def f75(n):
s = BigFloat(0)
for i in range(1, n + 1):
expr = 1 / (1 - 2**BigFloat(-i)) - 1
s += bigchoose(n, i) * 2**i * (-1)**(i + 1) * expr
return 1.0 / 2 * s
def calc_ratio(n):
l = BigFloat(0)
h = BigFloat(1)
m = (l + h) * 0.5
def calc_y1(x):
return x / n
def diff(x):
return (calc_y1(x) - (1 - sqrt(1 - (1 - x)**2)))
m_d = diff(m)
DIFF = BigFloat('1e-20')
while abs(m_d) > DIFF:
if m_d < 0:
l = m
else:
h = m
m = (l + h) * 0.5
m_d = diff(m)
x = x1 = m
y1 = calc_y1(x)
left_area = x1 * y1 * 0.5
right_area = ((y1 + 1) * (1 - x1) * 0.5 - asin(1 - x1) * 0.5)
return ((left_area + right_area) / L_sect_area)
def f66(n):
s1 = BigFloat(0)
for mu in range(1, MAX_MU):
s2 = BigFloat(0)
for i in range(0, n + 1):
s2 += bigchoose(n, i) * (-(2**(1 - mu)))**i
s1 += 1 - s2
return 1.0 / 2 * s1
def test_get_f(self):
alpha = math.pi / 4
beta = math.pi / 4
a = BigFloat.exact(0.2)
b = BigFloat.exact(0.6)
wavelength = BigFloat.exact(0.1)
f = processor.get_f(alpha, beta, a, b, wavelength)
self.assertAlmostEqual(f, 1.002 * 10 ** (-5))
def generate_random_gaussian(cls, n_dimensions, one_vector):
mean = np.array([BigFloat.exact("0", precision=110)] * n_dimensions)
sigma = np.array([BigFloat.exact("0", precision=110)] * n_dimensions)
for i in range(n_dimensions):
# TODO: Multivariate normal should accept 0 values, not require just a small value.
mean[i] = one_vector.component(i) + random.randint(-100, 100) / 50
# sigma[i][i] = random.randint(100, 1000) / 0.5
sigma[i] = 3e1
return Gaussian(mean, sigma)
def mk_bfc(self, x, y):
from bigfloat import BigFloat, precision
from mbrat.util import Arguments
with precision(self.prec):
bf_x = BigFloat.exact(x)
bf_y = BigFloat.exact(y)
return Arguments(
{'real': bf_x, 'imag': bf_y},
string="bfc(real='{0}', imag='{1}')".format(bf_x, bf_y) )
def f69(n):
odd_bound = int(math.floor((n - 1) / 2))
even_bound = int(math.floor(n / 2))
s1 = BigFloat(0)
for mu in range(1, MAX_MU):
s2 = BigFloat(0)
for k in range(0, odd_bound + 1):
s2 += bigchoose(n, 2 * k + 1) * 2**((1 - mu) * (2 * k + 1))
s3 = BigFloat(0)
for k in range(1, even_bound + 1):
s3 += bigchoose(n, 2 * k) * 2**((1 - mu) * 2 * k)
s1 += s2 - s3
return 1.0 / 2 * s1
def f74(n):
odd_bound = int(math.floor((n - 1) / 2))
even_bound = int(math.floor(n / 2))
s10 = BigFloat(0)
for k in range(0, odd_bound + 1):
s1 = 1 / (1 - 2**(-(2 * BigFloat(k) + 1)))
s10 += bigchoose(n, 2 * k + 1) * 2**(2 * k + 1) * (s1 - 1)
s20 = BigFloat(0)
for k in range(1, even_bound + 1):
s2 = 1 / (1 - 2**(-2 * BigFloat(k)))
s20 += bigchoose(n, 2 * k) * 2**(2 * k) * (s2 - 1)
return 1.0 / 2 * (s10 - s20)
def __json_list_to_numpy_list(self, jsonList):
newList = []
for v in iter(jsonList):
newList.append(
BigFloat.exact(v[Gaussian.__VALUE],
precision=v[Gaussian.__PRECISION]))
return np.array(newList)
def f76(n):
s = BigFloat(0)
for i in range(1, n + 1):
expr = 2**i / (2**i - 1)
s += bigchoose(n, i) * (-1)**(i + 1) * expr
return 1.0 / 2 * s
def compute_boltzmann(energies, debug):
# create Boltzmann distribution
# https://en.wikipedia.org/wiki/Boltzmann_distribution
# p_i = exp( -E_i / kT ) / ∑ exp( -E_j / kT )
# where:
# p_i is the probability of state i occuring
# E_i is the energy of state i
# E_j is the energy of state j, where the ∑ in the denominator
# iterates over all states j
# first we calculate exp( -E_i / kT ) for all states
if len(energies) == 0:
return []
if debug:
