Cubical interpolation (Newton scheme) for the HP-15C

This program is by P. J. Schüngel and is used here by permission.

This program is supplied without representation or warranty of any kind. P. J. Schüngel and The Museum of HP Calculators therefore assume no responsibility and shall have no liability, consequential or otherwise, of any kind arising from the use of this program material or any part thereof.

Overview

This programme interpolates data points to a cubical parabola for any given four points x_0 < x_1 < x_2 < x_3 following the simply programmed Newton approach. Points may be unequally spaced. Best results will be obtained if the interpolation point is between the two mid points.

Data points (x_n ; y_n) to be entered as per the following table:

x_0   REG 2       y_0   REG 3
x_1   REG 4       y_1   REG 5
x_2   REG 6       y_2   REG 7
x_3   REG 8       y_3   REG 9
(to leave R0 and R1 free for matrix operations)

Input:
Interpolation point, x_i (will be stored in R0)
Output:
Interpolated value, y_i

No storage registers needed beyond the above.
A division by zero error will occur if x_i matches any x_n
RCL- is required as RCL and ­ would lose the content of T multiple times
The programme should also work on the 42S but no other calculator features that command

Listing

000-               
001-    42.21.13 LBL C
002-    44 0     STO 0
003-    45 9     RCL 9
004-    45.30. 7 RCL- 7
005-    45 8     RCL 8
006-    45.30. 6 RCL- 6
007-    10       ÷
008-    45 7     RCL 7
009-    45.30. 5 RCL- 5
010-    45 6     RCL 6
011-    45.30. 4 RCL- 4
012-    10       ÷
013-    30       -
014-    43 36    LASTX
015-    45 5     RCL 5
016-    45.30. 3 RCL- 3
017-    45 4     RCL 4
018-    45.30. 2 RCL- 2
019-    10       ÷
020-    30       -
021-    43 36    LASTX
022-    34       x⇔y
023-    45 6     RCL 6
024-    45.30. 2 RCL- 2
025-    10       ÷
026-    43 33    R↑
027-    45 8     RCL 8
028-    45.30. 4 RCL- 4
029-    10       ÷
030-    34       x⇔y
031-    30       -
032-    43 36    LASTX
033-    34       x⇔y
034-    45 8     RCL 8
035-    45.30. 2 RCL- 2
036-    10       ÷
037-    45 0     RCL 0
038-    45.30. 6 RCL- 6
039-    20       ×
040-    40       +
041-    45 0     RCL 0
042-    45.30. 4 RCL- 4
043-    20       ×
044-    40       +
045-    45 0     RCL 0
046-    45.30. 2 RCL- 2
047-    20       ×
048-    45.40. 3 RCL+ 3
049-    43 32    RTN

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