HP15c program: y mod x

HP15c program: Calculate y mod x

command         display

f LBL B        001-42,21,12
   STO 3        002-    44 3       (store X in reg3)
   x><y         003-      34
   STO 4        004-    44 4       (store Y in reg4)
   x><y         005-      34
   divide       006-      10
g int          007-   43 44
   RCL 3        008-    45 3
   *            009-      20
   CHS          010-      16
   RCL 4        011-    45 4
   +            012-      40
g RTN          013-   43 32

This program uses the following label: LBL B
The program uses the registers (STO/RCL): 3 and 4

Using the program

The modulus of Y mod X is an integer number smaller than X and the reminder of y divided by x. Enter Y and X and then press "GSB B" The modulus is the number that is in X after the execution of the program.

The algorithm

The HP15c has an integer function to convert a floating point number into an integer number. We can use this to calculate the modulus:

y mod x = y - (x * int( y/x ))

Example to test the program:
15 mod 6 = 3

15
Enter
6
GSB B

Expected result (shown in the display):
3

Alternate implementation that uses only the stack

command         display

f LBL B        001-42,21,12
   x><y         002-      34
   Enter        003-      36
   R down       004-      33
   x><y         005-      34
   / (divide)   006-      10
g Last X       007-   43 36
   x><y         008-      34
g int          009-   43 44
   *            010-      20
   x><y         011-      34
   R down       012-      33
   -            013-      30
g RTN          014-   43 32

This program uses the following label: LBL B
The program uses the registers (STO/RCL): none