1 /* origin: FreeBSD /usr/src/lib/msun/src/s_erff.c */
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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
13 * ====================================================
19 erx
= 8.4506291151e-01, /* 0x3f58560b */
21 * Coefficients for approximation to erf on [0,0.84375]
23 efx8
= 1.0270333290e+00, /* 0x3f8375d4 */
24 pp0
= 1.2837916613e-01, /* 0x3e0375d4 */
25 pp1
= -3.2504209876e-01, /* 0xbea66beb */
26 pp2
= -2.8481749818e-02, /* 0xbce9528f */
27 pp3
= -5.7702702470e-03, /* 0xbbbd1489 */
28 pp4
= -2.3763017452e-05, /* 0xb7c756b1 */
29 qq1
= 3.9791721106e-01, /* 0x3ecbbbce */
30 qq2
= 6.5022252500e-02, /* 0x3d852a63 */
31 qq3
= 5.0813062117e-03, /* 0x3ba68116 */
32 qq4
= 1.3249473704e-04, /* 0x390aee49 */
33 qq5
= -3.9602282413e-06, /* 0xb684e21a */
35 * Coefficients for approximation to erf in [0.84375,1.25]
37 pa0
= -2.3621185683e-03, /* 0xbb1acdc6 */
38 pa1
= 4.1485610604e-01, /* 0x3ed46805 */
39 pa2
= -3.7220788002e-01, /* 0xbebe9208 */
40 pa3
= 3.1834661961e-01, /* 0x3ea2fe54 */
41 pa4
= -1.1089469492e-01, /* 0xbde31cc2 */
42 pa5
= 3.5478305072e-02, /* 0x3d1151b3 */
43 pa6
= -2.1663755178e-03, /* 0xbb0df9c0 */
44 qa1
= 1.0642088205e-01, /* 0x3dd9f331 */
45 qa2
= 5.4039794207e-01, /* 0x3f0a5785 */
46 qa3
= 7.1828655899e-02, /* 0x3d931ae7 */
47 qa4
= 1.2617121637e-01, /* 0x3e013307 */
48 qa5
= 1.3637083583e-02, /* 0x3c5f6e13 */
49 qa6
= 1.1984500103e-02, /* 0x3c445aa3 */
51 * Coefficients for approximation to erfc in [1.25,1/0.35]
53 ra0
= -9.8649440333e-03, /* 0xbc21a093 */
54 ra1
= -6.9385856390e-01, /* 0xbf31a0b7 */
55 ra2
= -1.0558626175e+01, /* 0xc128f022 */
56 ra3
= -6.2375331879e+01, /* 0xc2798057 */
57 ra4
= -1.6239666748e+02, /* 0xc322658c */
58 ra5
= -1.8460508728e+02, /* 0xc3389ae7 */
59 ra6
= -8.1287437439e+01, /* 0xc2a2932b */
60 ra7
= -9.8143291473e+00, /* 0xc11d077e */
61 sa1
= 1.9651271820e+01, /* 0x419d35ce */
62 sa2
= 1.3765776062e+02, /* 0x4309a863 */
63 sa3
= 4.3456588745e+02, /* 0x43d9486f */
64 sa4
= 6.4538726807e+02, /* 0x442158c9 */
65 sa5
= 4.2900814819e+02, /* 0x43d6810b */
66 sa6
= 1.0863500214e+02, /* 0x42d9451f */
67 sa7
= 6.5702495575e+00, /* 0x40d23f7c */
68 sa8
= -6.0424413532e-02, /* 0xbd777f97 */
70 * Coefficients for approximation to erfc in [1/.35,28]
72 rb0
= -9.8649431020e-03, /* 0xbc21a092 */
73 rb1
= -7.9928326607e-01, /* 0xbf4c9dd4 */
