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 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 bfangle_diff(a, b):
diff = a - b
twopi = 2.0 * bigfloat.const_pi(bfcontext)
while diff < 0.0:
diff += twopi
while diff >= twopi:
diff -= twopi
return diff
def bfbuild_nyk_ext(thetas, dups):
nt = len(thetas)
nyk_idx = [0] * nt
nyk = [0] * nt
pi = bigfloat.const_pi(bfcontext)
for i, theta in enumerate(thetas):
if i > 0:
nyk_idx[i] = nyk_idx[i - 1] - 1
nyk[i] = nyk[i - 1] - dups[i - 1]
while angle_diff(thetas[(i + nyk_idx[i]) % nt], theta) < pi:
nyk[i] += dups[(i + nyk_idx[i]) % nt]
nyk_idx[i] += 1
while angle_diff(thetas[(i + nyk_idx[i]) % nt], theta) > pi:
nyk_idx[i] -= 1
nyk[i] -= dups[(i + nyk_idx[i]) % nt]
return nyk, nyk_idx
def bfbuild_nyk(thetas):
nt = len(thetas)
nyk = [0] * nt
pi = bigfloat.const_pi(bfcontext)
for i, theta in enumerate(thetas):
if i > 0:
nyk[i] = nyk[i - 1] - 1
while (
angle_diff(thetas[(i + nyk[i]) % nt], theta) < pi
or thetas[(i + nyk[i] + 1) % nt] == thetas[(i + nyk[i]) % nt]
):
nyk[i] += 1
while (
angle_diff(thetas[(i + nyk[i]) % nt], theta) >= pi
or thetas[(i + nyk[i] - 1) % nt] == thetas[(i + nyk[i]) % nt]
):
nyk[i] -= 1
return nyk
#!/usr/bin/python
from bigfloat import const_pi, precision
from string import translate, maketrans
print translate(str(const_pi(precision(5482))), maketrans('0123456789', '.Hdlro lwe'))
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)
#!/usr/bin/python
from bigfloat import const_pi, precision
import math
import itertools
def convert_base(x, base=3, precision=None):
length_of_int = int(math.log(x, base))
iexps = range(length_of_int, -1, -1)
if precision == None:
fexps = itertools.count(-1, -1)
else:
fexps = range(-1, -int(precision + 1), -1)
def cbgen(x, base, exponents):
for e in exponents:
d = int(x // (base ** e))
x -= d * (base ** e)
yield d
if x == 0 and e < 0: break
return cbgen(int(x), base, iexps), cbgen(x - int(x), base, fexps)
gi, gf = convert_base(float(const_pi(precision(1000))), base=10)
print ''.join(map(str, gf))
#!/usr/bin/python from bigfloat import const_pi, precision from string import digits, maketrans, translate print translate(str(const_pi(precision(24746))), maketrans(digits, 'rd\neHwlo! ')) #print #print translate(str(const_pi(precision(5482))), maketrans(digits, '.Hdlro lwe'))
lower, upper = interval
out_interval = [bf.atan(lower, context_down), bf.atan(upper, context_up)]
derivs = [1 / (1 + lower**2), 0], [0, 1 / (1 + upper**2)]
return out_interval, derivs
# def interval_pow(interval, context_down, context_up):
# lower, upper = interval
# out_interval = [bf.log(lower, context_down), bf.log(upper, context_up)]
# derivs = [1 / lower, 0], [0, 1 / upper]
if __name__ == '__main__':
context_down = bf.precision(100) + bf.RoundTowardNegative
context_up = bf.precision(100) + bf.RoundTowardPositive
pi_down = bf.const_pi(context_down)
pi_up = bf.const_pi(context_up)
# Testing sin
(lower, upper), derivs = interval_sin([5 * pi_down / 6, 7 * pi_down / 4],
context_down, context_up)
assert lower == -1 and 0.4 < upper < 0.6
assert derivs[0][0] == derivs[1][0] == derivs[1][1] and derivs[0][1] < -0.5
(lower, upper), derivs = interval_sin([5 * pi_down / 4, 11 * pi_down / 6],
context_down, context_up)
assert lower == -1 and -0.6 < upper < -0.4
assert derivs[0][0] == derivs[1][0] == derivs[0][1] and 0.8 < derivs[1][
1] < 0.9
(lower, upper), derivs = interval_sin([pi_down / 3, 5 * pi_down / 6],