print("Boltzmann Distribution")
divisor = BigFloat.exact(0.0)
for energy in energies:
ep = bigfloat.exp(-energy)
if debug:
print("energy, ep = %g, %g" % (energy, ep))
# divisor = ∑ exp( -E_j / kT )
divisor += ep
probabilities = []
for energy in energies:
# p_i = exp( -E_i / kT ) / divisor
numerator = bigfloat.exp(-energy)
probability = numerator / divisor
# save probability to dictionary
probabilities.append(float(probability))
if debug:
print("%s / %s = %s" % (numerator, divisor, probability))
return probabilities
def __super_vectors_mean(svectors, weights):
dimensions = svectors[0].dimensions()
mean = np.array([BigFloat.exact("0", precision=110)] * dimensions)
for i in range(dimensions):
for svec_id in range(len(svectors)):
mean[i] += svectors[svec_id].component(i) * weights[svec_id]
mean[i] /= sum(weights)
return mean
def __init__(self, size, cellSize, distance):
self.size = np.array(size)
self.cellSize = np.array(cellSize).astype(BigFloat)
self.distance = BigFloat(distance)
# Angle binning of detector
self.anglePerCell = [
bf.atan(cellSize / self.distance) for cellSize in self.cellSize
]
def test_empty_format_matches_str(self):
test_values = [
BigFloat("0.0"),
BigFloat("-0.0"),
BigFloat("1.0"),
BigFloat("-2.3"),
BigFloat("1e100"),
BigFloat("1e-100"),
BigFloat("nan"),
BigFloat("inf"),
BigFloat("-inf"),
]
for value in test_values:
self.assertEqual(str(value), format(value, ""))
def test_empty_format_matches_str(self):
test_values = [
BigFloat('0.0'),
BigFloat('-0.0'),
BigFloat('1.0'),
BigFloat('-2.3'),
BigFloat('1e100'),
BigFloat('1e-100'),
BigFloat('nan'),
BigFloat('inf'),
BigFloat('-inf'),
]
for value in test_values:
self.assertEqual(str(value), format(value, ''))
def __init__(self, pos, directionAngles):
self.pos = np.array(pos)
self.directionAngles = np.array(directionAngles).astype(BigFloat)
assert (len(directionAngles) == 2)
self.dir = np.array([
BigFloat(1),
bf.atan(directionAngles[0]),
bf.atan(directionAngles[1])
])
def f73(n):
odd_bound = int(math.floor((n - 1) / 2))
even_bound = int(math.floor(n / 2))
s10 = BigFloat(0)
for k in range(0, odd_bound + 1):
s1 = BigFloat(0)
for mu in range(0, MAX_MU):
s1 += (2**(2 * k + 1))**(-mu)
s10 += bigchoose(n, 2 * k + 1) * 2**(2 * k + 1) * (s1 - 1)
s20 = BigFloat(0)
for k in range(1, even_bound + 1):
s2 = BigFloat(0)
for mu in range(0, MAX_MU):
s2 += (2**(2 * k))**(-mu)
s20 += bigchoose(n, 2 * k) * 2**(2 * k) * (s2 - 1)
return 1.0 / 2 * (s10 - s20)
def transform(s, l):
with precision(100):
ret = [BigFloat(0) for x in xrange(1 + s * (len(l)-1))]
prev = [1]
for i, v in enumerate(l):
if i > 0:
f = BigFloat(1) / (BigFloat(s) ** i)
new = [BigFloat(0) for x in xrange(1 + s * i)]
for faceval in xrange(1, s+1):
for idx, val in enumerate(prev):
new[idx+faceval] += val
if v > 0:
for idx, val in enumerate(new):
ret[idx] += val * v * f
prev = new
# while ret[-1] == 0:
# ret.pop()
print("s = ", s, " ; ret = ", ["%f" % x for x in ret])
sys.stdout.flush()
return [x/sum(ret) for x in ret]
def calcPhase(particle, detector, sim, waveLen):
"""Calculate the phase the particle has at the detector (current phase assumed to be 0)"""
detCellIdx = getBinnedDetCellIdx(particle, detector, sim)
#print("Target angles:", (detCellIdx - detector.size / 2) * detector.anglePerCell)
dx = detector.distance + (sim.size[0] - particle.pos[0]) * sim.cellSize[0]
dzdy = (detCellIdx - detector.size / 2) * detector.cellSize
