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ChiSquare (VSL_RNG_METHOD_CHISQUARE_CHI2GAMMA)

Random number generator of the chi-square distribution with degrees of freedom
v
. You can generate any successful random number
x
of the chi-square distribution as follows:
  1. If
    v
    = 1 and
    v
    = 3, a chi-square distributed number is generated as a sum of squares of
    v
    independent normal random numbers with parameter mean value
    a
    = 0 and standard deviation
    σ
    = 1.
  2. If
    v
    is even and 2 ≤
    v
    ≤ 16, a chi-square distributed random number is generated according to the formula:
    , where
    ui
    is a vector of successive random numbers uniformly distributed over the interval (0, 1).
  3. If
    v
    ≥ 17 or
    v
    is odd and 5 ≤
    v
    ≤ 15, the ChiSquare distribution is reduced to Gamma distribution with parameters shape
    α
    =
    v
    /2, offset
    a
    = 0, and scalefactor
    β
    = 2. Random numbers of the Gamma distribution are generated using method VSL_RNG_METHOD_GAMMA_GNORM.
See Intel® MKL Vector Statistics Random Number Generator Performance Data for test results summary and performance graphs.

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