If I want to simulate a digital oscillator (or phasor) to modulate an arbitrarily length signal: $$y(t) = \cos(2\pi f_ct)\quad\text{where}\quad t = \frac{n}{f_s}\quad\text{for sample}\quad n$$

What is the advantage of using a numerically controlled oscillator (Answered here) versus simply incrementing $n$ over the length of the input?

main(): 
  n = 0                 # total samples processed
  N = len(input)        # num samples in input
  blksz = N / 16        # don't create phasor all in one call
  # calculate phasor over multiple passes
  while ( n < N ) 
      update_phasor(blksz)
# calculate phasor
update_phasor(blksz):
  for (i = 0; i < blksz; i++)
      y[i] = exp(j*2*pi*fc*n/fs) 
      n++

The NCO referenced above and the pseudocode implementations give different results and I am trying to understand which makes more sense.

Also, what is the best way to synthesize the phasor if the desired frequency needs to change on the fly?

If I want to simulate a digital oscillator (or phasor) to modulate an arbitrarily length signal: $$y(t) = \cos(2\pi f_ct)\quad\text{where}\quad t = \frac{n}{f_s}\quad\text{for sample}\quad n$$

What is the advantage of using a numerically controlled oscillator (Answered here) versus simply incrementing $n$ over the length of the input?

main(): 
  n = 0                 # total samples processed
  N = len(input)        # num samples in input
  blksz = N / 16        # don't create phasor all in one call
  # calculate phasor over multiple passes
  while ( n < N ) 
      update_phasor(blksz)
# calculate phasor
update_phasor(blksz):
  for (i = 0; i < blksz; i++)
      y[i] = exp(j*2*pi*fc*n/fs) 
      n++

The NCO referenced above and the pseudocode implementations give different results and I am trying to understand which makes more sense.

Also, what is the best way to synthesize the phasor if the desired frequency needs to change on the fly?

If I want to simulate a digital oscillator (or phasor) to modulate an arbitrarily length signal:

$y(t) = cos(2\pi f_ct)$

where $t = n / f_s $ for sample n

What is the advantage of using a numerically controlled oscillator (Answered here) versus simply incrementing $n$ over the length of the input?

main(): 
  n = 0                 # total samples processed
  N = len(input)        # num samples in input
  blksz = N / 16        # don't create phasor all in one call
  # calculate phasor over multiple passes
  while ( n < N ) 
      update_phasor(blksz)
# calculate phasor
update_phasor(blksz):
  for (i = 0; i < blksz; i++)
      y[i] = exp(j*2*pi*fc*n/fs) 
      n++

The NCO referenced above and the pseudocode implementations give different results and I am trying to understand which makes more sense.

Also, what is the best way to synthesize the phasor if the desired frequency needs to change on the fly?

If I want to simulate a digital oscillator (or phasor) to modulate an arbitrarily length signal: $$y(t) = \cos(2\pi f_ct)\quad\text{where}\quad t = \frac{n}{f_s}\quad\text{for sample}\quad n$$

What is the advantage of using a numerically controlled oscillator (Answered here) versus simply incrementing $n$ over the length of the input?

main(): 
  n = 0                 # total samples processed
  N = len(input)        # num samples in input
  blksz = N / 16        # don't create phasor all in one call
  # calculate phasor over multiple passes
  while ( n < N ) 
      update_phasor(blksz)
# calculate phasor
update_phasor(blksz):
  for (i = 0; i < blksz; i++)
      y[i] = exp(j*2*pi*fc*n/fs) 
      n++

The NCO referenced above and the pseudocode implementations give different results and I am trying to understand which makes more sense.

Also, what is the best way to synthesize the phasor if the desired frequency needs to change on the fly?