[VA] SRC#003- New Year 2019 Special

[Thomas Klemm]

(01-15-2019 10:42 PM)Valentin Albillo Wrote:  Minimum Recommended Model would be the HP-11C or better

This program is for the HP-11C:

Code:

001-   42 34    CLEAR REG
002-   44 25    STO I
003-      33    R↓
004-    44 0    STO 0
005-       1    1
006-    44 3    STO 3
007-42,21, 0   ▸LBL 0
008-    45 3    RCL 3
009-    45 0    RCL 0
010-      20    ×
011-   42 16    π
012-44,20, 3    STO× 3
013-    45 2    RCL 2
014-44,40, 3    STO+ 3
015-      20    ×
016-    44 2    STO 2
017-      33    R↓
018-44,40, 2    STO+ 2
019-   43 36    LSTx
020-    45 0    RCL 0
021-      20    ×
022-      40    +
023-    45 1    RCL 1
024-44,40, 2    STO+ 2
025-44,40, 3    STO+ 3
026-   42 16    π
027-      20    ×
028-      40    +
029-44,10, 2    STO÷ 2
030-44,10, 3    STO÷ 3
031-       1    1
032-    44 1    STO 1
033-    42 5    DSE
034-    22 0    GTO 0
035-    45 2    RCL 2
036-      15    1/x

Example:

2019
ENTER
200
R/S

(this may take some time …)

12.63898232

Registers:

0: 2019 (or whatever you entered)
1: x
2: y
3: z


Starting with:

\(\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}=\begin{bmatrix}
0\\
0\\
1
\end{bmatrix}\)

The following matrix multiplication is iterated:

\(\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}\rightarrow \begin{bmatrix}
\pi & 2019 & 2019\\
1 & \pi & 2019\\
1 & 1 & \pi
\end{bmatrix}\cdot\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}\)

The resulting vector is reduced in lines 29-31 to avoid overflow.

\(\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}\rightarrow \begin{bmatrix}
1\\
\frac{y}{x}\\
\frac{z}{x}
\end{bmatrix}\)

Cheers
Thomas