s_erff.c revision 1dc9e472e19acfe6dc7f41e429236e7eef7ceda1 
1/* s_erff.c -- float version of s_erf.c.
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16#ifndef lint
17static char rcsid[] = "$FreeBSD: src/lib/msun/src/s_erff.c,v 1.7 2002/05/28 18:15:04 alfred Exp $";
18#endif
19
20#include "math.h"
21#include "math_private.h"
22
23static const float
24tiny	    = 1e-30,
25half=  5.0000000000e-01, /* 0x3F000000 */
26one =  1.0000000000e+00, /* 0x3F800000 */
27two =  2.0000000000e+00, /* 0x40000000 */
28	/* c = (subfloat)0.84506291151 */
29erx =  8.4506291151e-01, /* 0x3f58560b */
30/*
31 * Coefficients for approximation to  erf on [0,0.84375]
32 */
33efx =  1.2837916613e-01, /* 0x3e0375d4 */
34efx8=  1.0270333290e+00, /* 0x3f8375d4 */
35pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
36pp1  = -3.2504209876e-01, /* 0xbea66beb */
37pp2  = -2.8481749818e-02, /* 0xbce9528f */
38pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
39pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
40qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
41qq2  =  6.5022252500e-02, /* 0x3d852a63 */
42qq3  =  5.0813062117e-03, /* 0x3ba68116 */
43qq4  =  1.3249473704e-04, /* 0x390aee49 */
44qq5  = -3.9602282413e-06, /* 0xb684e21a */
45/*
46 * Coefficients for approximation to  erf  in [0.84375,1.25]
47 */
48pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
49pa1  =  4.1485610604e-01, /* 0x3ed46805 */
50pa2  = -3.7220788002e-01, /* 0xbebe9208 */
51pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
52pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
53pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
54pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
55qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
56qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
57qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
58qa4  =  1.2617121637e-01, /* 0x3e013307 */
59qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
60qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
61/*
62 * Coefficients for approximation to  erfc in [1.25,1/0.35]
63 */
64ra0  = -9.8649440333e-03, /* 0xbc21a093 */
65ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
66ra2  = -1.0558626175e+01, /* 0xc128f022 */
67ra3  = -6.2375331879e+01, /* 0xc2798057 */
68ra4  = -1.6239666748e+02, /* 0xc322658c */
69ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
70ra6  = -8.1287437439e+01, /* 0xc2a2932b */
71ra7  = -9.8143291473e+00, /* 0xc11d077e */
72sa1  =  1.9651271820e+01, /* 0x419d35ce */
73sa2  =  1.3765776062e+02, /* 0x4309a863 */
74sa3  =  4.3456588745e+02, /* 0x43d9486f */
75sa4  =  6.4538726807e+02, /* 0x442158c9 */
76sa5  =  4.2900814819e+02, /* 0x43d6810b */
77sa6  =  1.0863500214e+02, /* 0x42d9451f */
78sa7  =  6.5702495575e+00, /* 0x40d23f7c */
79sa8  = -6.0424413532e-02, /* 0xbd777f97 */
80/*
81 * Coefficients for approximation to  erfc in [1/.35,28]
82 */
83rb0  = -9.8649431020e-03, /* 0xbc21a092 */
84rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
85rb2  = -1.7757955551e+01, /* 0xc18e104b */
86rb3  = -1.6063638306e+02, /* 0xc320a2ea */
87rb4  = -6.3756646729e+02, /* 0xc41f6441 */
88rb5  = -1.0250950928e+03, /* 0xc480230b */
89rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
90sb1  =  3.0338060379e+01, /* 0x41f2b459 */
91sb2  =  3.2579251099e+02, /* 0x43a2e571 */
92sb3  =  1.5367296143e+03, /* 0x44c01759 */
93sb4  =  3.1998581543e+03, /* 0x4547fdbb */
94sb5  =  2.5530502930e+03, /* 0x451f90ce */
95sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
96sb7  = -2.2440952301e+01; /* 0xc1b38712 */
97
98float
99erff(float x)
100{
101	int32_t hx,ix,i;
102	float R,S,P,Q,s,y,z,r;
103	GET_FLOAT_WORD(hx,x);
104	ix = hx&0x7fffffff;
105	if(ix>=0x7f800000) {		/* erf(nan)=nan */
106	    i = ((u_int32_t)hx>>31)<<1;
107	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
108	}
109
110	if(ix < 0x3f580000) {		/* |x|<0.84375 */
111	    if(ix < 0x31800000) { 	/* |x|<2**-28 */
112	        if (ix < 0x04000000)
113		    /*avoid underflow */
114		    return (float)0.125*((float)8.0*x+efx8*x);
115		return x + efx*x;
116	    }
117	    z = x*x;
118	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
119	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
120	    y = r/s;
121	    return x + x*y;
122	}
123	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
124	    s = fabsf(x)-one;
125	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
126	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
127	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
128	}
129	if (ix >= 0x40c00000) {		/* inf>|x|>=6 */
130	    if(hx>=0) return one-tiny; else return tiny-one;
131	}
132	x = fabsf(x);
133 	s = one/(x*x);
134	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
135	    R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
136				ra5+s*(ra6+s*ra7))))));
137	    S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
138				sa5+s*(sa6+s*(sa7+s*sa8)))))));
139	} else {	/* |x| >= 1/0.35 */
140	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
141				rb5+s*rb6)))));
142	    S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
143				sb5+s*(sb6+s*sb7))))));
144	}
145	GET_FLOAT_WORD(ix,x);
146	SET_FLOAT_WORD(z,ix&0xfffff000);
147	r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
148	if(hx>=0) return one-r/x; else return  r/x-one;
149}
150
151float
152erfcf(float x)
153{
154	int32_t hx,ix;
155	float R,S,P,Q,s,y,z,r;
156	GET_FLOAT_WORD(hx,x);
157	ix = hx&0x7fffffff;
158	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
159						/* erfc(+-inf)=0,2 */
160	    return (float)(((u_int32_t)hx>>31)<<1)+one/x;
161	}
162
163	if(ix < 0x3f580000) {		/* |x|<0.84375 */
164	    if(ix < 0x23800000)  	/* |x|<2**-56 */
165		return one-x;
166	    z = x*x;
167	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
168	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
169	    y = r/s;
170	    if(hx < 0x3e800000) {  	/* x<1/4 */
171		return one-(x+x*y);
172	    } else {
173		r = x*y;
174		r += (x-half);
175	        return half - r ;
176	    }
177	}
178	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
179	    s = fabsf(x)-one;
180	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
181	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
182	    if(hx>=0) {
183	        z  = one-erx; return z - P/Q;
184	    } else {
185		z = erx+P/Q; return one+z;
186	    }
187	}
188	if (ix < 0x41e00000) {		/* |x|<28 */
189	    x = fabsf(x);
190 	    s = one/(x*x);
191	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
192	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
193				ra5+s*(ra6+s*ra7))))));
194	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
195				sa5+s*(sa6+s*(sa7+s*sa8)))))));
196	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
197		if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
198	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
199				rb5+s*rb6)))));
200	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
201				sb5+s*(sb6+s*sb7))))));
202	    }
203	    GET_FLOAT_WORD(ix,x);
204	    SET_FLOAT_WORD(z,ix&0xfffff000);
205	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
206			__ieee754_expf((z-x)*(z+x)+R/S);
207	    if(hx>0) return r/x; else return two-r/x;
208	} else {
209	    if(hx>0) return tiny*tiny; else return two-tiny;
210	}
211}
212