(42S) GAUSS LEGENDRE 16 POINT INTEGRATION

[Gerald H]

I note that some members (pito) have used the programme in some emulator contrary to my wish that we remain true to the original & exclusively use the programmes in the 42S.

However, recognising the scarcity & cost of a 42S I relent & permit usage in emulators.

go42S emulates very nicely using the original ROM, sadly incorporating the possibility of accelerating calculation speed by a factor of up to 32.

Free42 operates to a much higher level of accuracy & cannot operate at original speed - a sad comment on our times.

The following programme is adapted for Free42 - it will run on the original 42S, just at a slightly slower speed than the above programme - to make use of abscissae & weights of greater accuracy.

I would be pleased to hear of any actual improvement in calculating accuracy.

Code:

00 { 607-Byte Prgm }
01>LBL "GL16"
02 CLX
03 STO 04
04 RCL 02
05 RCL 01
06 STO 07
07 -
08 RCL 03
09 STO 05
10 STO+ ST X
11 ÷
12 STO 06
13>LBL 17
14 STO+ 07
15 16
16 STO 08
17>LBL 18
18 RCL 07
19 XEQ IND 08
20 RCL× 06
21 STO 09
22 -
23 XEQ IND 00
24 STO 10
25 RCL 07
26 RCL+ 09
27 XEQ IND 00
28 RCL+ 10
29 DSE 08
30 XEQ IND 08
31 ×
32 STO+ 04
33 DSE 08
34 GTO 18
35 RCL 06
36 STO+ 07
37 DSE 05
38 GTO 17
39 STO× 04
40 RCL 04
41 RTN
42>LBL 01
43 2.71524594117E-2
44 54094852E-21
45 +
46 RTN
47>LBL 02
48 9.89400934991E-1
49 649932596E-21
50 +
51 RTN
52>LBL 03
53 6.22535239386E-2
54 47892863E-21
55 +
56 RTN
57>LBL 04
58 9.44575023073E-1
59 232576078E-21
60 +
61 RTN
62>LBL 05
63 9.5158511682E-2
64 49278481E-20
65 +
66 RTN
67>LBL 06
68 8.65631202387E-1
69 83174388E-20
70 +
71 RTN
72>LBL 07
73 1.24628971255E-1
74 533872052E-21
75 +
76 RTN
77>LBL 08
78 7.55404408355E-1
79 3033895E-21
80 +
81 RTN
82>LBL 09
83 1.49595988816E-1
84 576732081E-21
85 +
86 RTN
87>LBL 10
88 6.17876244402E-1
89 643748447E-21
90 +
91 RTN
92>LBL 11
93 1.69156519395E-1
94 2538189E-21
95 +
96 RTN
97>LBL 12
98 4.58016777657E-1
99 227386342E-21
100 +
101 RTN
102>LBL 13
103 1.82603415044E-1
104 923588867E-21
105 +
106 RTN
107>LBL 14
108 2.81603550779E-1
109 25891323E-20
110 +
111 RTN
112>LBL 15
113 1.89450610455E-1
114 68496285E-21
115 +
116 RTN
117>LBL 16
118 9.50125098376E-2
119 37440185E-21
120 +
121 .END.