fast pwm calculation

"""
Inspiriert von
BitBastelei #398 - Die "Magie" hinter PWM (analogWrite, Timer, Preload, etc)
https://www.youtube.com/watch?v=nf8MB7FkRaI

"""


import math
from collections import namedtuple


class Frequency:
    def __init__(self, value):
        self.value = value

    def __float__(self):
        return float(self.value)

    def __index__(self):
        return int(self.value)

    def __str__(self):
        units = ("Hz", "kHz", "MHz")
        value = self.value
        for unit in units:
            if value < 1000:
                break
            value /= 1000
        return f"{value:.3f} {unit}"

    def __repr__(self):
        return f"{self.__class__.__name__}({self.value})"


def pwm_calc(freq, bits=8, board_freq=16_000_000):
    result = namedtuple(
        "Configuration",
        "board_freq scaled_freq prescaler count_bits count_start target_freq",
    )
    increments = 2 ** bits
    counter_max = increments - 1

    for prescaler in (2 ** n for n in range(11)):
        if (current_freq := board_freq / prescaler / increments) < freq:
            break

    # math.ceil aufrunden, math.floor abrunden
    offset = round(counter_max * current_freq / freq)
    resulting_freq = current_freq / offset * counter_max
    return result(
        Frequency(board_freq),
        Frequency(current_freq),
        prescaler,
        bits,
        counter_max - offset,
        Frequency(resulting_freq),
    )


result = pwm_calc(420)
print("Prescaler:", result.prescaler)
print("Frequency:", result.target_freq)
print("Counter-Start:", result.count_start)

# Prescaler: 256
# Frequency: 420.648 Hz
# Counter-Start: 107