that your code seeds the PRNG, then generates one pseudorandom number from the PRNG. The reason for the nonrandomness in xorshift128+ that you discovered is that xorshift128+ simply adds the two halves of the seed (and uses the result mod 264 as the generated number) before changing its state (review its source code). This makes that PRNG considerably different from a hash function.
What you see is the practical demonstration of quality of PRNG. Mersenne Twister is one of the best PRNGs with good performance, it passes DIEHARD tests. One should know that generating a random numbers is not an easy computational task, so looking for a better performance will inevitably result in poor quality. LCG is known to be simplest and worst PRNG ever designed and it clearly shows two-dimensional correlation as in your picture. The quality of Xorshift generators largely depend on bitness and parameters. They are definitely worse than Mersenne Twister, but some (xorshift128+) may work good enough to pass BigCrush battery of TestU01 tests.
In other words, if you are making an important physical modelling numerical experiment, you better continue to use Mersenne Twister as known to be a good trade-off between speed and quality and it comes in many standard libraries. On a less important case you may try to use xorshift128+ generator. For an ultimate results you need to use cryptographical-quality PRNG (none of mentioned here may be used for cryptographical purposes).
I'm trying to solve a problem from hacker rank over here.
The question is:
So to solve this, I tried with a simple maths equation:
4x + 7y = lucky_number
For example, to check 15 is a lucky_number or not, I could do start with x, y values 0 and substituting in the above equation until its equal or greater than (if so stop and say its not lucky number)
The above logic works fine. But the problem is with big number, imagine to check number 966888032206353 lucky or not, starting with x,y to 0 wont be an efficient idea.
Any guidance to it?
All numbers from 7*4=28 up (in fact even all mumbers from 18 up) are lucky, for the rest just precompute a smalll table.
Another way to think of it: All you need to do is plot the line
7y = -4x + 966888032206353
and identify any points where both x and y are integers.
So, you don't need a nested loop. Instead:
Iterate y as an integer. for y=0; y<966888032206353 / 7; y++
For each iteration, solve for x, using floating point math.
If x is an integer, the number is lucky.
This will require about 138T iterations.
Here's my code that I submitted to Hackerrank.
#include <bits/stdc++.h>
using namespace std;
int q; long long n; bool dp[1009];
int main() {
cin >> q;
dp[0] = true;
for(int i = 1; i <= 1000; i++) {
if(i >= 4 && dp[i - 4]) dp[i] = true;
if(i >= 7 && dp[i - 7]) dp[i] = true;
}
while(q--) {
cin >> n;
if(n >= 1000 || dp[n]) cout << "Yes" << endl;
else cout << "No" << endl;
}
}
This is dynamic programming, but if n >= 28 it is always ok.
One of your problems is that your problem description is very incomplete. You can infact represent any integer number as 4x + 7y, if you only allowed negative x and y. For example, 1 = 4*2 + (-1)*7 and you can get a solution for any number by multiplying with that factor.
I guess the best solution from an algorithmics point of view is to use dynamic programming. You can simply start checking numbers whether they are lucky in your sense or not. As soon as you find 4 consequtive lucky numbers, you can stop, because any number afterwards will be lucky by just adding 4 an appropriate number of times. I guess you will find a sequence of 4 consequtive lucky numbers very early.
Edit: my main question is that I want to replicate the TI-84 plus RNG algorithm on my computer, so I can write it in a language like Javascript or Lua, to test it faster.
I tried using an emulator, but it turned out to be slower than the calculator.
Just for the people concerned: There is another question like this, but answer to that question just says how to transfer already-generated numbers over to the computer. I don't want this. I already tried something like it, but I had to leave the calculator running all weekend, and it still wasn't done.
The algorithm being used is from the paper Efficient and portable combined random number generators by P. L'Ecuyer.
You can find the paper here and download it for free from here.
The algorithm used by the Ti calculators is on the RHS side of p. 747. I've included a picture.
