[unix-history] / usr / src / lib / libm / common_source / erf.c

/* @(#)erf.c	1.1 (ELEFUNT) %G% */

/*
	C program for floating point error function

	erf(x) returns the error function of its argument
	erfc(x) returns 1.0-erf(x)

	erf(x) is defined by
	${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$

	the entry for erfc is provided because of the
	extreme loss of relative accuracy if erf(x) is
	called for large x and the result subtracted
	from 1. (e.g. for x= 10, 12 places are lost).

	There are no error returns.

	Calls exp.

	Coefficients for large x are #5667 from Hart & Cheney (18.72D).
*/

#define M 7
#define N 9
static double torp = 1.1283791670955125738961589031;
static double p1[] = {
	0.804373630960840172832162e5,
	0.740407142710151470082064e4,
	0.301782788536507577809226e4,
	0.380140318123903008244444e2,
	0.143383842191748205576712e2,
	-.288805137207594084924010e0,
	0.007547728033418631287834e0,
};
static double q1[]  = {
	0.804373630960840172826266e5,
	0.342165257924628539769006e5,
	0.637960017324428279487120e4,
	0.658070155459240506326937e3,
	0.380190713951939403753468e2,
	0.100000000000000000000000e1,
	0.0,
};
static double p2[]  = {
	0.18263348842295112592168999e4,
	0.28980293292167655611275846e4,
	0.2320439590251635247384768711e4,
	0.1143262070703886173606073338e4,
	0.3685196154710010637133875746e3,
	0.7708161730368428609781633646e2,
	0.9675807882987265400604202961e1,
	0.5641877825507397413087057563e0,
	0.0,
};
static double q2[]  = {
	0.18263348842295112595576438e4,
	0.495882756472114071495438422e4,
	0.60895424232724435504633068e4,
	0.4429612803883682726711528526e4,
	0.2094384367789539593790281779e4,
	0.6617361207107653469211984771e3,
	0.1371255960500622202878443578e3,
	0.1714980943627607849376131193e2,
	1.0,
};

double
erf(arg) double arg;{
	double erfc();
	int sign;
	double argsq;
	double d, n;
	int i;

	sign = 1;
	if(arg < 0.){
		arg = -arg;
		sign = -1;
	}
	if(arg < 0.5){
		argsq = arg*arg;
		for(n=0,d=0,i=M-1; i>=0; i--){
			n = n*argsq + p1[i];
			d = d*argsq + q1[i];
		}
		return(sign*torp*arg*n/d);
	}
	if(arg >= 10.)
		return(sign*1.);
	return(sign*(1. - erfc(arg)));
}

double
erfc(arg) double arg;{
	double erf();
	double exp();
	double n, d;
	int i;

	if(arg < 0.)
		return(2. - erfc(-arg));
/*
	if(arg < 0.5)
		return(1. - erf(arg));
*/
	if(arg >= 10.)
		return(0.);

	for(n=0,d=0,i=N-1; i>=0; i--){
		n = n*arg + p2[i];
		d = d*arg + q2[i];
	}
	return(exp(-arg*arg)*n/d);
}
Commit	Line	Data
824cad0f ZAL	1	/* @(#)erf.c 1.1 (ELEFUNT) %G% */
	2
	3	/*
	4	C program for floating point error function
	5
	6	erf(x) returns the error function of its argument
	7	erfc(x) returns 1.0-erf(x)
	8
	9	erf(x) is defined by
	10	${2 over sqrt(pi)} int from 0 to x e sup {-t sup 2} dt$
	11
	12	the entry for erfc is provided because of the
	13	extreme loss of relative accuracy if erf(x) is
	14	called for large x and the result subtracted
	15	from 1. (e.g. for x= 10, 12 places are lost).
	16
	17	There are no error returns.
	18
	19	Calls exp.
	20
	21	Coefficients for large x are #5667 from Hart & Cheney (18.72D).
	22	*/
	23
	24	#define M 7
	25	#define N 9
	26	static double torp = 1.1283791670955125738961589031;
	27	static double p1[] = {
	28	0.804373630960840172832162e5,
	29	0.740407142710151470082064e4,
	30	0.301782788536507577809226e4,
	31	0.380140318123903008244444e2,
	32	0.143383842191748205576712e2,
	33	-.288805137207594084924010e0,
	34	0.007547728033418631287834e0,
	35	};
	36	static double q1[] = {
	37	0.804373630960840172826266e5,
	38	0.342165257924628539769006e5,
	39	0.637960017324428279487120e4,
	40	0.658070155459240506326937e3,
	41	0.380190713951939403753468e2,
	42	0.100000000000000000000000e1,
	43	0.0,
	44	};
	45	static double p2[] = {
	46	0.18263348842295112592168999e4,
	47	0.28980293292167655611275846e4,
	48	0.2320439590251635247384768711e4,
	49	0.1143262070703886173606073338e4,
	50	0.3685196154710010637133875746e3,
	51	0.7708161730368428609781633646e2,
	52	0.9675807882987265400604202961e1,
	53	0.5641877825507397413087057563e0,
	54	0.0,
	55	};
	56	static double q2[] = {
	57	0.18263348842295112595576438e4,
	58	0.495882756472114071495438422e4,
	59	0.60895424232724435504633068e4,
	60	0.4429612803883682726711528526e4,
	61	0.2094384367789539593790281779e4,
	62	0.6617361207107653469211984771e3,
	63	0.1371255960500622202878443578e3,
	64	0.1714980943627607849376131193e2,
65	1.0,
66	};
67
68	double
69	erf(arg) double arg;{
70	double erfc();
71	int sign;
72	double argsq;
73	double d, n;
74	int i;
75
76	sign = 1;
77	if(arg < 0.){
78	arg = -arg;
79	sign = -1;
80	}
81	if(arg < 0.5){
82	argsq = arg*arg;
83	for(n=0,d=0,i=M-1; i>=0; i--){
84	n = n*argsq + p1[i];
85	d = d*argsq + q1[i];
86	}
87	return(signtorparg*n/d);
88	}
89	if(arg >= 10.)
90	return(sign*1.);
91	return(sign*(1. - erfc(arg)));
92	}
93
94	double
95	erfc(arg) double arg;{
96	double erf();
97	double exp();
98	double n, d;
99	int i;
100
101	if(arg < 0.)
102	return(2. - erfc(-arg));
103	/*
104	if(arg < 0.5)
105	return(1. - erf(arg));
106	*/
107	if(arg >= 10.)
108	return(0.);
109
110	for(n=0,d=0,i=N-1; i>=0; i--){
111	n = n*arg + p2[i];
112	d = d*arg + q2[i];
113	}
114	return(exp(-argarg)n/d);
115	}