**HP 32SII: Some Algorithms For RPN Calculators**

Four programs ported to the HP 32SII calculator from algorithms designated for the 1973 HP 45 calculator.

**HP 32SII: Euclid Algorithm - Greatest Common Divisor (GCD**)

The HP 45 algorithm is found on page 228 in the Algorithms For RPN Calculators book. (see source below)

This algorithm takes up three labels.

**E01 LBL E**

**E02 INPUT M**

**E03 ENTER**

**E04 ENTER**

**E05 ENTER**

**E06 INPUT N**

**E07 x<>y**

**K01 LBL 1**

**K02 ÷**

**K03 FP**

**K04 ×**

**K05 1**

**K06 x>y?**

**K07 GTO L**

**K08 R↓**

**K09 ENTER**

**K10 ENTER**

**K11 R↓**

**K12 R↓**

**K13 GTO K**

**L01 LBL L**

**L02 R↓**

**L03 R↓**

**L04 RTN**

Sizes and Checksums:

E: 10.5 bytes, 9D4D

K: 19.5 bytes, F8AD

L: 6.0 bytes, C304

Total: 36.0 bytes

Instructions:

Press [ XEQ ] E, enter M and N.

Examples:

Input: M = 36, N = 28. Result: 4

Input: M = 48, N = 126. Result: 6

Input: M = 115, N = 300. Result: 5

**HP 32SII: GCD Using One Label - John Kenney **

The program was provided by Ross Barnes, and the algorithm is from the book ENTER by J. Daniel Dodlin and Keith Jarrett (ISBN 0-9615174-2-1, pg. 84). This is smart, one label program.

Enter both numbers in the stack before running the program.

**G01 LBL G**

**G02 ENTER**

**G03 ENTER**

**G04 -**

**G05 R↓**

**G06 x<>y**

**G07 LASTx**

**G08 /**

**G09 LASTx**

**G10 RDN**

**G11 IP**

**G12 x**

**G13 -**

**G14 x≠0?**

**G15 GTO G**

**G16 +**

**G17 RTN**

Size and Checksum: 25.5 bytes, 4E39

Posted with permission.

**HP 32SII: Tetens Equation**

The HP 45 algorithm is found on page 290 in the Algorithms For RPN Calculators book. The original algorithm took the temperature in Celsius.

Find the saturation of water vapor (e_m) in mmHg (millimeters of Mercury) given the temperature in °F.

Determined Formulas:

T (in °C) = (T°F - 32) * 5/9

α = T/(236.87 + T)

e_m = 4.579 * 10^(7.49 * α)

**T01 LBL T**

**T02 INPUT T**

**T03 →°C**

**T04 ENTER**

**T05 ENTER**

**T06 236.87**

**T07 +**

**T08 ÷**

**T09 7.49**

**T10 ×**

**T11 10^x**

**T12 4.579**

**T13 ×**

**T14 RTN**

Size and Checksum:

45.0 bytes, 404A

Examples:

T = 68 °F, Result: 17.53658 mmHg

T = 99 °F, Result: 47.63501 mmHg

**HP 32SII: Dew Point Given Relative Humidity and Air Temperature**

The HP 45 algorithm is found on page 290 in the Algorithms For RPN Calculators book. The original algorithm took the temperature in Celsius.

Relativity humidity (F) is to be entered as a decimal. For instance, instead of 20%, enter 0.20.

Determined Formulas:

T (in °C) = (T°F - 32) * 5/9

A = T/(T + 236.87)

B = 1/(log F/7.49 + A)

TD = 236.87/(B - 1)

TD = TD * 9/5 + 32

**D01 LBL D**

**D02 INPUT T**

**D03 →°C**

**D04 ENTER**

**D05 ENTER**

**D06 236.87**

**D07 STO A**

**D08 +**

**D09 ÷**

**D10 INPUT F**

**D11 LOG**

**D12 7.49**

**D13 ÷**

**D14 +**

**D15 1/x**

**D16 1**

**D17 -**

**D18 RCL÷ A**

**D19 1/x**

**D20 →°F**

**D21 RTN**

Size and Checksum:

47.5 bytes, 8677

Examples:

T = 80, F = 0.64, Result: 66.725

T = 95, F = 0.32, Result: 60.50684

**HP 32SII: Effective Temperature Due to Wind Velocity**

The HP 45 algorithm is found on page 291 in the Algorithms For RPN Calculators book. The original algorithm took the temperature in Fahrenheit.

Wind velocity is in miles per hour (mph).

Determined Formulas:

A = 0.634*(0.634 - log V)

ΔT = A*(T - 90)

Effective T = T - ΔT

**E01 LBL E**

**E02 0.634**

**E03 ENTER**

**E04 ENTER**

**E05 INPUT V**

**E06 LOG**

**E07 -**

**E08 ×**

**E09 INPUT T**

**E10 ENTER**

**E11 90**

**E12 -**

**E13 ×**

**E14 RCL T**

**E15 x<>y**

**E16 -**

**E17 RTN**

Size and Checksum:

33.5 bytes, 54F7

Examples:

V = 20 mph, T = 15 °F, Result: -16.71728

V = 15 mph, T = 86 °F, Result: 84.62526

Source:

Ball, John A. __Algorithms For RPN Calculators__ John Wiley & Sons: New York, NY. 1978. ISBN 0-471-03070-8

For the second GCD program:

Dodin, J. Daniel and Keith Jarrett. __ENTER: Reverse Polish Notation Made Easy__ Synthetix: Berkeley, CA ISBN 0-9612174-2-1 1984.

Special thanks and gratitude to Ross Barnes.

All original content copyright, © 2011-2022. 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.