Initial data commit

Task/Check-Machin-like-formulas/Python/check-machin-like-formulas.py

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