dydz = np.flipud(dzdy) + (sim.size[1:] / 2 -
particle.pos[1:]) * sim.cellSize[1:]
distance = bf.sqrt(dx**2 + dydz[0]**2 + dydz[1]**2)
phase = 2 * bf.const_pi() / BigFloat(waveLen) * distance
phase = bf.mod(phase, 2 * bf.const_pi())
return phase
def __probabilities_to_weights(probabilities):
weights = []
sums = np.array([BigFloat.exact("0", precision=110)] *
len(probabilities[0]))
for p in iter(probabilities):
weights.append(np.array(p))
sums += weights[len(weights) - 1]
for i in range(len(weights)):
weights[i] /= sums
return weights
def __super_vectors_sigma(svectors, mean, weights):
dimensions = svectors[0].dimensions()
values_from_dimensions = __supervectors_to_array_of_values_for_each_dimension(
svectors)
sigma = np.array([BigFloat.exact("0", precision=110)] * dimensions)
for i in range(dimensions):
sigma[i] = __weighted_variance(mean[i], values_from_dimensions[i],
weights)
# if math.isclose(sigma[i], 0, abs_tol=3.0e-20):
# print(sigma[i][i])
# raise NoVarianceException
# sigma[i] = 3.0e-20
return sigma
def calcPhaseFarField(particle, sim, waveLen):
"""Calculate the phase the particle has at the detector in the far field"""
# Only scatter in 1 direction
assert (particle.directionAngles[0] == 0
or particle.directionAngles[1] == 0)
# One of the sin is 0 -> Ok to use addition instead of a full projection
pathDiff = particle.pos[1] * sim.cellSize[1] * bf.sin(particle.directionAngles[0]) + \
particle.pos[2] * sim.cellSize[2] * bf.sin(particle.directionAngles[1])
# Negate as increasing position decreases phase
pathDiff = -pathDiff
phase = 2 * bf.const_pi() / BigFloat(waveLen) * pathDiff
phase = bf.mod(phase, 2 * bf.const_pi())
return phase
def invert(lower: BigFloat, upper: BigFloat, precision_of_result: int) -> ExactRealProgram:
context_down = bf.precision(precision_of_result) + bf.RoundTowardNegative
context_up = bf.precision(precision_of_result) + bf.RoundTowardPositive
# interval doesn't contain zero then invert and flip [1 / y2, 1 / y1]
if (lower > 0 and upper > 0) or (lower < 0 and upper < 0):
inv_lower = bf.div(1, upper, context_down)
inv_upper = bf.div(1, lower, context_up)
lw = [0, -float(inv_upper)**2]
uw = [-float(inv_lower)**2, 0]
# [lower, 0] -> [-infty, 1 / y1]
elif lower < 0 and upper == 0:
inv_lower = BigFloat('-inf')
inv_upper = bf.div(1, lower, context_up)
lw = [0, float('nan')]
uw = [-float(inv_lower)**2, 0]
# [0, upper] -> [1 / y2, infty]
elif lower == 0 and upper > 0:
inv_lower = bf.div(1, upper, context_down)
inv_upper = BigFloat('inf')
lw = [0, -float(inv_upper)**2]
uw = [float('nan'), 0]
# If the interval includes 0 just give up and return [-infty, infty]
# Note: an alternative is to split up intervals, but that's too tricky for now
elif lower < 0 < upper:
inv_lower = BigFloat('-inf')
inv_upper = BigFloat('inf')
lw = [0, float('nan')]
uw = [float('nan'), 0]
# Interval is probably such that lower is greater than upper
else:
raise ValueError("Input interval is invalid for division")
return inv_lower, inv_upper, lw, uw
def transform_brute(s, l):
with precision(100):
ret = [BigFloat(0) for x in xrange(1 + s * (len(l)-1))]
for i, v in enumerate(l):
if i == 0:
continue
def rec(sum_, c):
if i == c:
ret[sum_] += BigFloat(v)/(BigFloat(s)**i)
else:
for x in xrange(1, s+1):
rec(sum_+x, c+1)
rec(0, 0)
return [x/sum(ret) for x in ret]
def test_invalid_formats(self):
