Fast Modular Exponentiation algorithm in the Hewlett Packard HP48G language, code contributed by a generous student.

Unfortunately, I myself do not know the exact syntax of this language, so I cannot vouch for the correctness of it.

To use the program: enter the base (X), exponent (E), and modulus (m)
on the stack (in that order).  Then hit the variable name the program
is stored under.  The result will be X^E % m

<< 1 -> X E M Y
 << 
  DO
   IF E 2 MOD 0 == THEN  @ Exponent is even
    X X * M MOD 'X' STO  @ X <= X*X % m
    E 2 / 'E' STO  @ E <= E / 2
   ELSE
    X Y * M MOD 'Y' STO  @ Y <= X*Y % m
    'E' 1 STO-  @ E <= E - 1
   END
  UNTIL E 0 =  @ Use "less than or equal to" character instead of =
  END
  Y
 >>
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