1*05a0b428SJohn Marino /* s_erff.c -- float version of s_erf.c.
2*05a0b428SJohn Marino * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3*05a0b428SJohn Marino */
4*05a0b428SJohn Marino
5*05a0b428SJohn Marino /*
6*05a0b428SJohn Marino * ====================================================
7*05a0b428SJohn Marino * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8*05a0b428SJohn Marino *
9*05a0b428SJohn Marino * Developed at SunPro, a Sun Microsystems, Inc. business.
10*05a0b428SJohn Marino * Permission to use, copy, modify, and distribute this
11*05a0b428SJohn Marino * software is freely granted, provided that this notice
12*05a0b428SJohn Marino * is preserved.
13*05a0b428SJohn Marino * ====================================================
14*05a0b428SJohn Marino */
15*05a0b428SJohn Marino
16*05a0b428SJohn Marino #include "math.h"
17*05a0b428SJohn Marino #include "math_private.h"
18*05a0b428SJohn Marino
19*05a0b428SJohn Marino static const float
20*05a0b428SJohn Marino tiny = 1e-30,
21*05a0b428SJohn Marino half= 5.0000000000e-01, /* 0x3F000000 */
22*05a0b428SJohn Marino one = 1.0000000000e+00, /* 0x3F800000 */
23*05a0b428SJohn Marino two = 2.0000000000e+00, /* 0x40000000 */
24*05a0b428SJohn Marino /* c = (subfloat)0.84506291151 */
25*05a0b428SJohn Marino erx = 8.4506291151e-01, /* 0x3f58560b */
26*05a0b428SJohn Marino /*
27*05a0b428SJohn Marino * Coefficients for approximation to erf on [0,0.84375]
28*05a0b428SJohn Marino */
29*05a0b428SJohn Marino efx = 1.2837916613e-01, /* 0x3e0375d4 */
30*05a0b428SJohn Marino efx8= 1.0270333290e+00, /* 0x3f8375d4 */
31*05a0b428SJohn Marino pp0 = 1.2837916613e-01, /* 0x3e0375d4 */
32*05a0b428SJohn Marino pp1 = -3.2504209876e-01, /* 0xbea66beb */
33*05a0b428SJohn Marino pp2 = -2.8481749818e-02, /* 0xbce9528f */
34*05a0b428SJohn Marino pp3 = -5.7702702470e-03, /* 0xbbbd1489 */
35*05a0b428SJohn Marino pp4 = -2.3763017452e-05, /* 0xb7c756b1 */
36*05a0b428SJohn Marino qq1 = 3.9791721106e-01, /* 0x3ecbbbce */
37*05a0b428SJohn Marino qq2 = 6.5022252500e-02, /* 0x3d852a63 */
38*05a0b428SJohn Marino qq3 = 5.0813062117e-03, /* 0x3ba68116 */
39*05a0b428SJohn Marino qq4 = 1.3249473704e-04, /* 0x390aee49 */
40*05a0b428SJohn Marino qq5 = -3.9602282413e-06, /* 0xb684e21a */
41*05a0b428SJohn Marino /*
42*05a0b428SJohn Marino * Coefficients for approximation to erf in [0.84375,1.25]
43*05a0b428SJohn Marino */
44*05a0b428SJohn Marino pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */
45*05a0b428SJohn Marino pa1 = 4.1485610604e-01, /* 0x3ed46805 */
46*05a0b428SJohn Marino pa2 = -3.7220788002e-01, /* 0xbebe9208 */
47*05a0b428SJohn Marino pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */
48*05a0b428SJohn Marino pa4 = -1.1089469492e-01, /* 0xbde31cc2 */
49*05a0b428SJohn Marino pa5 = 3.5478305072e-02, /* 0x3d1151b3 */
50*05a0b428SJohn Marino pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */
51*05a0b428SJohn Marino qa1 = 1.0642088205e-01, /* 0x3dd9f331 */
52*05a0b428SJohn Marino qa2 = 5.4039794207e-01, /* 0x3f0a5785 */
53*05a0b428SJohn Marino qa3 = 7.1828655899e-02, /* 0x3d931ae7 */
54*05a0b428SJohn Marino qa4 = 1.2617121637e-01, /* 0x3e013307 */
55*05a0b428SJohn Marino qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */
56*05a0b428SJohn Marino qa6 = 1.1984500103e-02, /* 0x3c445aa3 */
57*05a0b428SJohn Marino /*
58*05a0b428SJohn Marino * Coefficients for approximation to erfc in [1.25,1/0.35]
59*05a0b428SJohn Marino */
60*05a0b428SJohn Marino ra0 = -9.8649440333e-03, /* 0xbc21a093 */
61*05a0b428SJohn Marino ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */
62*05a0b428SJohn Marino ra2 = -1.0558626175e+01, /* 0xc128f022 */
63*05a0b428SJohn Marino ra3 = -6.2375331879e+01, /* 0xc2798057 */
64*05a0b428SJohn Marino ra4 = -1.6239666748e+02, /* 0xc322658c */
65*05a0b428SJohn Marino ra5 = -1.8460508728e+02, /* 0xc3389ae7 */
