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1.1 root 1: #ifndef lint
2: static char sccsid[] = "@(#)j0.c 4.2 (Berkeley) 8/21/85";
3: #endif not lint
4:
5: /*
6: floating point Bessel's function
7: of the first and second kinds
8: of order zero
9:
10: j0(x) returns the value of J0(x)
11: for all real values of x.
12:
13: There are no error returns.
14: Calls sin, cos, sqrt.
15:
16: There is a niggling bug in J0 which
17: causes errors up to 2e-16 for x in the
18: interval [-8,8].
19: The bug is caused by an inappropriate order
20: of summation of the series. rhm will fix it
21: someday.
22:
23: Coefficients are from Hart & Cheney.
24: #5849 (19.22D)
25: #6549 (19.25D)
26: #6949 (19.41D)
27:
28: y0(x) returns the value of Y0(x)
29: for positive real values of x.
30: For x<=0, if on the VAX, error number EDOM is set and
31: the reserved operand fault is generated;
32: otherwise (an IEEE machine) an invalid operation is performed.
33:
34: Calls sin, cos, sqrt, log, j0.
35:
36: The values of Y0 have not been checked
37: to more than ten places.
38:
39: Coefficients are from Hart & Cheney.
40: #6245 (18.78D)
41: #6549 (19.25D)
42: #6949 (19.41D)
43: */
44:
45: #include <math.h>
46: #ifdef VAX
47: #include <errno.h>
48: #else /* IEEE double */
49: static double zero = 0.e0;
50: #endif
51: static double pzero, qzero;
52: static double tpi = .6366197723675813430755350535e0;
53: static double pio4 = .7853981633974483096156608458e0;
54: static double p1[] = {
55: 0.4933787251794133561816813446e21,
56: -.1179157629107610536038440800e21,
57: 0.6382059341072356562289432465e19,
58: -.1367620353088171386865416609e18,
59: 0.1434354939140344111664316553e16,
60: -.8085222034853793871199468171e13,
61: 0.2507158285536881945555156435e11,
62: -.4050412371833132706360663322e8,
63: 0.2685786856980014981415848441e5,
64: };
65: static double q1[] = {
66: 0.4933787251794133562113278438e21,
67: 0.5428918384092285160200195092e19,
68: 0.3024635616709462698627330784e17,
69: 0.1127756739679798507056031594e15,
70: 0.3123043114941213172572469442e12,
71: 0.6699987672982239671814028660e9,
72: 0.1114636098462985378182402543e7,
73: 0.1363063652328970604442810507e4,
74: 1.0
75: };
76: static double p2[] = {
77: 0.5393485083869438325262122897e7,
78: 0.1233238476817638145232406055e8,
79: 0.8413041456550439208464315611e7,
80: 0.2016135283049983642487182349e7,
81: 0.1539826532623911470917825993e6,
82: 0.2485271928957404011288128951e4,
83: 0.0,
84: };
85: static double q2[] = {
86: 0.5393485083869438325560444960e7,
87: 0.1233831022786324960844856182e8,
88: 0.8426449050629797331554404810e7,
89: 0.2025066801570134013891035236e7,
90: 0.1560017276940030940592769933e6,
91: 0.2615700736920839685159081813e4,
92: 1.0,
93: };
94: static double p3[] = {
95: -.3984617357595222463506790588e4,
96: -.1038141698748464093880530341e5,
97: -.8239066313485606568803548860e4,
98: -.2365956170779108192723612816e4,
99: -.2262630641933704113967255053e3,
100: -.4887199395841261531199129300e1,
101: 0.0,
102: };
103: static double q3[] = {
104: 0.2550155108860942382983170882e6,
105: 0.6667454239319826986004038103e6,
106: 0.5332913634216897168722255057e6,
107: 0.1560213206679291652539287109e6,
108: 0.1570489191515395519392882766e5,
109: 0.4087714673983499223402830260e3,
110: 1.0,
111: };
112: static double p4[] = {
113: -.2750286678629109583701933175e20,
114: 0.6587473275719554925999402049e20,
115: -.5247065581112764941297350814e19,
116: 0.1375624316399344078571335453e18,
117: -.1648605817185729473122082537e16,
118: 0.1025520859686394284509167421e14,
119: -.3436371222979040378171030138e11,
120: 0.5915213465686889654273830069e8,
121: -.4137035497933148554125235152e5,
122: };
123: static double q4[] = {
124: 0.3726458838986165881989980e21,
125: 0.4192417043410839973904769661e19,
126: 0.2392883043499781857439356652e17,
127: 0.9162038034075185262489147968e14,
128: 0.2613065755041081249568482092e12,
129: 0.5795122640700729537480087915e9,
130: 0.1001702641288906265666651753e7,
131: 0.1282452772478993804176329391e4,
132: 1.0,
133: };
134:
135: double
136: j0(arg) double arg;{
137: double argsq, n, d;
138: double sin(), cos(), sqrt();
139: int i;
140:
141: if(arg < 0.) arg = -arg;
142: if(arg > 8.){
143: asympt(arg);
144: n = arg - pio4;
145: return(sqrt(tpi/arg)*(pzero*cos(n) - qzero*sin(n)));
146: }
147: argsq = arg*arg;
148: for(n=0,d=0,i=8;i>=0;i--){
149: n = n*argsq + p1[i];
150: d = d*argsq + q1[i];
151: }
152: return(n/d);
153: }
154:
155: double
156: y0(arg) double arg;{
157: double argsq, n, d;
158: double sin(), cos(), sqrt(), log(), j0();
159: int i;
160:
161: if(arg <= 0.){
162: #ifdef VAX
163: extern double infnan();
164: return(infnan(EDOM)); /* NaN */
165: #else /* IEEE double */
166: return(zero/zero); /* IEEE machines: invalid operation */
167: #endif
168: }
169: if(arg > 8.){
170: asympt(arg);
171: n = arg - pio4;
172: return(sqrt(tpi/arg)*(pzero*sin(n) + qzero*cos(n)));
173: }
174: argsq = arg*arg;
175: for(n=0,d=0,i=8;i>=0;i--){
176: n = n*argsq + p4[i];
177: d = d*argsq + q4[i];
178: }
179: return(n/d + tpi*j0(arg)*log(arg));
180: }
181:
182: static
183: asympt(arg) double arg;{
184: double zsq, n, d;
185: int i;
186: zsq = 64./(arg*arg);
187: for(n=0,d=0,i=6;i>=0;i--){
188: n = n*zsq + p2[i];
189: d = d*zsq + q2[i];
190: }
191: pzero = n/d;
192: for(n=0,d=0,i=6;i>=0;i--){
193: n = n*zsq + p3[i];
194: d = d*zsq + q3[i];
195: }
196: qzero = (8./arg)*(n/d);
197: }
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