1*2fe8fb19SBen Gras /* s_erff.c -- float version of s_erf.c.
2*2fe8fb19SBen Gras * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*2fe8fb19SBen Gras */
4*2fe8fb19SBen Gras
5*2fe8fb19SBen Gras /*
6*2fe8fb19SBen Gras * ====================================================
7*2fe8fb19SBen Gras * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*2fe8fb19SBen Gras *
9*2fe8fb19SBen Gras * Developed at SunPro, a Sun Microsystems, Inc. business.
10*2fe8fb19SBen Gras * Permission to use, copy, modify, and distribute this
11*2fe8fb19SBen Gras * software is freely granted, provided that this notice
12*2fe8fb19SBen Gras * is preserved.
13*2fe8fb19SBen Gras * ====================================================
14*2fe8fb19SBen Gras */
15*2fe8fb19SBen Gras
16*2fe8fb19SBen Gras #include <sys/cdefs.h>
17*2fe8fb19SBen Gras #if defined(LIBM_SCCS) && !defined(lint)
18*2fe8fb19SBen Gras __RCSID("$NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $");
19*2fe8fb19SBen Gras #endif
20*2fe8fb19SBen Gras
21*2fe8fb19SBen Gras #include "math.h"
22*2fe8fb19SBen Gras #include "math_private.h"
23*2fe8fb19SBen Gras
24*2fe8fb19SBen Gras static const float
25*2fe8fb19SBen Gras tiny = 1e-30,
26*2fe8fb19SBen Gras half= 5.0000000000e-01, /* 0x3F000000 */
27*2fe8fb19SBen Gras one = 1.0000000000e+00, /* 0x3F800000 */
28*2fe8fb19SBen Gras two = 2.0000000000e+00, /* 0x40000000 */
29*2fe8fb19SBen Gras /* c = (subfloat)0.84506291151 */
30*2fe8fb19SBen Gras erx = 8.4506291151e-01, /* 0x3f58560b */
31*2fe8fb19SBen Gras /*
32*2fe8fb19SBen Gras * Coefficients for approximation to erf on [0,0.84375]
33*2fe8fb19SBen Gras */
34*2fe8fb19SBen Gras efx = 1.2837916613e-01, /* 0x3e0375d4 */
35*2fe8fb19SBen Gras efx8= 1.0270333290e+00, /* 0x3f8375d4 */
36*2fe8fb19SBen Gras pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
37*2fe8fb19SBen Gras pp1 = -3.2504209876e-01, /* 0xbea66beb */
38*2fe8fb19SBen Gras pp2 = -2.8481749818e-02, /* 0xbce9528f */
39*2fe8fb19SBen Gras pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
40*2fe8fb19SBen Gras pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
41*2fe8fb19SBen Gras qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
42*2fe8fb19SBen Gras qq2 = 6.5022252500e-02, /* 0x3d852a63 */
43*2fe8fb19SBen Gras qq3 = 5.0813062117e-03, /* 0x3ba68116 */
44*2fe8fb19SBen Gras qq4 = 1.3249473704e-04, /* 0x390aee49 */
45*2fe8fb19SBen Gras qq5 = -3.9602282413e-06, /* 0xb684e21a */
46*2fe8fb19SBen Gras /*
47*2fe8fb19SBen Gras * Coefficients for approximation to erf in [0.84375,1.25]
48*2fe8fb19SBen Gras */
49*2fe8fb19SBen Gras pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
50*2fe8fb19SBen Gras pa1 = 4.1485610604e-01, /* 0x3ed46805 */
51*2fe8fb19SBen Gras pa2 = -3.7220788002e-01, /* 0xbebe9208 */
52*2fe8fb19SBen Gras pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
53*2fe8fb19SBen Gras pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
54*2fe8fb19SBen Gras pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
55*2fe8fb19SBen Gras pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
56*2fe8fb19SBen Gras qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
57*2fe8fb19SBen Gras qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
58*2fe8fb19SBen Gras qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
59*2fe8fb19SBen Gras qa4 = 1.2617121637e-01, /* 0x3e013307 */
60*2fe8fb19SBen Gras qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
61*2fe8fb19SBen Gras qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
62*2fe8fb19SBen Gras /*
63*2fe8fb19SBen Gras * Coefficients for approximation to erfc in [1.25,1/0.35]
64*2fe8fb19SBen Gras */
65*2fe8fb19SBen Gras ra0 = -9.8649440333e-03, /* 0xbc21a093 */
66*2fe8fb19SBen Gras ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