66*05a0b428SJohn Marino ra6 = -8.1287437439e+01, /* 0xc2a2932b */
67*05a0b428SJohn Marino ra7 = -9.8143291473e+00, /* 0xc11d077e */
68*05a0b428SJohn Marino sa1 = 1.9651271820e+01, /* 0x419d35ce */
69*05a0b428SJohn Marino sa2 = 1.3765776062e+02, /* 0x4309a863 */
70*05a0b428SJohn Marino sa3 = 4.3456588745e+02, /* 0x43d9486f */
71*05a0b428SJohn Marino sa4 = 6.4538726807e+02, /* 0x442158c9 */
72*05a0b428SJohn Marino sa5 = 4.2900814819e+02, /* 0x43d6810b */
73*05a0b428SJohn Marino sa6 = 1.0863500214e+02, /* 0x42d9451f */
74*05a0b428SJohn Marino sa7 = 6.5702495575e+00, /* 0x40d23f7c */
75*05a0b428SJohn Marino sa8 = -6.0424413532e-02, /* 0xbd777f97 */
76*05a0b428SJohn Marino /*
77*05a0b428SJohn Marino * Coefficients for approximation to erfc in [1/.35,28]
78*05a0b428SJohn Marino */
79*05a0b428SJohn Marino rb0 = -9.8649431020e-03, /* 0xbc21a092 */
80*05a0b428SJohn Marino rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */
81*05a0b428SJohn Marino rb2 = -1.7757955551e+01, /* 0xc18e104b */
82*05a0b428SJohn Marino rb3 = -1.6063638306e+02, /* 0xc320a2ea */
83*05a0b428SJohn Marino rb4 = -6.3756646729e+02, /* 0xc41f6441 */
84*05a0b428SJohn Marino rb5 = -1.0250950928e+03, /* 0xc480230b */
85*05a0b428SJohn Marino rb6 = -4.8351919556e+02, /* 0xc3f1c275 */
86*05a0b428SJohn Marino sb1 = 3.0338060379e+01, /* 0x41f2b459 */
87*05a0b428SJohn Marino sb2 = 3.2579251099e+02, /* 0x43a2e571 */
88*05a0b428SJohn Marino sb3 = 1.5367296143e+03, /* 0x44c01759 */
89*05a0b428SJohn Marino sb4 = 3.1998581543e+03, /* 0x4547fdbb */
90*05a0b428SJohn Marino sb5 = 2.5530502930e+03, /* 0x451f90ce */
91*05a0b428SJohn Marino sb6 = 4.7452853394e+02, /* 0x43ed43a7 */
92*05a0b428SJohn Marino sb7 = -2.2440952301e+01; /* 0xc1b38712 */
93*05a0b428SJohn Marino
94*05a0b428SJohn Marino float
erff(float x)95*05a0b428SJohn Marino erff(float x)
96*05a0b428SJohn Marino {
97*05a0b428SJohn Marino int32_t hx,ix,i;
98*05a0b428SJohn Marino float R,S,P,Q,s,y,z,r;
99*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x);
100*05a0b428SJohn Marino ix = hx&0x7fffffff;
101*05a0b428SJohn Marino if(ix>=0x7f800000) { /* erf(nan)=nan */
102*05a0b428SJohn Marino i = ((u_int32_t)hx>>31)<<1;
103*05a0b428SJohn Marino return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
104*05a0b428SJohn Marino }
105*05a0b428SJohn Marino
106*05a0b428SJohn Marino if(ix < 0x3f580000) { /* |x|<0.84375 */
107*05a0b428SJohn Marino if(ix < 0x31800000) { /* |x|<2**-28 */
108*05a0b428SJohn Marino if (ix < 0x04000000)
109*05a0b428SJohn Marino /*avoid underflow */
110*05a0b428SJohn Marino return (float)0.125*((float)8.0*x+efx8*x);
111*05a0b428SJohn Marino return x + efx*x;
112*05a0b428SJohn Marino }
113*05a0b428SJohn Marino z = x*x;
114*05a0b428SJohn Marino r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
115*05a0b428SJohn Marino s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
116*05a0b428SJohn Marino y = r/s;
117*05a0b428SJohn Marino return x + x*y;
118*05a0b428SJohn Marino }
119*05a0b428SJohn Marino if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
120*05a0b428SJohn Marino s = fabsf(x)-one;
121*05a0b428SJohn Marino P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
122*05a0b428SJohn Marino Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
123*05a0b428SJohn Marino if(hx>=0) return erx + P/Q; else return -erx - P/Q;
124*05a0b428SJohn Marino }
125*05a0b428SJohn Marino if (ix >= 0x40c00000) { /* inf>|x|>=6 */
126*05a0b428SJohn Marino if(hx>=0) return one-tiny; else return tiny-one;
127*05a0b428SJohn Marino }
128*05a0b428SJohn Marino x = fabsf(x);
129*05a0b428SJohn Marino s = one/(x*x);
130*05a0b428SJohn Marino if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
131*05a0b428SJohn Marino R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
132*05a0b428SJohn Marino ra5+s*(ra6+s*ra7))))));
