def set_precision(number):
"""
Set the global gmpy2 precision.
Set the global precision for all gmpy2 computations and numbers in current
context. The gmpy2 precision is a bit width of stored numbers and it is
approximately 3 to 5 bits per digits (take 5 bits per digits into account).
Parameters
----------
number : int or str
Global gmpy2 precision in number of displayed digits.
Raises
------
error.PrecisionError
If `precision` has not acceptable format for precision.
"""
try:
gmpy2.get_context().precision = 5 * int(number)
debug("gmpy2 precision: {} bits".format(gmpy2.get_context().precision))
except:
raise error.PrecisionError
def N(value, prec=6):
pre_prec = gmp.get_context().precision
adj_prec = int((prec * (gmp.log(2) + gmp.log(5))) / gmp.log(2))
gmp.get_context().precision = adj_prec
try:
x, y = getattr(value, 'numerator'), getattr(value, 'denominator')
return x / y
except AttributeError:
return value
def compute(self):
gmpy2.get_context().precision = self.precision
x = mpfr(self.threshold)
ceilx = gmpy2.next_above(x)
gmpy2.get_context().precision = 53
ceilx = (x + ceilx) / 2
X = UniformDistr(self.lowerbound, self.upperbound)
self.error_prob = (X.get_piecewise_pdf().integrate(
x, ceilx)) / (X.get_piecewise_pdf().integrate(x, self.upperbound))
def compute(self):
gmpy2.get_context().precision = self.precision
x = mpfr(self.threshold)
ceilx = gmpy2.next_above(x)
floorx = gmpy2.next_below(x)
gmpy2.get_context().precision = 53
ceilx = (x + ceilx) / 2
floorx = (floorx + x) / 2
X = UniformDistr(self.lowerbound1, self.upperbound1)
Y = UniformDistr(self.lowerbound2, self.upperbound2)
Z = X + Y
self.error_prob = (((ceilx - x) / (ceilx - floorx)) *
Z.get_piecewise_pdf().integrate(x, ceilx))
def factorization(n, delta):
gmpy2.get_context().precision = 1000000
t = gmpy2.mpz(gmpy2.sqrt(n))
res = gmpy2.mpfr('0.0', 1000000)
steps = delta - t
print "Steps: %d" % steps
while True:
res = gmpy2.sqrt(t**2 - n)
if gmpy2.is_integer(res):
break
if res >= n / 2:
sys.stderr.write('I can\'t solve')
exit()
t += 1
steps -= 1
if steps % 1000 == 0:
print steps
p = t - gmpy2.mpz(res)
q = n / p
return {'p': int(q), 'q': int(p)}
def test1(self,n,p,prec,matrix_type,method):
'''
check the quality of tridiagonalization.
'''
if p==2:
assert(method=='qr' or method=='sqrtm')
else:
assert(method=='qr')
if prec is not None:
gmpy2.get_context().precision=prec
assert(matrix_type in ['array','sparse','mpc'])
v0=self.gen_randv0(n,p,matrix_type='array')
H0=self.gen_randomH(n,p,matrix_type=matrix_type)
if p is not None:
if method=='qr':
data,offset=tridiagonalize_qr(H0,q=v0,prec=prec)
else:
data,offset=tridiagonalize2(H0,q=v0,prec=prec)
else:
data,offset=tridiagonalize(H0,q=v0,prec=prec)
B=construct_tridmat(data,offset).toarray()
if sps.issparse(H0):
H0=H0.toarray()
H0=complex128(H0)
e1=eigvalsh(H0)
e2=eigvalsh(B)
assert_allclose(e1,e2)
def factorization(n, delta):
gmpy2.get_context().precision=1000000
t = gmpy2.mpz(gmpy2.sqrt(n))
res = gmpy2.mpfr('0.0', 1000000)
steps = delta-t
print "Steps: %d" % steps
while True:
res = gmpy2.sqrt(t**2 - n)
if gmpy2.is_integer(res):
break
if res >= n/2:
sys.stderr.write('I can\'t solve')
exit()
t += 1
steps -= 1
if steps % 1000 == 0:
print steps
p = t - gmpy2.mpz(res)
q = n/p
return {
'p': int(q),
'q': int(p)
}
def chudnovsky(digits):
# 20 safety digits because lots of calculations (only about 3 are needed)
scale = 10**(mpz(digits+20))
gmpy2.get_context().precision = int(math.log2(10) * (digits + 20))
k = mpz(1)
a_k = scale
a_sum = scale
b_sum = mpz(0)
C = mpz(640320)
C_cubed_over_24 = C**3 // 24
while True:
a_k *= -(6*k-5) * (2*k-1) * (6*k-1)
a_k //= k**3 * C_cubed_over_24
a_sum += a_k
b_sum += k * a_k
k += 1
if a_k == 0:
break
total_sum = mpfr(13591409 * a_sum + 545140134 * b_sum)
pi = (426880 * gmpy2.sqrt(mpfr(10005))) / total_sum
return pi*scale
def modulus_inutilis():
n = 17258212916191948536348548470938004244269544560039009244721959293554822498047075403658429865201816363311805874117705688359853941515579440852166618074161313773416434156467811969628473425365608002907061241714688204565170146117869742910273064909154666642642308154422770994836108669814632309362483307560217924183202838588431342622551598499747369771295105890359290073146330677383341121242366368309126850094371525078749496850520075015636716490087482193603562501577348571256210991732071282478547626856068209192987351212490642903450263288650415552403935705444809043563866466823492258216747445926536608548665086042098252335883
e = 3
ct = 243251053617903760309941844835411292373350655973075480264001352919865180151222189820473358411037759381328642957324889519192337152355302808400638052620580409813222660643570085177957
gmpy2.get_context().precision = 1000
plaintext = int(gmpy2.cbrt(ct))
return trans(plaintext)
def get_snapped_noise(self):
"""
Generates noise for Snapping Mechanism
See section 5.2 of Mironov (2012) for the definition of the snapping mechanism implemented below.
