72 lines
2.5 KiB
Python
72 lines
2.5 KiB
Python
import re
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from fractions import Fraction
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from pprint import pprint as pp
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equationtext = '''\
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pi/4 = arctan(1/2) + arctan(1/3)
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pi/4 = 2*arctan(1/3) + arctan(1/7)
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pi/4 = 4*arctan(1/5) - arctan(1/239)
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pi/4 = 5*arctan(1/7) + 2*arctan(3/79)
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pi/4 = 5*arctan(29/278) + 7*arctan(3/79)
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pi/4 = arctan(1/2) + arctan(1/5) + arctan(1/8)
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pi/4 = 4*arctan(1/5) - arctan(1/70) + arctan(1/99)
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pi/4 = 5*arctan(1/7) + 4*arctan(1/53) + 2*arctan(1/4443)
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pi/4 = 6*arctan(1/8) + 2*arctan(1/57) + arctan(1/239)
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pi/4 = 8*arctan(1/10) - arctan(1/239) - 4*arctan(1/515)
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pi/4 = 12*arctan(1/18) + 8*arctan(1/57) - 5*arctan(1/239)
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pi/4 = 16*arctan(1/21) + 3*arctan(1/239) + 4*arctan(3/1042)
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pi/4 = 22*arctan(1/28) + 2*arctan(1/443) - 5*arctan(1/1393) - 10*arctan(1/11018)
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pi/4 = 22*arctan(1/38) + 17*arctan(7/601) + 10*arctan(7/8149)
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pi/4 = 44*arctan(1/57) + 7*arctan(1/239) - 12*arctan(1/682) + 24*arctan(1/12943)
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pi/4 = 88*arctan(1/172) + 51*arctan(1/239) + 32*arctan(1/682) + 44*arctan(1/5357) + 68*arctan(1/12943)
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pi/4 = 88*arctan(1/172) + 51*arctan(1/239) + 32*arctan(1/682) + 44*arctan(1/5357) + 68*arctan(1/12944)
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'''
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def parse_eqn(equationtext=equationtext):
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eqn_re = re.compile(r"""(?mx)
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(?P<lhs> ^ \s* pi/4 \s* = \s*)? # LHS of equation
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(?: # RHS
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\s* (?P<sign> [+-])? \s*
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(?: (?P<mult> \d+) \s* \*)?
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\s* arctan\( (?P<numer> \d+) / (?P<denom> \d+)
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)""")
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found = eqn_re.findall(equationtext)
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machins, part = [], []
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for lhs, sign, mult, numer, denom in eqn_re.findall(equationtext):
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if lhs and part:
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machins.append(part)
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part = []
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part.append( ( (-1 if sign == '-' else 1) * ( int(mult) if mult else 1),
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Fraction(int(numer), (int(denom) if denom else 1)) ) )
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machins.append(part)
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return machins
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def tans(xs):
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xslen = len(xs)
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if xslen == 1:
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return tanEval(*xs[0])
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aa, bb = xs[:xslen//2], xs[xslen//2:]
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a, b = tans(aa), tans(bb)
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return (a + b) / (1 - a * b)
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def tanEval(coef, f):
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if coef == 1:
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return f
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if coef < 0:
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return -tanEval(-coef, f)
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ca = coef // 2
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cb = coef - ca
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a, b = tanEval(ca, f), tanEval(cb, f)
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return (a + b) / (1 - a * b)
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if __name__ == '__main__':
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machins = parse_eqn()
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#pp(machins, width=160)
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for machin, eqn in zip(machins, equationtext.split('\n')):
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ans = tans(machin)
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print('%5s: %s' % ( ('OK' if ans == 1 else 'ERROR'), eqn))
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