1 /* s_erff.c -- float version of s_erf.c.
2 */
3
4 /*
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunPro, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15 #if defined(LIBM_SCCS) && !defined(lint)
16 static char rcsid[] = "$NetBSD: s_erff.c,v 1.4 1995/05/10 20:47:07 jtc Exp $";
17 #endif
18
19 #include <errno.h>
20 #include <float.h>
21 #include <math.h>
22 #include <math-narrow-eval.h>
23 #include <math_private.h>
24 #include <math-underflow.h>
25 #include <libm-alias-float.h>
26 #include <fix-int-fp-convert-zero.h>
27
28 static const float
29 tiny = 1e-30,
30 half= 5.0000000000e-01, /* 0x3F000000 */
31 one = 1.0000000000e+00, /* 0x3F800000 */
32 two = 2.0000000000e+00, /* 0x40000000 */
33 /* c = (subfloat)0.84506291151 */
34 erx = 8.4506291151e-01, /* 0x3f58560b */
35 /*
36 * Coefficients for approximation to erf on [0,0.84375]
37 */
38 efx = 1.2837916613e-01, /* 0x3e0375d4 */
39 pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
40 pp1 = -3.2504209876e-01, /* 0xbea66beb */
41 pp2 = -2.8481749818e-02, /* 0xbce9528f */
42 pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
43 pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
44 qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
45 qq2 = 6.5022252500e-02, /* 0x3d852a63 */
46 qq3 = 5.0813062117e-03, /* 0x3ba68116 */
47 qq4 = 1.3249473704e-04, /* 0x390aee49 */
48 qq5 = -3.9602282413e-06, /* 0xb684e21a */
49 /*
50 * Coefficients for approximation to erf in [0.84375,1.25]
51 */
52 pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
53 pa1 = 4.1485610604e-01, /* 0x3ed46805 */
54 pa2 = -3.7220788002e-01, /* 0xbebe9208 */
55 pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
56 pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
57 pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
58 pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
59 qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
60 qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
61 qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
62 qa4 = 1.2617121637e-01, /* 0x3e013307 */
63 qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
64 qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
65 /*
66 * Coefficients for approximation to erfc in [1.25,1/0.35]
67 */
68 ra0 = -9.8649440333e-03, /* 0xbc21a093 */
69 ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
70 ra2 = -1.0558626175e+01, /* 0xc128f022 */
71 ra3 = -6.2375331879e+01, /* 0xc2798057 */
72 ra4 = -1.6239666748e+02, /* 0xc322658c */
73 ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
74 ra6 = -8.1287437439e+01, /* 0xc2a2932b */
75 ra7 = -9.8143291473e+00, /* 0xc11d077e */
76 sa1 = 1.9651271820e+01, /* 0x419d35ce */
77 sa2 = 1.3765776062e+02, /* 0x4309a863 */
78 sa3 = 4.3456588745e+02, /* 0x43d9486f */
79 sa4 = 6.4538726807e+02, /* 0x442158c9 */
80 sa5 = 4.2900814819e+02, /* 0x43d6810b */
81 sa6 = 1.0863500214e+02, /* 0x42d9451f */
82 sa7 = 6.5702495575e+00, /* 0x40d23f7c */
83 sa8 = -6.0424413532e-02, /* 0xbd777f97 */
84 /*
85 * Coefficients for approximation to erfc in [1/.35,28]
86 */
87 rb0 = -9.8649431020e-03, /* 0xbc21a092 */
88 rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
89 rb2 = -1.7757955551e+01, /* 0xc18e104b */
90 rb3 = -1.6063638306e+02, /* 0xc320a2ea */
91 rb4 = -6.3756646729e+02, /* 0xc41f6441 */
92 rb5 = -1.0250950928e+03, /* 0xc480230b */
93 rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
94 sb1 = 3.0338060379e+01, /* 0x41f2b459 */
95 sb2 = 3.2579251099e+02, /* 0x43a2e571 */
96 sb3 = 1.5367296143e+03, /* 0x44c01759 */
97 sb4 = 3.1998581543e+03, /* 0x4547fdbb */
98 sb5 = 2.5530502930e+03, /* 0x451f90ce */
99 sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
100 sb7 = -2.2440952301e+01; /* 0xc1b38712 */
101
102 float __erff(float x)
103 {
104 int32_t hx,ix,i;
105 float R,S,P,Q,s,y,z,r;
