399 lines
9.7 KiB
C++
399 lines
9.7 KiB
C++
///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
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// Digital Ltd. LLC
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//
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// All rights reserved.
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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// * Redistributions in binary form must reproduce the above
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// copyright notice, this list of conditions and the following disclaimer
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// in the documentation and/or other materials provided with the
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// distribution.
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// * Neither the name of Industrial Light & Magic nor the names of
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// its contributors may be used to endorse or promote products derived
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// from this software without specific prior written permission.
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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///////////////////////////////////////////////////////////////////////////
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#ifndef INCLUDED_IMATHRANDOM_H
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#define INCLUDED_IMATHRANDOM_H
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//-----------------------------------------------------------------------------
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//
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// Generators for uniformly distributed pseudo-random numbers and
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// functions that use those generators to generate numbers with
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// non-uniform distributions:
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//
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// class Rand32
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// class Rand48
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// solidSphereRand()
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// hollowSphereRand()
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// gaussRand()
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// gaussSphereRand()
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//
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// Note: class Rand48() calls erand48() and nrand48(), which are not
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// available on all operating systems. For compatibility we include
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// our own versions of erand48() and nrand48(). Our functions have
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// been reverse-engineered from the corresponding Unix/Linux man page.
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//
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//-----------------------------------------------------------------------------
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#include <stdlib.h>
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#include <math.h>
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namespace Imath {
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//-----------------------------------------------
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// Fast random-number generator that generates
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// a uniformly distributed sequence with a period
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// length of 2^32.
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//-----------------------------------------------
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class Rand32
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{
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public:
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//------------
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// Constructor
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//------------
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Rand32 (unsigned long int seed = 0);
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//--------------------------------
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// Re-initialize with a given seed
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//--------------------------------
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void init (unsigned long int seed);
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//----------------------------------------------------------
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// Get the next value in the sequence (range: [false, true])
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//----------------------------------------------------------
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bool nextb ();
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//---------------------------------------------------------------
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// Get the next value in the sequence (range: [0 ... 0xffffffff])
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//---------------------------------------------------------------
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unsigned long int nexti ();
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//------------------------------------------------------
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// Get the next value in the sequence (range: [0 ... 1[)
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//------------------------------------------------------
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float nextf ();
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//-------------------------------------------------------------------
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// Get the next value in the sequence (range [rangeMin ... rangeMax[)
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//-------------------------------------------------------------------
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float nextf (float rangeMin, float rangeMax);
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private:
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void next ();
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unsigned long int _state;
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};
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//--------------------------------------------------------
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// Random-number generator based on the C Standard Library
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// functions erand48(), nrand48() & company; generates a
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// uniformly distributed sequence.
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//--------------------------------------------------------
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class Rand48
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{
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public:
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//------------
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// Constructor
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//------------
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Rand48 (unsigned long int seed = 0);
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//--------------------------------
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// Re-initialize with a given seed
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//--------------------------------
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void init (unsigned long int seed);
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//----------------------------------------------------------
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// Get the next value in the sequence (range: [false, true])
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//----------------------------------------------------------
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bool nextb ();
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//---------------------------------------------------------------
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// Get the next value in the sequence (range: [0 ... 0x7fffffff])
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//---------------------------------------------------------------
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long int nexti ();
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//------------------------------------------------------
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// Get the next value in the sequence (range: [0 ... 1[)
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//------------------------------------------------------
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double nextf ();
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//-------------------------------------------------------------------
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// Get the next value in the sequence (range [rangeMin ... rangeMax[)
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//-------------------------------------------------------------------
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double nextf (double rangeMin, double rangeMax);
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private:
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unsigned short int _state[3];
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};
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//------------------------------------------------------------
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// Return random points uniformly distributed in a sphere with
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// radius 1 around the origin (distance from origin <= 1).
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//------------------------------------------------------------
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template <class Vec, class Rand>
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Vec
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solidSphereRand (Rand &rand);
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//-------------------------------------------------------------
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// Return random points uniformly distributed on the surface of
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// a sphere with radius 1 around the origin.
