s_erff.c revision a0ee07829a9ba7e99ef68e8c12551301cc797f0f 
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#include <sys/cdefs.h>
17__FBSDID("$FreeBSD$");
18
19#include "math.h"
20#include "math_private.h"
21
22static const float
23tiny	    = 1e-30,
24half=  5.0000000000e-01, /* 0x3F000000 */
25one =  1.0000000000e+00, /* 0x3F800000 */
26two =  2.0000000000e+00, /* 0x40000000 */
27	/* c = (subfloat)0.84506291151 */
28erx =  8.4506291151e-01, /* 0x3f58560b */
29/*
30 * Coefficients for approximation to  erf on [0,0.84375]
31 */
32efx =  1.2837916613e-01, /* 0x3e0375d4 */
33efx8=  1.0270333290e+00, /* 0x3f8375d4 */
34pp0  =  1.2837916613e-01, /* 0x3e0375d4 */
35pp1  = -3.2504209876e-01, /* 0xbea66beb */
36pp2  = -2.8481749818e-02, /* 0xbce9528f */
37pp3  = -5.7702702470e-03, /* 0xbbbd1489 */
38pp4  = -2.3763017452e-05, /* 0xb7c756b1 */
39qq1  =  3.9791721106e-01, /* 0x3ecbbbce */
40qq2  =  6.5022252500e-02, /* 0x3d852a63 */
41qq3  =  5.0813062117e-03, /* 0x3ba68116 */
42qq4  =  1.3249473704e-04, /* 0x390aee49 */
43qq5  = -3.9602282413e-06, /* 0xb684e21a */
44/*
45 * Coefficients for approximation to  erf  in [0.84375,1.25]
46 */
47pa0  = -2.3621185683e-03, /* 0xbb1acdc6 */
48pa1  =  4.1485610604e-01, /* 0x3ed46805 */
49pa2  = -3.7220788002e-01, /* 0xbebe9208 */
50pa3  =  3.1834661961e-01, /* 0x3ea2fe54 */
51pa4  = -1.1089469492e-01, /* 0xbde31cc2 */
52pa5  =  3.5478305072e-02, /* 0x3d1151b3 */
53pa6  = -2.1663755178e-03, /* 0xbb0df9c0 */
54qa1  =  1.0642088205e-01, /* 0x3dd9f331 */
55qa2  =  5.4039794207e-01, /* 0x3f0a5785 */
56qa3  =  7.1828655899e-02, /* 0x3d931ae7 */
57qa4  =  1.2617121637e-01, /* 0x3e013307 */
58qa5  =  1.3637083583e-02, /* 0x3c5f6e13 */
59qa6  =  1.1984500103e-02, /* 0x3c445aa3 */
60/*
61 * Coefficients for approximation to  erfc in [1.25,1/0.35]
62 */
63ra0  = -9.8649440333e-03, /* 0xbc21a093 */
64ra1  = -6.9385856390e-01, /* 0xbf31a0b7 */
65ra2  = -1.0558626175e+01, /* 0xc128f022 */
66ra3  = -6.2375331879e+01, /* 0xc2798057 */
67ra4  = -1.6239666748e+02, /* 0xc322658c */
68ra5  = -1.8460508728e+02, /* 0xc3389ae7 */
69ra6  = -8.1287437439e+01, /* 0xc2a2932b */
70ra7  = -9.8143291473e+00, /* 0xc11d077e */
71sa1  =  1.9651271820e+01, /* 0x419d35ce */
72sa2  =  1.3765776062e+02, /* 0x4309a863 */
73sa3  =  4.3456588745e+02, /* 0x43d9486f */
74sa4  =  6.4538726807e+02, /* 0x442158c9 */
75sa5  =  4.2900814819e+02, /* 0x43d6810b */
76sa6  =  1.0863500214e+02, /* 0x42d9451f */
77sa7  =  6.5702495575e+00, /* 0x40d23f7c */
78sa8  = -6.0424413532e-02, /* 0xbd777f97 */
79/*
80 * Coefficients for approximation to  erfc in [1/.35,28]
81 */
82rb0  = -9.8649431020e-03, /* 0xbc21a092 */
83rb1  = -7.9928326607e-01, /* 0xbf4c9dd4 */
84rb2  = -1.7757955551e+01, /* 0xc18e104b */
85rb3  = -1.6063638306e+02, /* 0xc320a2ea */
86rb4  = -6.3756646729e+02, /* 0xc41f6441 */
87rb5  = -1.0250950928e+03, /* 0xc480230b */
88rb6  = -4.8351919556e+02, /* 0xc3f1c275 */
89sb1  =  3.0338060379e+01, /* 0x41f2b459 */
90sb2  =  3.2579251099e+02, /* 0x43a2e571 */
91sb3  =  1.5367296143e+03, /* 0x44c01759 */
92sb4  =  3.1998581543e+03, /* 0x4547fdbb */
93sb5  =  2.5530502930e+03, /* 0x451f90ce */
94sb6  =  4.7452853394e+02, /* 0x43ed43a7 */
95sb7  = -2.2440952301e+01; /* 0xc1b38712 */
96
97float
98erff(float x)
99{
100	int32_t hx,ix,i;
101	float R,S,P,Q,s,y,z,r;
102	GET_FLOAT_WORD(hx,x);
103	ix = hx&0x7fffffff;
104	if(ix>=0x7f800000) {		/* erf(nan)=nan */
105	    i = ((u_int32_t)hx>>31)<<1;
106	    return (float)(1-i)+one/x;	/* erf(+-inf)=+-1 */
