HP 35s Remainder Function

[SRMac]

Mathmatically, how does the RMDR function manage negative numbers?  for example:  using an argument of

(-187,360), the RMDR function gives 173.  Clearly it can be seen, that 187 + 173 = 360, but it is unclear as to how internally, the calculator makes the adjustment.  Any ideas?

SRMac

[BartdB]

Hi,

The RMDR function cannot handle negative numbers, the answer it gave is wrong.

Ignoring the negative, what you were asking for was the remainder of 187/360, which is 187 (as the numerator is already smaller than the denominator).

What the calculator gave you was the remainder for 360/187 (which = 1 & 173/360, i.e. remainder is 173).

The RMDR function is also known as the MOD function, which is often calculated as MOD(x,y) = x-y*Floor(x/y), where Floor is the greatest integer that is less than or equal to the argument.

From this we can see the error:

x-y*Floor(x/y)

= -187-360*Floor(-187/360)

= -187-360*Floor(-0.5194')

= -187-360*(-1)

= -187+360

= 173  (which is incorrect)

I suggest you avoid using negatives in the RMDR function.

Hope this helps.