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//-------------------------------------------------------------
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template <class Vec, class Rand>
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Vec
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hollowSphereRand (Rand &rand);
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//-----------------------------------------------
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// Return random numbers with a normal (Gaussian)
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// distribution with zero mean and unit variance.
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//-----------------------------------------------
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template <class Rand>
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float
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gaussRand (Rand &rand);
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//----------------------------------------------------
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// Return random points whose distance from the origin
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// has a normal (Gaussian) distribution with zero mean
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// and unit variance.
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//----------------------------------------------------
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template <class Vec, class Rand>
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Vec
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gaussSphereRand (Rand &rand);
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//---------------------------------
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// erand48(), nrand48() and friends
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//---------------------------------
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double erand48 (unsigned short state[3]);
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double drand48 ();
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long int nrand48 (unsigned short state[3]);
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long int lrand48 ();
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void srand48 (long int seed);
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//---------------
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// Implementation
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//---------------
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inline void
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Rand32::init (unsigned long int seed)
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{
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_state = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL;
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}
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inline
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Rand32::Rand32 (unsigned long int seed)
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{
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init (seed);
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}
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inline void
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Rand32::next ()
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{
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_state = 1664525L * _state + 1013904223L;
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}
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inline bool
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Rand32::nextb ()
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{
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next ();
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// Return the 31st (most significant) bit, by and-ing with 2 ^ 31.
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return !!(_state & 2147483648UL);
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}
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inline unsigned long int
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Rand32::nexti ()
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{
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next ();
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return _state & 0xffffffff;
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}
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inline float
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Rand32::nextf (float rangeMin, float rangeMax)
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{
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float f = nextf();
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return rangeMin * (1 - f) + rangeMax * f;
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}
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inline void
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Rand48::init (unsigned long int seed)
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{
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seed = (seed * 0xa5a573a5L) ^ 0x5a5a5a5aL;
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_state[0] = (unsigned short int) (seed & 0xFFFF);
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_state[1] = (unsigned short int) ((seed >> 16) & 0xFFFF);
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_state[2] = (unsigned short int) (seed & 0xFFFF);
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}
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inline
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Rand48::Rand48 (unsigned long int seed)
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{
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init (seed);
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}
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inline bool
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Rand48::nextb ()
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{
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return Imath::nrand48 (_state) & 1;
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}
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inline long int
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Rand48::nexti ()
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{
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return Imath::nrand48 (_state);
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}
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inline double
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Rand48::nextf ()
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{
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return Imath::erand48 (_state);
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}
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inline double
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Rand48::nextf (double rangeMin, double rangeMax)
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{
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double f = nextf();
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return rangeMin * (1 - f) + rangeMax * f;
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}
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template <class Vec, class Rand>
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Vec
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solidSphereRand (Rand &rand)
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{
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Vec v;
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do
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{
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for (unsigned int i = 0; i < Vec::dimensions(); i++)
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v[i] = (typename Vec::BaseType) rand.nextf (-1, 1);
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}
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while (v.length2() > 1);
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return v;
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}
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template <class Vec, class Rand>
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Vec
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hollowSphereRand (Rand &rand)
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{
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Vec v;
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typename Vec::BaseType length;
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do
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{
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for (unsigned int i = 0; i < Vec::dimensions(); i++)
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v[i] = (typename Vec::BaseType) rand.nextf (-1, 1);
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length = v.length();
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}
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while (length > 1 || length == 0);
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return v / length;
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}
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template <class Rand>
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float
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gaussRand (Rand &rand)
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{
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float x; // Note: to avoid numerical problems with very small
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float y; // numbers, we make these variables singe-precision
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float length2; // floats, but later we call the double-precision log()
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// and sqrt() functions instead of logf() and sqrtf().
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do
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{
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x = float (rand.nextf (-1, 1));
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y = float (rand.nextf (-1, 1));
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length2 = x * x + y * y;
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}
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while (length2 >= 1 || length2 == 0);
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return x * sqrt (-2 * log (double (length2)) / length2);
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}
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template <class Vec, class Rand>
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Vec
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gaussSphereRand (Rand &rand)
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{
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return hollowSphereRand <Vec> (rand) * gaussRand (rand);
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}
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} // namespace Imath
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#endif
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