"""
gmpy2.get_context().precision = self.precision
# scale mechanism input by sensitivity
mechanism_input_scaled = self.mechanism_input / self.sensitivity
# generate random sign and draw from Unif(0,1)
sign = gmpy2.mpfr(
2 * secrets.randbits(1) - 1
) # using mpfr precision here, even though it's an integer, so that the
# precision carries through in later steps
u_star_sample = self._sample_from_uniform()
inner_result = self._clamp(mechanism_input_scaled, self._B_scaled) + (
sign * 1 / self.epsilon_prime * crlibm.log_rn(u_star_sample))
# perform rounding/snapping
inner_result_rounded = self._get_closest_multiple_of_Lambda(
inner_result, self._m)
private_estimate = self._clamp(
self.sensitivity * inner_result_rounded,
self.B) # put private estimate back on original scale
snapped_noise = private_estimate - self.mechanism_input
return (snapped_noise)
def aks_test(n):
"""
Implement the AKS primality test.
"""
get_context().precision = bit_length(n)
# Check if n is a perfect power. If so, return composite.
if is_power(n):
return "composite"
# Find the smallest r such that the multiplicative order of n modulo r
# is greater than log(n, 2)^2
r = get_r(n)
# If 1 < gcd(a, n) < n for some a <= r, return composite
for a in range(1, r):
if gcd(a, n) > 1 and gcd(a, n) < n:
return "composite"
# If n <= r, return prime
if n <= r:
return "prime"
# Check if (x + a)^n mod (x^r - 1, n) != (x^n + a) mod (x^r - 1, n)
if False in ray.get([
is_congruent.remote(a, n, r)
for a in range(1, mpz(floor(sqrt(phi(r)) * log2(n))))
]):
return "composite"
return "prime"
def solve_first(N): gmpy2.get_context().precision = 1000 Nsqrt = gmpy2.sqrt(N) A = gmpy2.mpz(gmpy2.rint_ceil(Nsqrt)) A2 = A*A x = gmpy2.isqrt(A2 - N) print "#1 ----> P is: " + str(A-x)
def _ptwise_vals_equal(mp_val, np_val, epsilon):
"""Pointwise value comparison"""
ptwise_diff = abs(mp_val - mpfr(np_val))
if epsilon == None:
P = gmpy2.get_context().precision
epsilon = mpfr("0b" + "0" * P + "1")
return ptwise_diff < epsilon
def legendre_symbol():
p = 101524035174539890485408575671085261788758965189060164484385690801466167356667036677932998889725476582421738788500738738503134356158197247473850273565349249573867251280253564698939768700489401960767007716413932851838937641880157263936985954881657889497583485535527613578457628399173971810541670838543309159139
ints = [
25081841204695904475894082974192007718642931811040324543182130088804239047149283334700530600468528298920930150221871666297194395061462592781551275161695411167049544771049769000895119729307495913024360169904315078028798025169985966732789207320203861858234048872508633514498384390497048416012928086480326832803,
45471765180330439060504647480621449634904192839383897212809808339619841633826534856109999027962620381874878086991125854247108359699799913776917227058286090426484548349388138935504299609200377899052716663351188664096302672712078508601311725863678223874157861163196340391008634419348573975841578359355931590555,
17364140182001694956465593533200623738590196990236340894554145562517924989208719245429557645254953527658049246737589538280332010533027062477684237933221198639948938784244510469138826808187365678322547992099715229218615475923754896960363138890331502811292427146595752813297603265829581292183917027983351121325,
14388109104985808487337749876058284426747816961971581447380608277949200244660381570568531129775053684256071819837294436069133592772543582735985855506250660938574234958754211349215293281645205354069970790155237033436065434572020652955666855773232074749487007626050323967496732359278657193580493324467258802863,
4379499308310772821004090447650785095356643590411706358119239166662089428685562719233435615196994728767593223519226235062647670077854687031681041462632566890129595506430188602238753450337691441293042716909901692570971955078924699306873191983953501093343423248482960643055943413031768521782634679536276233318,
85256449776780591202928235662805033201684571648990042997557084658000067050672130152734911919581661523957075992761662315262685030115255938352540032297113615687815976039390537716707854569980516690246592112936796917504034711418465442893323439490171095447109457355598873230115172636184525449905022174536414781771,
50576597458517451578431293746926099486388286246142012476814190030935689430726042810458344828563913001012415702876199708216875020997112089693759638454900092580746638631062117961876611545851157613835724635005253792316142379239047654392970415343694657580353333217547079551304961116837545648785312490665576832987,
96868738830341112368094632337476840272563704408573054404213766500407517251810212494515862176356916912627172280446141202661640191237336568731069327906100896178776245311689857997012187599140875912026589672629935267844696976980890380730867520071059572350667913710344648377601017758188404474812654737363275994871,
