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/*
Copyright 2020...2021 Adam Lavrik <lavrik.adam@gmail.com>
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on
an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND,
either express or implied. See the License for the specific
language governing permissions and limitations under the License.
*/
package u64
// Fibonacci(index) returns Fibonacci sequence member with corresponding index:
// - Fibonacci(0) == 0
// - Fibonacci(1) == Fibonacci(2) == 1
// - Fibonacci(3) == 2
// - Fibonacci(4) == 3
// ...
// Result is calculated via matrix ((1, 1), (1, 0)) fast raising to `index` power.
func Fibonacci(index uint) T {
v0, v1 := T(0), T(1) // Result vector
for m00, m01, m10, m11 := v1, v1, v1, v0; index > 0; index >>= 1 { // `index` fast division by 2
if (index & 1) != 0 { // If index is odd
v0, v1 = v0 * m00 + v1 * m10, v0 * m01 + v1 * m11 // If power is odd then multiply result vector by matrix
}
m00, m01, m10, m11 = m00 * m00 + m01 * m10, m00 * m01 + m01 * m11, m10 * m00 + m11 * m10, m10 * m01 + m11 * m11 // Square the matrix
}
return v0
}
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