zlacker

Good point. To indemnify youself from this type of data loss, change math.log10() to np.log10() and use Decimal() for tasks involving precise number crunching.

EDIT: Setting Decimal module's precision manually via getcontext() may be required if you work with "long" numbers.

    import math
    import numpy as np
    from decimal import getcontext, Decimal

    def digit_length_correct(n):
        return len(str(n))
    
    def digit_length_clever_2(n):
        if n ==0:
            return 1
        else:
            return math.floor((np.log10(Decimal(n)))) + 1 # You can use np.floor() and eschew the use of math. module altogether, but I left it intact to show the minimal necessary modifications
    
    def generate_cases(n):
        getcontext().prec = n + 3
        return (
        [10 ** i for i in range(n)] +
        [(10 ** i) - 1 for i in range(n)]
    )
    
    cases = generate_cases(300)
    
    for t in cases:
        a = digit_length_correct(t)
        b = digit_length_clever_2(t)
        assert a == b, (t, a, b)
    
    for t in cases[-2:]:
        print(t)
        print(digit_length_correct(t))
        print(digit_length_clever_2(t))

>>gspetr+(OP)
Using arbitrary precision arithmetic kind of defeats the point of not using loops.