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1.1 root 1: #ifndef lint
2: static char sccsid[] = "@(#)j1.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 one
9:
10: j1(x) returns the value of J1(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 J1 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: #6050 (20.98D)
25: #6750 (19.19D)
26: #7150 (19.35D)
27:
28: y1(x) returns the value of Y1(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, j1.
35:
36: The values of Y1 have not been checked
37: to more than ten places.
38:
39: Coefficients are from Hart & Cheney.
40: #6447 (22.18D)
41: #6750 (19.19D)
42: #7150 (19.35D)
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: 0.581199354001606143928050809e21,
56: -.6672106568924916298020941484e20,
57: 0.2316433580634002297931815435e19,
58: -.3588817569910106050743641413e17,
59: 0.2908795263834775409737601689e15,
60: -.1322983480332126453125473247e13,
61: 0.3413234182301700539091292655e10,
62: -.4695753530642995859767162166e7,
63: 0.2701122710892323414856790990e4,
64: };
65: static double q1[] = {
66: 0.1162398708003212287858529400e22,
67: 0.1185770712190320999837113348e20,
68: 0.6092061398917521746105196863e17,
69: 0.2081661221307607351240184229e15,
70: 0.5243710262167649715406728642e12,
71: 0.1013863514358673989967045588e10,
72: 0.1501793594998585505921097578e7,
73: 0.1606931573481487801970916749e4,
74: 1.0,
75: };
76: static double p2[] = {
77: -.4435757816794127857114720794e7,
78: -.9942246505077641195658377899e7,
79: -.6603373248364939109255245434e7,
80: -.1523529351181137383255105722e7,
81: -.1098240554345934672737413139e6,
82: -.1611616644324610116477412898e4,
83: 0.0,
84: };
85: static double q2[] = {
86: -.4435757816794127856828016962e7,
87: -.9934124389934585658967556309e7,
88: -.6585339479723087072826915069e7,
89: -.1511809506634160881644546358e7,
90: -.1072638599110382011903063867e6,
91: -.1455009440190496182453565068e4,
92: 1.0,
93: };
94: static double p3[] = {
95: 0.3322091340985722351859704442e5,
96: 0.8514516067533570196555001171e5,
97: 0.6617883658127083517939992166e5,
98: 0.1849426287322386679652009819e5,
99: 0.1706375429020768002061283546e4,
100: 0.3526513384663603218592175580e2,
101: 0.0,
102: };
103: static double q3[] = {
104: 0.7087128194102874357377502472e6,
105: 0.1819458042243997298924553839e7,
106: 0.1419460669603720892855755253e7,
107: 0.4002944358226697511708610813e6,
108: 0.3789022974577220264142952256e5,
109: 0.8638367769604990967475517183e3,
110: 1.0,
111: };
112: static double p4[] = {
113: -.9963753424306922225996744354e23,
114: 0.2655473831434854326894248968e23,
115: -.1212297555414509577913561535e22,
116: 0.2193107339917797592111427556e20,
117: -.1965887462722140658820322248e18,
118: 0.9569930239921683481121552788e15,
119: -.2580681702194450950541426399e13,
120: 0.3639488548124002058278999428e10,
121: -.2108847540133123652824139923e7,
122: 0.0,
123: };
124: static double q4[] = {
125: 0.5082067366941243245314424152e24,
126: 0.5435310377188854170800653097e22,
127: 0.2954987935897148674290758119e20,
128: 0.1082258259408819552553850180e18,
129: 0.2976632125647276729292742282e15,
130: 0.6465340881265275571961681500e12,
131: 0.1128686837169442121732366891e10,
132: 0.1563282754899580604737366452e7,
133: 0.1612361029677000859332072312e4,
134: 1.0,
135: };
136:
137: double
138: j1(arg) double arg;{
139: double xsq, n, d, x;
140: double sin(), cos(), sqrt();
141: int i;
142:
143: x = arg;
144: if(x < 0.) x = -x;
145: if(x > 8.){
146: asympt(x);
147: n = x - 3.*pio4;
148: n = sqrt(tpi/x)*(pzero*cos(n) - qzero*sin(n));
149: if(arg <0.) n = -n;
150: return(n);
151: }
152: xsq = x*x;
153: for(n=0,d=0,i=8;i>=0;i--){
154: n = n*xsq + p1[i];
155: d = d*xsq + q1[i];
156: }
157: return(arg*n/d);
158: }
159:
160: double
161: y1(arg) double arg;{
162: double xsq, n, d, x;
163: double sin(), cos(), sqrt(), log(), j1();
164: int i;
165:
166: x = arg;
167: if(x <= 0.){
168: #ifdef VAX
169: extern double infnan();
170: return(infnan(EDOM)); /* NaN */
171: #else /* IEEE double */
172: return(zero/zero); /* IEEE machines: invalid operation */
173: #endif
174: }
175: if(x > 8.){
176: asympt(x);
177: n = x - 3*pio4;
178: return(sqrt(tpi/x)*(pzero*sin(n) + qzero*cos(n)));
179: }
180: xsq = x*x;
181: for(n=0,d=0,i=9;i>=0;i--){
182: n = n*xsq + p4[i];
183: d = d*xsq + q4[i];
184: }
185: return(x*n/d + tpi*(j1(x)*log(x)-1./x));
186: }
187:
188: static
189: asympt(arg) double arg;{
190: double zsq, n, d;
191: int i;
192: zsq = 64./(arg*arg);
193: for(n=0,d=0,i=6;i>=0;i--){
194: n = n*zsq + p2[i];
195: d = d*zsq + q2[i];
196: }
197: pzero = n/d;
198: for(n=0,d=0,i=6;i>=0;i--){
199: n = n*zsq + p3[i];
200: d = d*zsq + q3[i];
201: }
202: qzero = (8./arg)*(n/d);
203: }
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