invalid_formats = [
# Can't specify fill/align *and* zero padding at once ...
"X<010.2f",
">010.2f",
" ^010.2f",
"=010.2f",
# ... even if the fill/align matches the zero padding!
"0=010.2f",
# a . must be followed by a precision.
".f",
"10.g",
]
for fmt in invalid_formats:
with self.assertRaises(ValueError):
format(BigFloat(2), fmt)
def calc_variance_brute(x12):
s = 20
with precision(100):
s_sq = [0, 0, 0]
for i, v in enumerate(x12):
if i > 0:
f = BigFloat(1) / (BigFloat(s) ** i)
print("i = ", i)
def rec(s_sq, sum_, c):
if (c == i):
s_sq[0] += f * v * sum_ * sum_
s_sq[1] += f * v * sum_
s_sq[2] += f * v
else:
for x in xrange(1, 21):
rec(s_sq, sum_+x, c+1)
rec(s_sq, 0, 0)
print("s_sq = ", s_sq)
return (BigFloat(s_sq[0])/BigFloat(s_sq[2]) -
((BigFloat(s_sq[1])/BigFloat(s_sq[2]))**2))
def test_format(self):
# Fixed precision formatting.
test_triples = [
(BigFloat(2), ".6f", "2.000000"),
# 'F' behaves the same as 'f' except for infinities and nans.
(BigFloat(2), ".6F", "2.000000"),
# Extra zeros in the precision should be fine.
(BigFloat(2), ".06f", "2.000000"),
(BigFloat(2), ".5f", "2.00000"),
# . only retained with 'alternate' formatting
(BigFloat(2), ".0f", "2"),
# Default precision is 6.
(BigFloat(2), "f", "2.000000"),
(BigFloat('nan'), "f", "nan"),
(BigFloat('-nan'), "f", "nan"),
(BigFloat('inf'), "f", "inf"),
(BigFloat('-inf'), "f", "-inf"),
(BigFloat('nan'), "F", "NAN"),
(BigFloat('-nan'), "F", "NAN"),
(BigFloat('inf'), "F", "INF"),
(BigFloat('-inf'), "F", "-INF"),
# Rounding behaviour.
(BigFloat('3.1415926535'), ".6f", "3.141593"),
(BigFloat('3.1415926535'), ".5f", "3.14159"),
(BigFloat('3.1415926535'), ".4f", "3.1416"),
(BigFloat('3.1415926535'), ".3f", "3.142"),
(BigFloat('3.1415926535'), ".2f", "3.14"),
(BigFloat('3.1415926535'), ".1f", "3.1"),
(BigFloat('3.1415926535'), ".0f", "3"),
# Sign specification.
(BigFloat(+2), "+.3f", "+2.000"),
(BigFloat(-2), "+.3f", "-2.000"),
(BigFloat(+2), " .3f", " 2.000"),
(BigFloat(-2), " .3f", "-2.000"),
(BigFloat(+2), "-.3f", "2.000"),
(BigFloat(-2), "-.3f", "-2.000"),
(BigFloat(+2), ".3f", "2.000"),
(BigFloat(-2), ".3f", "-2.000"),
# With infinities and nans; note that MPFR doesn't include
# these signs.
(BigFloat('+inf'), "+.3f", "+inf"),
(BigFloat('-inf'), "+.3f", "-inf"),
(BigFloat('+nan'), "+.3f", "+nan"),
(BigFloat('+inf'), "-.3f", "inf"),
(BigFloat('-inf'), "-.3f", "-inf"),
(BigFloat('+nan'), "-.3f", "nan"),
(BigFloat('+inf'), " .3f", " inf"),
(BigFloat('-inf'), " .3f", "-inf"),
(BigFloat('+nan'), " .3f", " nan"),
# Alternate formatting.
(BigFloat(2), "#.0f", "2."),
(BigFloat(2), "+#.0f", "+2."),
# Minimum field width.
(BigFloat(2), "10.3f", " 2.000"),
(BigFloat(2), "6.3f", " 2.000"),
