def pi_gmpy(prec):
"""gmpy.mpf"""
set_minprec(prec)
lasts, t, s, n, na, d, da = mpf(0), mpf(3), mpf(3), mpf(1), mpf(0), mpf(
0), mpf(24)
while s != lasts:
lasts = s
n, na = n + na, na + 8
d, da = d + da, da + 32
t = (t * n) / d
s += t
return s
def fermat_factor(N, minutes=10, verbose=False):
"""
Code based on Sage code from FactHacks, a joint work by
Daniel J. Bernstein, Nadia Heninger, and Tanja Lange.
http://facthacks.cr.yp.to/
N - integer to attempt to factor using Fermat's Last Theorem
minutes - number of minutes to run the algorithm before giving up
verbose - (bool) Periodically show how many iterations have been
attempted
"""
from time import time
current_time = int(time())
end_time = current_time + int(minutes * 60)
def sqrt(n):
return gmpy.fsqrt(n)
def is_square(n):
sqrt_n = sqrt(n)
return sqrt_n.floor() == sqrt_n
if verbose:
print "Starting factorization..."
gmpy.set_minprec(4096)
N = gmpy.mpf(N)
if N <= 0: return [1,N]
if N % 2 == 0: return [2,N/2]
a = gmpy.mpf(gmpy.ceil(sqrt(N)))
count = 0
while not is_square(gmpy.mpz(a ** 2 - N)):
a += 1
count += 1
if verbose:
if (count % 1000000 == 0):
sys.stdout.write("\rCurrent iterations: %d" % count)
sys.stdout.flush()
if time() > end_time:
if verbose: print "\nTime expired, returning [1,N]"
return [1,N]
b = sqrt(gmpy.mpz(a ** 2 - N))
print "\nModulus factored!"
return [long(a - b), long(a + b)]
def fermat_factor(N, minutes=10, verbose=False):
"""
Code based on Sage code from FactHacks, a joint work by
Daniel J. Bernstein, Nadia Heninger, and Tanja Lange.
http://facthacks.cr.yp.to/
N - integer to attempt to factor using Fermat's Last Theorem
minutes - number of minutes to run the algorithm before giving up
verbose - (bool) Periodically show how many iterations have been
attempted
"""
from time import time
current_time = int(time())
end_time = current_time + int(minutes * 60)
def sqrt(n):
return gmpy.fsqrt(n)
def is_square(n):
sqrt_n = sqrt(n)
return sqrt_n.floor() == sqrt_n
if verbose:
print "Starting factorization..."
gmpy.set_minprec(4096)
N = gmpy.mpf(N)
if N <= 0: return [1,N]
if N % 2 == 0: return [2,N/2]
a = gmpy.mpf(gmpy.ceil(sqrt(N)))
count = 0
while not is_square(gmpy.mpz(a ** 2 - N)):
a += 1
count += 1
if verbose:
if (count % 1000000 == 0):
sys.stdout.write("\rCurrent iterations: %d" % count)
sys.stdout.flush()
if time() > end_time:
if verbose: print "\nTime expired, returning [1,N]"
return [1,N]
b = sqrt(gmpy.mpz(a ** 2 - N))
print "\nModulus factored!"
return [long(a - b), long(a + b)]
import gmpy
from gmpy import mpz
gmpy.set_minprec(700)
N1 = mpz(
'179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581'
)
N2 = mpz(
'648455842808071669662824265346772278726343720706976263060439070378797308618081116462714015276061417569195587321840254520655424906719892428844841839353281972988531310511738648965962582821502504990264452100885281673303711142296421027840289307657458645233683357077834689715838646088239640236866252211790085787877'
)
N = N1
def try_midpoint(N, midpoint):
delta = gmpy.sqrt(midpoint * midpoint - N)
p = midpoint - delta
q = midpoint + delta
if p * q == N:
return min(p, q)
else:
return False
def try_weightedavg(N, weightedavg2sq):
# gmpy.set_minprec(1000)
# print weightedavg2 - 2*gmpy.ceil(gmpy.fsqrt(6*N))
import pdb
# pdb.set_trace()
# radical = gmpy.fsqrt(weightedavg2sq - 24*N)
#!/usr/bin/python # Calculate digits of e # Marcus Kazmierczak, [email protected] # July 29th, 2004 # the formula # e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ... 1/N! # You should chop off the last five digits returned # they aren't necessarily accurate # precision library import gmpy # how many digits (roughly) N = 1000 gmpy.set_minprec(int(N*3.5+16)) e = gmpy.mpf('1.0') for n in range(1,N+3): e = gmpy.fdigits(gmpy.mpf(e) + (gmpy.mpf('1.0') / gmpy.fac(n))) print e
#!/usr/bin/env python
import gmpy
import sys
gmpy.set_minprec(20000)
f = sys.stdin
t = int(f.next())
for case in range(1, t + 1):
n = int(f.next())
s = 3 + gmpy.fsqrt(5)
res = long(s**n)
print "Case #%s: %s" % (case, str(res)[-3:].rjust(3, '0'))
def num_longest_period(length):
#Minimum accuracy to get the correct answer - 10000.
