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dma: add required headers if they are not present
[dragonfly.git] / lib / libm / src / s_erff.c
blob273a068972e5921becaba76c6208e26d1f342d2b
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 * $NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $
16 * $DragonFly: src/lib/libm/src/s_erff.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
17 */
18
19 #include <math.h>
20 #include "math_private.h"
21
22 static const float
23 tiny = 1e-30,
24 half= 5.0000000000e-01, /* 0x3F000000 */
25 one = 1.0000000000e+00, /* 0x3F800000 */
26 two = 2.0000000000e+00, /* 0x40000000 */
27 /* c = (subfloat)0.84506291151 */
28 erx = 8.4506291151e-01, /* 0x3f58560b */
29 /*
30 * Coefficients for approximation to erf on [0,0.84375]
31 */
32 efx = 1.2837916613e-01, /* 0x3e0375d4 */
33 efx8= 1.0270333290e+00, /* 0x3f8375d4 */
34 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
35 pp1 = -3.2504209876e-01, /* 0xbea66beb */
36 pp2 = -2.8481749818e-02, /* 0xbce9528f */
37 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
38 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
39 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
40 qq2 = 6.5022252500e-02, /* 0x3d852a63 */
41 qq3 = 5.0813062117e-03, /* 0x3ba68116 */
42 qq4 = 1.3249473704e-04, /* 0x390aee49 */
43 qq5 = -3.9602282413e-06, /* 0xb684e21a */
44 /*
45 * Coefficients for approximation to erf in [0.84375,1.25]
46 */
47 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
48 pa1 = 4.1485610604e-01, /* 0x3ed46805 */
49 pa2 = -3.7220788002e-01, /* 0xbebe9208 */
50 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
51 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
52 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
53 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
54 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
55 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
56 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
57 qa4 = 1.2617121637e-01, /* 0x3e013307 */
58 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
59 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
60 /*
61 * Coefficients for approximation to erfc in [1.25,1/0.35]
62 */
63 ra0 = -9.8649440333e-03, /* 0xbc21a093 */
64 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
65 ra2 = -1.0558626175e+01, /* 0xc128f022 */
66 ra3 = -6.2375331879e+01, /* 0xc2798057 */
67 ra4 = -1.6239666748e+02, /* 0xc322658c */
68 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
69 ra6 = -8.1287437439e+01, /* 0xc2a2932b */
70 ra7 = -9.8143291473e+00, /* 0xc11d077e */
71 sa1 = 1.9651271820e+01, /* 0x419d35ce */
72 sa2 = 1.3765776062e+02, /* 0x4309a863 */
73 sa3 = 4.3456588745e+02, /* 0x43d9486f */
74 sa4 = 6.4538726807e+02, /* 0x442158c9 */
75 sa5 = 4.2900814819e+02, /* 0x43d6810b */
76 sa6 = 1.0863500214e+02, /* 0x42d9451f */
77 sa7 = 6.5702495575e+00, /* 0x40d23f7c */
78 sa8 = -6.0424413532e-02, /* 0xbd777f97 */
79 /*
80 * Coefficients for approximation to erfc in [1/.35,28]
81 */
82 rb0 = -9.8649431020e-03, /* 0xbc21a092 */
83 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
84 rb2 = -1.7757955551e+01, /* 0xc18e104b */
85 rb3 = -1.6063638306e+02, /* 0xc320a2ea */
86 rb4 = -6.3756646729e+02, /* 0xc41f6441 */
87 rb5 = -1.0250950928e+03, /* 0xc480230b */
88 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
89 sb1 = 3.0338060379e+01, /* 0x41f2b459 */
90 sb2 = 3.2579251099e+02, /* 0x43a2e571 */
91 sb3 = 1.5367296143e+03, /* 0x44c01759 */
92 sb4 = 3.1998581543e+03, /* 0x4547fdbb */
93 sb5 = 2.5530502930e+03, /* 0x451f90ce */
94 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
95 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
96
97 float
98 erff(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 = expf(-z*z-(float)0.5625)*expf((z-x)*(z+x)+R/S);
147 if(hx>=0) return one-r/x; else return r/x-one;
148 }
149
150 float
151 erfcf(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 = expf(-z*z-(float)0.5625)*
205 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 }
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