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