"""
This script calculates solutions to some of the problems from the
"Many Digits" competition:
http://www.cs.ru.nl/~milad/manydigits/problems.php

Run with:

    python manydigits.py

"""
from mpmath import *
from mpmath.libmp import to_fixed, bin_to_radix

dps = 100
mp.dps = dps + 10

def pr(x):
    """Return the first dps digits after the decimal point"""
    x = x._mpf_
    p = int(dps*3.33 + 10)
    t = to_fixed(x, p)
    d = bin_to_radix(t, p, 10, dps)
    s = str(d).zfill(dps)[-dps:]
    return s[:dps//2] + "\n" + s[dps//2:]

print("""
This script prints answers to a selection of the "Many Digits"
competition problems: http://www.cs.ru.nl/~milad/manydigits/problems.php

The output for each problem is the first 100 digits after the
decimal point in the result.
""")

print("C01: sin(tan(cos(1)))")
print(pr(sin(tan(cos(1)))))
print()

print("C02: sqrt(e/pi)")
print(pr(sqrt(e/pi)))
print()

print("C03: sin((e+1)^3)")
print(pr(sin((e+1)**3)))
print()

print("C04: exp(pi*sqrt(2011))")
mp.dps += 65
print(pr(exp(pi*sqrt(2011))))
mp.dps -= 65
print()

print("C05: exp(exp(exp(1/2)))")
print(pr(exp(exp(exp(0.5)))))
print()

print("C06: arctanh(1-arctanh(1-arctanh(1-arctanh(1/pi))))")
print(pr(atanh(1-atanh(1-atanh(1-atanh(1/pi))))))
print()

print("C07: pi^1000")
mp.dps += 505
print(pr(pi**1000))
mp.dps -= 505
print()

print("C08: sin(6^(6^6))")
print(pr(sin(6**(6**6))))
print()

print("C09: sin(10*arctan(tanh(pi*(2011^(1/2))/3)))")
mp.dps += 150
print(pr(sin(10*atan(tanh(pi*sqrt(2011)/3)))))
mp.dps -= 150
print()

print("C10: (7+2^(1/5)-5*(8^(1/5)))^(1/3) + 4^(1/5)-2^(1/5)")
a = mpf(1)/5
print(pr(((7 + 2**a - 5*(8**a))**(mpf(1)/3) + 4**a - 2**a)))
print()

print("C11: tan(2^(1/2))+arctanh(sin(1))")
print(pr((tan(sqrt(2)) + atanh(sin(1)))))
print()

print("C12: arcsin(1/e^2) + arcsinh(e^2)")
print(pr(asin(1/exp(2)) + asinh(exp(2))))
print()

print("C17: S= -4*Zeta(2) - 2*Zeta(3) + 4*Zeta(2)*Zeta(3) + 2*Zeta(5)")
print(pr(-4*zeta(2) - 2*zeta(3) + 4*zeta(2)*zeta(3) + 2*zeta(5)))
print()

print("C18: Catalan G = Sum{i=0}{\infty}(-1)^i/(2i+1)^2")
print(pr(catalan))
print()

print("C21: Equation exp(cos(x)) = x")
print(pr(findroot(lambda x: exp(cos(x))-x, 1)))
print()

print("C22: J = integral(sin(sin(sin(x)))), x=0..1")
print(pr(quadts(lambda x: sin(sin(sin(x))), [0, 1])))
print()
