HP 12C: Error Function Approximation
Introduction
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.
HP 12C Program Error Function
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
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
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.
HP 12C Program Error Function
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
Eddie
All original content copyright, © 2011-2019. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
