def khinchin_fixed(prec):
wp = int(prec + prec**0.5 + 15)
s = MPZ_ZERO
fac = from_int(4)
t = ONE = MPZ_ONE << wp
pi = mpf_pi(wp)
pipow = twopi2 = mpf_shift(mpf_mul(pi, pi, wp), 2)
n = 1
while 1:
zeta2n = mpf_abs(mpf_bernoulli(2*n, wp))
zeta2n = mpf_mul(zeta2n, pipow, wp)
zeta2n = mpf_div(zeta2n, fac, wp)
zeta2n = to_fixed(zeta2n, wp)
term = (((zeta2n - ONE) * t) // n) >> wp
if term < 100:
break
#if not n % 10:
# print n, math.log(int(abs(term)))
s += term
t += ONE//(2*n+1) - ONE//(2*n)
n += 1
fac = mpf_mul_int(fac, (2*n)*(2*n-1), wp)
pipow = mpf_mul(pipow, twopi2, wp)
s = (s << wp) // ln2_fixed(wp)
K = mpf_exp(from_man_exp(s, -wp), wp)
K = to_fixed(K, prec)
return K
def khinchin_fixed(prec):
wp = int(prec + prec**0.5 + 15)
s = MP_ZERO
fac = from_int(4)
t = ONE = MP_ONE << wp
pi = mpf_pi(wp)
pipow = twopi2 = mpf_shift(mpf_mul(pi, pi, wp), 2)
n = 1
while 1:
zeta2n = mpf_abs(mpf_bernoulli(2 * n, wp))
zeta2n = mpf_mul(zeta2n, pipow, wp)
zeta2n = mpf_div(zeta2n, fac, wp)
zeta2n = to_fixed(zeta2n, wp)
term = (((zeta2n - ONE) * t) // n) >> wp
if term < 100:
break
#if not n % 100:
# print n, nstr(ln(term))
s += term
t += ONE // (2 * n + 1) - ONE // (2 * n)
n += 1
fac = mpf_mul_int(fac, (2 * n) * (2 * n - 1), wp)
pipow = mpf_mul(pipow, twopi2, wp)
s = (s << wp) // ln2_fixed(wp)
K = mpf_exp(from_man_exp(s, -wp), wp)
K = to_fixed(K, prec)
return K
def euler_fixed(prec):
extra = 30
prec += extra
# choose p such that exp(-4*(2**p)) < 2**-n
p = int(math.log((prec/4) * math.log(2), 2)) + 1
n = 2**p
A = U = -p*ln2_fixed(prec)
B = V = MPZ_ONE << prec
k = 1
while 1:
B = B*n**2//k**2
A = (A*n**2//k + B)//k
U += A
V += B
if max(abs(A), abs(B)) < 100:
break
k += 1
return (U<<(prec-extra))//V
def euler_fixed(prec):
extra = 30
prec += extra
# choose p such that exp(-4*(2**p)) < 2**-n
p = int(math.log((prec / 4) * math.log(2), 2)) + 1
n = 2**p
A = U = -p * ln2_fixed(prec)
B = V = MP_ONE << prec
k = 1
while 1:
B = B * n**2 // k**2
A = (A * n**2 // k + B) // k
U += A
V += B
if max(abs(A), abs(B)) < 100:
break
k += 1
return (U << (prec - extra)) // V