Enoncé du problème sur le forum Silicium

PREC  = 60
SCALE = 10 ** PREC

def ln2():
    result = 0
    power = SCALE // 3
    base  = SCALE // 9
    k = 0
    while True:
        term = power // (2 * k + 1)
        if term == 0: break
        result += term
        power = (power * SCALE) // (9 * SCALE // SCALE)
        power = (power * SCALE) // (9 * SCALE)
        k += 1
    return 2 * result

def ln2_direct():
    result = 0
    num   = SCALE // 3
    denom = 9
    k = 0
    while True:
        term = num // (2 * k + 1)
        if term == 0: break
        result += term
        num = num // denom
        k += 1
    return 2 * result

def f_series(x):
    result = 0
    xk = (x * x) // SCALE   # x^2
    k  = 2
    while True:
        term = xk // k
        if term == 0: break
        if k % 2 == 0: result += term
        else: result -= term
        xk = (xk * x) // SCALE
        k  += 1
    return result

def int_to_digits(n, nb):
    digits = []
    for _ in range(nb):
        n, r = divmod(n, 10)
        digits.append(r)
    digits.reverse()
    return digits

def affiche(n, val):
    if val < 0: s, val = "-", -val
    else: s = ""
    entier = val // SCALE
    frac   = val % SCALE
    e_digits = int_to_digits(entier, 1)
    f_digits = int_to_digits(frac, PREC)
    ligne = "u(" + str(n) + ") = " + s
    for d in e_digits: ligne += str(d)
    ligne += "."
    for d in f_digits: ligne += str(d)
    print(ligne)

u = SCALE
affiche(0, u)
u = SCALE - ln2_direct()
affiche(1, u)
for n in range(1, 8):
    u = f_series(u)
    affiche(n + 1, u)