(12C) Error Function Approximation
10-02-2019, 03:21 AM (This post was last modified: 10-02-2019 03:25 AM by Eddie W. Shore.)
Post: #1
 Eddie W. Shore Senior Member Posts: 1,290 Joined: Dec 2013
(12C) Error Function Approximation
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:
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
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 Messages In This Thread (12C) Error Function Approximation - Eddie W. Shore - 10-02-2019 03:21 AM RE: (12C) Error Function Approximation - Albert Chan - 10-05-2019, 12:26 PM

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