(BigFloat(2), "5.3f", "2.000"),
(BigFloat(2), "4.3f", "2.000"),
(BigFloat(2), "1.3f", "2.000"),
# Minimum field width in combination with sign.
(BigFloat(2), "+10.3f", " +2.000"),
(BigFloat(-23), "+10.3f", " -23.000"),
# Zero padding.
(BigFloat(2), "010.3f", "000002.000"),
(BigFloat(2), "+010.3f", "+00002.000"),
(BigFloat(2), " 010.3f", " 00002.000"),
(BigFloat(2), "0010.3f", "000002.000"),
# Alignment and filling.
(BigFloat(2), "<10.3f", "2.000 "),
(BigFloat(2), ">10.3f", " 2.000"),
(BigFloat(2), "^10.3f", " 2.000 "),
(BigFloat(2), "<10.2f", "2.00 "),
(BigFloat(2), ">10.2f", " 2.00"),
(BigFloat(2), "^10.2f", " 2.00 "),
(BigFloat(2), "<4.2f", "2.00"),
(BigFloat(2), ">4.2f", "2.00"),
(BigFloat(2), "^4.2f", "2.00"),
(BigFloat(2), "<3.2f", "2.00"),
(BigFloat(2), ">3.2f", "2.00"),
(BigFloat(2), "^3.2f", "2.00"),
(BigFloat(2), "X<10.3f", "2.000XXXXX"),
(BigFloat(2), "X>10.3f", "XXXXX2.000"),
(BigFloat(2), "X^10.3f", "XX2.000XXX"),
(BigFloat(2), "X<10.2f", "2.00XXXXXX"),
(BigFloat(2), "X>10.2f", "XXXXXX2.00"),
(BigFloat(2), "X^10.2f", "XXX2.00XXX"),
(BigFloat(2), "X<4.2f", "2.00"),
(BigFloat(2), "X>4.2f", "2.00"),
(BigFloat(2), "X^4.2f", "2.00"),
(BigFloat(2), "X<3.2f", "2.00"),
(BigFloat(2), "X>3.2f", "2.00"),
(BigFloat(2), "X^3.2f", "2.00"),
(BigFloat(2), "X=+10.3f", "+XXXX2.000"),
(BigFloat(2), " =+10.3f", "+ 2.000"),
(BigFloat(2), "0=+10.3f", "+00002.000"),
(BigFloat(2), "\x00=+10.3f", "+\x00\x00\x00\x002.000"),
(BigFloat(2), "\n=+10.3f", "+\n\n\n\n2.000"),
# e-style formatting
(BigFloat(2), ".6e", "2.000000e+00"),
(BigFloat(3.141592653589793), ".6e", "3.141593e+00"),
(BigFloat(3.141592653589793), ".6E", "3.141593E+00"),
(BigFloat(314.1592653589793), ".6e", "3.141593e+02"),
(BigFloat(314.1592653589793), ".6E", "3.141593E+02"),
(BigFloat('nan'), "e", "nan"),
(BigFloat('-nan'), "e", "nan"),
(BigFloat('inf'), "e", "inf"),
(BigFloat('-inf'), "e", "-inf"),
(BigFloat('nan'), "E", "NAN"),
(BigFloat('-nan'), "E", "NAN"),
(BigFloat('inf'), "E", "INF"),
(BigFloat('-inf'), "E", "-INF"),
(BigFloat(314.1592653589793), ".0e", "3e+02"),
(BigFloat(314.1592653589793), "#.0e", "3.e+02"),
(BigFloat(314.1592653589793), "e", "3.1415926535897933e+02"),
(BigFloat(314.1592653589793), "6e", "3.1415926535897933e+02"),
# g-style formatting
(BigFloat(3.141592653589793), ".7g", "3.141593"),
(BigFloat(3.141592653589793), ".7G", "3.141593"),
(BigFloat(314.1592653589793), ".7g", "314.1593"),
(BigFloat(31415.92653589793), ".7g", "31415.93"),
(BigFloat(3141592.653589793), ".7g", "3141593"),
(BigFloat(3141592.653589793), ".7G", "3141593"),
(BigFloat(31415926.53589793), ".7g", "3.141593e+07"),
(BigFloat(31415926.53589793), ".7G", "3.141593E+07"),
