POK
erff.c
1 /*
2  * POK header
3  *
4  * The following file is a part of the POK project. Any modification should
5  * made according to the POK licence. You CANNOT use this file or a part of
6  * this file is this part of a file for your own project
7  *
8  * For more information on the POK licence, please see our LICENCE FILE
9  *
10  * Please follow the coding guidelines described in doc/CODING_GUIDELINES
11  *
12  * Copyright (c) 2007-2009 POK team
13  *
14  * Created by julien on Fri Jan 30 14:41:34 2009
15  */
16 
17 /* s_erff.c -- float version of s_erf.c.
18  * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
19  */
20 
21 /*
22  * ====================================================
23  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
24  *
25  * Developed at SunPro, a Sun Microsystems, Inc. business.
26  * Permission to use, copy, modify, and distribute this
27  * software is freely granted, provided that this notice
28  * is preserved.
29  * ====================================================
30  */
31 
32 #ifdef POK_NEEDS_LIBMATH
33 
34 #include <libm.h>
35 #include "math_private.h"
36 
37 static const float
38 tiny = 1e-30,
39 half= 5.0000000000e-01, /* 0x3F000000 */
40 one = 1.0000000000e+00, /* 0x3F800000 */
41 two = 2.0000000000e+00, /* 0x40000000 */
42  /* c = (subfloat)0.84506291151 */
43 erx = 8.4506291151e-01, /* 0x3f58560b */
44 /*
45  * Coefficients for approximation to erf on [0,0.84375]
46  */
47 efx = 1.2837916613e-01, /* 0x3e0375d4 */
48 efx8= 1.0270333290e+00, /* 0x3f8375d4 */
49 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
50 pp1 = -3.2504209876e-01, /* 0xbea66beb */
51 pp2 = -2.8481749818e-02, /* 0xbce9528f */
52 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
53 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
54 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
55 qq2 = 6.5022252500e-02, /* 0x3d852a63 */
56 qq3 = 5.0813062117e-03, /* 0x3ba68116 */
57 qq4 = 1.3249473704e-04, /* 0x390aee49 */
58 qq5 = -3.9602282413e-06, /* 0xb684e21a */
59 /*
60  * Coefficients for approximation to erf in [0.84375,1.25]
61  */
62 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
63 pa1 = 4.1485610604e-01, /* 0x3ed46805 */
64 pa2 = -3.7220788002e-01, /* 0xbebe9208 */
65 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
66 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
67 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
68 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
69 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
70 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
71 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
72 qa4 = 1.2617121637e-01, /* 0x3e013307 */
73 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
74 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
75 /*
76  * Coefficients for approximation to erfc in [1.25,1/0.35]
77  */
78 ra0 = -9.8649440333e-03, /* 0xbc21a093 */
79 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
80 ra2 = -1.0558626175e+01, /* 0xc128f022 */
81 ra3 = -6.2375331879e+01, /* 0xc2798057 */
82 ra4 = -1.6239666748e+02, /* 0xc322658c */
83 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
84 ra6 = -8.1287437439e+01, /* 0xc2a2932b */
85 ra7 = -9.8143291473e+00, /* 0xc11d077e */
86 sa1 = 1.9651271820e+01, /* 0x419d35ce */
87 sa2 = 1.3765776062e+02, /* 0x4309a863 */
88 sa3 = 4.3456588745e+02, /* 0x43d9486f */
89 sa4 = 6.4538726807e+02, /* 0x442158c9 */
90 sa5 = 4.2900814819e+02, /* 0x43d6810b */
91 sa6 = 1.0863500214e+02, /* 0x42d9451f */
92 sa7 = 6.5702495575e+00, /* 0x40d23f7c */
93 sa8 = -6.0424413532e-02, /* 0xbd777f97 */
94 /*
95  * Coefficients for approximation to erfc in [1/.35,28]
96  */
97 rb0 = -9.8649431020e-03, /* 0xbc21a092 */
98 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
99 rb2 = -1.7757955551e+01, /* 0xc18e104b */
100 rb3 = -1.6063638306e+02, /* 0xc320a2ea */
101 rb4 = -6.3756646729e+02, /* 0xc41f6441 */
102 rb5 = -1.0250950928e+03, /* 0xc480230b */