67*2fe8fb19SBen Gras ra2 = -1.0558626175e+01, /* 0xc128f022 */
68*2fe8fb19SBen Gras ra3 = -6.2375331879e+01, /* 0xc2798057 */
69*2fe8fb19SBen Gras ra4 = -1.6239666748e+02, /* 0xc322658c */
70*2fe8fb19SBen Gras ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
71*2fe8fb19SBen Gras ra6 = -8.1287437439e+01, /* 0xc2a2932b */
72*2fe8fb19SBen Gras ra7 = -9.8143291473e+00, /* 0xc11d077e */
73*2fe8fb19SBen Gras sa1 = 1.9651271820e+01, /* 0x419d35ce */
74*2fe8fb19SBen Gras sa2 = 1.3765776062e+02, /* 0x4309a863 */
75*2fe8fb19SBen Gras sa3 = 4.3456588745e+02, /* 0x43d9486f */
76*2fe8fb19SBen Gras sa4 = 6.4538726807e+02, /* 0x442158c9 */
77*2fe8fb19SBen Gras sa5 = 4.2900814819e+02, /* 0x43d6810b */
78*2fe8fb19SBen Gras sa6 = 1.0863500214e+02, /* 0x42d9451f */
79*2fe8fb19SBen Gras sa7 = 6.5702495575e+00, /* 0x40d23f7c */
80*2fe8fb19SBen Gras sa8 = -6.0424413532e-02, /* 0xbd777f97 */
81*2fe8fb19SBen Gras /*
82*2fe8fb19SBen Gras * Coefficients for approximation to erfc in [1/.35,28]
83*2fe8fb19SBen Gras */
84*2fe8fb19SBen Gras rb0 = -9.8649431020e-03, /* 0xbc21a092 */
85*2fe8fb19SBen Gras rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
86*2fe8fb19SBen Gras rb2 = -1.7757955551e+01, /* 0xc18e104b */
87*2fe8fb19SBen Gras rb3 = -1.6063638306e+02, /* 0xc320a2ea */
88*2fe8fb19SBen Gras rb4 = -6.3756646729e+02, /* 0xc41f6441 */
89*2fe8fb19SBen Gras rb5 = -1.0250950928e+03, /* 0xc480230b */
90*2fe8fb19SBen Gras rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
91*2fe8fb19SBen Gras sb1 = 3.0338060379e+01, /* 0x41f2b459 */
92*2fe8fb19SBen Gras sb2 = 3.2579251099e+02, /* 0x43a2e571 */
93*2fe8fb19SBen Gras sb3 = 1.5367296143e+03, /* 0x44c01759 */
94*2fe8fb19SBen Gras sb4 = 3.1998581543e+03, /* 0x4547fdbb */
95*2fe8fb19SBen Gras sb5 = 2.5530502930e+03, /* 0x451f90ce */
96*2fe8fb19SBen Gras sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
97*2fe8fb19SBen Gras sb7 = -2.2440952301e+01; /* 0xc1b38712 */
98*2fe8fb19SBen Gras
99*2fe8fb19SBen Gras float
erff(float x)100*2fe8fb19SBen Gras erff(float x)
101*2fe8fb19SBen Gras {
102*2fe8fb19SBen Gras int32_t hx,ix,i;
103*2fe8fb19SBen Gras float R,S,P,Q,s,y,z,r;
104*2fe8fb19SBen Gras GET_FLOAT_WORD(hx,x);
105*2fe8fb19SBen Gras ix = hx&0x7fffffff;
106*2fe8fb19SBen Gras if(ix>=0x7f800000) { /* erf(nan)=nan */
107*2fe8fb19SBen Gras i = ((u_int32_t)hx>>31)<<1;
108*2fe8fb19SBen Gras return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
109*2fe8fb19SBen Gras }
110*2fe8fb19SBen Gras
111*2fe8fb19SBen Gras if(ix < 0x3f580000) { /* |x|<0.84375 */
112*2fe8fb19SBen Gras if(ix < 0x31800000) { /* |x|<2**-28 */
113*2fe8fb19SBen Gras if (ix < 0x04000000)
114*2fe8fb19SBen Gras /*avoid underflow */
115*2fe8fb19SBen Gras return (float)0.125*((float)8.0*x+efx8*x);
116*2fe8fb19SBen Gras return x + efx*x;
117*2fe8fb19SBen Gras }
118*2fe8fb19SBen Gras z = x*x;
119*2fe8fb19SBen Gras r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
120*2fe8fb19SBen Gras s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
121*2fe8fb19SBen Gras y = r/s;
122*2fe8fb19SBen Gras return x + x*y;
123*2fe8fb19SBen Gras }
124*2fe8fb19SBen Gras if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
125*2fe8fb19SBen Gras s = fabsf(x)-one;
126*2fe8fb19SBen Gras P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
127*2fe8fb19SBen Gras Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
128*2fe8fb19SBen Gras if(hx>=0) return erx + P/Q; else return -erx - P/Q;
129*2fe8fb19SBen Gras }
130*2fe8fb19SBen Gras if (ix >= 0x40c00000) { /* inf>|x|>=6 */
131*2fe8fb19SBen Gras if(hx>=0) return one-tiny; else return tiny-one;
132*2fe8fb19SBen Gras }
133*2fe8fb19SBen Gras x = fabsf(x);
134*2fe8fb19SBen Gras s = one/(x*x);
135*2fe8fb19SBen Gras if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
