71 lines
2.7 KiB
D
71 lines
2.7 KiB
D
import std.stdio, std.regex, std.conv, std.string, std.range,
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arithmetic_rational;
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struct Pair { int x; Rational r; }
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Pair[][] parseEquations(in string text) /*pure nothrow*/ {
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auto r = regex(r"\s*(?P<sign>[+-])?\s*(?:(?P<mul>\d+)\s*\*)?\s*" ~
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r"arctan\((?P<num>\d+)/(?P<denom>\d+)\)");
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Pair[][] machins;
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foreach (const line; text.splitLines) {
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Pair[] formula;
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foreach (part; line.split("=")[1].matchAll(r)) {
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immutable mul = part["mul"],
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num = part["num"],
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denom = part["denom"];
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formula ~= Pair((part["sign"] == "-" ? -1 : 1) *
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(mul.empty ? 1 : mul.to!int),
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Rational(num.to!int,
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denom.empty ? 1 : denom.to!int));
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}
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machins ~= formula;
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}
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return machins;
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}
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Rational tans(in Pair[] xs) pure nothrow {
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static Rational tanEval(in int coef, in Rational f)
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pure nothrow {
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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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immutable a = tanEval(coef / 2, f),
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b = tanEval(coef - coef / 2, f);
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return (a + b) / (1 - a * b);
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}
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if (xs.length == 1)
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return tanEval(xs[0].tupleof);
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immutable a = xs[0 .. $ / 2].tans,
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b = xs[$ / 2 .. $].tans;
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return (a + b) / (1 - a * b);
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}
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void main() {
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immutable 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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const machins = equationText.parseEquations;
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foreach (const machin, const eqn; machins.zip(equationText.splitLines)) {
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immutable ans = machin.tans;
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writefln("%5s: %s", ans == 1 ? "OK" : "ERROR", eqn);
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}
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}
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