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-narrow-eval.h>
24#include <math_private.h>
25#include <math-underflow.h>
26#include <libm-alias-float.h>
27#include <fix-int-fp-convert-zero.h>
28
29static const float
30tiny = 1e-30,
31half= 5.0000000000e-01, /* 0x3F000000 */
32one = 1.0000000000e+00, /* 0x3F800000 */
33two = 2.0000000000e+00, /* 0x40000000 */
34 /* c = (subfloat)0.84506291151 */
35erx = 8.4506291151e-01, /* 0x3f58560b */
36/*
37 * Coefficients for approximation to erf on [0,0.84375]
38 */
39efx = 1.2837916613e-01, /* 0x3e0375d4 */
40pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
41pp1 = -3.2504209876e-01, /* 0xbea66beb */
42pp2 = -2.8481749818e-02, /* 0xbce9528f */
43pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
44pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
45qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
46qq2 = 6.5022252500e-02, /* 0x3d852a63 */
47qq3 = 5.0813062117e-03, /* 0x3ba68116 */
48qq4 = 1.3249473704e-04, /* 0x390aee49 */
49qq5 = -3.9602282413e-06, /* 0xb684e21a */
50/*
51 * Coefficients for approximation to erf in [0.84375,1.25]
52 */
53pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
54pa1 = 4.1485610604e-01, /* 0x3ed46805 */
55pa2 = -3.7220788002e-01, /* 0xbebe9208 */
56pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
57pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
58pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
59pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
60qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
61qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
62qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
63qa4 = 1.2617121637e-01, /* 0x3e013307 */
64qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
65qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
66/*
67 * Coefficients for approximation to erfc in [1.25,1/0.35]
68 */
69ra0 = -9.8649440333e-03, /* 0xbc21a093 */
70ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
71ra2 = -1.0558626175e+01, /* 0xc128f022 */
72ra3 = -6.2375331879e+01, /* 0xc2798057 */
73ra4 = -1.6239666748e+02, /* 0xc322658c */
74ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
75ra6 = -8.1287437439e+01, /* 0xc2a2932b */
76ra7 = -9.8143291473e+00, /* 0xc11d077e */
77sa1 = 1.9651271820e+01, /* 0x419d35ce */
78sa2 = 1.3765776062e+02, /* 0x4309a863 */
79sa3 = 4.3456588745e+02, /* 0x43d9486f */
80sa4 = 6.4538726807e+02, /* 0x442158c9 */
81sa5 = 4.2900814819e+02, /* 0x43d6810b */
82sa6 = 1.0863500214e+02, /* 0x42d9451f */
83sa7 = 6.5702495575e+00, /* 0x40d23f7c */
84sa8 = -6.0424413532e-02, /* 0xbd777f97 */
85/*
86 * Coefficients for approximation to erfc in [1/.35,28]
87 */
88rb0 = -9.8649431020e-03, /* 0xbc21a092 */
89rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
90rb2 = -1.7757955551e+01, /* 0xc18e104b */
91rb3 = -1.6063638306e+02, /* 0xc320a2ea */
92rb4 = -6.3756646729e+02, /* 0xc41f6441 */
93rb5 = -1.0250950928e+03, /* 0xc480230b */
94rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
95sb1 = 3.0338060379e+01, /* 0x41f2b459 */
96sb2 = 3.2579251099e+02, /* 0x43a2e571 */
97sb3 = 1.5367296143e+03, /* 0x44c01759 */
98sb4 = 3.1998581543e+03, /* 0x4547fdbb */
99sb5 = 2.5530502930e+03, /* 0x451f90ce */
100sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
101sb7 = -2.2440952301e+01; /* 0xc1b38712 */
102
103float __erff(float x)
104{
105 int32_t hx,ix,i;
106 float R,S,P,Q,s,y,z,r;
107 GET_FLOAT_WORD(hx,x);
108 ix = hx&0x7fffffff;
109 if(ix>=0x7f800000) { /* erf(nan)=nan */
110 i = ((uint32_t)hx>>31)<<1;
111 return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
112 }