I've translated this into a C++ program
#include <iostream>
#include <iomanip>
using namespace std;
long s1,s2;
double Uniform(){
long Z,k;
k = s1 / 53668;
s1 = 40014*(s1-k*53668)-k*12211;
if(s1<0)
s1 = s1+2147483563;
k = s2/52774;
s2 = 40692*(s2-k*52774)-k*3791;
if(s2<0)
s2 = s2+2147483399;
Z=s1-s2;
if(Z<1)
Z = Z+2147483562;
return Z*(4.656613e-10);
}
int main(){
s1 = 12345; //Gotta love these seed values!
s2 = 67890;
for(int i=0;i<10;i++)
cout<<std::setprecision(10)<<Uniform()<<endl;
}
Note that the initial seeds are s1 = 12345 and s2 = 67890.
And got an output from a Ti-83 (sorry, I couldn't find a Ti-84 ROM) emulator:
This matches what my implementation produces
I've just cranked the output precision on my implementation and get the following results:
0.9435973904
0.9083188494
0.1466878273
0.5147019439
0.4058096366
0.7338123019
0.04399198693
0.3393625207
Note that they diverge from Ti's results in the less significant digits. This may be a difference in the way the two processors (Ti's Z80 versus my X86) perform floating point calculations. If so, it will be hard to overcome this issue. Nonetheless, the random numbers will still generate in the same sequence (with the caveat below) since the sequence relies on only integer mathematics, which are exact.
I've also used the long type to store intermediate values. There's some risk that the Ti implementation relies on integer overflow (I didn't read L'Ecuyer's paper too carefully), in which case you would have to adjust to int32_t or a similar type to emulate this behaviour. Assuming, again, that the processors perform similarly.
Edit
This site provides a Ti-Basic implementation of the code as follows:
:2147483563→mod1
:2147483399→mod2
:40014→mult1
:40692→mult2
#The RandSeed Algorithm
:abs(int(n))→n
:If n=0 Then
: 12345→seed1
: 67890→seed2
:Else
: mod(mult1*n,mod1)→seed1
: mod(n,mod2)→seed2
:EndIf
#The rand() Algorithm
:Local result
:mod(seed1*mult1,mod1)→seed1
:mod(seed2*mult2,mod2)→seed2
:(seed1-seed2)/mod1→result
:If result<0
: result+1→result
:Return result
I translated this into C++ for testing:
#include <iostream>
#include <iomanip>
using namespace std;
long mod1 = 2147483563;
long mod2 = 2147483399;
long mult1 = 40014;
long mult2 = 40692;
long seed1,seed2;
void Seed(int n){
if(n<0) //Perform an abs
n = -n;
if(n==0){
seed1 = 12345; //Gotta love these seed values!
seed2 = 67890;
} else {
seed1 = (mult1*n)%mod1;
seed2 = n%mod2;
}
}
double Generate(){
double result;
seed1 = (seed1*mult1)%mod1;
seed2 = (seed2*mult2)%mod2;
result = (double)(seed1-seed2)/(double)mod1;
if(result<0)
result = result+1;
return result;
}
int main(){
Seed(0);
for(int i=0;i<10;i++)
cout<<setprecision(10)<<Generate()<<endl;
}
This gave the following results:
0.9435974025
0.908318861
0.1466878292
0.5147019502
0.405809642
0.7338123114
0.04399198747
0.3393625248
0.9954663411
0.2003402617
which match those achieved with the implementation based on the original paper.
I implemented rand, randInt, randM and randBin in Python. Thanks Richard for the C code. All implemented commands work as expected. You can also find it in this Gist.
