RNG147

March 28, 2017

We have looked at random number generators in several previous exercises, but most of them returned integers. In today’s exercise we look at a simple random number generator that returns floating-point numbers. The generator is simple: Given a seed between zero and one, the next number in the sequence is the fractional portion of 147 times the seed.

Your task is to implement the random number generator described above, and to assess its suitability. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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3 Responses to “RNG147”

  1. Rutger said

    In python 3

    def rng147(seed):
    	while True:
    		yield seed
    		seed = (147.0 * seed) % 1.0
    
    
    r = rng147(0.1234)
    
    for v in range(10):
    	print(next(r))
    
  2. Graham said

    Your sine trick only moves the problem elsewhere; try seeding with pi/6 (arcsin of 1/2).

    Solution in Haskell, using the Stream package for explicitly infinite lists:

    module Main where
    
    import           Data.Fixed  (mod')
    import           Data.Stream (Stream)
    import qualified Data.Stream as S
    
    rng147 :: Double -> Stream Double
    rng147 = S.iterate (\x -> (147 * x) `mod'` 1)
    
    main :: IO ()
    main = mapM_ print . S.take 10 . rng147 $ pi / 10
    
  3. Globules said

    Here’s another Haskell version. With an integer argument, n, it prints the first n random numbers. With no arguments it converts the stream of random Doubles into a stream of 32-bit unsigned integers. The purpose is to feed that binary data to the dieharder program, which evaluates its randomness. We don’t make use of all the bits in the Double; it’s just an easy way of getting the data to dieharder in a form that it likes.

    {-# LANGUAGE ScopedTypeVariables #-}
    
    import Control.Monad (void)
    import Data.Word (Word32)
    import Foreign.Marshal.Alloc (alloca)
    import Foreign.Storable (poke, sizeOf)
    import System.Environment (getArgs)
    import System.IO (hPutBuf, stdout)
    
    -- A stream of "random" numbers.  (We take the tail to exclude the seed from the
    -- values.)
    rng147 :: RealFrac b => b -> [b]
    rng147 = tail . iterate step
      where step x = let (_ :: Int, f) = properFraction (147 * x) in f
    
    main :: IO ()
    main = do
      let rs = rng147 (0.1234567 :: Double)
      ns <- fmap (map read) getArgs :: IO [Int]
      case ns of
        -- Output an endless stream of 32-bit binary data for dieharder.
        []  -> put $ map cvt rs
        
        -- Print the first n random values.
        [n] -> mapM_ print $ take n rs
        
        -- Invalid argument(s).
        _   -> putStrLn "Usage: rng147 [n]"
      
    -- Convert a value to an 32-bit unsigned integer, possibly throwing away the
    -- least significant bits of the argument.
    cvt :: RealFrac a => a -> Word32
    cvt x = round $ fromIntegral (maxBound :: Word32) * x
    
    -- Output the unsigned 32-bit values as binary data.
    put :: [Word32] -> IO ()
    put is = let n = sizeOf (0 :: Word32)
             in alloca (\p -> void (mapM_ (\i -> poke p i >> hPutBuf stdout p n) is))
    
    $ ./rng147 10
    0.14813489999999874
    0.7758302999998143
    4.705409997271204e-2
    0.9169526959886696
    0.7920463103344275
    0.430807619160845
    0.3287200166442119
    0.32184244669915074
    0.310839664775159
    0.6934307219483742
    

    Here’s the result of feeding the output to dieharder. I won’t try to interpret the results, here. (The -a argument tells it to run all the tests it has; -g 200 says that stdin is a series of 32-bit unsigned integers.) The summary is that 82 tests passed, 27 failed and 5 were weak.

