```   1: /*	@(#)j0.c	4.1	12/25/82	*/
2:
3: /*
4: 	floating point Bessel's function
5: 	of the first and second kinds
6: 	of order zero
7:
8: 	j0(x) returns the value of J0(x)
9: 	for all real values of x.
10:
11: 	There are no error returns.
12: 	Calls sin, cos, sqrt.
13:
14: 	There is a niggling bug in J0 which
15: 	causes errors up to 2e-16 for x in the
16: 	interval [-8,8].
17: 	The bug is caused by an inappropriate order
18: 	of summation of the series.  rhm will fix it
19: 	someday.
20:
21: 	Coefficients are from Hart & Cheney.
22: 	#5849 (19.22D)
23: 	#6549 (19.25D)
24: 	#6949 (19.41D)
25:
26: 	y0(x) returns the value of Y0(x)
27: 	for positive real values of x.
28: 	For x<=0, error number EDOM is set and a
29: 	large negative value is returned.
30:
31: 	Calls sin, cos, sqrt, log, j0.
32:
33: 	The values of Y0 have not been checked
34: 	to more than ten places.
35:
36: 	Coefficients are from Hart & Cheney.
37: 	#6245 (18.78D)
38: 	#6549 (19.25D)
39: 	#6949 (19.41D)
40: */
41:
42: #include <math.h>
43: #include <errno.h>
44:
45: int errno;
46: static double pzero, qzero;
47: static double tpi   = .6366197723675813430755350535e0;
48: static double pio4  = .7853981633974483096156608458e0;
49: static double p1[] = {
50:     0.4933787251794133561816813446e21,
51:     -.1179157629107610536038440800e21,
52:     0.6382059341072356562289432465e19,
53:     -.1367620353088171386865416609e18,
54:     0.1434354939140344111664316553e16,
55:     -.8085222034853793871199468171e13,
56:     0.2507158285536881945555156435e11,
57:     -.4050412371833132706360663322e8,
58:     0.2685786856980014981415848441e5,
59: };
60: static double q1[] = {
61:     0.4933787251794133562113278438e21,
62:     0.5428918384092285160200195092e19,
63:     0.3024635616709462698627330784e17,
64:     0.1127756739679798507056031594e15,
65:     0.3123043114941213172572469442e12,
66:     0.6699987672982239671814028660e9,
67:     0.1114636098462985378182402543e7,
68:     0.1363063652328970604442810507e4,
69:     1.0
70: };
71: static double p2[] = {
72:     0.5393485083869438325262122897e7,
73:     0.1233238476817638145232406055e8,
74:     0.8413041456550439208464315611e7,
75:     0.2016135283049983642487182349e7,
76:     0.1539826532623911470917825993e6,
77:     0.2485271928957404011288128951e4,
78:     0.0,
79: };
80: static double q2[] = {
81:     0.5393485083869438325560444960e7,
82:     0.1233831022786324960844856182e8,
83:     0.8426449050629797331554404810e7,
84:     0.2025066801570134013891035236e7,
85:     0.1560017276940030940592769933e6,
86:     0.2615700736920839685159081813e4,
87:     1.0,
88: };
89: static double p3[] = {
90:     -.3984617357595222463506790588e4,
91:     -.1038141698748464093880530341e5,
92:     -.8239066313485606568803548860e4,
93:     -.2365956170779108192723612816e4,
94:     -.2262630641933704113967255053e3,
95:     -.4887199395841261531199129300e1,
96:     0.0,
97: };
98: static double q3[] = {
99:     0.2550155108860942382983170882e6,
100:     0.6667454239319826986004038103e6,
101:     0.5332913634216897168722255057e6,
102:     0.1560213206679291652539287109e6,
103:     0.1570489191515395519392882766e5,
104:     0.4087714673983499223402830260e3,
105:     1.0,
106: };
107: static double p4[] = {
108:     -.2750286678629109583701933175e20,
109:     0.6587473275719554925999402049e20,
110:     -.5247065581112764941297350814e19,
111:     0.1375624316399344078571335453e18,
112:     -.1648605817185729473122082537e16,
113:     0.1025520859686394284509167421e14,
114:     -.3436371222979040378171030138e11,
115:     0.5915213465686889654273830069e8,
116:     -.4137035497933148554125235152e5,
117: };
118: static double q4[] = {
119:     0.3726458838986165881989980e21,
120:     0.4192417043410839973904769661e19,
121:     0.2392883043499781857439356652e17,
122:     0.9162038034075185262489147968e14,
123:     0.2613065755041081249568482092e12,
124:     0.5795122640700729537480087915e9,
125:     0.1001702641288906265666651753e7,
126:     0.1282452772478993804176329391e4,
127:     1.0,
128: };
129:
130: double
131: j0(arg) double arg;{
132:     double argsq, n, d;
133:     double sin(), cos(), sqrt();
134:     int i;
135:
136:     if(arg < 0.) arg = -arg;
137:     if(arg > 8.){
138:         asympt(arg);
139:         n = arg - pio4;
140:         return(sqrt(tpi/arg)*(pzero*cos(n) - qzero*sin(n)));
141:     }
142:     argsq = arg*arg;
143:     for(n=0,d=0,i=8;i>=0;i--){
144:         n = n*argsq + p1[i];
145:         d = d*argsq + q1[i];
146:     }
147:     return(n/d);
148: }
149:
150: double
151: y0(arg) double arg;{
152:     double argsq, n, d;
153:     double sin(), cos(), sqrt(), log(), j0();
154:     int i;
155:
156:     errno = 0;
157:     if(arg <= 0.){
158:         errno = EDOM;
159:         return(-HUGE);
160:     }
161:     if(arg > 8.){
162:         asympt(arg);
163:         n = arg - pio4;
164:         return(sqrt(tpi/arg)*(pzero*sin(n) + qzero*cos(n)));
165:     }
166:     argsq = arg*arg;
167:     for(n=0,d=0,i=8;i>=0;i--){
168:         n = n*argsq + p4[i];
169:         d = d*argsq + q4[i];
170:     }
171:     return(n/d + tpi*j0(arg)*log(arg));
172: }
173:
174: static
175: asympt(arg) double arg;{
176:     double zsq, n, d;
177:     int i;
178:     zsq = 64./(arg*arg);
179:     for(n=0,d=0,i=6;i>=0;i--){
180:         n = n*zsq + p2[i];
181:         d = d*zsq + q2[i];
182:     }
183:     pzero = n/d;
184:     for(n=0,d=0,i=6;i>=0;i--){
185:         n = n*zsq + p3[i];
186:         d = d*zsq + q3[i];
187:     }
188:     qzero = (8./arg)*(n/d);
189: }
```

#### Defined functions

asympt defined in line 174; used 2 times
j0 defined in line 130; used 12 times

#### Defined variables

errno defined in line 45; used 2 times
p1 defined in line 49; used 1 times
p2 defined in line 71; used 1 times
p3 defined in line 89; used 1 times
p4 defined in line 107; used 1 times
pio4 defined in line 48; used 2 times
pzero defined in line 46; used 3 times
q1 defined in line 60; used 1 times
q2 defined in line 80; used 1 times
q3 defined in line 98; used 1 times
q4 defined in line 118; used 1 times
qzero defined in line 46; used 3 times
tpi defined in line 47; used 3 times
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