1 /* s_erff.c -- float version of s_erf.c.
2 * 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 * ====================================================
16 #if defined(LIBM_SCCS) && !defined(lint)
17 static char rcsid
[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
23 #include <math_private.h>
24 #include <fix-int-fp-convert-zero.h>
28 half
= 5.0000000000e-01, /* 0x3F000000 */
29 one
= 1.0000000000e+00, /* 0x3F800000 */
30 two
= 2.0000000000e+00, /* 0x40000000 */
31 /* c = (subfloat)0.84506291151 */
32 erx
= 8.4506291151e-01, /* 0x3f58560b */
34 * Coefficients for approximation to erf on [0,0.84375]
36 efx
= 1.2837916613e-01, /* 0x3e0375d4 */
37 pp0
= 1.2837916613e-01, /* 0x3e0375d4 */
38 pp1
= -3.2504209876e-01, /* 0xbea66beb */
39 pp2
= -2.8481749818e-02, /* 0xbce9528f */
40 pp3
= -5.7702702470e-03, /* 0xbbbd1489 */
41 pp4
= -2.3763017452e-05, /* 0xb7c756b1 */
42 qq1
= 3.9791721106e-01, /* 0x3ecbbbce */
43 qq2
= 6.5022252500e-02, /* 0x3d852a63 */
44 qq3
= 5.0813062117e-03, /* 0x3ba68116 */
45 qq4
= 1.3249473704e-04, /* 0x390aee49 */
46 qq5
= -3.9602282413e-06, /* 0xb684e21a */
48 * Coefficients for approximation to erf in [0.84375,1.25]
50 pa0
= -2.3621185683e-03, /* 0xbb1acdc6 */
51 pa1
= 4.1485610604e-01, /* 0x3ed46805 */
52 pa2
= -3.7220788002e-01, /* 0xbebe9208 */
53 pa3
= 3.1834661961e-01, /* 0x3ea2fe54 */
54 pa4
= -1.1089469492e-01, /* 0xbde31cc2 */
55 pa5
= 3.5478305072e-02, /* 0x3d1151b3 */
56 pa6
= -2.1663755178e-03, /* 0xbb0df9c0 */
57 qa1
= 1.0642088205e-01, /* 0x3dd9f331 */
58 qa2
= 5.4039794207e-01, /* 0x3f0a5785 */
59 qa3
= 7.1828655899e-02, /* 0x3d931ae7 */
60 qa4
= 1.2617121637e-01, /* 0x3e013307 */
61 qa5
= 1.3637083583e-02, /* 0x3c5f6e13 */
62 qa6
= 1.1984500103e-02, /* 0x3c445aa3 */
64 * Coefficients for approximation to erfc in [1.25,1/0.35]
66 ra0
= -9.8649440333e-03, /* 0xbc21a093 */
67 ra1
= -6.9385856390e-01, /* 0xbf31a0b7 */
68 ra2
= -1.0558626175e+01, /* 0xc128f022 */
69 ra3
= -6.2375331879e+01, /* 0xc2798057 */
70 ra4
= -1.6239666748e+02, /* 0xc322658c */
71 ra5
= -1.8460508728e+02, /* 0xc3389ae7 */
72 ra6
= -8.1287437439e+01, /* 0xc2a2932b */
73 ra7
= -9.8143291473e+00, /* 0xc11d077e */
74 sa1
= 1.9651271820e+01, /* 0x419d35ce */
75 sa2
= 1.3765776062e+02, /* 0x4309a863 */
76 sa3
= 4.3456588745e+02, /* 0x43d9486f */
77 sa4
= 6.4538726807e+02, /* 0x442158c9 */
78 sa5
= 4.2900814819e+02, /* 0x43d6810b */
79 sa6
= 1.0863500214e+02, /* 0x42d9451f */
80 sa7
= 6.5702495575e+00, /* 0x40d23f7c */
81 sa8
= -6.0424413532e-02, /* 0xbd777f97 */
83 * Coefficients for approximation to erfc in [1/.35,28]
85 rb0
= -9.8649431020e-03, /* 0xbc21a092 */
86 rb1
= -7.9928326607e-01, /* 0xbf4c9dd4 */
87 rb2
= -1.7757955551e+01, /* 0xc18e104b */
88 rb3
= -1.6063638306e+02, /* 0xc320a2ea */
89 rb4
= -6.3756646729e+02, /* 0xc41f6441 */
90 rb5
= -1.0250950928e+03, /* 0xc480230b */
91 rb6
= -4.8351919556e+02, /* 0xc3f1c275 */
92 sb1
= 3.0338060379e+01, /* 0x41f2b459 */
93 sb2
= 3.2579251099e+02, /* 0x43a2e571 */
94 sb3
= 1.5367296143e+03, /* 0x44c01759 */
95 sb4
= 3.1998581543e+03, /* 0x4547fdbb */
96 sb5
= 2.5530502930e+03, /* 0x451f90ce */
97 sb6
= 4.7452853394e+02, /* 0x43ed43a7 */
98 sb7
= -2.2440952301e+01; /* 0xc1b38712 */