4881261656846638800623549662943393234361061827128610120046315649707078244180313661063004390750821317096754282796876479695558644108492317407662131441224257537276274962372021273583478509416358764706098471849536036184924640593888902859441388472856822541452041181244337124767666161645827145408781917658423571721,
18237936726367556664171427575475596460727369368246286138804284742124256700367133250078608537129877968287885457417957868580553371999414227484737603688992620953200143688061024092623556471053006464123205133894607923801371986027458274343737860395496260538663183193877539815179246700525865152165600985105257601565
]
x = -1
for i in ints:
if euler_criterion(
i, p) == 1: # 1 means that the number is a quadratic residue
x = i # this is the quadratic residue
# a^2 = x mod p
# b^p cong b mod p
gmpy2.get_context().precision = 10000
# temp = gmpy2.div(p+1, 4)
# print(temp)
a = pow(x, int(gmpy2.div(p + 1, 4)), p)
# a = (pow(x, p/2, p))
# print(int(a) == a)
print(a)
def verif_quadra(phi, N):
# coefficients are initialized
a = 1
b = phi - N - 1
c = N
#calculation of the determinant
delta = b * b - 4 * a * c
if delta < 0:
return False
#processing the roots
n = gmpy2.mpz(delta)
gmpy2.get_context().precision = 2048
det = gmpy2.sqrt(n)
num1 = (-b + det)
num2 = (-b - det)
den = 2 * a
k1 = int(num1 // den)
r1 = num1 - k1 * den
k2 = int(num2 // den)
r2 = num2 - k2 * den
if r1 == 0.0 and r2 == 0.0:
return True
else:
return False
def worker(number, data, ppc):
gmpy2.get_context().precision = 100
m = 1
setup(ppc)
temp_data = [[0 for i in range(N)] for i in range(N)]
mm = [[gmpy2.mpfr(0.0) for i in range(N)] for ii in range(N)]
ss = [[0 for i in range(N)] for ii in range(N)]
v0 = 0.0 #v([])
vector = list(range(N))
while (True):
for i in range(0, m, N):
shuffle(vector)
prev_v = v0
spruik_solver()
for ii, vv in enumerate(vector): #size ii, player vv
new_v = v(vector[0:ii + 1])
x = new_v - prev_v
prev_v = new_v
mm[ii][vv] += x
mm[N - ii - 1][vv] += x
ss[ii][vv] += 1
ss[N - ii - 1][vv] += 1
for i in range(N):
for ii in range(N):
temp_data[i][ii] = mm[i][ii] / ss[i][ii] if ss[i][
ii] > 0 else 0 #indsplus*random()*2.0/N #random()*1000
data[number] = [
float(sum([temp_data[o][i] for o in range(N)]) / N)
for i in range(N)
]
def _read_sighash_config(self, sig_cfgf):
# get pool/poolkey config from given .mbrat file
self.cfgparser.read(path.abspath(sig_cfgf))
print path.abspath(sig_cfgf)
# set precision try
try:
prec = self.cfgparser.getint('poolkey', 'prec')
except ConfigParser.NoOptionError:
return None
gmpy2.get_context().precision = prec
# check to see if the poolkey already exists, else create it
# sig_pool =
sig_d = {}
for sec in self.cfgparser.sections():
if sec == 'poolkey':
sig_d[sec] = { 'name': self.cfgparser.get(sec, 'name'),
'prec': prec,
'iters': self.cfgparser.getint(sec, 'iters'),
'mpoint': mpc( self.cfgparser.get(sec, 'mpoint') ),
}
elif sec == 'signature':
hash_sig_s = self.cfgparser.get(sec, 'hash_sig')
sig_d[sec] = { 'hash_sig': [mpc(pt) for pt in hash_sig_s.split('\n')] }
return sig_d
def callfunc2(a, b):
# print("Number of arguments", emb.numargs())
gmpy2.get_context().precision = 100
print(gmpy2.sqrt(5))
mp.dps = 50
print(mpf(2) ** mpf("0.5"))
x = 21.3
s = "a*x+1 * math.sin(3)"
result = eval(s)
print(result)
mycode = """print ('hello world from mycode')"""
exec(mycode)
def f(x):
x = x + 12
return x
print(f(4))
print("Will compute", a, "times", b)
c = 0
for i in range(0, a):
c = c + b
return c
def Run_MFun(self, itermax, Z_0):
""" Expects gmpy2.mpc type for Z_0. """
if not gmpy2.get_context().precision == self.prec:
gmpy2.get_context().precision = self.prec
Z = Z_0
while self.iters < itermax:
Z = add( gmpy2.mul(Z,Z), self.C )
if norm(Z) > 4.0:
break
self.iters += 1
if self.iters == itermax:
self.inmset = True
def create(self, string, round=0):
ctx = gmpy2.ieee(self.format)
ctx.round = MPFR_Data.rounding[round]
gmpy2.set_context(ctx)
fpo = gmpy2.mpfr(string)
ctx = gmpy2.get_context() # Get the results
self.ctx = ctx.copy() # Copy the context for later status
return fpo
def precision_hook(self, value):
fp_format = {'single': 32, 'double': 64}.get(value, None)
if fp_format is not None:
value = gmpy2.ieee(fp_format).precision - 1
if isinstance(value, str):
value = int(value)
gmpy2.get_context().precision = value + 1
return value
def testSquare(num):
gmpy2.get_context().precision = 100000
sqrt = int(gmpy2.sqrt(num))
# print("Square: " + str(sqrt))
for i in range(sqrt, 1, -1):
if (num % i) == 0:
print("Result: " + str(i) + " q: " + str(num // i))
return i, num // i
def main():
from sys import argv
if len(argv) > 1:
gmpy2.get_context().precision = 5000
if argv[1] == '--sign':
sign()
if argv[1] == '--check':
check()
def create(self,string,round=0):
ctx=gmpy2.ieee(self.format)
ctx.round=MPFR_Data.rounding[round]
gmpy2.set_context(ctx)
fpo=gmpy2.mpfr(string)
ctx=gmpy2.get_context() # Get the results
self.ctx=ctx.copy() # Copy the context for later status
return fpo
def is_square(integer):
itg = gmpy2.mpz(integer)
gmpy2.get_context().precision = 2048
root = gmpy2.sqrt(itg)