106 GET_FLOAT_WORD(hx,x);
107 ix = hx&0x7fffffff;
108 if(ix>=0x7f800000) { /* erf(nan)=nan */
109 i = ((uint32_t)hx>>31)<<1;
110 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
111 }
112
113 if(ix < 0x3f580000) { /* |x|<0.84375 */
114 if(ix < 0x31800000) { /* |x|<2**-28 */
115 if (ix < 0x04000000)
116 {
117 /* Avoid spurious underflow. */
118 float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
119 math_check_force_underflow (ret);
120 return ret;
121 }
122 return x + efx*x;
123 }
124 z = x*x;
125 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
126 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
127 y = r/s;
128 return x + x*y;
129 }
130 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
131 s = fabsf(x)-one;
132 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
133 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
134 if(hx>=0) return erx + P/Q; else return -erx - P/Q;
135 }
136 if (ix >= 0x40c00000) { /* inf>|x|>=6 */
137 if(hx>=0) return one-tiny; else return tiny-one;
138 }
139 x = fabsf(x);
140 s = one/(x*x);
141 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
142 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
143 ra5+s*(ra6+s*ra7))))));
144 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
145 sa5+s*(sa6+s*(sa7+s*sa8)))))));
146 } else { /* |x| >= 1/0.35 */
147 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
148 rb5+s*rb6)))));
149 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
150 sb5+s*(sb6+s*sb7))))));
151 }
152 GET_FLOAT_WORD(ix,x);
153 SET_FLOAT_WORD(z,ix&0xfffff000);
154 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
155 if(hx>=0) return one-r/x; else return r/x-one;
156 }
157 libm_alias_float (__erf, erf)
158
159 float __erfcf(float x)
160 {
161 int32_t hx,ix;
162 float R,S,P,Q,s,y,z,r;
163 GET_FLOAT_WORD(hx,x);
164 ix = hx&0x7fffffff;
165 if(ix>=0x7f800000) { /* erfc(nan)=nan */
166 /* erfc(+-inf)=0,2 */
167 float ret = (float)(((uint32_t)hx>>31)<<1)+one/x;
168 if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f)
169 return 0.0f;
170 return ret;
171 }
172
173 if(ix < 0x3f580000) { /* |x|<0.84375 */
174 if(ix < 0x32800000) /* |x|<2**-26 */
175 return one-x;
176 z = x*x;
177 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
178 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
179 y = r/s;
180 if(hx < 0x3e800000) { /* x<1/4 */
181 return one-(x+x*y);
182 } else {
183 r = x*y;
184 r += (x-half);
185 return half - r ;
186 }
187 }
188 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
189 s = fabsf(x)-one;
190 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
191 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
192 if(hx>=0) {
193 z = one-erx; return z - P/Q;
194 } else {
195 z = erx+P/Q; return one+z;
196 }
197 }
198 if (ix < 0x41e00000) { /* |x|<28 */
199 x = fabsf(x);
200 s = one/(x*x);
201 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
202 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
203 ra5+s*(ra6+s*ra7))))));
204 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
205 sa5+s*(sa6+s*(sa7+s*sa8)))))));
206 } else { /* |x| >= 1/.35 ~ 2.857143 */
207 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
208 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
209 rb5+s*rb6)))));
210 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
211 sb5+s*(sb6+s*sb7))))));
212 }
213 GET_FLOAT_WORD(ix,x);
214 SET_FLOAT_WORD(z,ix&0xffffe000);
215 r = __ieee754_expf(-z*z-(float)0.5625)*
216 __ieee754_expf((z-x)*(z+x)+R/S);
217 if(hx>0) {
218 float ret = math_narrow_eval (r/x);
219 if (ret == 0)
220 __set_errno (ERANGE);
221 return ret;
222 } else
223 return two-r/x;
224 } else {
225 if(hx>0) {
226 __set_errno (ERANGE);
227 return tiny*tiny;
228 } else
229 return two-tiny;
230 }
231 }
232 libm_alias_float (__erfc, erfc)