uno timer0 prescale

Question

I have a project where I need to get a low frequency to get a pwm suited from my project. The problem is that after I modify the frequency of timer0 the millis() becomes slower or faster depending on prescalar. So a fix as stated here is to change prescalar in wiring.c. But I don't know for what reason when I set it to 256 or 1024 the millis return 0. For 1-64 works fine.

Timer 0 uses a prescale factor which is set to 64 by default
To set the prescale factor use this line in the setup function

Setting                          Prescale_factor
TCCR0B = _BV(CS00);              1
TCCR0B = _BV(CS01);              8
TCCR0B = _BV(CS00) | _BV(CS01);  64
TCCR0B = _BV(CS02);              256
TCCR0B = _BV(CS00) | _BV(CS02);  1024

To use Fast PWM on Timer 0
Write this line in the setup function
TCCR0A = _BV(COM0A1) | _BV(COM0B1) | _BV(WGM01) | _BV(WGM00); 
And to calculate the PWM frequency, use
Fast_PWM_frequency = (16 000 000)/(Prescale_factor*256); 

To use Phase-correct PWM on Timer 0 (half the frequency of Fast PWM)
Write this line in the setup function
TCCR0A = _BV(COM0A1) | _BV(COM0B1) | _BV(WGM00); 
And to calculate the PWM frequency, use
Phase_correct_PWM_frequency = (16 000 000)/(Prescale_factor*510); 

Changing the prescale factor on Timer0 will affect functions
millis(), micros(), delay(),...

To adjust millis(), micros(), delay(),... accordingly,
You can modify a line in the wiring.c function in the Arduino program files
hardware\arduino\cores\arduino\wiring.c

In the beginning of wiring.c you can find:
// the prescaler is set so that timer0 ticks every 64 clock cycles, and the
// the overflow handler is called every 256 ticks.
#define MICROSECONDS_PER_TIMER0_OVERFLOW (clockCyclesToMicroseconds(64 * 256))

You need to modify the prescale factor in this function to the corresponding line

For fast PWM (default):
#define MICROSECONDS_PER_TIMER0_OVERFLOW (clockCyclesToMicroseconds(PRESCALE_FACTOR* 256))
For phase-correct PWM :
#define MICROSECONDS_PER_TIMER0_OVERFLOW (clockCyclesToMicroseconds(PRESCALE_FACTOR * 510))

Answer 1

Integer math in C is done in an int or unsigned int by default. int is 16-bit on AVR. 256 * 256 overflows to 0, as does 1024 * 256. You will need to tell the compiler to perform the math in a longer type.

#define MICROSECONDS_PER_TIMER0_OVERFLOW (clockCyclesToMicroseconds(256 * 256L))