# root = math.sqrt(integer)
if int(root) ** 2 == integer:
return True
else:
return False
def set_context_precision(mantissa, exponent):
ctx = gmpy2.get_context()
#precision is already +1, meaning in single precision is 24 (and not 23)
ctx.precision = mantissa
ctx.emax = 2**(exponent - 1)
# 4-emax-precision
#https://github.com/aleaxit/gmpy/issues/103
ctx.emin = 4 - ctx.emax - ctx.precision
return ctx
def avg_error(coeffs, trials, max):
gmpy2.get_context().precision = 256
total_error = 0
for i in range(trials):
x = random.random()*max
expected = gmpy2.log(x) * 2**64
result = fxp_ln(int(x*2**64), coeffs)
total_error += abs(result - expected)/expected
return total_error/trials
def fib_eig(k):
import gmpy2
ctx = gmpy2.get_context()
ctx.precision += 1000
sqrt5 = gmpy2.sqrt(5)
lambda1 = (1 + sqrt5) / 2
lambda2 = (1 - sqrt5) / 2
fk = (lambda1**k - lambda2**k) / (lambda1 - lambda2)
return int(fk)
def calc():
# gmpy2.get_context().precision = 3321925
start = time.time()
for i in range(3321925, 3321930):
t = time.time()
gmpy2.get_context().precision = i
res = str(gmpy2.sqrt(2))
print("精度设置为{}, 运算长度为{}, 第一百万位数字是{}, 本次用时{}".format(i, len(res), res[-1], time.time() - t))
end = time.time()
print("总用时{}秒".format(end - start))
def main():
gmpy2.set_context(gmpy2.context())
gmpy2.get_context().precision = 75
T = int(input())
if T < 1 or T > 100:
raise RuntimeError("T is not within the valid range")
for i in range(T):
n = int(input())
r = Numbers(n)
print("Case #" + str(i + 1) + ": " + r)
def __init__(self):
#set the precision for gmpy to very high
gmpy2.get_context().precision=5000
self.N = 0
self.p = 0
self.q = 0
self.e = 0
self.d = 0
self.pi_of_N = 0
self.pkcsByte = "02"
self.separatorByte = "00"
def recover_msg(N1, N2, N3, C1, C2, C3):
m = 42
# your code starts here: to calculate the original message - m
# Note 'm' should be an integer
N = N1 * N2 * N3
#y1 = N / N1
#y2 = N / N2
#y3 = N / N3
s = [1, 0]
r = [(N / N1), N1]
i = 2
temp = (N / N1) % N1
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(temp)
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z1 = s[i - 2]
s = [1, 0]
r = [(N / N2), N2]
i = 2
temp = (N / N2) % N2
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(temp)
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z2 = s[i - 2]
s = [1, 0]
r = [(N / N3), N3]
i = 2
temp = (N / N3) % N3
while (temp > 0):
temp = r[i - 2] % r[i - 1]
r.append(r[i - 2] % r[i - 1])
s.append(s[i - 2] - (r[i - 2] / r[i - 1]) * s[i - 1])
i += 1
z3 = s[i - 2]
if z1 < 0: z1 += N1
if z2 < 0: z2 += N2
if z3 < 0: z3 += N3
x = (z1 * C1 * (N / N1) + z2 * C2 * (N / N2) + z3 * C3 * (N / N3)) % N
gmpy2.set_context(gmpy2.context())
gmpy2.get_context().precision = 1000000
m = int(gmpy2.cbrt(x))
# your code ends here
# convert the int to message string
msg = hex(m).rstrip('L')[2:].decode('hex')
return msg
def machin_gmpy2(digits):
# Precision + 20 bits for safety
gmpy2.get_context().precision = int(math.log2(10) * digits) + 20
one_5th = mpfr("1") / 5
one_239th = mpfr("1") / 239
pi_fourths = 4*gmpy2.atan(one_5th) - gmpy2.atan(one_239th)
pi = 4*pi_fourths
return pi
def __init__(self):
# Set number of bits to keep around
gmpy2.get_context().precision = 2000
# These are values taken from the OEIS which I use when
# checking my results.
self.lambdainf = mpfr(
"3.5699456718709449018420051513864989367638369115148323781079755299213628875001367775263210342163"
)
self.delta = mpfr(
"4.669201609102990671853203820466201617258185577475768632745651343004134330211314"
)
def get_prec():
prec = 3000000
while True:
gmpy2.get_context().precision = prec
res = str(gmpy2.sqrt(2))
print(prec, len(res))
if len(res) >= 1000002:
print(res[-1], len(res), prec)
break
else:
prec += 1
return prec
def main():
gmpy2.get_context().precision = 100
for dir_entry in os.scandir():
try:
run_record = read_pcreo_file(dir_entry)
print("Successfully read PCreo output file:", dir_entry.name)
except:
print("File", dir_entry.name, "is not a PCreo output file.")
sys.exit(0)
continue
print(len(defect_classes(run_record)))
povray_draw(run_record, 800, dir_entry.name)
def find_nearest_power(number):
gmpy2.get_context().precision = 10000
smallest_r = number
nearest_xy = 0
for i in range(2, int(math.log(number, 2))):
floor = int(gmpy2.root(mpfr(number), i))**i
if number - floor < smallest_r:
if floor > number:
print("error at %d" % i)
smallest_r = number - floor
nearest_xy = floor
return smallest_r
def check_context(self):
""" Check that the context settings including precision and inexact arithmetic
flags are set properly. """
if self.precision_set != True:
return False
ctx = gmpy2.get_context()
if ctx.precision != self.context.precision:
return False
else:
return (ctx.trap_inexact and ctx.trap_overflow and ctx.trap_erange \
and ctx.trap_divzero and ctx.trap_invalid and ctx.trap_expbound \
and ctx.trap_underflow)
def run_sign(self, args, return_dict=False):
"""
Method to sign a hash of a given file, returning either True or a dict if return_dict==True.
