Contents

MCG31m1

This is a 31-bit multiplicative congruential generator:
  
MCG31m1 belongs to linear congruential generators with the period length of approximately 2
31
. Such generators are still used as default random number generators in various software systems, mainly due to the simplicity of the portable versions implementation, speed and compatibility with the earlier systems versions. However, their period length does not meet the requirements for modern basic generators. Still, the MCG31m1 generator possesses good statistic properties and you may successfully use it to generate random numbers of different distributions for small samplings.
Real Implementation (Single and Double Precision)
The output vector is the sequence of the floating-point values
u
0
,
u
1
, ...
Integer Implementation
The output vector of 32-bit integers
x
0
,
x
1
, ...
Stream Initialization by Function
vslNewStream
MCG31m1 generates the stream and initializes it specifying the input 32-bit parameter seed :
  1. Assume
    x0 = seed mod 0x7FFFFFFF
  2. If
    x
    0
    = 0, assume
    x
    0
    = 1.
Stream Initialization by Function
vslNewStreamEx
MCG31m1 generates the stream and initializes it specifying the array
params[]
of
n
32-bit integers:
  1. If
    n
    = 0, assume
    x
    0
    = 1
  2. Otherwise, assume
    x0 = params[0] mod 0x7FFFFFFF
    If
    x
    0
    = 0, assume
    x
    0
    = 1.
Subsequences Selection Methods
vslSkipAheadStream
Supported
vslSkipAheadStreamEx
Not supported
vslLeapfrogStream
Supported
Generator Period
Lattice Structure
M
8
= 0.72771, M
16
= 0.61996, M
32
= 0.61996 (for more details see [L'Ecu94]).
Empirical Testing Results Summary
Test Name
vsRngUniform
vdRngUniform
viRngUniform
viRngUniformBits
3D Spheres Test
OK (10% errors)
OK (10% errors)
Not applicable
OK (10% errors)
Birthday Spacing Test
Not applicable
Not applicable
Not applicable
OK (0% errors)
Bitstream Test
Not applicable
Not applicable
Not applicable
OK (10% errors)
Rank of 31x31 Binary Matrices Test
Not applicable
Not applicable
Not applicable
OK (10% errors)
Rank of 32x32 Binary Matrices Test
Not applicable
Not applicable
Not applicable
Not applicable
Rank of 6x8 Binary Matrices Test
Not applicable
Not applicable
Not applicable
OK (0% errors)
Counts-the-1’s Test (stream of bits)
Not applicable
Not applicable
Not applicable
OK (20% errors)
Counts-the-1’s Test (stream of specific bytes)
Not applicable
Not applicable
Not applicable
OK (0% errors)
Craps Test
OK (20% errors)
OK (20% errors)
OK (20% errors)
OK (20% errors)
Parking Lot Test
OK (10% errors)
OK (10% errors)
Not applicable
OK (10% errors)
2D Self-Avoiding Random Walk Test
OK (20% errors)
OK (20% errors)
Not applicable
OK (20% errors)
Note
  1. The tabulated data is obtained using the one-level (threshold) testing technique. The OK result indicates FAIL < 50%. The run fails when p-value falls outside the interval [0.05, 0.95].
  2. The stream tested is generated by calling the function
    vslNewStream
    with seed=7,777,777.

Product and Performance Information

1

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804