def exact_fft(x, debug=False):
''' Calculates the exact DFT using gmpy2
Has ~N^2 efficiency but I tried to optimize the calculation a bit.
'''
N = x.shape[0]
start = time.clock()
arg = -2j * (gmpy2.const_pi() / N)
exp1d = np.array([gmpy2.exp(arg * idx) for idx in range(N)])
exp = np.diag(exp1d)
for i in range(N):
for j in range(i+1):
exp[j, i] = exp[i, j] = exp1d[(j * i) % N]
stop = time.clock()
if debug:
print('preparation %.2fms' % ((stop-start)*1e3))
start = time.clock()
x = np.array([gmpy2.mpc(xi) for xi in x])
# fsum solution - I noticed no difference except that it ran slower
# y = []
# for i in range(N):
# mul = x * exp[i, :]
# y.append(gmpy2.fsum([m.real for m in mul]) + 1j *
# gmpy2.fsum([m.imag for m in mul]))
# y = np.array(y, dtype=np.complex128)
y = np.sum(exp * x, axis=-1)
y = np.array(y, dtype=np.complex128)
stop = time.clock()
if debug:
print('calculation %.2fms' % ((stop-start)*1e3))
return y
def calc_pi():
if mem.libmath == np:
pi = np.pi
elif mem.libmath == gmpy2:
pi = gmpy2.const_pi()
else:
raise TypeError("Constants not implemented. Error in 'mem.libmath'")
return pi
### FUNCTIONS ###
def mp(num):
return mpfr(str(num))
def backf(num, digits=5):
return float(round(num, digits))
def listf(l):
return list(map(backf, l))
pi = const_pi(bits)
e = const_euler(bits)
def propagation1D(i_max, n_max, ratio, l):
global pi
global e
eps_0 = mp(8.85418782) * 10**-12 # Farad/m
mi_0 = 4 * pi * 10**-7 # Hen/m
c = mp(299792458) # m/s
dx = mp(0.001)
dt = 0.9 * dx / c
parser.add_argument(
'--prefix',
help='Prefix to the C style functions to generate (include the "_"!)',
default="my_")
parser.add_argument(
'--lgamma',
help='Whether or not to include an implementation of the `lgamma` function',
action='store_true')
args = parser.parse_args()
# set precision to the requested one
gmpy2.get_context().precision = args.prec
# pi & e, but to full precision within gmpy2
pi = const_pi()
e = exp(1)
# factorial, product of all integers <= x
@lru_cache
def factorial(x):
return math.factorial(x)
# double factorial, if n is even, product of all even numbers <= n, otherwise the product of all odd numbers <= n
@lru_cache
def double_factorial(n):
if n <= 1:
return 1
else:
>>> from gmpy2 import mpq
>>> mpq(1,7)
mpq(1,7)
>>> mpq(1,7) * 11
mpq(11,7)
>>> mpq(11,7)/13
mpq(11,91)
#gmpy2: Multiple-precision Reals
>>> import gmpy2
>>> from gmpy2 import mpfr
>>> mpfr('1.2')
>>> gmpy2.const_pi(100000)
>>> gmpy2.get_context().precision=100
>>> gmpy2.atan2(mpfr("+0.0"),mpfr("-0.0"))
>>> gmpy2.sqrt(5)
mpfr('2.2360679774997898')
>>> gmpy2.get_context().precision=100
>>> gmpy2.sqrt(5)
mpfr('2.2360679774997896964091736687316',100)
>>> with gmpy2.local_context(gmpy2.context(), precision=100) as ctx:
print(gmpy2.sqrt(2))
ctx.precision += 100
print(gmpy2.sqrt(2))
initializer = (str(num1) + "." + str(num2) + str(num3) + "e" +
str(exponent))
if (randint(0, 1) == 1):
initializer = "-" + initializer
return Numeric(initializer)
def eval(self):
return self
def getexponent(self):
return int(gmpy2.floor(self.log().val))
PI = Numeric(gmpy2.const_pi())
PI.latex = lambda: '\pi'
E = Numeric(gmpy2.exp(1))
class Model1(Expression):
def __init__(self):
self.value = Numeric.new()
self.text = str(self.value)
def gen(self):
x = randint(1, 550)
if (x < 120):
z = Numeric.create(self.value.getexponent() - 1,
self.value.getexponent() + 1)
self.text = z.latex() + " + " + self.value.latex()
def compute_timings():
# operations = [bf.add, bf.mul, bf.sub, bf.div]
operations = [gp.add, gp.mul, gp.sub, gp.div]
labels = ["add", "mul", "sub", "div"]
for label, operation in zip(labels, operations):
precisions, times = [], []
for i in range(3, 45):
p = int(1.3**i)
precisions.append(p)
gp.set_context(gp.context(precision=p))
start = time.time()
pi = gp.const_pi()
e = gp.exp(1)
a = operation(e, pi)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
# pi = bf.const_pi(context)
# e = bf.exp(1, context)
# a = operation(e, pi, context)
end = time.time()
times.append(end-start)
plt.plot(precisions, times, label=label)
plt.legend()
plt.xlabel('Precision')
plt.ylabel('Time')
plt.show()
#////////////////////////////////////////////////// #Code developed to genetare ADS-B message////////// #////////////////////////////////////////////////// import math import sys import gmpy2 #multi precision module from gmpy2 import mpz, mpq, mpfr, mpc import numpy from numpy import * #-------------Globals----------------------------------- gmpy2.get_context().precision = 32 #set gmpy precision to 128 bits Dlat0 = 6 # Even message Dlat1 = mpfr(6.101694915254237288135593220339) # Odd message pi = mpfr(gmpy2.const_pi(), 56) airID = 0x8D # bit 1 to 5 DF format 17 and 6 to 8 CA type 3 altitude = 0 evenMsg = mpz(1) oddMsg = mpz(1) CRCOdd = mpz(1) CRCEven = mpz(1) #-----------For testing ------------------------- t_aid = 'ab7444' t_alt = 40000 t_lat = mpfr(49.925827) t_lon = mpfr(89.193542) #-------------------------------------------------