"""
from mbrat.spi.sign import SignSPI
spi = SignSPI(mandelfun)
print "Signing '{0}' with profile '{1}:{2}' and pool '{3}:{4}' ...".format(
args.file, self.config.get('name'), self.privkey_cfg.get('name'),
self.pool_cfg.get('name'), self.poolkey_cfg.get('name')
)
# put together arguments for the SPI
args.spi['iters'] = int(self.pool_cfg.get('iters')) + \
int(self.privkey_cfg.get_from_section('pool', 'iters'))
# set the precision
args.spi['prec'] = int(self.privkey_cfg.get('prec'))
gmpy2.get_context().precision = args.spi['prec']
# format the keys for mpc
args.spi['poolkey'] = mpc( self.poolkey_cfg.get('real') + " " \
+ self.poolkey_cfg.get('imag') )
args.spi['privkey'] = mpc( self.privkey_cfg.get('real') + " " \
+ self.privkey_cfg.get('imag') )
######## sign the hash ########
hash_sig = spi.run(args)
# init a ConfigParser compat dict with a top-section of 'mhash'
sig_d = {'mhash': {'prec': args.spi['prec']}}
for sec in ['pool', 'poolkey']:
sig_d[sec] = self.cfgmgr.secmgr[sec].get_as_args(
subsection=sec, return_dict=True)
sig_d['signature'] = { 'hash_sig': hash_sig } # add hash_sig
# return a dict if desired ...
if return_dict:
return sig_d
# ... or get the filename for the signature 'BASENAME.mbrat' file
sig_cfgf = path.splitext(path.basename(args.file))[0] + ".mbrat"
sig_cfgf = path.join( path.dirname(path.abspath(args.file)),
sig_cfgf )
self._write_sig_config(sig_d, sig_cfgf)
return True
def solve_second(N):
gmpy2.get_context().precision = 1000
Nsqrt = gmpy2.isqrt(N)
for A in range(Nsqrt , Nsqrt+2**20):
A2 = A*A
diff = A2 - N
if diff > 0:
possible_x = gmpy2.isqrt(A2 - N)
if (A-possible_x) * (A+possible_x) == N:
print "#2 ----> P is: " + str(A-possible_x)
break
else:
print "Error: P not found!"
def test_roundings(self):
gmpy2.get_context().real_round = gmpy2.RoundToNearest
for test_vector in scalar_decomp_test_vectors:
scalar = test_vector[0]
# alpha_tilde = floor(ell_i * m / mu) ~ round((alpha_hat_i / N) * scalar)
alpha_tildes = scalar_decomposition.calculate_alpha_tildes(scalar)
alpha_hats = scalar_decomposition.calculate_alpha_hats()
# the values of alpha_tilde should be equal to round((alpha_hat / N) * m)
for alpha_tilde, alpha_hat in zip(alpha_tildes, alpha_hats):
alpha_rounded = round(mpq(alpha_hat * scalar, constants.N))
# computing the rounding in this way means the answer can be out by 1 in some cases
diff = alpha_rounded - alpha_tilde
self.assertTrue(0 <= diff <= 1)
def fermat_factorization(n):
factor_list = []
gmpy2.get_context().precision = 2048
a = int(gmpy2.sqrt(n))
a2 = a * a
b2 = gmpy2.sub(a2, n)
while True:
a += 1
b2 = a * a - n
if gmpy2.is_square(b2):
b2 = gmpy2.mpz(b2)
gmpy2.get_context().precision = 2048
b = int(gmpy2.sqrt(b2))
factor_list.append([a + b, a - b])
if len(factor_list) == 2:
break
return factor_list
def main():
gmpy2.get_context().precision = 10000
p = 0x16498bf7cc48a7465416e0f9ec8034f4030991e73aff9524ef74cc574228e36e6e1944c7686f69f0d1186a69b7aa77d7e954edc8a6932f006786f4648ecc8d4f4d3f6c03d9a1ee9fe61b28b6dd2791a63be581b8811a8ac90a387241ea68b7d36b4a274f64c7a721ad55cfcef23cd14c72542f576e4b507c11c4fa198e80021d484691b
e = 0x69420
ct1 = 0xa82b37d57b6476fa98f6ee7c278d934bd96c49aa1c5399552d25211230d76cb16ade049572bf631e3849903638d41c884957b9592d0aa072b2bdc3105fe0e3253284f85286ec613966f9cde77ae06e2053dc2254e44ca673b4c76879eff84e5fc32af976c1bfafe147a277d72aad674db749ed8f34d2ebe8189cf12afc9baa17764e4b
phi = p - 1
const = 32
e //= const
d = gmpy2.invert(e, phi)
# print(d)
p32 = pow(ct1, d, p)
# print(p32)
while (const != 1):
const //= 2
p32 = tonelli_shanks(p32, p)
# print(trans(-p32%p))
# FIRST PART OF THE FLAG BABY: HTB{why_d1d_y0u_m3ss_3v3ryth1ng_up_1ts_n0t_th4t_h4rd
p = 0x16498bf7cc48a7465416e0f9ec8034f4030991e73aff9524ef74cc574228e36e6e1944c7686f69f0d1186a69b7aa77d7e954edc8a6932f006786f4648ecc8d4f4d3f6c03d9a1ee9fe61b28b6dd2791a63be581b8811a8ac90a387241ea68b7d36b4a274f64c7a721ad55cfcef23cd14c72542f576e4b507c11c4fa198e80021d484691b
