Generates Cauchy distributed random values.


template<typename RealType = float, typename Method = cauchy_method::by_default>
class cauchy {
using method_type = Method;
using result_type = RealType;
cauchy(): cauchy((RealType)0.0, (RealType)1.0){}
explicit cauchy(RealType a, RealType b);
RealType a() const;
RealType b() const;

Devices supported: Host, CPU, and GPU.

Include Files

  • oneapi/mkl/rng.hpp


The oneapi::mkl::rng::cauchy class object is used in the oneapi::mkl::rng::generate function to provide Cauchy distributed random numbers with displacement (a) and scalefactor (b, β), where a, β∈R ; β > 0.

The probability density function is given by:


The cumulative distribution function is as follows:


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

This notice covers the following instruction sets: SSE2, SSE4.2, AVX2, AVX-512.

Template Parameters

typename RealType = float

Type of the produced values. The specific values are as follows: float double

typename Method = oneapi::mkl::rng::cauchy_method::by_default

Generation method. The specific values are as follows: oneapi::mkl::rng::cauchy_method::icdf See brief descriptions of the methods in Distributions Template Parameter Method Values

Input Parameters





RealType (float, double)

Displacement a.


RealType (float, double)

Scalefactor b.