    $ ./rng147 | dieharder -a -g 200
    #=============================================================================#
    #            dieharder version 3.31.1 Copyright 2003 Robert G. Brown          #
    #=============================================================================#
       rng_name    |rands/second|   Seed   |
    stdin_input_raw|  1.01e+07  |2776686247|
    #=============================================================================#
            test_name   |ntup| tsamples |psamples|  p-value |Assessment
    #=============================================================================#
       diehard_birthdays|   0|       100|     100|0.64044752|  PASSED  
          diehard_operm5|   0|   1000000|     100|0.00000000|  FAILED  
      diehard_rank_32x32|   0|     40000|     100|0.45366134|  PASSED  
        diehard_rank_6x8|   0|    100000|     100|0.97658733|  PASSED  
       diehard_bitstream|   0|   2097152|     100|0.72508491|  PASSED  
            diehard_opso|   0|   2097152|     100|0.00000000|  FAILED  
            diehard_oqso|   0|   2097152|     100|0.00000000|  FAILED  
             diehard_dna|   0|   2097152|     100|0.00000000|  FAILED  
    diehard_count_1s_str|   0|    256000|     100|0.00000000|  FAILED  
    diehard_count_1s_byt|   0|    256000|     100|0.00000000|  FAILED  
     diehard_parking_lot|   0|     12000|     100|0.00000000|  FAILED  
        diehard_2dsphere|   2|      8000|     100|0.00000000|  FAILED  
        diehard_3dsphere|   3|      4000|     100|0.00000000|  FAILED  
         diehard_squeeze|   0|    100000|     100|0.00000000|  FAILED  
            diehard_sums|   0|       100|     100|0.06709806|  PASSED  
            diehard_runs|   0|    100000|     100|0.00000000|  FAILED  
            diehard_runs|   0|    100000|     100|0.00000000|  FAILED  
           diehard_craps|   0|    200000|     100|0.13428702|  PASSED  
           diehard_craps|   0|    200000|     100|0.00096831|   WEAK   
     marsaglia_tsang_gcd|   0|  10000000|     100|0.00000000|  FAILED  
     marsaglia_tsang_gcd|   0|  10000000|     100|0.00000000|  FAILED  
             sts_monobit|   1|    100000|     100|0.03994929|  PASSED  
                sts_runs|   2|    100000|     100|0.22979976|  PASSED  
              sts_serial|   1|    100000|     100|0.98471576|  PASSED  
              sts_serial|   2|    100000|     100|0.31624292|  PASSED  
              sts_serial|   3|    100000|     100|0.13274265|  PASSED  
              sts_serial|   3|    100000|     100|0.06274970|  PASSED  
              sts_serial|   4|    100000|     100|0.10906298|  PASSED  
              sts_serial|   4|    100000|     100|0.71359846|  PASSED  
              sts_serial|   5|    100000|     100|0.00790811|  PASSED  
              sts_serial|   5|    100000|     100|0.07231695|  PASSED  
              sts_serial|   6|    100000|     100|0.17659272|  PASSED  
              sts_serial|   6|    100000|     100|0.18513720|  PASSED  
              sts_serial|   7|    100000|     100|0.04315090|  PASSED  
              sts_serial|   7|    100000|     100|0.45634930|  PASSED  
              sts_serial|   8|    100000|     100|0.14826946|  PASSED  
              sts_serial|   8|    100000|     100|0.42520026|  PASSED  
              sts_serial|   9|    100000|     100|0.71305937|  PASSED  
              sts_serial|   9|    100000|     100|0.20822407|  PASSED  
              sts_serial|  10|    100000|     100|0.97154428|  PASSED  
              sts_serial|  10|    100000|     100|0.69812982|  PASSED  
              sts_serial|  11|    100000|     100|0.53454147|  PASSED  
              sts_serial|  11|    100000|     100|0.08444014|  PASSED  
              sts_serial|  12|    100000|     100|0.22453592|  PASSED  
              sts_serial|  12|    100000|     100|0.72236320|  PASSED  
              sts_serial|  13|    100000|     100|0.78366045|  PASSED  
              sts_serial|  13|    100000|     100|0.37616667|  PASSED  
              sts_serial|  14|    100000|     100|0.95764809|  PASSED  
              sts_serial|  14|    100000|     100|0.14472891|  PASSED  
              sts_serial|  15|    100000|     100|0.43901688|  PASSED  
              sts_serial|  15|    100000|     100|0.76714556|  PASSED  
              sts_serial|  16|    100000|     100|0.58587727|  PASSED  
              sts_serial|  16|    100000|     100|0.67425978|  PASSED  
             rgb_bitdist|   1|    100000|     100|0.05846675|  PASSED  
