In this article, you will find a fast generator for Random Variable, namely normal and exponential distributions. It is based on George Marsaglia's and Wai Wan Tsang's work.
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// PathHull.h: interface for the CPathHull class.
//
//////////////////////////////////////////////////////////////////////
#if !defined(AFX_PATHHULL_H__50C639BA_585B_4272_9AF4_4632128D8938__INCLUDED_)
#define AFX_PATHHULL_H__50C639BA_585B_4272_9AF4_4632128D8938__INCLUDED_
#if _MSC_VER > 1000
#pragma once
#endif // _MSC_VER > 1000
#ifndef NULL
#define NULL 0
#endif
#define DP_PUSH_OP 0 /* Operation names saved in history stack */
#define DP_TOP_OP 1
#define DP_BOT_OP 2
#ifndef FALSE
#define FALSE 0
#endif
#ifndef TRUE
#define TRUE 1
#endif
typedef double DP_POINT[2]; /* Most data is cartesian points */
typedef double DP_HOMOG[3]; /* Some partial calculations are homogeneous */
#define DP_XX 0
#define DP_YY 1
#define DP_WW 2
#define DP_CROSSPROD_2CCH(p, q, r) /* 2-d cartesian to homog cross product */\
(r)[DP_WW] = (p)[DP_XX] * (q)[DP_YY] - (p)[DP_YY] * (q)[DP_XX];\
(r)[DP_XX] = - (q)[DP_YY] + (p)[DP_YY];\
(r)[DP_YY] = (q)[DP_XX] - (p)[DP_XX];
#define DP_DOTPROD_2CH(p, q) /* 2-d cartesian to homog dot product */\
(q)[DP_WW] + (p)[DP_XX]*(q)[DP_XX] + (p)[DP_YY]*(q)[DP_YY]
#define DP_DOTPROD_2C(p, q) /* 2-d cartesian dot product */\
(p)[DP_XX]*(q)[DP_XX] + (p)[DP_YY]*(q)[DP_YY]
#define DP_LINCOMB_2C(a, p, b, q, r) /* 2-d cartesian linear combination */\
(r)[DP_XX] = (a) * (p)[DP_XX] + (b) * (q)[DP_XX];\
(r)[DP_YY] = (a) * (p)[DP_YY] + (b) * (q)[DP_YY];
#define DP_SGN(a) (a >= 0)
#define DP_MIN(a,b) ( a < b ? a : b)
#define DP_MAX(a,b) ( a > b ? a : b)
class CPathHull
{
public:
CPathHull();
virtual ~CPathHull();
void SetMaxSize(int iHullMax);
int GetHp() const
{ return m_iHp;};
int GetBot() const
{ return m_iBot;};
int GetTop() const
{ return m_iTop;};
DP_POINT* GetpElt(int i)
{ return m_ppElt[i];};
DP_POINT* GetpHelt(int i)
{ return m_ppHelt[i];};
int* GetpOp()
{ return m_pOp;};
void SetHp(int hp)
{ m_iHp=hp;};
void UpHp() { m_iHp++;};
void UpTop() { m_iTop++;};
void UpBot() { m_iBot++;};
void DownHp() { m_iHp--;};
void DownTop() { m_iTop--;};
void DownBot() { m_iBot--;};
void SetTopElt(DP_POINT* p)
{ m_ppElt[m_iTop]=p;};
void SetBotElt(DP_POINT* p)
{ m_ppElt[m_iBot]=p;};
void Split(DP_POINT *e);
void FindExtreme(DP_HOMOG line, DP_POINT ** e, double * dist);
void Init(DP_POINT* e1, DP_POINT* e2)
{
/* Initialize path hull and history */
m_ppElt[m_iHullMax] = e1;
m_ppElt[m_iTop = m_iHullMax + 1] =
m_ppElt[m_iBot = m_iHullMax - 1] =
m_ppHelt[m_iHp = 0] = e2;
m_pOp[0] = DP_PUSH_OP;
}
void Push(DP_POINT* e)
{
/* Push element $e$ onto path hull $h$ */
m_ppElt[++m_iTop] = m_ppElt[--m_iBot] = m_ppHelt[++m_iHp] = e;
m_pOp[m_iHp] = DP_PUSH_OP;
}
void PopTop()
{ /* Pop from top */
m_ppHelt[++m_iHp] = m_ppElt[m_iTop--];
m_pOp[m_iHp] = DP_TOP_OP;
}
void PopBot()
{
/* Pop from bottom */
m_ppHelt[++m_iHp] = m_ppElt[m_iBot++];
m_pOp[m_iHp] = DP_BOT_OP;
}
void Add(DP_POINT* p);
int LeftOfTop(DP_POINT* c)
{
/* Determine if point c is left of line a to b */
return (((*m_ppElt[m_iTop])[DP_XX] - (*c)[DP_XX])*((*m_ppElt[m_iTop-1])[DP_YY] - (*c)[DP_YY])
>= ((*m_ppElt[m_iTop-1])[DP_XX] - (*c)[DP_XX])*((*m_ppElt[m_iTop])[DP_YY] - (*c)[DP_YY]));
}
int LeftOfBot(DP_POINT* c)
{
/* Determine if point c is left of line a to b */
return (((*m_ppElt[m_iBot+1])[DP_XX] - (*c)[DP_XX])*((*m_ppElt[m_iBot])[DP_YY] - (*c)[DP_YY])
>= ((*m_ppElt[m_iBot])[DP_XX] - (*c)[DP_XX])*((*m_ppElt[m_iBot+1])[DP_YY] - (*c)[DP_YY]));
}
int SlopeSign(int p, int q, DP_HOMOG l)
{
/* Return the sign of the projection
of $h[q] - h[p]$ onto the normal
to line $l$ */
return (int)(DP_SGN((l[DP_XX])*((*m_ppElt[q])[DP_XX] - (*m_ppElt[p])[DP_XX])
+ (l[DP_YY])*((*m_ppElt[q])[DP_YY] - (*m_ppElt[p])[DP_YY]))) ;
};
protected:
/// Maxium number of elements in hull
int m_iHullMax;
/// internal values
int m_iTop;
int m_iBot;
int m_iHp;
int *m_pOp;
DP_POINT **m_ppElt;
DP_POINT **m_ppHelt;
};
#endif // !defined(AFX_PATHHULL_H__50C639BA_585B_4272_9AF4_4632128D8938__INCLUDED_)
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Jonathan de Halleux is Civil Engineer in Applied Mathematics. He finished his PhD in 2004 in the rainy country of Belgium. After 2 years in the Common Language Runtime (i.e. .net), he is now working at Microsoft Research on Pex (http://research.microsoft.com/pex).