'Test accuracy of math.hypot()'

from math import hypot, frexp, ldexp
from random import expovariate, triangular, gauss, shuffle
from decimal import Decimal, getcontext
from collections import Counter
from pprint import pprint
from sys import version_info

getcontext().prec = 200

hist = Counter()

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

n = 1_000_000
reverse = True

for k in (2, 3, 5, 10, 100, 1_000, 10_000):
    if k > 2 and version_info[:2] <= (3, 8):
        # 3.7 and prior only support the two argument form
        continue
    for i in range(n):
        args = [gauss(1_000_000_000, 300_000_000) for i in range(min(3, k))]
        args += [expovariate(1.0) for i in range(len(args) - k)]    
        shuffle(args)
        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:,d}, n={n:,d}, reverse={reverse!r}')
    pprint(sorted(hist.items()), width=30)