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) |
17 | static 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 | |
29 | static const float |
30 | tiny = 1e-30, |
31 | half= 5.0000000000e-01, /* 0x3F000000 */ |
32 | one = 1.0000000000e+00, /* 0x3F800000 */ |
33 | two = 2.0000000000e+00, /* 0x40000000 */ |
34 | /* c = (subfloat)0.84506291151 */ |
35 | erx = 8.4506291151e-01, /* 0x3f58560b */ |
36 | /* |
37 | * Coefficients for approximation to erf on [0,0.84375] |
38 | */ |
39 | efx = 1.2837916613e-01, /* 0x3e0375d4 */ |
40 | pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ |
41 | pp1 = -3.2504209876e-01, /* 0xbea66beb */ |
42 | pp2 = -2.8481749818e-02, /* 0xbce9528f */ |
43 | pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ |
44 | pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ |
45 | qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ |
46 | qq2 = 6.5022252500e-02, /* 0x3d852a63 */ |
47 | qq3 = 5.0813062117e-03, /* 0x3ba68116 */ |
48 | qq4 = 1.3249473704e-04, /* 0x390aee49 */ |
49 | qq5 = -3.9602282413e-06, /* 0xb684e21a */ |
50 | /* |
51 | * Coefficients for approximation to erf in [0.84375,1.25] |
52 | */ |
53 | pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ |
54 | pa1 = 4.1485610604e-01, /* 0x3ed46805 */ |
55 | pa2 = -3.7220788002e-01, /* 0xbebe9208 */ |
56 | pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ |
57 | pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ |
58 | pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ |
59 | pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ |
60 | qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ |
61 | qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ |
62 | qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ |
63 | qa4 = 1.2617121637e-01, /* 0x3e013307 */ |
64 | qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ |
65 | qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ |
66 | /* |
67 | * Coefficients for approximation to erfc in [1.25,1/0.35] |
68 | */ |
69 | ra0 = -9.8649440333e-03, /* 0xbc21a093 */ |
70 | ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ |
71 | ra2 = -1.0558626175e+01, /* 0xc128f022 */ |
72 | ra3 = -6.2375331879e+01, /* 0xc2798057 */ |
73 | ra4 = -1.6239666748e+02, /* 0xc322658c */ |
74 | ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ |
75 | ra6 = -8.1287437439e+01, /* 0xc2a2932b */ |
76 | ra7 = -9.8143291473e+00, /* 0xc11d077e */ |
77 | sa1 = 1.9651271820e+01, /* 0x419d35ce */ |
78 | sa2 = 1.3765776062e+02, /* 0x4309a863 */ |
79 | sa3 = 4.3456588745e+02, /* 0x43d9486f */ |
80 | sa4 = 6.4538726807e+02, /* 0x442158c9 */ |
81 | sa5 = 4.2900814819e+02, /* 0x43d6810b */ |
82 | sa6 = 1.0863500214e+02, /* 0x42d9451f */ |
83 | sa7 = 6.5702495575e+00, /* 0x40d23f7c */ |
84 | sa8 = -6.0424413532e-02, /* 0xbd777f97 */ |
85 | /* |
86 | * Coefficients for approximation to erfc in [1/.35,28] |
87 | */ |
88 | rb0 = -9.8649431020e-03, /* 0xbc21a092 */ |
89 | rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ |
90 | rb2 = -1.7757955551e+01, /* 0xc18e104b */ |
91 | rb3 = -1.6063638306e+02, /* 0xc320a2ea */ |
92 | rb4 = -6.3756646729e+02, /* 0xc41f6441 */ |
93 | rb5 = -1.0250950928e+03, /* 0xc480230b */ |
94 | rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ |
95 | sb1 = 3.0338060379e+01, /* 0x41f2b459 */ |
96 | sb2 = 3.2579251099e+02, /* 0x43a2e571 */ |
97 | sb3 = 1.5367296143e+03, /* 0x44c01759 */ |
98 | sb4 = 3.1998581543e+03, /* 0x4547fdbb */ |
99 | sb5 = 2.5530502930e+03, /* 0x451f90ce */ |
100 | sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ |
101 | sb7 = -2.2440952301e+01; /* 0xc1b38712 */ |
102 | |
103 | float __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 | } |
158 | libm_alias_float (__erf, erf) |
159 | |
160 | float __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 | } |
233 | libm_alias_float (__erfc, erfc) |
234 | |