boxmuller.hpp

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/*
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// This file implements the Box-Muller method for generating gaussian
// random variables (GRVs).  Box-Muller has the advantage of
// deterministically requiring exactly two uniform random variables as
// input and producing exactly two GRVs as output, which makes it
// especially well-suited to the counter-based generators in
// Random123.  Other methods (e.g., Ziggurat, polar) require an
// indeterminate number of inputs for each output and so require a
// 'MicroURNG' to be used with Random123.  The down side of Box-Muller
// is that it calls sincos, log and sqrt, which may be slow.  However,
// on GPUs, these functions are remarkably fast, which makes
// Box-Muller the fastest GRV generator we know of on GPUs.
//
// This file exports two structs and one overloaded function,
// all in the r123 namespace:
//   struct r123::float2{ float x,y; }
//   struct r123::double2{ double x,y; }
//
//   r123::float2  r123::boxmuller(uint32_t u0, uint32_t u1);
//   r123::double2 r123::boxmuller(uint64_t u0, uint64_t u1);
//
// float2 and double2 are identical to their synonymous global-
// namespace structures in CUDA.
//
// This file may not be as portable, and has not been tested as
// rigorously as other files in the library, e.g., the generators.
// Nevertheless, we hope it is useful and we encourage developers to
// copy it and modify it for their own use.  We invite comments and
// improvements.
 
#ifndef _r123_BOXMULLER_HPP__
#define _r123_BOXMULLER_HPP__
 
#include <Random123/features/compilerfeatures.h>
#include <Random123/uniform.hpp>
#include <math.h>
 
namespace r123 {
 
#if !defined(__CUDACC__)
typedef struct {
    float x, y;
} float2;
typedef struct {
    double x, y;
} double2;
#else
typedef ::float2 float2;
typedef ::double2 double2;
#endif
 
#if !defined(R123_NO_SINCOS) && defined(__APPLE__)
/* MacOS X 10.10.5 (2015) doesn't have sincosf */
#define R123_NO_SINCOS 1
#endif
 
#if R123_NO_SINCOS /* enable this if sincos and sincosf are not in the math library */
R123_CUDA_DEVICE R123_STATIC_INLINE void sincosf(float x, float* s, float* c) {
    *s = sinf(x);
    *c = cosf(x);
}
 
R123_CUDA_DEVICE R123_STATIC_INLINE void sincos(double x, double* s, double* c) {
    *s = sin(x);
    *c = cos(x);
}
#endif /* sincos is not in the math library */
 
#if !defined(CUDART_VERSION) || CUDART_VERSION < 5000 /* enabled if sincospi and sincospif are not in math lib */
 
R123_CUDA_DEVICE R123_STATIC_INLINE void sincospif(float x, float* s, float* c) {
    float const PIf = 3.1415926535897932f;
    sincosf(PIf * x, s, c);
}
 
R123_CUDA_DEVICE R123_STATIC_INLINE void sincospi(double x, double* s, double* c) {
    double const PI = 3.1415926535897932;
    sincos(PI * x, s, c);
}
#endif /* sincospi is not in math lib */
 
/*
 * take two 32bit unsigned random values and return a float2 with
 * two random floats in a normal distribution via a Box-Muller transform
 */
R123_CUDA_DEVICE R123_STATIC_INLINE float2 boxmuller(uint32_t u0, uint32_t u1) {
    float r;
    float2 f;
    sincospif(uneg11<float>(u0), &f.x, &f.y);
    r = sqrtf(-2.f * logf(u01<float>(u1))); // u01 is guaranteed to avoid 0.
    f.x *= r;
    f.y *= r;
    return f;
}
 
/*
 * take two 64bit unsigned random values and return a double2 with
 * two random doubles in a normal distribution via a Box-Muller transform
 */
R123_CUDA_DEVICE R123_STATIC_INLINE double2 boxmuller(uint64_t u0, uint64_t u1) {
    double r;
    double2 f;
 
    sincospi(uneg11<double>(u0), &f.x, &f.y);
    r = sqrt(-2. * log(u01<double>(u1))); // u01 is guaranteed to avoid 0.
    f.x *= r;
    f.y *= r;
    return f;
}
} // namespace r123
 
#endif /* BOXMULLER_H__ */