MRG32k3a Combined recursive generator (pseudo-code)

   /* Constants */
   /* First generator */
   a1 = [0, 1403580, -810728]
   m1 = 2**32 - 209
   /* Second Generator */
   a2 = [527612, 0, -1370589]
   m2 = 2**32 - 22853
    
   d = m1 + 1
   
   class MRG32k3a
       x1 = [0, 0, 0]  /* list of three last values of gen #1 */
       x2 = [0, 0, 0]  /* list of three last values of gen #2 */
       
       method seed(u64 seed_state)
           assert seed_state in range >0 and < d 
           x1 = [seed_state, 0, 0]
           x2 = [seed_state, 0, 0]
       end method
           
       method next_int()
           x1i = (a1[0]*x1[0] + a1[1]*x1[1] + a1[2]*x1[2]) mod m1
           x2i = (a2[0]*x2[0] + a2[1]*x2[1] + a2[2]*x2[2]) mod m2
           x1 = [x1i, x1[0], x1[1]]    /* Keep last three */
           x2 = [x2i, x2[0], x2[1]]    /* Keep last three */
           z = (x1i - x2i) % m1
           answer = (z + 1)
           
           return answer
       end method
       
       method next_float():
           return float next_int() / d
       end method
       
   end class


MRG32k3a Use:
   random_gen = instance MRG32k3a
   random_gen.seed(1234567)
   print(random_gen.next_int())   /* 1459213977 */
   print(random_gen.next_int())   /* 2827710106 */
   print(random_gen.next_int())   /* 4245671317 */
   print(random_gen.next_int())   /* 3877608661 */
   print(random_gen.next_int())   /* 2595287583 */
   
       

Task
 Generate a class/set of functions that generates pseudo-random
numbers as shown above.

 Show that the first five integers generated with the seed `1234567`
are as shown above

 Show that for an initial seed of '987654321' the counts of 100_000
repetitions of

   floor(random_gen.next_float() * 5)

Is as follows:

   0: 20002, 1: 20060, 2: 19948, 3: 20059, 4: 19931

 Show your output here, on this page.


def mod(x, y)
    m = x % y
    if m < 0 then
        if y < 0 then
            return m - y
        else
            return m + y
        end
    end
    return m
end
 
# Constants
# First generator
A1 = [0, 1403580, -810728]
A1.freeze
M1 = (1 << 32) - 209
# Second generator
A2 = [527612, 0, -1370589]
A2.freeze
M2 = (1 << 32) - 22853
 
D = M1 + 1
 
# the last three values of the first generator
$x1 = [0, 0, 0]
# the last three values of the second generator
$x2 = [0, 0, 0]
 
def seed(seed_state)
    $x1 = [seed_state, 0, 0]
    $x2 = [seed_state, 0, 0]
end
 
def next_int()
    x1i = mod((A1[0] * $x1[0] + A1[1] * $x1[1] + A1[2] * $x1[2]), M1)
    x2i = mod((A2[0] * $x2[0] + A2[1] * $x2[1] + A2[2] * $x2[2]), M2)
    z = mod(x1i - x2i, M1)
 
    $x1 = [x1i, $x1[0], $x1[1]]
    $x2 = [x2i, $x2[0], $x2[1]]
 
    return z + 1
end
 
def next_float()
    return 1.0 * next_int() / D
end
 
########################################
 
seed(1234567)
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print "\n"
 
counts = [0, 0, 0, 0, 0]
seed(987654321)
for i in 1 .. 100000
    value = (next_float() * 5.0).floor
    counts[value] = counts[value] + 1
end
counts.each_with_index { |v,i|
    print i, ": ", v, "\n"
}