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// // SPDX-License-Identifier: BSD-3-Clause // Copyright Contributors to the OpenEXR Project. // // // Generators for uniformly distributed pseudo-random numbers and // functions that use those generators to generate numbers with // non-uniform distributions // // Note: class Rand48() calls erand48() and nrand48(), which are not // available on all operating systems. For compatibility we include // our own versions of erand48() and nrand48(). Our functions // have been reverse-engineered from the corresponding Unix/Linux // man page. // #ifndef INCLUDED_IMATHRANDOM_H #define INCLUDED_IMATHRANDOM_H #include "ImathExport.h" #include "ImathNamespace.h" #include #include IMATH_INTERNAL_NAMESPACE_HEADER_ENTER /// Fast random-number generator that generates /// a uniformly distributed sequence with a period /// length of 2^32. class Rand32 { public: /// Constructor, given a seed IMATH_HOSTDEVICE Rand32 (unsigned long int seed = 0); /// Re-initialize with a given seed IMATH_HOSTDEVICE void init (unsigned long int seed); /// Get the next value in the sequence (range: [false, true]) IMATH_HOSTDEVICE bool nextb (); /// Get the next value in the sequence (range: [0 ... 0xffffffff]) IMATH_HOSTDEVICE unsigned long int nexti (); /// Get the next value in the sequence (range: [0 ... 1[) IMATH_HOSTDEVICE IMATH_EXPORT float nextf (); /// Get the next value in the sequence (range [rangeMin ... rangeMax[) IMATH_HOSTDEVICE float nextf (float rangeMin, float rangeMax); private: IMATH_HOSTDEVICE void next (); unsigned long int _state; }; /// Random-number generator based on the C Standard Library /// functions erand48(), nrand48() & company; generates a /// uniformly distributed sequence. class Rand48 { public: /// Constructor IMATH_HOSTDEVICE Rand48 (unsigned long int seed = 0); /// Re-initialize with a given seed IMATH_HOSTDEVICE void init (unsigned long int seed); /// Get the next value in the sequence (range: [false, true]) IMATH_HOSTDEVICE bool nextb (); /// Get the next value in the sequence (range: [0 ... 0x7fffffff]) IMATH_HOSTDEVICE long int nexti (); /// Get the next value in the sequence (range: [0 ... 1[) IMATH_HOSTDEVICE double nextf (); /// Get the next value in the sequence (range [rangeMin ... rangeMax[) IMATH_HOSTDEVICE double nextf (double rangeMin, double rangeMax); private: unsigned short int _state[3]; }; /// Return random points uniformly distributed in a sphere with /// radius 1 around the origin (distance from origin <= 1). template IMATH_HOSTDEVICE Vec solidSphereRand (Rand& rand); /// Return random points uniformly distributed on the surface of /// a sphere with radius 1 around the origin. template IMATH_HOSTDEVICE Vec hollowSphereRand (Rand& rand); /// Return random numbers with a normal (Gaussian) /// distribution with zero mean and unit variance. template IMATH_HOSTDEVICE float gaussRand (Rand& rand); /// Return random points whose distance from the origin /// has a normal (Gaussian) distribution with zero mean /// and unit variance. template IMATH_HOSTDEVICE Vec gaussSphereRand (Rand& rand); //--------------------------------- // erand48(), nrand48() and friends //--------------------------------- /// @cond Doxygen_Suppress IMATH_HOSTDEVICE IMATH_EXPORT double erand48 (unsigned short state[3]); IMATH_HOSTDEVICE IMATH_EXPORT double drand48 (); IMATH_HOSTDEVICE IMATH_EXPORT long int nrand48 (unsigned short state[3]); IMATH_HOSTDEVICE IMATH_EXPORT long int lrand48 (); IMATH_HOSTDEVICE IMATH_EXPORT void srand48 (long int seed); /// @endcond //--------------- // Implementation //--------------- IMATH_HOSTDEVICE inline void Rand32::init (unsigned long int seed) { _state = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL; } IMATH_HOSTDEVICE inline Rand32::Rand32 (unsigned long int seed) { init (seed); } IMATH_HOSTDEVICE inline void Rand32::next () { _state = 1664525L * _state + 1013904223L; } IMATH_HOSTDEVICE inline bool Rand32::nextb () { next (); // Return the 31st (most significant) bit, by and-ing with 2 ^ 31. return !!(_state & 2147483648UL); } IMATH_HOSTDEVICE inline unsigned long int Rand32::nexti () { next (); return _state & 0xffffffff; } IMATH_HOSTDEVICE inline float Rand32::nextf (float rangeMin, float rangeMax) { float f = nextf (); return rangeMin * (1 - f) + rangeMax * f; } IMATH_HOSTDEVICE inline void Rand48::init (unsigned long int seed) { seed = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL; _state[0] = (unsigned short int) (seed & 0xFFFF); _state[1] = (unsigned short int) ((seed >> 16) & 0xFFFF); _state[2] = (unsigned short int) (seed & 0xFFFF); } IMATH_HOSTDEVICE inline Rand48::Rand48 (unsigned long int seed) { init (seed); } IMATH_HOSTDEVICE inline bool Rand48::nextb () { return nrand48 (_state) & 1; } IMATH_HOSTDEVICE inline long int Rand48::nexti () { return nrand48 (_state); } IMATH_HOSTDEVICE inline double Rand48::nextf () { return erand48 (_state); } IMATH_HOSTDEVICE inline double Rand48::nextf (double rangeMin, double rangeMax) { double f = nextf (); return rangeMin * (1 - f) + rangeMax * f; } template IMATH_HOSTDEVICE Vec solidSphereRand (Rand& rand) { Vec v; do { for (unsigned int i = 0; i < Vec::dimensions (); i++) v[i] = (typename Vec::BaseType) rand.nextf (-1, 1); } while (v.length2 () > 1); return v; } template IMATH_HOSTDEVICE Vec hollowSphereRand (Rand& rand) { Vec v; typename Vec::BaseType length; do { for (unsigned int i = 0; i < Vec::dimensions (); i++) v[i] = (typename Vec::BaseType) rand.nextf (-1, 1); length = v.length (); } while (length > 1 || length == 0); return v / length; } template IMATH_HOSTDEVICE float gaussRand (Rand& rand) { float x; // Note: to avoid numerical problems with very small float y; // numbers, we make these variables singe-precision float length2; // floats, but later we call the double-precision log() // and sqrt() functions instead of logf() and sqrtf(). do { x = float (rand.nextf (-1, 1)); y = float (rand.nextf (-1, 1)); length2 = x * x + y * y; } while (length2 >= 1 || length2 == 0); return x * sqrt (-2 * log (double (length2)) / length2); } template IMATH_HOSTDEVICE Vec gaussSphereRand (Rand& rand) { return hollowSphereRand (rand) * gaussRand (rand); } IMATH_INTERNAL_NAMESPACE_HEADER_EXIT #endif // INCLUDED_IMATHRANDOM_H