107	}
108
109	if(ix < 0x3f580000) {		/* |x|<0.84375 */
110	    if(ix < 0x31800000) { 	/* |x|<2**-28 */
111	        if (ix < 0x04000000)
112		    /*avoid underflow */
113		    return (float)0.125*((float)8.0*x+efx8*x);
114		return x + efx*x;
115	    }
116	    z = x*x;
117	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
118	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
119	    y = r/s;
120	    return x + x*y;
121	}
122	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
123	    s = fabsf(x)-one;
124	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
125	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
126	    if(hx>=0) return erx + P/Q; else return -erx - P/Q;
127	}
128	if (ix >= 0x40c00000) {		/* inf>|x|>=6 */
129	    if(hx>=0) return one-tiny; else return tiny-one;
130	}
131	x = fabsf(x);
132 	s = one/(x*x);
133	if(ix< 0x4036DB6E) {	/* |x| < 1/0.35 */
134	    R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
135				ra5+s*(ra6+s*ra7))))));
136	    S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
137				sa5+s*(sa6+s*(sa7+s*sa8)))))));
138	} else {	/* |x| >= 1/0.35 */
139	    R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
140				rb5+s*rb6)))));
141	    S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
142				sb5+s*(sb6+s*sb7))))));
143	}
144	GET_FLOAT_WORD(ix,x);
145	SET_FLOAT_WORD(z,ix&0xfffff000);
146	r  =  __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
147	if(hx>=0) return one-r/x; else return  r/x-one;
148}
149
150float
151erfcf(float x)
152{
153	int32_t hx,ix;
154	float R,S,P,Q,s,y,z,r;
155	GET_FLOAT_WORD(hx,x);
156	ix = hx&0x7fffffff;
157	if(ix>=0x7f800000) {			/* erfc(nan)=nan */
158						/* erfc(+-inf)=0,2 */
159	    return (float)(((u_int32_t)hx>>31)<<1)+one/x;
160	}
161
162	if(ix < 0x3f580000) {		/* |x|<0.84375 */
163	    if(ix < 0x23800000)  	/* |x|<2**-56 */
164		return one-x;
165	    z = x*x;
166	    r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
167	    s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
168	    y = r/s;
169	    if(hx < 0x3e800000) {  	/* x<1/4 */
170		return one-(x+x*y);
171	    } else {
172		r = x*y;
173		r += (x-half);
174	        return half - r ;
175	    }
176	}
177	if(ix < 0x3fa00000) {		/* 0.84375 <= |x| < 1.25 */
178	    s = fabsf(x)-one;
179	    P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
180	    Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
181	    if(hx>=0) {
182	        z  = one-erx; return z - P/Q;
183	    } else {
184		z = erx+P/Q; return one+z;
185	    }
186	}
187	if (ix < 0x41e00000) {		/* |x|<28 */
188	    x = fabsf(x);
189 	    s = one/(x*x);
190	    if(ix< 0x4036DB6D) {	/* |x| < 1/.35 ~ 2.857143*/
191	        R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
192				ra5+s*(ra6+s*ra7))))));
193	        S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
194				sa5+s*(sa6+s*(sa7+s*sa8)))))));
195	    } else {			/* |x| >= 1/.35 ~ 2.857143 */
196		if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
197	        R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
198				rb5+s*rb6)))));
199	        S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
200				sb5+s*(sb6+s*sb7))))));
201	    }
202	    GET_FLOAT_WORD(ix,x);
203	    SET_FLOAT_WORD(z,ix&0xfffff000);
204	    r  =  __ieee754_expf(-z*z-(float)0.5625)*
205			__ieee754_expf((z-x)*(z+x)+R/S);
206	    if(hx>0) return r/x; else return two-r/x;
207	} else {
208	    if(hx>0) return tiny*tiny; else return two-tiny;
209	}
210}
211