Search for the seed of the rand () function TI-84

Question

I have researched this rand () TI-84 function a lot. It uses the L'Ecuyer algorithm to generate pseudo random numbers. I have an interesting case.

If the proper seed is given to the rand () function, it will always generate the same numbers. So, given the first random number that the rand () function generates, is it possible to find the seed of the function?

Let the variable X represent an unknown seed.

    X->rand
    rand->D
    Disp D

Conclusion:

    0.114820491

Based on this information, is it possible to calculate the seed of the rand () function? Can you somehow step back from the rand () TI-84 algorithm?

Answer 1

, , , . :

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

int64_t mod1  = 2147483563;
int64_t mod2  = 2147483399;
int64_t mult1 = 40014;
int64_t mult2 = 40692;
int64_t seed1,seed2;

void Seed(int64_t 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(int argc, char **argv){
  double x = 0.114820491; // Mattkx4 value
  double r;
  int64_t n;
  int i;

  if (argc > 2) {
    printf("USAGE: %s <1st generated random number>\n", argv[0]);
    return 1;
  } else if (argc == 2) {
    x = atof(argv[1]);
    printf("[Looking for seed generating %.10f]\n", x);
  } else {
    printf("[Looking for seed generating default value of %.10f]\n", x);
  }

  for (n=0; n<= 2147483647; n++) {
    Seed(n);
    r = Generate();
    if (fabs(r-x) < 10e-10) {
      printf("HIT: seed is %ld; G()=%.10f, G()-x=%.12f\n", (long) n, r, r-x);
      for (i=0; i<5; i++) {
        printf("  G() = %.10f\n", Generate());
      }
    }
  }

  return 0;
}

OPs :

$ time ./a.out
[Looking for seed generating default value of 0.1148204910]
HIT: seed is 41817; G()=0.1148204909, G()-x=-0.000000000055
  G() = 0.1928098124
  G() = 0.8785866698
  G() = 0.7541802051
  G() = 0.3236799652
  G() = 0.2698472063
HIT: seed is 196206349; G()=0.1148204909, G()-x=-0.000000000055
  G() = 0.7255189385
  G() = 0.3079613984
  G() = 0.8041985209
  G() = 0.0959226401
  G() = 0.7729820570
HIT: seed is 392370881; G()=0.1148204909, G()-x=-0.000000000055
  G() = 0.2582281409
  G() = 0.7373361269
  G() = 0.8542168367
  G() = 0.8681653150
  G() = 0.2761169842
HIT: seed is 588535413; G()=0.1148204909, G()-x=-0.000000000055
  G() = 0.7909372669
  G() = 0.1667108555
  G() = 0.9042350761
  G() = 0.6404079899
  G() = 0.7792519113
HIT: seed is 1869313916; G()=0.1148204919, G()-x=0.000000000876
  G() = 0.9421831845
  G() = 0.2660259263
  G() = 0.9001868100
  G() = 0.3563914254
  G() = 0.3884731955
HIT: seed is 2065478448; G()=0.1148204919, G()-x=0.000000000876
  G() = 0.4748923105
  G() = 0.6954006549
  G() = 0.9502050494
  G() = 0.1286341003
  G() = 0.8916080463

real    1m24.132s
user    1m24.179s
sys 0m0.000s

, , , @richard, this stackoverflow. , .

Answer 2

, . , rand.

0→C

Repeat X=0.114820491
Disp C
C→rand
rand→X
C+1→C
End

Disp "Done!"

rand , , .

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. @JimD. .