10-02-2019, 03:21 AM
The program for the HP 12C calculator approximates the error function defined as
erf(x) = 2 / √π * ∫ e^-(t^2) dt from t = 0 to t = x
by using the series
erf(x) = (2*x) / √π * Σ( (-x^2)^n / (n!*(2*n+1)), n = 0 to ∞)
In the approximation, up to 69 terms are calculated for the sum (the loop stops when n = 69).
Since there is no π constant on the HP 12C, the approximation 355/113 for π is used.
Program:
Examples
(FIX 5)
erf(0.5) ≈ 0.52050
erf(1.6) ≈ 0.97635
erf(2.3) ≈ 0.99886
Source
Ball, John A. Algorithms for PRN Calculators John Wiley & Sons: New York 1978 ISBN (10) 0-471-0370-8
erf(x) = 2 / √π * ∫ e^-(t^2) dt from t = 0 to t = x
by using the series
erf(x) = (2*x) / √π * Σ( (-x^2)^n / (n!*(2*n+1)), n = 0 to ∞)
In the approximation, up to 69 terms are calculated for the sum (the loop stops when n = 69).
Since there is no π constant on the HP 12C, the approximation 355/113 for π is used.
Program:
Code:
Step; Key Code; Key
01; 44,1; STO 1
02; 35; CLx
03; 44, 2; STO 2
04; 44, 3; STO 3
05; 45, 1; RCL 1
06; 2; 2
07; 21; y^x
08; 16; CHS
09; 45, 2; RCL 2
10; 21; y^x
11; 45, 2; RCL 2
12; 43, 3; n!
13; 45, 2; RCL 2
14; 2; 2
15; 20; *
16; 1; 1
17; 40; +
18; 20; *
19; 10; ÷
20; 44,40,3; STO+ 3
21; 43, 35; x=0
22; 43,33,31; GTO 31
23; 1; 1
24; 44,40,2; STO+ 2
25; 45, 2; RCL 2
26; 6; 6
27; 9; 9
28; 43,34; x≤y
29; 43,33,31; GTO 31
30; 43,33,05; GTO 05
31; 45,3; RCL 3
32; 45,1; RCL 1
33; 20; *
34; 2; 2
35; 20; *
36; 3; 3
37; 5; 5
38; 5; 5
39; 36; ENTER
40; 1; 1
41; 1; 1
42; 3; 3
43; 10; ÷
44; 43,21; √
45; 10; ÷
46; 43,33,00; STO 00
Examples
(FIX 5)
erf(0.5) ≈ 0.52050
erf(1.6) ≈ 0.97635
erf(2.3) ≈ 0.99886
Source
Ball, John A. Algorithms for PRN Calculators John Wiley & Sons: New York 1978 ISBN (10) 0-471-0370-8