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Check Machin-like formulas: Difference between revisions
Updated D entry
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This uses the module of the Arithmetic Rational Task.
{{trans|Python}}
<lang d>import std.stdio, std.regex, std.conv, std.string, std.
immutable 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)";▼
Pair[][] parseEquations(in string text) /*pure nothrow*/ {▼
▲alias Pair = Tuple!(int, Rational);
▲Pair[][] parseEquations(in string text) {
auto r = regex(r"\s*(?P<sign>[+-])?\s*(?:(?P<mul>\d+)\s*\*)?\s*" ~
r"arctan\((?P<num>\d+)/(?P<denom>\d+)\)
Pair[][] machins;
foreach (const line; text.splitLines
Pair[] formula;
foreach (/*const*/ part;
immutable
formula ~= Pair((part["sign"] == "-" ? -1 : 1) *
(mul.empty ? 1 : mul.to!int
Rational(num.to!int
denom.empty ? 1 : denom.to!int
}
machins ~= formula;
Line 87 ⟶ 67:
if (coef < 0)
return -tanEval(-coef, f);
/*const*/ auto a = tanEval(coef / 2, f)
return (a + b) / (1 - a * b);
}
Line 94 ⟶ 74:
if (xs.length == 1)
return tanEval(xs[0].tupleof);
/*const*/ auto a =
return (a + b) / (1 - a * b);
}
void main() {
▲ immutable equationText =
/*const*/ auto machins = parseEquations(equationText);▼
▲"pi/4 = arctan(1/2) + arctan(1/3)
foreach (machin, eqn; zip(machins, equationText.splitLines())) {▼
▲pi/4 = 2*arctan(1/3) + arctan(1/7)
/*const*/ auto ans = tans(machin);▼
▲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)";
writefln("%5s: %s", ans == 1 ? "OK" : "ERROR", eqn);
}
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