103 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
104 sb1 = 3.0338060379e+01, /* 0x41f2b459 */
105 sb2 = 3.2579251099e+02, /* 0x43a2e571 */
106 sb3 = 1.5367296143e+03, /* 0x44c01759 */
107 sb4 = 3.1998581543e+03, /* 0x4547fdbb */
108 sb5 = 2.5530502930e+03, /* 0x451f90ce */
109 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
110 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
111 
112 float
113 erff(float x)
114 {
115  int32_t hx,ix,i;
116  float R,S,P,Q,s,y,z,r;
117  GET_FLOAT_WORD(hx,x);
118  ix = hx&0x7fffffff;
119  if(ix>=0x7f800000) { /* erf(nan)=nan */
120  i = ((uint32_t)hx>>31)<<1;
121  return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
122  }
123 
124  if(ix < 0x3f580000) { /* |x|<0.84375 */
125  if(ix < 0x31800000) { /* |x|<2**-28 */
126  if (ix < 0x04000000)
127  /*avoid underflow */
128  return (float)0.125*((float)8.0*x+efx8*x);
129  return x + efx*x;
130  }
131  z = x*x;
132  r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
133  s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
134  y = r/s;
135  return x + x*y;
136  }
137  if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
138  s = fabsf(x)-one;
139  P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
140  Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
141  if(hx>=0) return erx + P/Q; else return -erx - P/Q;
142  }
143  if (ix >= 0x40c00000) { /* inf>|x|>=6 */
144  if(hx>=0) return one-tiny; else return tiny-one;
145  }
146  x = fabsf(x);
147  s = one/(x*x);
148  if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
149  R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
150  ra5+s*(ra6+s*ra7))))));
151  S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
152  sa5+s*(sa6+s*(sa7+s*sa8)))))));
153  } else { /* |x| >= 1/0.35 */
154  R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
155  rb5+s*rb6)))));
156  S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
157  sb5+s*(sb6+s*sb7))))));
158  }
159  GET_FLOAT_WORD(ix,x);
160  SET_FLOAT_WORD(z,ix&0xfffff000);
161  r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
162  if(hx>=0) return one-r/x; else return r/x-one;
163 }
164 
165 float
166 erfcf(float x)
167 {
168  int32_t hx,ix;
169  float R,S,P,Q,s,y,z,r;
170  GET_FLOAT_WORD(hx,x);
171  ix = hx&0x7fffffff;
172  if(ix>=0x7f800000) { /* erfc(nan)=nan */
173  /* erfc(+-inf)=0,2 */
174  return (float)(((uint32_t)hx>>31)<<1)+one/x;
175  }
176 
177  if(ix < 0x3f580000) { /* |x|<0.84375 */
178  if(ix < 0x23800000) /* |x|<2**-56 */
179  return one-x;
180  z = x*x;
181  r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
182  s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
183  y = r/s;
184  if(hx < 0x3e800000) { /* x<1/4 */
185  return one-(x+x*y);
186  } else {
187  r = x*y;
188  r += (x-half);
189  return half - r ;
190  }
191  }
192  if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
193  s = fabsf(x)-one;
194  P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
195  Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
196  if(hx>=0) {
197  z = one-erx; return z - P/Q;
198  } else {
199  z = erx+P/Q; return one+z;
200  }
201  }
202  if (ix < 0x41e00000) { /* |x|<28 */
203  x = fabsf(x);
204  s = one/(x*x);
205  if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
206  R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
207  ra5+s*(ra6+s*ra7))))));
208  S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
209  sa5+s*(sa6+s*(sa7+s*sa8)))))));
210  } else { /* |x| >= 1/.35 ~ 2.857143 */
211  if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
212  R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
213  rb5+s*rb6)))));
214  S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
215  sb5+s*(sb6+s*sb7))))));
216  }
217  GET_FLOAT_WORD(ix,x);
218  SET_FLOAT_WORD(z,ix&0xfffff000);
219  r = __ieee754_expf(-z*z-(float)0.5625)*
220  __ieee754_expf((z-x)*(z+x)+R/S);
221  if(hx>0) return r/x; else return two-r/x;
222  } else {
223  if(hx>0) return tiny*tiny; else return two-tiny;
224  }
225 }
226 
227 #endif