(30b) 16-Point Gauss-Legendre Integration

[Gerald H]

Gauss-Legendre 16-point integration
0 P0
1 0
2 STO 4
3 RCL 2
4 RCL 1
5 STO 7
6 -
7 RCL 3
8 STO 5
9 2
10 *
11 /
12 STO 6
13 Lbl 17
14 STO+ 7
15 1
16 6
17 STO 0
18 Lbl 18
19 RCL 7
20 RCL Data
21 RCL* 6
22 STO 9
23 -
24 Call19
25 STO 8
26 RCL 7
27 RCL+ 9
28 Call19
29 RCL+ 8
30 DSE 0
31 RCL Data
32 *
33 STO+ 4
34 DSE 0
35 Gto 18
36 RCL 6
37 STO+ 7
38 DSE 5
39 Gto 17
40 STO* 4
41 RCL 4
42 RTN

The following MAGIC NUMBERS should be stored as data in consecutive storage points from Y1 to X9 (do not store the indices 1 to 16):

1. 271524594118E-13
2. 989400934992E-12
3. 622535239386E-13
4. 944575023073E-12
5. 951585116825E-13
6. 865631202388E-12
7. 124628971256E-12
8. 755404408355E-12
9. 149595988817E-12
10. 617876244403E-12
11. 169156519395E-12
12. 458016777657E-12
13. 182603415045E-12
14. 281603550779E-12
15. 189450610455E-12
16. 950125098376E-13

Enter function (taking a real value from the stack & returning a real value to the stack) to integrate as a programme under Lbl 19, store lower limit of integration as 1, upper limit as 2 & integer number of divisions of integral range as 3, then run programme to return integral in X register.