(BigFloat('nan'), "g", "nan"),
(BigFloat('-nan'), "g", "nan"),
(BigFloat('inf'), "g", "inf"),
(BigFloat('-inf'), "g", "-inf"),
(BigFloat('nan'), "G", "NAN"),
(BigFloat('-nan'), "G", "NAN"),
(BigFloat('inf'), "G", "INF"),
(BigFloat('-inf'), "G", "-INF"),
(BigFloat(314.1592653589793), ".0g", "3e+02"),
(BigFloat(314.1592653589793), ".1g", "3e+02"),
(BigFloat(314.1592653589793), "#.0g", "3.e+02"),
(BigFloat(314.1592653589793), "#.1g", "3.e+02"),
(BigFloat(314.1592653589793), "g", "314.159"),
(BigFloat(314.1592653589793), "6g", "314.159"),
# Trailing zeros are stripped, except in alternate style.
(BigFloat(2), ".6g", "2"),
(BigFloat(0.000023), ".6g", "2.3e-05"),
(BigFloat(0.00023), ".6g", "0.00023"),
(BigFloat(2.3), ".6g", "2.3"),
(BigFloat(230), ".6g", "230"),
(BigFloat(230000), ".6g", "230000"),
(BigFloat(2300000), ".6g", "2.3e+06"),
(BigFloat(2), "#.6g", "2.00000"),
# %-formatting
(BigFloat(3.141592653589793), ".2%", "314.16%"),
(BigFloat(3.141592653589793), ".1%", "314.2%"),
(BigFloat(3.141592653589793), ".0%", "314%"),
(BigFloat(3.141592653589793), "%", "314.159265%"),
(BigFloat(0.0234), ".3%", "2.340%"),
(BigFloat(0.00234), ".3%", "0.234%"),
(BigFloat(0.000234), ".3%", "0.023%"),
(BigFloat(0.000234), ".3U%", "0.024%"),
(BigFloat(0.0000234), ".3%", "0.002%"),
(BigFloat(0.00000234), ".3%", "0.000%"),
(BigFloat(0.00000234), ".3Y%", "0.001%"),
(BigFloat(-3.141592653589793), ".2%", "-314.16%"),
(BigFloat(-3.141592653589793), ".1%", "-314.2%"),
(BigFloat(-3.141592653589793), ".0%", "-314%"),
(BigFloat(-3.141592653589793), "%", "-314.159265%"),
(BigFloat(-0.0234), ".3%", "-2.340%"),
(BigFloat(-0.00234), ".3%", "-0.234%"),
(BigFloat(-0.000234), ".3%", "-0.023%"),
(BigFloat(-0.000234), ".3U%", "-0.023%"),
(BigFloat(-0.0000234), ".3%", "-0.002%"),
(BigFloat(-0.00000234), ".3%", "-0.000%"),
(BigFloat(-0.00000234), ".3Y%", "-0.001%"),
(BigFloat('0'), ".3%", "0.000%"),
(BigFloat('-0'), ".3%", "-0.000%"),
# We should see the '%' even on infinities and nans.
(BigFloat('inf'), ".3%", "inf%"),
(BigFloat('-inf'), ".3%", "-inf%"),
(BigFloat('nan'), ".3%", "nan%"),
(BigFloat('inf'), "+.3%", "+inf%"),
(BigFloat('-inf'), "+.3%", "-inf%"),
(BigFloat('nan'), "+.3%", "+nan%"),
# Hexadecimal formatting. It's not 100% clear how MPFR
# chooses the exponent here.
(BigFloat(1.5), ".6a", "0x1.800000p+0"),
(BigFloat(1.5), ".5a", "0x1.80000p+0"),
(BigFloat(1.5), ".1a", "0x1.8p+0"),
(BigFloat(1.5), ".0a", "0xcp-3"),
(BigFloat(1.5), ".6A", "0X1.800000P+0"),
(BigFloat(3.0), ".6a", "0x3.000000p+0"),
(BigFloat(3.141592653589793), ".6a", "0x3.243f6bp+0"),
(BigFloat(3.141592653589793), ".5a", "0x3.243f7p+0"),
(BigFloat(3.141592653589793), ".4a", "0x3.243fp+0"),
