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1.1 root 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: }
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