|
9 | 9 | //
|
10 | 10 | //===----------------------------------------------------------------------===//
|
11 | 11 |
|
12 |
| -extension BinaryInteger { |
| 12 | +/// The greatest common divisor of `a` and `b`. |
| 13 | +/// |
| 14 | +/// If both inputs are zero, the result is zero. If one input is zero, the |
| 15 | +/// result is the absolute value of the other input. |
| 16 | +/// |
| 17 | +/// [wiki]: https://en.wikipedia.org/wiki/Greatest_common_divisor |
| 18 | +@inlinable |
| 19 | +public func gcd<T: BinaryInteger>(_ a: T, _ b: T) -> T { |
| 20 | + var x = a.magnitude |
| 21 | + var y = b.magnitude |
13 | 22 |
|
14 |
| - /// The greatest common divisor of `a` and `b`. |
15 |
| - /// |
16 |
| - /// If both inputs are zero, the result is zero. If one input is zero, the |
17 |
| - /// result is the absolute value of the other input. |
18 |
| - /// |
19 |
| - /// [wiki]: https://en.wikipedia.org/wiki/Greatest_common_divisor |
20 |
| - @inlinable |
21 |
| - public static func gcd(_ a: Self, _ b: Self) -> Self { |
22 |
| - var x = a.magnitude |
23 |
| - var y = b.magnitude |
24 |
| - |
25 |
| - if x == 0 { return Self(y) } |
26 |
| - if y == 0 { return Self(x) } |
27 |
| - |
28 |
| - let xtz = x.trailingZeroBitCount |
29 |
| - let ytz = y.trailingZeroBitCount |
30 |
| - |
31 |
| - x >>= xtz |
32 |
| - y >>= ytz |
33 |
| - |
34 |
| - // The binary GCD algorithm |
35 |
| - // |
36 |
| - // At the top of the loop both x and y are odd. Each pass removes at least |
37 |
| - // one low-order bit from the larger of the two, so the number of iterations |
38 |
| - // is bounded by the sum of the bit-widths of the inputs. |
39 |
| - while x != 0 { |
40 |
| - if x < y { swap(&x, &y) } |
41 |
| - x -= y |
42 |
| - x >>= x.trailingZeroBitCount |
43 |
| - } |
44 |
| - |
45 |
| - return Self(y << min(xtz, ytz)) |
| 23 | + if x == 0 { return T(y) } |
| 24 | + if y == 0 { return T(x) } |
| 25 | + |
| 26 | + let xtz = x.trailingZeroBitCount |
| 27 | + let ytz = y.trailingZeroBitCount |
| 28 | + |
| 29 | + x >>= xtz |
| 30 | + y >>= ytz |
| 31 | + |
| 32 | + // The binary GCD algorithm |
| 33 | + // |
| 34 | + // At the top of the loop both x and y are odd. Each pass removes at least |
| 35 | + // one low-order bit from the larger of the two, so the number of iterations |
| 36 | + // is bounded by the sum of the bit-widths of the inputs. |
| 37 | + while x != 0 { |
| 38 | + if x < y { swap(&x, &y) } |
| 39 | + x -= y |
| 40 | + x >>= x.trailingZeroBitCount |
46 | 41 | }
|
| 42 | + |
| 43 | + return T(y << min(xtz, ytz)) |
47 | 44 | }
|
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