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from gmpy2 import mpz
def halley(digits):
BASE = mpz(2)**int(digits/0.301)#mpz(10)**digits
m, n = mpz(9369319), mpz(6625109)
x = (m * BASE) // n
for _ in range(int(mpz(digits).bit_length() // 2 + 2)):
x_sq = (x * x) // BASE
numerator = 2 * (2 * BASE - x_sq) # 2*(2 - x^2)
denominator = 3 * x_sq + 2 * BASE # 3x^2 + 2
correction = (BASE + (numerator * BASE // denominator) )
x = (x * correction) // BASE
return (x*mpz(10)**digits)//BASE
def halley2(digits):
bin_shift = int(digits / 0.301)
BASE = mpz(2)**bin_shift
DEC_BASE = mpz(10)**digits
m, n = mpz(9369319), mpz(6625109)
x = (m * BASE) // n
for _ in range(int(mpz(digits).bit_length() // 2 + 2)):
x_sq = (x * x) >> bin_shift
numerator = ((BASE << 1) - x_sq)<<1 # 2*(2 - x^2)
denominator = 3 * x_sq + (BASE << 1) # 3x^2 + 2
correction = BASE + (numerator * BASE) // denominator
x = (x * correction) >> bin_shift
return (x * DEC_BASE) >> bin_shifthalley(1000000) runs as fast as halley2(1000000) in x64 Linux, but it runs much slower than halley2 in arm Linux
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