133*05a0b428SJohn Marino S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
134*05a0b428SJohn Marino sa5+s*(sa6+s*(sa7+s*sa8)))))));
135*05a0b428SJohn Marino } else { /* |x| >= 1/0.35 */
136*05a0b428SJohn Marino R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
137*05a0b428SJohn Marino rb5+s*rb6)))));
138*05a0b428SJohn Marino S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
139*05a0b428SJohn Marino sb5+s*(sb6+s*sb7))))));
140*05a0b428SJohn Marino }
141*05a0b428SJohn Marino GET_FLOAT_WORD(ix,x);
142*05a0b428SJohn Marino SET_FLOAT_WORD(z,ix&0xfffff000);
143*05a0b428SJohn Marino r = expf(-z*z-(float)0.5625)*expf((z-x)*(z+x)+R/S);
144*05a0b428SJohn Marino if(hx>=0) return one-r/x; else return r/x-one;
145*05a0b428SJohn Marino }
146*05a0b428SJohn Marino
147*05a0b428SJohn Marino float
erfcf(float x)148*05a0b428SJohn Marino erfcf(float x)
149*05a0b428SJohn Marino {
150*05a0b428SJohn Marino int32_t hx,ix;
151*05a0b428SJohn Marino float R,S,P,Q,s,y,z,r;
152*05a0b428SJohn Marino GET_FLOAT_WORD(hx,x);
153*05a0b428SJohn Marino ix = hx&0x7fffffff;
154*05a0b428SJohn Marino if(ix>=0x7f800000) { /* erfc(nan)=nan */
155*05a0b428SJohn Marino /* erfc(+-inf)=0,2 */
156*05a0b428SJohn Marino return (float)(((u_int32_t)hx>>31)<<1)+one/x;
157*05a0b428SJohn Marino }
158*05a0b428SJohn Marino
159*05a0b428SJohn Marino if(ix < 0x3f580000) { /* |x|<0.84375 */
160*05a0b428SJohn Marino if(ix < 0x23800000) /* |x|<2**-56 */
161*05a0b428SJohn Marino return one-x;
162*05a0b428SJohn Marino z = x*x;
163*05a0b428SJohn Marino r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4)));
164*05a0b428SJohn Marino s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5))));
165*05a0b428SJohn Marino y = r/s;
166*05a0b428SJohn Marino if(hx < 0x3e800000) { /* x<1/4 */
167*05a0b428SJohn Marino return one-(x+x*y);
168*05a0b428SJohn Marino } else {
169*05a0b428SJohn Marino r = x*y;
170*05a0b428SJohn Marino r += (x-half);
171*05a0b428SJohn Marino return half - r ;
172*05a0b428SJohn Marino }
173*05a0b428SJohn Marino }
174*05a0b428SJohn Marino if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
175*05a0b428SJohn Marino s = fabsf(x)-one;
176*05a0b428SJohn Marino P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6)))));
177*05a0b428SJohn Marino Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6)))));
178*05a0b428SJohn Marino if(hx>=0) {
179*05a0b428SJohn Marino z = one-erx; return z - P/Q;
180*05a0b428SJohn Marino } else {
181*05a0b428SJohn Marino z = erx+P/Q; return one+z;
182*05a0b428SJohn Marino }
183*05a0b428SJohn Marino }
184*05a0b428SJohn Marino if (ix < 0x41e00000) { /* |x|<28 */
185*05a0b428SJohn Marino x = fabsf(x);
186*05a0b428SJohn Marino s = one/(x*x);
187*05a0b428SJohn Marino if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
188*05a0b428SJohn Marino R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
189*05a0b428SJohn Marino ra5+s*(ra6+s*ra7))))));
190*05a0b428SJohn Marino S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
191*05a0b428SJohn Marino sa5+s*(sa6+s*(sa7+s*sa8)))))));
192*05a0b428SJohn Marino } else { /* |x| >= 1/.35 ~ 2.857143 */
193*05a0b428SJohn Marino if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */
194*05a0b428SJohn Marino R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
195*05a0b428SJohn Marino rb5+s*rb6)))));
196*05a0b428SJohn Marino S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
197*05a0b428SJohn Marino sb5+s*(sb6+s*sb7))))));
198*05a0b428SJohn Marino }
199*05a0b428SJohn Marino GET_FLOAT_WORD(ix,x);
200*05a0b428SJohn Marino SET_FLOAT_WORD(z,ix&0xfffff000);
201*05a0b428SJohn Marino r = expf(-z*z-(float)0.5625) * expf((z-x)*(z+x)+R/S);
202*05a0b428SJohn Marino if(hx>0) return r/x; else return two-r/x;
203*05a0b428SJohn Marino } else {
204*05a0b428SJohn Marino if(hx>0) return tiny*tiny; else return two-tiny;
205*05a0b428SJohn Marino }
206*05a0b428SJohn Marino }
207