(BigFloat(3.141592653589793), ".3a", "0x3.244p+0"),
(BigFloat(3.141592653589793), ".2a", "0x3.24p+0"),
(BigFloat(3.141592653589793), ".1a", "0x3.2p+0"),
(BigFloat(3.141592653589793), ".0a", "0xdp-2"),
# With no precision, outputs enough digits to give an
# exact representation.
(BigFloat(3.141592653589793), "a", "0x3.243f6a8885a3p+0"),
(BigFloat(10.0), ".6a", "0xa.000000p+0"),
(BigFloat(16.0), ".6a", "0x1.000000p+4"),
(BigFloat('nan'), "a", "nan"),
(BigFloat('-nan'), "a", "nan"),
(BigFloat('inf'), "a", "inf"),
(BigFloat('-inf'), "a", "-inf"),
(BigFloat('nan'), "A", "NAN"),
(BigFloat('-nan'), "A", "NAN"),
(BigFloat('inf'), "A", "INF"),
(BigFloat('-inf'), "A", "-INF"),
# Binary formatting.
(BigFloat('2.25'), "b", '1.001p+1'),
(BigFloat('-2.25'), "b", '-1.001p+1'),
(BigFloat('nan'), "b", 'nan'),
(BigFloat('inf'), "b", "inf"),
(BigFloat('-inf'), "b", "-inf"),
# Rounding mode.
# Round up.
(BigFloat('-56.127'), ".2Uf", "-56.12"),
(BigFloat('-56.125'), ".2Uf", "-56.12"),
(BigFloat('-56.123'), ".2Uf", "-56.12"),
(BigFloat('56.123'), ".2Uf", "56.13"),
(BigFloat('56.125'), ".2Uf", "56.13"),
(BigFloat('56.127'), ".2Uf", "56.13"),
# Round down.
(BigFloat('-56.127'), ".2Df", "-56.13"),
(BigFloat('-56.125'), ".2Df", "-56.13"),
(BigFloat('-56.123'), ".2Df", "-56.13"),
(BigFloat('56.123'), ".2Df", "56.12"),
(BigFloat('56.125'), ".2Df", "56.12"),
(BigFloat('56.127'), ".2Df", "56.12"),
# Round away from zero.
(BigFloat('-56.127'), ".2Yf", "-56.13"),
(BigFloat('-56.125'), ".2Yf", "-56.13"),
(BigFloat('-56.123'), ".2Yf", "-56.13"),
(BigFloat('56.123'), ".2Yf", "56.13"),
(BigFloat('56.125'), ".2Yf", "56.13"),
(BigFloat('56.127'), ".2Yf", "56.13"),
# Round toward zero.
(BigFloat('-56.127'), ".2Zf", "-56.12"),
(BigFloat('-56.125'), ".2Zf", "-56.12"),
(BigFloat('-56.123'), ".2Zf", "-56.12"),
(BigFloat('56.123'), ".2Zf", "56.12"),
(BigFloat('56.125'), ".2Zf", "56.12"),
(BigFloat('56.127'), ".2Zf", "56.12"),
# Round to nearest (ties to even).
(BigFloat('-56.127'), ".2Nf", "-56.13"),
(BigFloat('-56.125'), ".2Nf", "-56.12"),
(BigFloat('-56.123'), ".2Nf", "-56.12"),
(BigFloat('56.123'), ".2Nf", "56.12"),
(BigFloat('56.125'), ".2Nf", "56.12"),
(BigFloat('56.127'), ".2Nf", "56.13"),
# Missing rounding mode implies round to nearest.
(BigFloat('-56.127'), ".2f", "-56.13"),
(BigFloat('-56.125'), ".2f", "-56.12"),
(BigFloat('-56.123'), ".2f", "-56.12"),
(BigFloat('56.123'), ".2f", "56.12"),
(BigFloat('56.125'), ".2f", "56.12"),
(BigFloat('56.127'), ".2f", "56.13"),
# Missing type behaves like str formatting.
(BigFloat('123'), ".0", "1e+02"),
(BigFloat('123'), ".1", "1e+02"),
(BigFloat('123'), ".2", "1.2e+02"),
(BigFloat('123'), ".2U", "1.3e+02"),
