'Test accuracy of math.hypot()'

from math import hypot, frexp, ldexp
from random import expovariate, triangular
from decimal import Decimal
from collections import Counter
from pprint import pprint

hist = Counter()

def ulp(x):
    mant, exp = frexp(x)
    return ldexp(0.5, exp - 52)

k = 10_000
n = 1_000
reverse = True

for i in range(n):
    args = [triangular(0.999, 1.001) for i in range(k)]
    args.sort(reverse=reverse)
    expected = float(sum(x**2 for x in map(Decimal, args)).sqrt())
    actual = hypot(*args)
    ulps = (actual - expected) / ulp(expected)
    hist[ulps] += 1
    #print(expected.hex(), actual.hex(), ulps)

print(f'k={k}, n={n}, reverse={reverse!r}')
pprint(sorted(hist.items()), width=30)