100 float __erff(float x
)
103 float R
,S
,P
,Q
,s
,y
,z
,r
;
104 GET_FLOAT_WORD(hx
,x
);
106 if(ix
>=0x7f800000) { /* erf(nan)=nan */
107 i
= ((u_int32_t
)hx
>>31)<<1;
108 return (float)(1-i
)+one
/x
; /* erf(+-inf)=+-1 */
111 if(ix
< 0x3f580000) { /* |x|<0.84375 */
112 if(ix
< 0x31800000) { /* |x|<2**-28 */
115 /* Avoid spurious underflow. */
116 float ret
= 0.0625f
* (16.0f
* x
+ (16.0f
* efx
) * x
);
117 math_check_force_underflow (ret
);
123 r
= pp0
+z
*(pp1
+z
*(pp2
+z
*(pp3
+z
*pp4
)));
124 s
= one
+z
*(qq1
+z
*(qq2
+z
*(qq3
+z
*(qq4
+z
*qq5
))));
128 if(ix
< 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
130 P
= pa0
+s
*(pa1
+s
*(pa2
+s
*(pa3
+s
*(pa4
+s
*(pa5
+s
*pa6
)))));
131 Q
= one
+s
*(qa1
+s
*(qa2
+s
*(qa3
+s
*(qa4
+s
*(qa5
+s
*qa6
)))));
132 if(hx
>=0) return erx
+ P
/Q
; else return -erx
- P
/Q
;
134 if (ix
>= 0x40c00000) { /* inf>|x|>=6 */
135 if(hx
>=0) return one
-tiny
; else return tiny
-one
;
139 if(ix
< 0x4036DB6E) { /* |x| < 1/0.35 */
140 R
=ra0
+s
*(ra1
+s
*(ra2
+s
*(ra3
+s
*(ra4
+s
*(
141 ra5
+s
*(ra6
+s
*ra7
))))));
142 S
=one
+s
*(sa1
+s
*(sa2
+s
*(sa3
+s
*(sa4
+s
*(
143 sa5
+s
*(sa6
+s
*(sa7
+s
*sa8
)))))));
144 } else { /* |x| >= 1/0.35 */
145 R
=rb0
+s
*(rb1
+s
*(rb2
+s
*(rb3
+s
*(rb4
+s
*(
147 S
=one
+s
*(sb1
+s
*(sb2
+s
*(sb3
+s
*(sb4
+s
*(
148 sb5
+s
*(sb6
+s
*sb7
))))));
150 GET_FLOAT_WORD(ix
,x
);
151 SET_FLOAT_WORD(z
,ix
&0xfffff000);
152 r
= __ieee754_expf(-z
*z
-(float)0.5625)*__ieee754_expf((z
-x
)*(z
+x
)+R
/S
);
153 if(hx
>=0) return one
-r
/x
; else return r
/x
-one
;
155 weak_alias (__erff
, erff
)
157 float __erfcf(float x
)
160 float R
,S
,P
,Q
,s
,y
,z
,r
;
161 GET_FLOAT_WORD(hx
,x
);
163 if(ix
>=0x7f800000) { /* erfc(nan)=nan */
164 /* erfc(+-inf)=0,2 */
165 float ret
= (float)(((u_int32_t
)hx
>>31)<<1)+one
/x
;
166 if (FIX_INT_FP_CONVERT_ZERO
&& ret
== 0.0f
)
171 if(ix
< 0x3f580000) { /* |x|<0.84375 */
172 if(ix
< 0x32800000) /* |x|<2**-26 */
175 r
= pp0
+z
*(pp1
+z
*(pp2
+z
*(pp3
+z
*pp4
)));
176 s
= one
+z
*(qq1
+z
*(qq2
+z
*(qq3
+z
*(qq4
+z
*qq5
))));
178 if(hx
< 0x3e800000) { /* x<1/4 */
186 if(ix
< 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
188 P
= pa0
+s
*(pa1
+s
*(pa2
+s
*(pa3
+s
*(pa4
+s
*(pa5
+s
*pa6
)))));
189 Q
= one
+s
*(qa1
+s
*(qa2
+s
*(qa3
+s
*(qa4
+s
*(qa5
+s
*qa6
)))));
191 z
= one
-erx
; return z
- P
/Q
;
193 z
= erx
+P
/Q
; return one
+z
;
196 if (ix
< 0x41e00000) { /* |x|<28 */
199 if(ix
< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
200 R
=ra0
+s
*(ra1
+s
*(ra2
+s
*(ra3
+s
*(ra4
+s
*(
201 ra5
+s
*(ra6
+s
*ra7
))))));
202 S
=one
+s
*(sa1
+s
*(sa2
+s
*(sa3
+s
*(sa4
+s
*(
203 sa5
+s
*(sa6
+s
*(sa7
+s
*sa8
)))))));
204 } else { /* |x| >= 1/.35 ~ 2.857143 */
205 if(hx
<0&&ix
>=0x40c00000) return two
-tiny
;/* x < -6 */
206 R
=rb0
+s
*(rb1
+s
*(rb2
+s
*(rb3
+s
*(rb4
+s
*(
208 S
=one
+s
*(sb1
+s
*(sb2
+s
*(sb3
+s
*(sb4
+s
*(
209 sb5
+s
*(sb6
+s
*sb7
))))));
211 GET_FLOAT_WORD(ix
,x
);
212 SET_FLOAT_WORD(z
,ix
&0xffffe000);
213 r
= __ieee754_expf(-z
*z
-(float)0.5625)*
214 __ieee754_expf((z
-x
)*(z
+x
)+R
/S
);
216 float ret
= math_narrow_eval (r
/x
);
218 __set_errno (ERANGE
);
224 __set_errno (ERANGE
);
230 weak_alias (__erfcf
, erfcf
)