turtle.setworldscoordinates() and floating point precision

Start by running the supplied turtle spiral reproducer and inspect Lib/turtle.py around line 1105. Trace how setworldcoordinates updates xscale and yscale, then compare the Tk floating-point error with the RawTurtle ZeroDivisionError. Done means the precision-limit behavior is handled without a blank screen or crash, with coverage for the reported boundary conditions.

I made a turtle draw a spiral while rescaling the screen according to the last position of the turtle.

Simple code to reproduce (increasing the speed variable will make it crash sooner):

"""Crash a Turtle with negative infinity canvas scale"""
import turtle

speed = 3

angle = 0
radius = 1
boundaries = {'llx': -1.0, 'lly': -1.0, 'urx': 1.0, 'ury': 1.0}
pen = turtle.Turtle()
pen.speed(10)
pen.getscreen().tracer(1e3)
while True:
    print(f"radius {radius}, angle {angle}")
    print(f"screen xscale {pen.getscreen().xscale}")
    print(f"screen yscale {pen.getscreen().yscale}")
    pen.circle(radius, angle)
    radius *= speed
    angle += 1
    pos = pen.pos()
    boundaries['llx'] = min(boundaries['llx'], pos[0])
    boundaries['lly'] = min(boundaries['lly'], pos[1])
    boundaries['urx'] = max(boundaries['urx'], pos[0])
    boundaries['ury'] = max(boundaries['ury'], pos[1])
    pen.getscreen().setworldcoordinates(**boundaries)

This will raise _tkinter.TclError: expected floating-point number but got "floating" when x or y scale gets near 1e-306.

But in the code I'm using with a RawTurtle and a TurtleScreen I get ZeroDivisionError because somewhere after 6.7e-307 (in my machine) both TurtleScreen's x and y scales becomes 0.0, RawTurtle's position becomes (-inf, -inf) and then this line of code is reached: https://github.com/python/cpython/blob/3ef9f6b508a8524f385cdc9fdd4b4afca0eac59b/Lib/turtle.py#L1105

I had to set this in my code to prevent screen becoming blank (because of scale becoming 0.0), so I could stop drawing before it crashes:

precision: int = 1e-306
while True:
    logger.debug(f"""
boundaries = {boundaries}
screen.xscale = {screen.xscale}
screen.yscale = {screen.yscale}
""")
    try:
        1 / screen.xscale
        1 / screen.yscale
    except ZeroDivisionError:
        logger.warning(f"reached infinity")
        break
    if precision != min(precision, screen.xscale, screen.yscale):
        logger.warning(f"reached floating point precision limit")
        break
    screen.setworldcoordinates(**boundaries)
## Make screen still without going blank
root.mainloop()