Rational interpolation program for the HP 42S

for the HP 42S RI - Rational interpolaton
Rational interpolation is suitable for interpolating logarithmic or exponential relations of the data points
e.g. NTC thermistor characteristics than Lagrange interpolation, with its better accuracy and less computational complexity.

Input

REG X  : x
REG 01  : x₁
REG 02  : x₂
REG 03  : x₃
REG 04  : y₁
REG 05  : y₂
REG 06  : y₃

Resources to be used

FLAG 01
LBL "RI" : entry point
REG 01~03: x values
REG 04~06: y values

Output

REG Y : x
REG X : y

Program list for the HP 42S

RI - Rev.1.10 Sep. 30 2011


00 { 84-Byte Prgm }
01 LBL "RI"
02 ENTER
03 ENTER
04 ENTER
05 RCL 03
06 -
07 ABS
08 X<>Y
09 RCL- 01
10 ABS
11 -
12 CF 01
13 X>0?
14 SF 01
15 R↓
16 RCL- 03
17 RCL 02
18 RCL- 01
19 ×
20 RCL 05
21 RCL- 06
22 ×
23 X<>Y
24 RCL- 01
25 RCL 02
26 RCL- 03
27 ×
28 RCL 05
29 RCL- 04
30 ×
31 FS? 01
32 X<>Y
33 X=0?
34 GTO E
35 ÷
36 X<>Y
37 RCL 06
38 RCL 04
39 FS? 01
40 X<>Y
41 R↑
42 ×
43 LASTX
44 R↓
45 -
46 1
47 R↑
48 -
49 X=0?
50 GTO E
51 ÷
52 RTN
53 LBL E
54 BEEP
55 RTN
56 .END.

Download

'RI' (ri.raw, 87 byte, raw program file for the Free42)

Formulas used

Rational interpolation

Examples

Note Interpolation
Common logarithms Reverse interpolation
Temperature V.S. Resistance characteristic of an NTC thermistor
Operation
2.8 STO 01 3.0 STO 02 3.2 STO 03 0.44715803 STO 04 0.47712125 STO 05 0.50514998 ST0 06 3.1 XEQ RI
12.478 STO 01 8.068 STO 02 5.353 STO 03 20 STO 04 30 STO 05 40 STO 06 10.000 XEQ RI
Results
Y: 3.100000000 X: 0.491365525
Y: 10.00000000 X: 24.94306610

Program list for the HP 42S

Download

Formulas used

Examples

SEE ALSO