Description

Calculate either the length of a right triangle’s hypotenuse given the lengths of the legs, or one leg given the other and the hypotenuse.

Usage

Hypotenuse: Put legs a and b on the stack, then g GTO 000 R/S

Other Leg: Put hypotenuse c on the stack followed by leg a, then g GTO 007 R/S

Resources

X and Y are consumed, with the answer in X.

• X: leg length on input, answer on output
• Y: hypotenuse (GTO 000) or other leg (GTO 007) on input
• variables: none
• flags: none

Compatibility

I wrote this using the RLM 12c Platinum simulator, and it is directly openable as such.

Because this simulator’s program save format does not include a pretty-printed version, I provide it inline here, including comments to document the register contents:

001  x²         ; T Z a b²
002  x≷y        ; T Z b² a
003  x²         ; T Z b² a²
004  +          ; T T Z a²+b²
005  √x         ; T T Z c
006  g GTO 000  ; “RTN” in 12c-speak

Notice that even a program this short exhibits a few of the extended HP 12c Platinum features:

1. The dedicated x² operation.

   The trivial effect of replacing the Platinum’s single-instruction operation with 2 yˣ on the 12C is that it pushes the next program’s starting address down two steps since this program uses this operation twice.

   Less obvious is that doing this destroys the Z value from the first step; the starting register contents become T a b 2. Contrast a 12c Platinum, where we see above that the former Z is preserved as the new Y.

   In a strange quirk of HP RPN behavior, there is at the same time no change in the end state of T. Stack-end duplication logic causes both the 12C and the Platinum to copy T down as the new Z.

2. 3-digit GTO addresses.

   That makes the “RTN” equivalent on the 12C g GTO 0 0.

   Between this and the above point, the starting address for the next program on a 12C becomes not 009 but 09.

Now let us show the corresponding “leg” program:

007  x²         ; T Z c b²
008  x≷y        ; T Z b² c
009  x²         ; T Z b² c²
010  x≷y        ; T Z c² b²
011  -          ; T T Z c²-b²
012  √x         ; T T Z a
013  g GTO 000  ; “RTN” in 12c-speak

You might wish to contrast this with the versions for the HP 15C and the SwissMicros DM32.

See Also

Motivation here, plus other variants, including a version of the “leg” program with the HP-12C modification suggested above, plus adaptation to its weaker calling syntax.