n = 0xbe30ccaf896c16f53515e298df25df9158d0a95295c119f0444398b94fae26c0b4cf3a43b120cf0fb657069e0621eb1d2dd832eef3065e80ddbc35854dd4585cc41fd6a5b36339c0d9fcc066272be6818be6a624f75482bbb9c408010ac8c27b20397d870bfcb14e6318097b1601f99e391c9b68c5c586f8da561ff8507be9212713b910b748370ce692c11afa09b74ce80c5f5dd72046415aeed85e1ecedca14abe17ed19ab97729b859120699d9f80dd13f8483773df15b938b8399702a6e846b8728a70f1940d4c6e5835a06a89925eb1ec91a796f270e2d9be1a2c4bee5517109c161f04333d9c0d4034fbbd2dcf69fe734b759a89937f4d8ea0ee6b8385aae14a2cce361
# generator
g = 0x69420
ct2 = 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
# print(n)
# print(g)
# print(ct2)
q = n // p
# print(q)
# found using alpertron for g^xp = ct2 mod p
kp = 0
xp = 1333647771826129906056278980508785116695001357398405010264712880010822066437928270470093887443647579332557329757513503832688236838814545646539928049413880950956136391197700699813257009513030650710096103937450573603079886862042789301653172344151731360918260335579808862271014412080624561537897979314727207446470188301\
+ 2100597191236862411973123184673222390029361412634375676811383630091967723602897705208854139513327705418840522104410271985778087477636285771639551773018473451844243204190875248518748762236574766561778114516538828518726261981381313004189199195300204873125911752732961129454366019842676645748294495098918135199007126669 * kp
kq = 0
xq = 2248237925279582319646346402167252499424555860028602832387207824347301477610684362756745372458799004275280799304910420404269790625413034441525997676464275232206297649095612480172888211521015846455387388707653809767187874172857528680924943045273311447383766726890650161662310150531795567852223701545458237821806704227\
+ 25737553036453033170874873232492616472696251153498345345893349066914349319700028526259065151440470760781885101651616163782998343068021108194360596481454344775056268387636520767391616783538213196153998980567585557740463660083917063025907541863194906635695830144597030344814258845557193440907517374289359866191267367218 * kq
assert (pow(g, xp, p) == ct2 % p)
assert (pow(g, xq, q) == ct2 % q)
m = [p - 1, q - 1] # modulo
v = [xp, xq]
ret = crt(m, v)
print(ret[0]) # gives x in g^x
# # check
assert (xp == ret[0] % (p - 1))
assert (xq == ret[0] % (q - 1))
print(trans(ret[0]))
def getFinalMaxValue(self, supVal):
if not gmpy2.is_finite(supVal):
print("Error cannot compute intervals with infinity")
exit(-1)
bkpCtx = gmpy2.get_context().copy()
i = 0
while not gmpy2.is_finite(gmpy2.next_above(supVal)):
set_context_precision(self.precision + i, self.exponent + i)
i = i + 1
prec = printMPFRExactly(gmpy2.next_above(supVal))
gmpy2.set_context(bkpCtx)
return prec
def _assert_mp_equals_np(mp_array, np_array):
"""Compares an MPMatrix and np array, checking for equality.
Returns an equality bool and an error string."""
m, n = np_array.shape
coordinates = itertools.product(range(m), range(n))
P = gmpy2.get_context().precision # TODO: need this to be relative
epsilon = mpfr("0b" + "0" * P + "1")
for coord in coordinates:
mp_val = mp_array[coord]
np_val = np_array[coord]
if not _ptwise_vals_equal(mp_val, np_val, epsilon):
return (False, "Distinct values mp: {}, np: {} at coord {}".format(
mp_val, np_val, coord))
return (True, "")
def main():
# Configure precision to deal with large integers
# The right factor(3) must be found by trial and error; turns out that to solve these
# problems a precision of around 900 digits is necessary
num_digits = len(N1)
precision = 3 * num_digits
print "The required precision is {} digits".format(precision)
gmpy2.get_context().precision = precision
print "Q1)"
solve_q1()
print "Q2)"
solve_q2()
print "Q3)"
solve_q3()
print "Decrpyt:", decrypt()
def FermatFacotorization(n):
# a = math.ceil(math.sqrt(N))
N = gmpy2.mpz(n)
gmpy2.get_context().precision = 2048
a = gmpy2.sqrt(N)
# print a
b2 = a ** 2 - N
# print b2
while not is_sqr(b2):
a += 1
b2 = a ** 2 - N
print a
print "a is " + str(a)
print "b2 is " + str(b2)
# a = math.sqrt(a2)
b = math.sqrt(b2)
return (a + b, a - b)
def display(self, modes=False, indent="", string=False):
s = "%s MPFR Data:" % indent
lcl = "%s " % indent
if modes:
s = "%s\n%sRoundAwayZero: %s" % (s, lcl, gmpy2.RoundAwayZero)
s = "%s\n%sRoundDown: %s" % (s, lcl, gmpy2.RoundDown)
s = "%s\n%sRoundToNearest: %s" % (s, lcl, gmpy2.RoundToNearest)
s = "%s\n%sRoundToZero: %s" % (s, lcl, gmpy2.RoundToZero)
s = "%s\n%sRoundUp: %s" % (s, lcl, gmpy2.RoundUp)
