''' Determine when log1p starts to be better than log(1+p).
    IOW, what is meant by "when x is near zero"?
'''

from decimal import getcontext, Decimal
from math import log, log1p
from random import random
from collections import Counter

getcontext().prec = 100

def best_method(x):
    regular_log = log(1.0 + x)
    offset_log = log1p(x)
    if regular_log == offset_log:
        return 'equal'
    correct = (1 + Decimal(x)).ln()
    if abs(Decimal(regular_log) - correct) < abs(Decimal(offset_log) - correct):
        return 'regular_log'
    return 'offset_log'

n = 100_000
print(Counter(best_method(random()) for i in range(n)))
print(Counter(best_method(-random()) for i in range(n)))