import math
class TIprng(object):
def __init__(self):
self.mod1 = 2147483563
self.mod2 = 2147483399
self.mult1 = 40014
self.mult2 = 40692
self.seed1 = 12345
self.seed2 = 67890
def seed(self, n):
n = math.fabs(math.floor(n))
if (n == 0):
self.seed1 = 12345
self.seed2 = 67890
else:
self.seed1 = (self.mult1 * n) % self.mod1
self.seed2 = (n)% self.mod2
def rand(self, times = 0):
# like TI, this will return a list (array in python) if times == 1,
# or an integer if times isn't specified
if not(times):
self.seed1 = (self.seed1 * self.mult1) % self.mod1
self.seed2 = (self.seed2 * self.mult2)% self.mod2
result = (self.seed1 - self.seed2)/self.mod1
if(result<0):
result = result+1
return result
else:
return [self.rand() for _ in range(times)]
def randInt(self, minimum, maximum, times = 0):
# like TI, this will return a list (array in python) if times == 1,
# or an integer if times isn't specified
if not(times):
if (minimum < maximum):
return (minimum + math.floor((maximum- minimum + 1) * self.rand()))
else:
return (maximum + math.floor((minimum - maximum + 1) * self.rand()))
else:
return [self.randInt(minimum, maximum) for _ in range(times)]
def randBin(self, numtrials, prob, times = 0):
if not(times):
return sum([(self.rand() < prob) for _ in range(numtrials)])
else:
return [self.randBin(numtrials, prob) for _ in range(times)]
def randM(self, rows, columns):
# this will return an array of arrays
matrixArr = [[0 for x in range(columns)] for x in range(rows)]
# we go from bottom to top, from right to left
for row in reversed(range(rows)):
for column in reversed(range(columns)):
matrixArr[row][column] = self.randInt(-9, 9)
return matrixArr
testPRNG = TIprng()
testPRNG.seed(0)
print(testPRNG.randInt(0,100))
testPRNG.seed(0)
print(testPRNG.randM(3,4))
The algorithm used by the TI-Basic rand command is L'Ecuyer's algorithm according to TIBasicDev.
rand generates a uniformly-distributed pseudorandom number (this page
and others will sometimes drop the pseudo- prefix for simplicity)
between 0 and 1. rand(n) generates a list of n uniformly-distributed
pseudorandom numbers between 0 and 1. seed→rand seeds (initializes)
the built-in pseudorandom number generator. The factory default seed
is 0.
L'Ecuyer's algorithm is used by TI calculators to generate
pseudorandom numbers.
Unfortunately I have not been able to find any source published by Texas Instruments backing up this claim, so I cannot with certainty that this is the algorthm used. I am also uncertain what exactly is referred to by L'Ecuyer's algorithm.
Here is a C++ program that works:
#include<cmath>
#include<iostream>
#include<iomanip>
using namespace std;
int main()
{
double seed1 = 12345;
double seed2 = 67890;
double mod1 = 2147483563;
double mod2 = 2147483399;
double result;
for(int i=0; i<10; i++)
{
seed1 = seed1*40014-mod1*floor((seed1*40014)/mod1);
seed2 = seed2*40692-mod2*floor((seed2*40692)/mod2);
result = (seed1 - seed2)/mod1;
if(result < 0)
{result = result + 1;}
cout<<setprecision(10)<<result<<endl;
}
return 0;
}
I need some help to parallelize the pi calculation with the monte carlo method with openmp by a given random number generator, which is not thread safe.
First: This SO thread didn't help me.
My own try is the following #pragma omp statements. I thought the i, x and y vars should be init by each thread and should than be private. z ist the sum of all hits in the circle, so it should be summed after the implied barriere after the for loop.
Think the main problem ist the static state var of the random number generator. I made a critical section where the functions are called, so that only one thread per time could execute it. But the Pi solutions doesn't scale with more higher values.
Note: I should not use another RNG, but its okay to make little changes on it.
int main (int argc, char *argv[]) {
int i, z = 0, threads = 8, iters = 100000;
double x,y, pi;
#pragma omp parallel firstprivate(i,x,y) reduction(+:z) num_threads(threads)
for (i=0; i<iters; ++i) {
#pragma omp critical
{
x = rng_doub(1.0);
y = rng_doub(1.0);
}
if ((x*x+y*y) <= 1.0)
z++;
}
pi = ((double) z / (double) (iters*threads))*4.0;
printf("Pi: %lf\n", pi);;
return 0;
}
This RNG is actually an included file, but as I'm not sure if I create the header file correct, I integrated it in the other program file, so I have only one .c file.
#define RNG_MOD 741025
int rng_int(void) {
static int state = 0;
return (state = (1366 * state + 150889) % RNG_MOD);
}
double rng_doub(double range) {
return ((double) rng_int()) / (double) ((RNG_MOD - 1)/range);
}
I've also tried to make the static int state global, but it doesn't change my result, maybe I done it wrong. So please could you help me make the correct changes? Thank you very much!
Your original linear congruent PRNG has a cycle length of 49400, therefore you are only getting 29700 unique test points. This is a terrible generator to be used for any kind of Monte Carlo simulations. Even if you make 100000000 trials, you won't get any closer to the true value of Pi because you are simply repeating the same points over and over again and as a result both the final value of z and iters are simply multiplied by the same constant, which cancel in the end during the division.