(BigFloat('123'), ".2D", "1.2e+02"),
(BigFloat('123'), ".3", "123"),
# 'alternate' flag is currently ignored.
(BigFloat('123'), "#.3", "123"),
(BigFloat('123'), ".4", "123.0"),
(BigFloat('123'), "#.4", "123.0"),
(BigFloat('123'), ".0", "1e+02"),
(BigFloat('123'), "", "123.00000000000000"),
(BigFloat('nan'), "", "nan"),
(BigFloat('inf'), "", "inf"),
(BigFloat('-inf'), "", "-inf"),
]
for bf, fmt, expected_output in test_triples:
result = format(bf, fmt)
self.assertEqual(result,
expected_output,
msg=(bf, fmt, expected_output))
#!/usr/bin/env python
import sys
import math
from bigfloat import BigFloat, precision
if sys.version_info > (3, ):
long = int
xrange = range
with precision(20000):
N_tosses = 1000
h_probs = [
math.factorial(N_tosses) /
(math.factorial(x) * math.factorial(N_tosses - x)) *
(BigFloat('0.5')**N_tosses) for x in xrange(N_tosses + 1)
]
s = 0
h_sums = [0]
for x in h_probs:
s += x
h_sums.append(s + 0)
def calc_prob(f, h_sums):
h = N_tosses + 0
money = (1 + 2 * f)**h
while money > 1e9:
h -= 1
money *= (1 - f) / (1 + 2 * f)
h += 1
return h
def main():
assert_ratio(1, 0.5, 1e-8)
assert_ratio(2, BigFloat(36.46) / 100, 1e-2)
assert_ratio(15, 0.1, 1e-2)
print_less_than(0.1)
print_less_than(BigFloat('1e-3'))
self.a = self.b = None
def __iter__(self):
for value in self.values():
self.a, self.b = self.b, value
yield value
def values(self):
yield Fraction(2, 1)
yield Fraction(-4, 1)
while True:
def f(y, z):
a = Fraction(111, 1)
b = Fraction(1130, 1) / y
c = Fraction(3000, 1) / (z * y)
return a - b + c
yield f(self.b, self.a)
print(list(take(10, JMM())))
with precision(9000):
for a, b in zip(forever(0), JMM()):
fnumerator = BigFloat(b.numerator)
fdenominator = BigFloat(b.denominator)
big = fnumerator / fdenominator
strbig = str(big)[:140]
print(f"{a:>5}: {strbig} {b}")
def rec(sum_, c):
if i == c:
ret[sum_] += BigFloat(v)/(BigFloat(s)**i)
else:
for x in xrange(1, s+1):
rec(sum_+x, c+1)
def __init__(self, constant: float):
context_down = bf.precision(53) + bf.RoundTowardNegative
context_up = bf.precision(53) + bf.RoundTowardPositive
super(ExactConstant, self).__init__([], BigFloat(constant, context_down), BigFloat(constant, context_up))
import sys
from bigfloat import precision, BigFloat, const_pi, sqrt, asin
if sys.version_info > (3, ):
long = int
with precision(100):
L_sect_area = (1 - BigFloat(const_pi()) / 4)
def calc_ratio(n):
l = BigFloat(0)
h = BigFloat(1)
m = (l + h) * 0.5
def calc_y1(x):
return x / n
def diff(x):
return (calc_y1(x) - (1 - sqrt(1 - (1 - x)**2)))
m_d = diff(m)
DIFF = BigFloat('1e-20')
while abs(m_d) > DIFF:
if m_d < 0:
l = m
else:
h = m
m = (l + h) * 0.5
m_d = diff(m)
x = x1 = m
y1 = calc_y1(x)