microcontroller - Help understanding the code

I am new to C programming. I need your help in understanding the some particular lines in a code segment for sensored control of a brushless dc motor. It was written for a 16-bit MCU (dsPIC33FJ32MC710). This particular section is from the interrupt service routine, and contains two ISRs. Can you please explain to me in simple words, the lines marked by //???? What is being done there, and why? Any other comments are also welcome.

int DesiredSpeed;
int ActualSpeed;
int SpeedError;
long SpeedIntegral = 0, SpeedIntegral_n_1 = 0, SpeedProportional = 0;
long DutyCycle = 0;
unsigned int Kps = 20000;                   // Proportional gain
unsigned int Kis = 2000;                    // Integral gain

void __attribute__((interrupt, no_auto_psv)) _T1Interrupt (void)

{
#ifdef CLOSEDLOOP
    ActualSpeed = SPEEDMULT/timer3avg;
    SpeedError = DesiredSpeed - ActualSpeed;
    SpeedProportional = (int)(((long)Kps*(long)SpeedError) >> 15);                 // ???
    SpeedIntegral = SpeedIntegral_n_1 + (int)(((long)Kis*(long)SpeedError) >> 15);   //???      
    SpeedIntegral_n_1 = SpeedIntegral;
    DutyCycle = SpeedIntegral + SpeedProportional;
    PDC1 = (int)(((long)(PTPER*2)*(long)DutyCycle) >> 15);  // ???  PWM duty cycle 
    1PDC2 = PDC1;

    PDC3 = PDC1;
#endif                              // in closed loop algorithm

    IFS0bits.T1IF = 0;
}

void __attribute__((interrupt, no_auto_psv)) _IC1Interrupt (void)
{
    int Hall_Index;


    IFS0bits.IC1IF = 0; // Clear interrupt flag
    HallValue = (unsigned int)((PORTB >> 1) & 0x0007);  // Read halls

    if (Flags.Direction)
    {
        OVDCON = StateTableFwd[HallValue];
        Hall_Index = HALL_INDEX_F;
        }
    else
    {

        OVDCON = StateTableRev[HallValue];
        Hall_Index = HALL_INDEX_R;
        }

// The code below is uses TMR3 to calculate the speed of the rotor
    if (HallValue == Hall_Index)  // has the same position been sensed?
        if (polecount++ == POLEPAIRS)  //has one mech rev elasped?         // ???
        {                               // yes then read timer 3
        timer3value = TMR3;
        TMR3 = 0;

        timer3avg = ((timer3avg + timer3value) >> 1);    // ???
        polecount = 1;
        } 
}