Check Machin-like formulas: Difference between revisions
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You can store the equations in any convenient data structure, but for extra credit parse them from human-readable [[Check_Machin-like_formulas/text_equations|text input]]. |
You can store the equations in any convenient data structure, but for extra credit parse them from human-readable [[Check_Machin-like_formulas/text_equations|text input]]. |
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=={{header|Go}}== |
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{{trans|Python}} |
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<lang go>package main |
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import ( |
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"fmt" |
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"math/big" |
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) |
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type mTerm struct { |
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a, n, d int64 |
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} |
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var testCases = [][]mTerm{ |
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{{1, 1, 2}, {1, 1, 3}}, |
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{{2, 1, 3}, {1, 1, 7}}, |
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{{4, 1, 5}, {-1, 1, 239}}, |
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{{5, 1, 7}, {2, 3, 79}}, |
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{{1, 1, 2}, {1, 1, 5}, {1, 1, 8}}, |
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{{4, 1, 5}, {-1, 1, 70}, {1, 1, 99}}, |
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{{5, 1, 7}, {4, 1, 53}, {2, 1, 4443}}, |
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{{6, 1, 8}, {2, 1, 57}, {1, 1, 239}}, |
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{{8, 1, 10}, {-1, 1, 239}, {-4, 1, 515}}, |
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{{12, 1, 18}, {8, 1, 57}, {-5, 1, 239}}, |
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{{16, 1, 21}, {3, 1, 239}, {4, 3, 1042}}, |
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{{22, 1, 28}, {2, 1, 443}, {-5, 1, 1393}, {-10, 1, 11018}}, |
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{{22, 1, 38}, {17, 7, 601}, {10, 7, 8149}}, |
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{{44, 1, 57}, {7, 1, 239}, {-12, 1, 682}, {24, 1, 12943}}, |
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{{88, 1, 172}, {51, 1, 239}, {32, 1, 682}, {44, 1, 5357}, {68, 1, 12943}}, |
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{{88, 1, 172}, {51, 1, 239}, {32, 1, 682}, {44, 1, 5357}, {68, 1, 12944}}, |
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} |
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func main() { |
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for _, m := range testCases { |
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fmt.Printf("tan %v = %v\n", m, tans(m)) |
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} |
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} |
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var one = big.NewRat(1, 1) |
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func tans(m []mTerm) *big.Rat { |
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if len(m) == 1 { |
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return tanEval(m[0].a, big.NewRat(m[0].n, m[0].d)) |
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} |
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half := len(m) / 2 |
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a := tans(m[:half]) |
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b := tans(m[half:]) |
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r := new(big.Rat) |
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return r.Quo(new(big.Rat).Add(a, b), r.Sub(one, r.Mul(a, b))) |
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} |
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func tanEval(coef int64, f *big.Rat) *big.Rat { |
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if coef == 1 { |
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return f |
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} |
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if coef < 0 { |
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r := tanEval(-coef, f) |
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return r.Neg(r) |
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} |
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ca := coef / 2 |
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cb := coef - ca |
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a := tanEval(ca, f) |
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b := tanEval(cb, f) |
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r := new(big.Rat) |
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return r.Quo(new(big.Rat).Add(a, b), r.Sub(one, r.Mul(a, b))) |
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}</lang> |
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{{out}} |
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Last line edited to show only most significant digits of fraction which is near, but not exactly equal to 1. |
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<pre> |
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tan [{1 1 2} {1 1 3}] = 1/1 |
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tan [{2 1 3} {1 1 7}] = 1/1 |
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tan [{4 1 5} {-1 1 239}] = 1/1 |
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tan [{5 1 7} {2 3 79}] = 1/1 |
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tan [{1 1 2} {1 1 5} {1 1 8}] = 1/1 |
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tan [{4 1 5} {-1 1 70} {1 1 99}] = 1/1 |
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tan [{5 1 7} {4 1 53} {2 1 4443}] = 1/1 |
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tan [{6 1 8} {2 1 57} {1 1 239}] = 1/1 |
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tan [{8 1 10} {-1 1 239} {-4 1 515}] = 1/1 |
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tan [{12 1 18} {8 1 57} {-5 1 239}] = 1/1 |
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tan [{16 1 21} {3 1 239} {4 3 1042}] = 1/1 |
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tan [{22 1 28} {2 1 443} {-5 1 1393} {-10 1 11018}] = 1/1 |
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tan [{22 1 38} {17 7 601} {10 7 8149}] = 1/1 |
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tan [{44 1 57} {7 1 239} {-12 1 682} {24 1 12943}] = 1/1 |
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tan [{88 1 172} {51 1 239} {32 1 682} {44 1 5357} {68 1 12943}] = 1/1 |
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tan [{88 1 172} {51 1 239} {32 1 682} {44 1 5357} {68 1 12944}] = |
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100928801... / |
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100928883... |
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</pre> |
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=={{header|Haskell}}== |
=={{header|Haskell}}== |
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