The per-thread seed introduced by Z boson improves the situation a little bit with the number of unique points increasing with the total number of OpenMP threads. The increase is not linear since if the seed of one PRNG falls in the sequence of another PRNG, both PRNGs produce the same sequence shifted with no more than 49400 elements. Given the cycle length, each PRNG covers 49400/RNG_MOD = 6,7% of the total output range and that is the probability of two PRNGs being synchronised. There are a total of RNG_MOD/49400 = 15 unique sequences possible. It basically means that in the best seeding case scenario you won't be able to get past 30 threads as any other thread would simply repeat the result of some of the others. The multiplier 2 comes from the fact that each point uses two elements from the sequence and therefore it is possible to get a different set of points if you shift the sequence by one element.
The ultimate solution is to completely drop your PRNG and stick to something like Mersenne twister MT19937, which has a cycle length of 219937 − 1 and a very strong seeding algorithm. If you are not able to use another PRNG as you state in your question, at least modify the constants of the LCG to match those used in rand():
int rng_int(void) {
static int state = 1;
// & 0x7fffffff is equivalent to modulo with RNG_MOD = 2^31
return (state = (state * 1103515245 + 12345) & 0x7fffffff);
}
Note that rand() is not a good PRNG - it is still bad. It is just a little better than the one used in your code.
Try the code below. It makes a private state for each thread. I did something similar with the at rand_r function Why does calculation with OpenMP take 100x more time than with a single thread?
Edit: I updated my code using some of Hristo's suggestions. I used threadprivate (for the first time). I also used a better rand function which gives a better estimate of pi but it's still not good enough.
One strange things was I had to define the function rng_int after threadprivate otherwise I got an error "error: 'state' declared 'threadprivate' after first use". I should probably ask a question about this.
//gcc -O3 -Wall -pedantic -fopenmp main.c
#include <omp.h>
#include <stdio.h>
#define RNG_MOD 0x80000000
int state;
int rng_int(void);
double rng_doub(double range);
int main() {
int i, numIn, n;
double x, y, pi;
n = 1<<30;
numIn = 0;
#pragma omp threadprivate(state)
#pragma omp parallel private(x, y) reduction(+:numIn)
{
state = 25234 + 17 * omp_get_thread_num();
#pragma omp for
for (i = 0; i <= n; i++) {
x = (double)rng_doub(1.0);
y = (double)rng_doub(1.0);
if (x*x + y*y <= 1) numIn++;
}
}
pi = 4.*numIn / n;
printf("asdf pi %f\n", pi);
return 0;
}
int rng_int(void) {
// & 0x7fffffff is equivalent to modulo with RNG_MOD = 2^31
return (state = (state * 1103515245 + 12345) & 0x7fffffff);
}
double rng_doub(double range) {
return ((double)rng_int()) / (((double)RNG_MOD)/range);
}
You can see the results (and edit and run the code) at http://coliru.stacked-crooked.com/a/23c1753a1b7d1b0d
I'm writing a code that performs a random scan over a set of 4 numbers. I'd like to scan 10000 points (millions later). I just learned about rand(), so here's the relevant part:
int numPoints = 10000;
double A,B,C,D;
for (i=0; i<=numPoints1;i++) {
srand ( time(NULL) );
A = rand() % 500 + 100;
B = rand() % 500 + 100;
C = rand() % 100 - 100;
D = rand() % 5 + 2.5;
Then these four variable are fed into a function (A,B,C,D).
The code performs some checks and calculations inside the loop.
}
However, I noticed in the output file that many times, the same set of A,B,C,D is picked.
Q: Any suggestions as to how can I improve the situation?
You should move the call to srand out of the loop. Like this:
srand(time(NULL));
for (i = 0; i <= numPoints1; i++)
{
...
}
What's happening is that you're re-initializing the random number generator with each iteration. As I recall, time returns the time as a number of seconds. So time(NULL) will only change once per second, meaning that you'll be seeding the random number with the same seed multiple times.
That said, this won't guarantee that a set of numbers isn't repeated. It will, however, make duplicates much less likely.