s = "%s\n%sfpo: %s" % (s, lcl, self.fpo)
s = "%s\n%sformat: %s" % (s, lcl, self.format)
# Get Base 2 mantissa and base 10 exponent
# man,exp,mpfr_prec=self.fpo.digits(2)
s = "%s\n%smpfr prec:%s 0x%X" % (s, lcl, self.dprec, self.dprec)
s = "%s\n%smpfr sign: %s" % (s, lcl, self.isign)
if not self.ic:
s = "%s\n%smpfr man: %s (%s digits)" % (s, lcl, self.digits, len(self.digits))
# % (s,lcl,digits[0],len(digits[0]))
s = "%s\n%smpfr exp: %s 0x%X" % (s, lcl, self.dexp, self.dexp)
else:
l = self.format // 8
dcd = bfp.BFPRound.decode[l]
s = "%s\n%sdecode: %s" % (s, lcl, dcd)
byts = fp.FP.str2bytes(self.ic)
ic_sign, ic_frac, ic_exp, ic_attr = dcd.decode(byts)
ic_frac = fp.rounding_mode.list2str(ic_frac, 2)
s = "%s\n%sifmt big: %s" % (s, lcl, fp.FP.bytes2str(byts))
b = int.from_bytes(byts, byteorder="big", signed=False)
s = "%s\n%sifmt sign:%s" % (s, lcl, ic_sign)
s = "%s\n%sifmt exp: %s" % (s, lcl, ic_exp)
bexp = exp + dcd.bias
s = "%s\n%sifmt bias:%s 0x%X" % (s, lcl, bexp, bexp)
s = "%s\n%smpfr exp: %s 0x%X" % (s, lcl, exp, exp)
s = "%s\n%smpfr man: %s (%s digits)" % (s, lcl, man, len(man))
#% (s,lcl,digits[0],len(digits[0]))
s = "%s\n%sifmt frac: %s (%s digits)" % (s, lcl, ic_frac, len(ic_frac))
s = "%s\n%sattr: %s" % (s, lcl, ic_attr)
ctx = gmpy2.get_context()
s = "%s\n%s%s" % (s, lcl, ctx)
s = "%s\n" % s
if string:
return s
print(s)
def checkPQDistance(self, keys):
if not isinstance(keys, (tuple, list)):
keys = [keys]
ctx = gmpy2.get_context()
ctx.precision = 5000
ctx.round = gmpy2.RoundDown
ctx.real_round = gmpy2.RoundDown
gmpy2.set_context(ctx)
for key in keys:
gmpy_key = gmpy2.mpfr(key)
skey = int(gmpy2.sqrt(gmpy_key))
skey2 = skey ** 2
if (skey2 > key) or (((skey + 1) ** 2) < key):
print skey2
print (skey+1)**2
raise Exception("WTF")
bits = int(gmpy2.log2(key - skey2))
if bits < 480:
print '%d Has p, q distance of %d bits' % (key, bits)
def chudnovsky_bs(digits):
gmpy2.get_context().precision = int(math.log2(10) * (digits + 20))
# Use binary splitting
digits += 20
C = mpz(640320)
C_cubed_over_24 = C**3 // 24
def bs(a, b):
# a(a) = +/- (13591409 + 545140134a)
# p(a) = (6a-5)(2a-1)(6a-1)
# b(a) = 1
# q(a) = a^3 * C_cubed_over_24
if b - a == 1:
# Directly compute
if a == 0:
Pab = Qab = mpz(1)
else:
Pab = (6*a-5) * (2*a-1) * (6*a-1)
Qab = a**3 * C_cubed_over_24
Tab = Pab * (13591409 + 545140134*a)
if a & 1:
Tab *= -1
else:
m = (a+b) // 2 # Midpoint
# Recursively divide and conquer
Pam, Qam, Tam = bs(a, m)
Pmb, Qmb, Tmb = bs(m, b)
Pab = Pam * Pmb
Qab = Qam * Qmb
Tab = Qmb * Tam + Pam * Tmb
return Pab, Qab, Tab
digits_per_term = math.log10(C_cubed_over_24/72)
N = int(digits/digits_per_term + 1)
P, Q, T = bs(mpz(0), mpz(N))
Q, T = mpfr(Q), mpfr(T)
return (Q * 426880 * gmpy2.sqrt(mpfr(10005))) / T
def worker(xs, results, updates, trials, max):
gmpy2.get_context().precision = 256
ys = (map(gmpy2.log2, x) for x in xs)
polys = (scipy.interpolate.lagrange(x, y) for x, y in itertools.izip(xs, ys))
coeffs = [[int(a_i*2**64) for a_i in reversed(p.coeffs)] for p in polys]
updates.put("Generated %d polynomials to test." % len(coeffs))
min_err = float('inf')
min_cs = None
for cs in coeffs:
try:
err = avg_error(cs, trials, max)
if err < min_err:
min_err = err
min_cs = cs
except Exception as exc:
updates.put(str(exc))
results.put((float('inf'), None))
return
updates.put("Checked %d polynomials." % len(coeffs))
results.put((min_err, min_cs))
def gauss_legendre(digits):
gmpy2.get_context().precision = int(math.log2(10) * (digits + 5))
iterations = int(math.log2(digits))
# Direct translation of algorithm
a = mpfr(1)
b = 1 / gmpy2.sqrt(mpfr(2))
t = mpfr(1)/4
x = mpfr(1)
for i in range(iterations):
y = a
a = (a + b) / 2
b = gmpy2.sqrt(b * y)
t = t - x * (y-a)**2
x = 2 * x
pi = ((a+b)**2) / (4*t)
return pi
def borwein(digits):
gmpy2.get_context().precision = int(math.log2(10) * (digits + 10))
sqrt_2 = gmpy2.sqrt(mpfr(2))
a_n = sqrt_2
b_n = mpz(0)
p_n = 2 + sqrt_2
while True:
sqrt_a_n = gmpy2.sqrt(a_n)
a_n1 = (sqrt_a_n + 1/sqrt_a_n) / 2
b_n1 = (1 + b_n) * sqrt_a_n / (a_n + b_n)
p_n1 = (1 + a_n1) * p_n * b_n1 / (1 + b_n1)
if p_n1 == p_n:
break
a_n = a_n1
b_n = b_n1
p_n = p_n1
return p_n
def _init_from(self, args):
