for i in range(4):
a = mpf_mul(a, mpf_sub(fone, ppowers[i]), wp)
ppowers[i] = mpf_mul(ppowers[i], primes[i], wp)
a = mpf_pow_int(a, -I(n), wp)
if mpf_pos(a, prec+10, 'n') == fone:
break
#from libmpf import to_str
#print n, to_str(mpf_sub(fone, a), 6)
res = mpf_mul(res, a, wp)
n += 1
res = mpf_mul(res, from_int(3*15*35), wp)
res = mpf_div(res, from_int(4*16*36), wp)
return to_fixed(res, prec)
mpf_euler = def_mpf_constant(euler_fixed)
mpf_apery = def_mpf_constant(apery_fixed)
mpf_khinchin = def_mpf_constant(khinchin_fixed)
mpf_glaisher = def_mpf_constant(glaisher_fixed)
mpf_catalan = def_mpf_constant(catalan_fixed)
mpf_mertens = def_mpf_constant(mertens_fixed)
mpf_twinprime = def_mpf_constant(twinprime_fixed)
#-----------------------------------------------------------------------#
# #
# Bernoulli numbers #
# #
#-----------------------------------------------------------------------#
MAX_BERNOULLI_CACHE = 3000
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
mpf_euler = def_mpf_constant(euler_fixed)
mpf_apery = def_mpf_constant(apery_fixed)
mpf_khinchin = def_mpf_constant(khinchin_fixed)
mpf_glaisher = def_mpf_constant(glaisher_fixed)
mpf_catalan = def_mpf_constant(catalan_fixed)
# Note: computation of cos(pi*x) and sin(pi*x) is needed by
# reflection formulas for gamma, polygamma, zeta, etc
def mpf_cos_sin_pi(x, prec, rnd=round_fast):
"""Accurate computation of (cos(pi*x), sin(pi*x))
for x close to an integer"""
sign, man, exp, bc = x
if not man:
return cos_sin(x, prec, rnd)
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
mpf_euler = def_mpf_constant(euler_fixed)
mpf_apery = def_mpf_constant(apery_fixed)
mpf_khinchin = def_mpf_constant(khinchin_fixed)
mpf_glaisher = def_mpf_constant(glaisher_fixed)
mpf_catalan = def_mpf_constant(catalan_fixed)
# Note: computation of cos(pi*x) and sin(pi*x) is needed by
# reflection formulas for gamma, polygamma, zeta, etc
def mpf_cos_sin_pi(x, prec, rnd=round_fast):
"""Accurate computation of (cos(pi*x), sin(pi*x))
for x close to an integer"""
for i in range(4):
a = mpf_mul(a, mpf_sub(fone, ppowers[i]), wp)
ppowers[i] = mpf_mul(ppowers[i], primes[i], wp)
a = mpf_pow_int(a, -I(n), wp)
if mpf_pos(a, prec + 10, 'n') == fone:
break
#from libmpf import to_str
#print n, to_str(mpf_sub(fone, a), 6)
res = mpf_mul(res, a, wp)
n += 1
res = mpf_mul(res, from_int(3 * 15 * 35), wp)
res = mpf_div(res, from_int(4 * 16 * 36), wp)
return to_fixed(res, prec)
mpf_euler = def_mpf_constant(euler_fixed)
mpf_apery = def_mpf_constant(apery_fixed)
mpf_khinchin = def_mpf_constant(khinchin_fixed)
mpf_glaisher = def_mpf_constant(glaisher_fixed)
mpf_catalan = def_mpf_constant(catalan_fixed)
mpf_mertens = def_mpf_constant(mertens_fixed)
mpf_twinprime = def_mpf_constant(twinprime_fixed)
#-----------------------------------------------------------------------#
# #
# Bernoulli numbers #
# #
#-----------------------------------------------------------------------#
MAX_BERNOULLI_CACHE = 3000
"""