             rgb_bitdist|   2|    100000|     100|0.00004623|   WEAK   
             rgb_bitdist|   3|    100000|     100|0.66589418|  PASSED  
             rgb_bitdist|   4|    100000|     100|0.00026565|   WEAK   
             rgb_bitdist|   5|    100000|     100|0.07969442|  PASSED  
             rgb_bitdist|   6|    100000|     100|0.17850326|  PASSED  
             rgb_bitdist|   7|    100000|     100|0.25911992|  PASSED  
             rgb_bitdist|   8|    100000|     100|0.00045592|   WEAK   
             rgb_bitdist|   9|    100000|     100|0.00642740|  PASSED  
             rgb_bitdist|  10|    100000|     100|0.27514527|  PASSED  
             rgb_bitdist|  11|    100000|     100|0.91420132|  PASSED  
             rgb_bitdist|  12|    100000|     100|0.09738292|  PASSED  
    rgb_minimum_distance|   2|     10000|    1000|0.00000000|  FAILED  
    rgb_minimum_distance|   3|     10000|    1000|0.00000000|  FAILED  
    rgb_minimum_distance|   4|     10000|    1000|0.00000000|  FAILED  
    rgb_minimum_distance|   5|     10000|    1000|0.01232138|  PASSED  
        rgb_permutations|   2|    100000|     100|0.55323173|  PASSED  
        rgb_permutations|   3|    100000|     100|0.00000000|  FAILED  
        rgb_permutations|   4|    100000|     100|0.00000000|  FAILED  
        rgb_permutations|   5|    100000|     100|0.00000000|  FAILED  
          rgb_lagged_sum|   0|   1000000|     100|0.76792249|  PASSED  
          rgb_lagged_sum|   1|   1000000|     100|0.59838659|  PASSED  
          rgb_lagged_sum|   2|   1000000|     100|0.95607401|  PASSED  
          rgb_lagged_sum|   3|   1000000|     100|0.28565715|  PASSED  
          rgb_lagged_sum|   4|   1000000|     100|0.95085961|  PASSED  
          rgb_lagged_sum|   5|   1000000|     100|0.45582064|  PASSED  
          rgb_lagged_sum|   6|   1000000|     100|0.60565985|  PASSED  
          rgb_lagged_sum|   7|   1000000|     100|0.04195406|  PASSED  
          rgb_lagged_sum|   8|   1000000|     100|0.30831976|  PASSED  
          rgb_lagged_sum|   9|   1000000|     100|0.36546234|  PASSED  
          rgb_lagged_sum|  10|   1000000|     100|0.19936994|  PASSED  
          rgb_lagged_sum|  11|   1000000|     100|0.07303233|  PASSED  
          rgb_lagged_sum|  12|   1000000|     100|0.34645127|  PASSED  
          rgb_lagged_sum|  13|   1000000|     100|0.29195838|  PASSED  
          rgb_lagged_sum|  14|   1000000|     100|0.30094975|  PASSED  
          rgb_lagged_sum|  15|   1000000|     100|0.99790005|   WEAK   
          rgb_lagged_sum|  16|   1000000|     100|0.75196523|  PASSED  
          rgb_lagged_sum|  17|   1000000|     100|0.38809626|  PASSED  
          rgb_lagged_sum|  18|   1000000|     100|0.61180091|  PASSED  
          rgb_lagged_sum|  19|   1000000|     100|0.19440479|  PASSED  
          rgb_lagged_sum|  20|   1000000|     100|0.57917094|  PASSED  
          rgb_lagged_sum|  21|   1000000|     100|0.83129601|  PASSED  
          rgb_lagged_sum|  22|   1000000|     100|0.57292407|  PASSED  
          rgb_lagged_sum|  23|   1000000|     100|0.10381929|  PASSED  
          rgb_lagged_sum|  24|   1000000|     100|0.93651195|  PASSED  
          rgb_lagged_sum|  25|   1000000|     100|0.50848729|  PASSED  
          rgb_lagged_sum|  26|   1000000|     100|0.81756629|  PASSED  
          rgb_lagged_sum|  27|   1000000|     100|0.29194323|  PASSED  
          rgb_lagged_sum|  28|   1000000|     100|0.14934239|  PASSED  
          rgb_lagged_sum|  29|   1000000|     100|0.96722837|  PASSED  
          rgb_lagged_sum|  30|   1000000|     100|0.41045537|  PASSED  
          rgb_lagged_sum|  31|   1000000|     100|0.33379469|  PASSED  
          rgb_lagged_sum|  32|   1000000|     100|0.67528985|  PASSED  
         rgb_kstest_test|   0|     10000|    1000|0.12422629|  PASSED  
         dab_bytedistrib|   0|  51200000|       1|1.00000000|  FAILED  
                 dab_dct| 256|     50000|       1|0.00000000|  FAILED  
    Preparing to run test 207.  ntuple = 0
            dab_filltree|  32|  15000000|       1|0.00000000|  FAILED  
            dab_filltree|  32|  15000000|       1|0.00000000|  FAILED  
    Preparing to run test 208.  ntuple = 0
           dab_filltree2|   0|   5000000|       1|0.00000000|  FAILED  
           dab_filltree2|   1|   5000000|       1|0.00000000|  FAILED  
    Preparing to run test 209.  ntuple = 0
            dab_monobit2|  12|  65000000|       1|1.00000000|  FAILED  
    $ 
    

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