136*2fe8fb19SBen Gras R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
137*2fe8fb19SBen Gras ra5+s*(ra6+s*ra7))))));
138*2fe8fb19SBen Gras S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
139*2fe8fb19SBen Gras sa5+s*(sa6+s*(sa7+s*sa8)))))));
140*2fe8fb19SBen Gras } else { /* |x| >= 1/0.35 */
141*2fe8fb19SBen Gras R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
142*2fe8fb19SBen Gras rb5+s*rb6)))));
143*2fe8fb19SBen Gras S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
144*2fe8fb19SBen Gras sb5+s*(sb6+s*sb7))))));
145*2fe8fb19SBen Gras }
146*2fe8fb19SBen Gras GET_FLOAT_WORD(ix,x);
147*2fe8fb19SBen Gras SET_FLOAT_WORD(z,ix&0xfffff000);
148*2fe8fb19SBen Gras r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S);
149*2fe8fb19SBen Gras if(hx>=0) return one-r/x; else return r/x-one;
150*2fe8fb19SBen Gras }
151*2fe8fb19SBen Gras
152*2fe8fb19SBen Gras float
erfcf(float x)153*2fe8fb19SBen Gras erfcf(float x)
154*2fe8fb19SBen Gras {
155*2fe8fb19SBen Gras int32_t hx,ix;
156*2fe8fb19SBen Gras float R,S,P,Q,s,y,z,r;
157*2fe8fb19SBen Gras GET_FLOAT_WORD(hx,x);
158*2fe8fb19SBen Gras ix = hx&0x7fffffff;
159*2fe8fb19SBen Gras if(ix>=0x7f800000) { /* erfc(nan)=nan */
160*2fe8fb19SBen Gras /* erfc(+-inf)=0,2 */
161*2fe8fb19SBen Gras return (float)(((u_int32_t)hx>>31)<<1)+one/x;
162*2fe8fb19SBen Gras }
163*2fe8fb19SBen Gras
164*2fe8fb19SBen Gras if(ix < 0x3f580000) { /* |x|<0.84375 */
165*2fe8fb19SBen Gras if(ix < 0x23800000) /* |x|<2**-56 */
166*2fe8fb19SBen Gras return one-x;
167*2fe8fb19SBen Gras z = x*x;
168*2fe8fb19SBen Gras r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
169*2fe8fb19SBen Gras s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
170*2fe8fb19SBen Gras y = r/s;
171*2fe8fb19SBen Gras if(hx < 0x3e800000) { /* x<1/4 */
172*2fe8fb19SBen Gras return one-(x+x*y);
173*2fe8fb19SBen Gras } else {
174*2fe8fb19SBen Gras r = x*y;
175*2fe8fb19SBen Gras r += (x-half);
176*2fe8fb19SBen Gras return half - r ;
177*2fe8fb19SBen Gras }
178*2fe8fb19SBen Gras }
179*2fe8fb19SBen Gras if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
180*2fe8fb19SBen Gras s = fabsf(x)-one;
181*2fe8fb19SBen Gras P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
182*2fe8fb19SBen Gras Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
183*2fe8fb19SBen Gras if(hx>=0) {
184*2fe8fb19SBen Gras z = one-erx; return z - P/Q;
185*2fe8fb19SBen Gras } else {
186*2fe8fb19SBen Gras z = erx+P/Q; return one+z;
187*2fe8fb19SBen Gras }
188*2fe8fb19SBen Gras }
189*2fe8fb19SBen Gras if (ix < 0x41e00000) { /* |x|<28 */
190*2fe8fb19SBen Gras x = fabsf(x);
191*2fe8fb19SBen Gras s = one/(x*x);
192*2fe8fb19SBen Gras if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
193*2fe8fb19SBen Gras R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
194*2fe8fb19SBen Gras ra5+s*(ra6+s*ra7))))));
195*2fe8fb19SBen Gras S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
196*2fe8fb19SBen Gras sa5+s*(sa6+s*(sa7+s*sa8)))))));
197*2fe8fb19SBen Gras } else { /* |x| >= 1/.35 ~ 2.857143 */
198*2fe8fb19SBen Gras if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
199*2fe8fb19SBen Gras R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
200*2fe8fb19SBen Gras rb5+s*rb6)))));
201*2fe8fb19SBen Gras S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
202*2fe8fb19SBen Gras sb5+s*(sb6+s*sb7))))));
203*2fe8fb19SBen Gras }
204*2fe8fb19SBen Gras GET_FLOAT_WORD(ix,x);
205*2fe8fb19SBen Gras SET_FLOAT_WORD(z,ix&0xfffff000);
206*2fe8fb19SBen Gras r = __ieee754_expf(-z*z-(float)0.5625)*
207*2fe8fb19SBen Gras __ieee754_expf((z-x)*(z+x)+R/S);
208*2fe8fb19SBen Gras if(hx>0) return r/x; else return two-r/x;
209*2fe8fb19SBen Gras } else {
210*2fe8fb19SBen Gras if(hx>0) return tiny*tiny; else return two-tiny;
211*2fe8fb19SBen Gras }
212*2fe8fb19SBen Gras }
213