gmpy.set_minprec(10000)
#We search only prime numbers, because they have the longest periods
fact_lst = Factors(length).make_sieve()
return max(((period(1 / gmpy.mpf(i)), i) for i in fact_lst), key=itemgetter(0))
import gmpy
from gmpy import mpz
gmpy.set_minprec(700)
N1 = mpz('179769313486231590772930519078902473361797697894230657273430081157732675805505620686985379449212982959585501387537164015710139858647833778606925583497541085196591615128057575940752635007475935288710823649949940771895617054361149474865046711015101563940680527540071584560878577663743040086340742855278549092581')
N2 = mpz('648455842808071669662824265346772278726343720706976263060439070378797308618081116462714015276061417569195587321840254520655424906719892428844841839353281972988531310511738648965962582821502504990264452100885281673303711142296421027840289307657458645233683357077834689715838646088239640236866252211790085787877')
N = N1
def try_midpoint(N, midpoint):
delta = gmpy.sqrt(midpoint*midpoint - N)
p = midpoint - delta
q = midpoint + delta
if p*q == N:
return min(p,q)
else:
return False
def try_weightedavg(N, weightedavg2sq):
# gmpy.set_minprec(1000)
# print weightedavg2 - 2*gmpy.ceil(gmpy.fsqrt(6*N))
import pdb
# pdb.set_trace()
# radical = gmpy.fsqrt(weightedavg2sq - 24*N)
# numerators = [gmpy.fsqrt(weightedavg2sq) + x for x in [radical, -radical]]
# for n in numerators:
# p = gmpy.cdivmod(mpz(gmpy.fround(n)), 6)[0] # +/- 1?
# # q = gmpy.cdivmod(weightedavg2 - 3*p, 2)[0]
# if(gmpy.cdivmod(N,p)[1] == 0):
# print("found divisor")
# print p
import sys
from math import sqrt
from gmpy import mpf, mpz, set_minprec
def fib(n):
"""
Returns n-th fibonacci number using Binet's formula
"""
gr = (1 + mpf(5).sqrt()) / 2
return mpz((gr**n - (1-gr)**n)/mpf(5).sqrt())
def find_term(length):
'''
Find Fibonacci's term number for number that contains over lenght digits
'''
index = 0
num = mpz(0)
while True:
index += 1
num = fib(index)
if num.numdigits() >= length:
# help(numdigits) says it's can be off by one some times
return (index, index + 1)
set_minprec(1024)
print find_term(int(sys.argv[1]))
from flask import Flask, request, redirect
import subprocess
import gmpy
gmpy.set_minprec(200)
app = Flask(__name__)
@app.route('/')
def hello_world():
args = dict(x=0, y=0, wid=2, iters=10)
for k, v in request.args.iteritems():
args[k] = v
args["i2"] = int(int(args["iters"]) * 1.2)
return """
<html>
<body>
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.2/jquery.min.js"></script>
<script type="text/javascript">
$(function(){
$("#i").click(function(e){
var ox = e.offsetX;
var oy = e.offsetY;
console.log(ox, oy);
window.location = "/s/" + ox + "/" + oy + "" + window.location.search;
})
})
</script>
<dl>
<dt>X</dt><dd>%(x)s</dd>