113
114 if(ix < 0x3f580000) { /* |x|<0.84375 */
115 if(ix < 0x31800000) { /* |x|<2**-28 */
116 if (ix < 0x04000000)
117 {
118 /* Avoid spurious underflow. */
119 float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
120 math_check_force_underflow (ret);
121 return ret;
122 }
123 return x + efx*x;
124 }
125 z = x*x;
126 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
127 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
128 y = r/s;
129 return x + x*y;
130 }
131 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
132 s = fabsf(x)-one;
133 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
134 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
135 if(hx>=0) return erx + P/Q; else return -erx - P/Q;
136 }
137 if (ix >= 0x40c00000) { /* inf>|x|>=6 */
138 if(hx>=0) return one-tiny; else return tiny-one;
139 }
140 x = fabsf(x);
141 s = one/(x*x);
142 if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
143 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
144 ra5+s*(ra6+s*ra7))))));
145 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
146 sa5+s*(sa6+s*(sa7+s*sa8)))))));
147 } else { /* |x| >= 1/0.35 */
148 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
149 rb5+s*rb6)))));
150 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
151 sb5+s*(sb6+s*sb7))))));
152 }
153 GET_FLOAT_WORD(ix,x);
154 SET_FLOAT_WORD(z,ix&0xfffff000);
155 r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
156 if(hx>=0) return one-r/x; else return r/x-one;
157}
158libm_alias_float (__erf, erf)
159
160float __erfcf(float x)
161{
162 int32_t hx,ix;
163 float R,S,P,Q,s,y,z,r;
164 GET_FLOAT_WORD(hx,x);
165 ix = hx&0x7fffffff;
166 if(ix>=0x7f800000) { /* erfc(nan)=nan */
167 /* erfc(+-inf)=0,2 */
168 float ret = (float)(((uint32_t)hx>>31)<<1)+one/x;
169 if (FIX_INT_FP_CONVERT_ZERO && ret == 0.0f)
170 return 0.0f;
171 return ret;
172 }
173
174 if(ix < 0x3f580000) { /* |x|<0.84375 */
175 if(ix < 0x32800000) /* |x|<2**-26 */
176 return one-x;
177 z = x*x;
178 r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
179 s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
180 y = r/s;
181 if(hx < 0x3e800000) { /* x<1/4 */
182 return one-(x+x*y);
183 } else {
184 r = x*y;
185 r += (x-half);
186 return half - r ;
187 }
188 }
189 if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
190 s = fabsf(x)-one;
191 P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
192 Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
193 if(hx>=0) {
194 z = one-erx; return z - P/Q;
195 } else {
196 z = erx+P/Q; return one+z;
197 }
198 }
199 if (ix < 0x41e00000) { /* |x|<28 */
200 x = fabsf(x);
201 s = one/(x*x);
202 if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
203 R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
204 ra5+s*(ra6+s*ra7))))));
205 S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
206 sa5+s*(sa6+s*(sa7+s*sa8)))))));
207 } else { /* |x| >= 1/.35 ~ 2.857143 */
208 if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
209 R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
210 rb5+s*rb6)))));
211 S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
212 sb5+s*(sb6+s*sb7))))));
213 }
214 GET_FLOAT_WORD(ix,x);
215 SET_FLOAT_WORD(z,ix&0xffffe000);
216 r = __ieee754_expf(-z*z-(float)0.5625)*
217 __ieee754_expf((z-x)*(z+x)+R/S);
218 if(hx>0) {
219 float ret = math_narrow_eval (r/x);
220 if (ret == 0)
221 __set_errno (ERANGE);
222 return ret;
223 } else
224 return two-r/x;
225 } else {
226 if(hx>0) {
227 __set_errno (ERANGE);
228 return tiny*tiny;
229 } else
230 return two-tiny;
231 }
232}
233libm_alias_float (__erfc, erfc)
234