74 rb2
= -1.7757955551e+01, /* 0xc18e104b */
75 rb3
= -1.6063638306e+02, /* 0xc320a2ea */
76 rb4
= -6.3756646729e+02, /* 0xc41f6441 */
77 rb5
= -1.0250950928e+03, /* 0xc480230b */
78 rb6
= -4.8351919556e+02, /* 0xc3f1c275 */
79 sb1
= 3.0338060379e+01, /* 0x41f2b459 */
80 sb2
= 3.2579251099e+02, /* 0x43a2e571 */
81 sb3
= 1.5367296143e+03, /* 0x44c01759 */
82 sb4
= 3.1998581543e+03, /* 0x4547fdbb */
83 sb5
= 2.5530502930e+03, /* 0x451f90ce */
84 sb6
= 4.7452853394e+02, /* 0x43ed43a7 */
85 sb7
= -2.2440952301e+01; /* 0xc1b38712 */
87 static float erfc1(float x
)
92 P
= pa0
+s
*(pa1
+s
*(pa2
+s
*(pa3
+s
*(pa4
+s
*(pa5
+s
*pa6
)))));
93 Q
= 1+s
*(qa1
+s
*(qa2
+s
*(qa3
+s
*(qa4
+s
*(qa5
+s
*qa6
)))));
97 static float erfc2(uint32_t ix
, float x
)
102 if (ix
< 0x3fa00000) /* |x| < 1.25 */
107 if (ix
< 0x4036db6d) { /* |x| < 1/0.35 */
108 R
= ra0
+s
*(ra1
+s
*(ra2
+s
*(ra3
+s
*(ra4
+s
*(
109 ra5
+s
*(ra6
+s
*ra7
))))));
110 S
= 1.0f
+s
*(sa1
+s
*(sa2
+s
*(sa3
+s
*(sa4
+s
*(
111 sa5
+s
*(sa6
+s
*(sa7
+s
*sa8
)))))));
112 } else { /* |x| >= 1/0.35 */
113 R
= rb0
+s
*(rb1
+s
*(rb2
+s
*(rb3
+s
*(rb4
+s
*(
115 S
= 1.0f
+s
*(sb1
+s
*(sb2
+s
*(sb3
+s
*(sb4
+s
*(
116 sb5
+s
*(sb6
+s
*sb7
))))));
118 GET_FLOAT_WORD(ix
, x
);
119 SET_FLOAT_WORD(z
, ix
&0xffffe000);
120 return expf(-z
*z
- 0.5625f
) * expf((z
-x
)*(z
+x
) + R
/S
)/x
;
129 GET_FLOAT_WORD(ix
, x
);
132 if (ix
>= 0x7f800000) {
133 /* erf(nan)=nan, erf(+-inf)=+-1 */
134 return 1-2*sign
+ 1/x
;
136 if (ix
< 0x3f580000) { /* |x| < 0.84375 */
137 if (ix
< 0x31800000) { /* |x| < 2**-28 */
139 return 0.125f
*(8*x
+ efx8
*x
);
142 r
= pp0
+z
*(pp1
+z
*(pp2
+z
*(pp3
+z
*pp4
)));
143 s
= 1+z
*(qq1
+z
*(qq2
+z
*(qq3
+z
*(qq4
+z
*qq5
))));
147 if (ix
< 0x40c00000) /* |x| < 6 */
151 return sign
? -y
: y
;
160 GET_FLOAT_WORD(ix
, x
);
163 if (ix
>= 0x7f800000) {
164 /* erfc(nan)=nan, erfc(+-inf)=0,2 */
168 if (ix
< 0x3f580000) { /* |x| < 0.84375 */
169 if (ix
< 0x23800000) /* |x| < 2**-56 */
172 r
= pp0
+z
*(pp1
+z
*(pp2
+z
*(pp3
+z
*pp4
)));
173 s
= 1.0f
+z
*(qq1
+z
*(qq2
+z
*(qq3
+z
*(qq4
+z
*qq5
))));
175 if (sign
|| ix
< 0x3e800000) /* x < 1/4 */
176 return 1.0f
- (x
+x
*y
);
177 return 0.5f
- (x
- 0.5f
+ x
*y
);
179 if (ix
< 0x41e00000) { /* |x| < 28 */
180 return sign
? 2 - erfc2(ix
,x
) : erfc2(ix
,x
);
182 return sign
? 2 - 0x1p
-120f
: 0x1p
-120f
*0x1p
-120f
;