//////////////////////////////////////////////////////////////////////////
///////////////利用梯形法生成符合標準正態分佈的累積函from  Dain//////////////////
//////////////////////////////////////////////////////////////////////////
#include "iostream.h"
#include "fstream.h"
#include "math.h"
#include "errno.h"

const double PI=3.1415926;

double Normal(double z)
{
	double temp;
	temp=exp((-1)*z*z/2)/sqrt(2*PI);
	return temp;
	
}
/***************************************************************/
/* 返回標準正態分佈的累積函式，該分佈的平均值為 0，標準偏差為 1。                           */
/***************************************************************/
double NormSDist(const double z)
{
	// this guards against overflow
	if(z > 6) return 1;
	if(z < -6) return 0; 
	
	static const double gamma =  0.231641900,
		a1  =  0.319381530,
		a2  = -0.356563782,
		a3  =  1.781477973,
		a4  = -1.821255978,
		a5  =  1.330274429; 
	
	double k = 1.0 / (1 + fabs(z) * gamma);
	double n = k * (a1 + k * (a2 + k * (a3 + k * (a4 + k * a5))));
	n = 1 - Normal(z) * n;
	if(z < 0)
		return 1.0 - n; 
	
	return n;
} 


/***************************************************************/
/* 返回標準正態分佈累積函式的逆函式。該分佈的平均值為 0，標準偏差為 1。                    */
/***************************************************************/ 
double normsinv(const double p)
{
	static const double LOW  = 0.02425;
	static const double HIGH = 0.97575;
	
	/* Coefficients in rational approximations. */
	static const double a[] =
	{
		-3.969683028665376e+01,
			2.209460984245205e+02,
			-2.759285104469687e+02,
			1.383577518672690e+02,
			-3.066479806614716e+01,
			2.506628277459239e+00
	}; 
	
	static const double b[] =
	{
		-5.447609879822406e+01,
			1.615858368580409e+02,
			-1.556989798598866e+02,
			6.680131188771972e+01,
			-1.328068155288572e+01
	}; 
	
	static const double c[] =
	{
		-7.784894002430293e-03,
			-3.223964580411365e-01,
			-2.400758277161838e+00,
			-2.549732539343734e+00,
			4.374664141464968e+00,
			2.938163982698783e+00
	}; 
	
	static const double d[] =
	{
		7.784695709041462e-03,
			3.224671290700398e-01,
			2.445134137142996e+00,
			3.754408661907416e+00
	}; 
	
	double q, r; 
	
	errno = 0; 
	
	if (p < 0 || p > 1)
	{
		errno = EDOM;
		return 0.0;
	}
	else if (p == 0)
	{
		errno = ERANGE;
		return -HUGE_VAL /* minus "infinity" */;
	}
	else if (p == 1)
	{
		errno = ERANGE;
		return HUGE_VAL /* "infinity" */;
	}
	else if (p < LOW)
	{
		/* Rational approximation for lower region */
		q = sqrt(-2*log(p));
		return (((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
			((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1);
	}
	else if (p > HIGH)
	{
		/* Rational approximation for upper region */
		q  = sqrt(-2*log(1-p));
		return -(((((c[0]*q+c[1])*q+c[2])*q+c[3])*q+c[4])*q+c[5]) /
			((((d[0]*q+d[1])*q+d[2])*q+d[3])*q+1);
	}
	else
	{
		/* Rational approximation for central region */
		q = p - 0.5;
		r = q*q;
		return (((((a[0]*r+a[1])*r+a[2])*r+a[3])*r+a[4])*r+a[5])*q /
			(((((b[0]*r+b[1])*r+b[2])*r+b[3])*r+b[4])*r+1);
	}
} 

void main()
{
	ofstream out1;
	out1.open("正態分佈累積函式.xls");
	for(int i=0;i<1200;i++)
		out1<<(-6)+i*0.01<<"\t"<<NormSDist((-6)+i*0.01)<<"\n";
	out1.close();
	out1.open("正態分佈累積函式的逆函式.xls");
    for(i=0;i<1000;i++)
		out1<<0.001*i<<"\t"<<normsinv(0.001*i)<<"\n";
	out1.close();
}