# from mbrat.util import Arguments
# 1st set the precision ...
if not hasattr(args, 'prec'):
args.prec = MBRAT_DEF_PRECISION
self.prec = int(args.prec)
gmpy2.get_context().precision = self.prec
# ... make sure lims dict is right ...
if not hasattr(args, 'lims'):
self.limits = { 'low': mpc(mpfr(args.x_lo), mpfr(args.y_lo)),
'high': mpc(mpfr(args.x_hi), mpfr(args.y_hi)), }
else:
self.limits = args.lims
# ... init the core stuff ...
self._init_new(args)
# ... if 'ini_d' dict provided then init more depending...
if hasattr(args, 'ini_d'):
if 'image' in args.ini_d:
self.gen_mscreen_from_img( args.ini_d['image'] )
import gmpy2
from gmpy2 import root
gmpy2.get_context().precision = 4096
import codecs
e = 3
c1 = 261345950255088824199206969589297492768083568554363001807292202086148198406422015406837306712350185001004539557263392747990052517553733793783164539246862722846027251864430884218012651143187891041767278036834613455255679627575565220404720823343734717216496823882624775291829042065791328110144692179931720656184
n1 = 1001191535967882284769094654562963158339094991366537360172618359025855097846977704928598237040115495676223744383629803332394884046043603063054821999994629411352862317941517957323746992871914047324555019615398720677218748535278252779545622933662625193622517947605928420931496443792865516592262228294965047903627
c2 = 147535246350781145803699087910221608128508531245679654307942476916759248177533099119747011361428805549054451656981174660189536226806378907786889467354024644240879320253207532952949102143188764785409228498939338911381114763011074430123706304767125057179745262429033988355639559021251950099792930724833562784673
n2 = 405864605704280029572517043538873770190562953923346989456102827133294619540434679181357855400199671537151039095796094162418263148474324455458511633891792967156338297585653540910958574924436510557629146762715107527852413979916669819333765187674010542434580990241759130158992365304284892615408513239024879592309
c3 = 633230627388596886579908367739501184580838393691617645602928172655297372011548865034935604403952733958738640693591337661775300212965321256493515985362225064130164637923136989033908516462412694733923594235845265750167194852656423103420952926986457914303614556562367709542082728589329045460298763797973333272805
n3 = 1204664380009414697639782865058772653140636684336678901863196025928054706723976869222235722439176825580211657044153004521482757717615318907205106770256270292154250168657084197056536811063984234635803887040926920542363612936352393496049379544437329226857538524494283148837536712608224655107228808472106636903723
def chinese_remainder_theorem(items):
# Determine N, the product of all n_i
N = 1
for a, n in items:
N *= n
# Find the solution (mod N)
result = 0
for a, n in items:
m = N // n
r, s, d = extended_gcd(n, m)
if d != 1:
raise "Input not pairwise co-prime"
result += a * s * m
# Make sure we return the canonical solution.
return result % N
#!/usr/bin/env python #Author : Karthik C #////////////////////////////////////////////////// #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)
import numpy import gmpy2 import math from collections import defaultdict from gmpy2 import mpz gmpy2.get_context().precision=10000 N = 179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581 N=179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581 N=648455842808071669662824265346772278726343720706976263060439070378797308618081116462714015276061417569195587321840254520655424906719892428844841839353281972988531310511738648965962582821502504990264452100885281673303711142296421027840289307657458645233683357077834689715838646088239640236866252211790085787877 N=720062263747350425279564435525583738338084451473999841826653057981916355690188337790423408664187663938485175264994017897083524079135686877441155132015188279331812309091996246361896836573643119174094961348524639707885238799396839230364676670221627018353299443241192173812729276147530748597302192751375739387929 N= mpz(N)*6 A=gmpy2.ceil(gmpy2.sqrt(gmpy2.mpz(N))) B=numpy.powmod(2,20,N) for i in range(0,B+1): print i #x=mpz(A*A) -N A=mpz(A) z=mpz(A)*mpz(A) #print mpz(z)+1 y=mpz(z)-mpz(N) x=gmpy2.sqrt(gmpy2.mpz(y)) p=mpz(A)-mpz(x) q=mpz(A)+mpz(x) #print p #print mpz(p)
#!/usr/bin/python2
import gmpy2
#import matplotlib.pyplot as plt
import os
import bisect
from numpy import linspace
# gmpy2 precision initialization
BITS = (1 << 10)
BYTES = BITS/8
gmpy2.get_context().precision = BITS # a whole lotta bits
def random():
seed = int(os.urandom(BYTES).encode('hex'), 16)
return gmpy2.mpfr_random(gmpy2.random_state(seed))
# Useful constants as mpfr
PI = gmpy2.acos(-1)
LOG2E = gmpy2.log2(gmpy2.exp(1))
LN2 = gmpy2.log(2)
# Same, as 192.64 fixedpoint
FX_PI = int(PI * 2**64)
FX_LOG2E = int(LOG2E * 2**64)
FX_LN2 = int(LN2 * 2**64)
FX_ONE = 1 << 64
## The index of a poly is the power of x,
## the val at the index is the coefficient.
##
## An nth degree poly is a list of len n + 1.
##
## The vals in a poly must all be floating point
## numbers.
