A faster signed remainder when divisor is power of 2

[Dan Lewis]

The following C code:

int Rem8(int n)
    {
    return n % 8 ;
    }

is recognized as a special case (divisor is power of 2) and compiled by gcc version 8.2 with -O3 into:

Rem8: rsbs r3, r0, #0
        and r3, r3, #7
        and r0, r0, #7
        it pl
        rsbpl r0, r3, #0
        bx lr

However, I believe there's a simpler and faster solution (see below). Computing the remainder for other powers of 2 is simply a matter of changing the constant 7 to 2^k-1 and the constant 3 to k.

Rem8: LSRS R1,R0,31
  ANDS R0,R0,7
  IT NE
  SUBNE R0,R0,R1,LSL 3
  BX LR