Blame Imath/ImathRandom.h

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///////////////////////////////////////////////////////////////////////////
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//
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// Copyright (c) 2002-2012, 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 "ImathNamespace.h"
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#include "ImathExport.h"
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#include <stdlib.h>
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#include <math.h>
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IMATH_INTERNAL_NAMESPACE_HEADER_ENTER
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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 IMATH_EXPORT 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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IMATH_EXPORT double     erand48 (unsigned short state[3]);
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IMATH_EXPORT double     drand48 ();
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IMATH_EXPORT long int   nrand48 (unsigned short state[3]);
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IMATH_EXPORT long int   lrand48 ();
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IMATH_EXPORT 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 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 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 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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IMATH_INTERNAL_NAMESPACE_HEADER_EXIT
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#endif // INCLUDED_IMATHRANDOM_H