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s_erff.c (6784B)
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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
17 static 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
23 static const float
24 tiny = 1e-30,
25 half= 5.0000000000e-01, /* 0x3F000000 */
26 one = 1.0000000000e+00, /* 0x3F800000 */
27 two = 2.0000000000e+00, /* 0x40000000 */
28 /* c = (subfloat)0.84506291151 */
29 erx = 8.4506291151e-01, /* 0x3f58560b */
30 /*
31 * Coefficients for approximation to erf on [0,0.84375]
32 */
33 efx = 1.2837916613e-01, /* 0x3e0375d4 */
34 efx8= 1.0270333290e+00, /* 0x3f8375d4 */
35 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
36 pp1 = -3.2504209876e-01, /* 0xbea66beb */
37 pp2 = -2.8481749818e-02, /* 0xbce9528f */
38 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
39 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
40 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
41 qq2 = 6.5022252500e-02, /* 0x3d852a63 */
42 qq3 = 5.0813062117e-03, /* 0x3ba68116 */
43 qq4 = 1.3249473704e-04, /* 0x390aee49 */
44 qq5 = -3.9602282413e-06, /* 0xb684e21a */
45 /*
46 * Coefficients for approximation to erf in [0.84375,1.25]
47 */
48 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
49 pa1 = 4.1485610604e-01, /* 0x3ed46805 */
50 pa2 = -3.7220788002e-01, /* 0xbebe9208 */
51 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
52 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
53 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
54 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
55 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
56 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
57 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
58 qa4 = 1.2617121637e-01, /* 0x3e013307 */
59 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
60 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
61 /*
62 * Coefficients for approximation to erfc in [1.25,1/0.35]
63 */
64 ra0 = -9.8649440333e-03, /* 0xbc21a093 */
65 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
66 ra2 = -1.0558626175e+01, /* 0xc128f022 */
67 ra3 = -6.2375331879e+01, /* 0xc2798057 */
68 ra4 = -1.6239666748e+02, /* 0xc322658c */
69 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
70 ra6 = -8.1287437439e+01, /* 0xc2a2932b */
71 ra7 = -9.8143291473e+00, /* 0xc11d077e */
72 sa1 = 1.9651271820e+01, /* 0x419d35ce */
73 sa2 = 1.3765776062e+02, /* 0x4309a863 */
74 sa3 = 4.3456588745e+02, /* 0x43d9486f */
75 sa4 = 6.4538726807e+02, /* 0x442158c9 */
76 sa5 = 4.2900814819e+02, /* 0x43d6810b */
77 sa6 = 1.0863500214e+02, /* 0x42d9451f */
78 sa7 = 6.5702495575e+00, /* 0x40d23f7c */
79 sa8 = -6.0424413532e-02, /* 0xbd777f97 */
80 /*
81 * Coefficients for approximation to erfc in [1/.35,28]
82 */
83 rb0 = -9.8649431020e-03, /* 0xbc21a092 */
84 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
85 rb2 = -1.7757955551e+01, /* 0xc18e104b */
86 rb3 = -1.6063638306e+02, /* 0xc320a2ea */
87 rb4 = -6.3756646729e+02, /* 0xc41f6441 */
88 rb5 = -1.0250950928e+03, /* 0xc480230b */
89 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
90 sb1 = 3.0338060379e+01, /* 0x41f2b459 */
91 sb2 = 3.2579251099e+02, /* 0x43a2e571 */
92 sb3 = 1.5367296143e+03, /* 0x44c01759 */
93 sb4 = 3.1998581543e+03, /* 0x4547fdbb */
94 sb5 = 2.5530502930e+03, /* 0x451f90ce */
95 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
96 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
97
98 float
99 erff(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
151 float
152 erfcf(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 }