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Insane Decimal Math -- 624 digits of Phi
""" Really exercise the Decimal Math processor.
Calculates two weird identities of the irrational number Phi using an insane number of digits.
Phi**2 + Phi**-2 == 3
8 * Phi**2 - Phi**6 == 3
"""
from __future__ import print_function
digits = ("1.61803398874989484820458683436563811772030917980576286213544862270526046281890"
"244970720720418939113748475408807538689175212663386222353693179318006076672635"
"443338908659593958290563832266131992829026788067520876689250171169620703222104"
"321626954862629631361443814975870122034080588795445474924618569536486444924104"
"432077134494704956584678850987433944221254487706647809158846074998871240076521"
"705751797883416625624940758906970400028121042762177111777805315317141011704666"
"599146697987317613560067087480710131795236894275219484353056783002287856997829"
"778347845878228911097625003026961561700250464338243776486102838312683303724292")
import decimal
def compress_print(d):
s = str(d)
reps = 0
digit = s[2]
i = 3
while s[i] == digit:
i += 1
reps += 1
return '{} and {} more "{}"s then {}'.format(s[:3], reps, digit, s[i:])
with decimal.localcontext() as context:
context.prec = len(digits)-1
phi = decimal.Decimal(digits)
id1 = phi**2 + phi**-2 # Identity 1 (== 3)
id2 = 8 * phi**2 - phi**6 # Identity 2 (== 3)
print('Phi is {} digits long, {}...{}'.format(len(digits) - 1, digits[:5], digits[-5:]))
print('The 1st identity is', compress_print(id1))
print('The 2nd identity is', compress_print(id2))
print('Equal?', id1 == id2)
print('The difference is=', id2 - id1)
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