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improve documentation for fast_power

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This commit is contained in:
Krishna Vedala
2020-05-27 15:14:39 -04:00
parent d262065492
commit a436cd7a1b
1 changed files with 15 additions and 11 deletions
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26
math/fast_power.cpp
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@@ -1,15 +1,16 @@
/**
* @file
Program that computes \f$a^b\f$ in \f$O(logN)\f$ time.
It is based on formula that:
1. if \f$b\f$ is even: \f$a^b = a^\frac{b}{2} \cdot a^\frac{b}{2} =
{a^\frac{b}{2}}^2\f$
2. if \f$b\f$ is odd: \f$a^b = a^\frac{b-1}{2} \cdot
a^\frac{b-1}{2} \cdot a = {a^\frac{b-1}{2}}^2 \cdot a\f$
We can compute \f$a^b\f$
recursively using above algorithm.
*/
* @brief Faster computation for \f$a^b\f$
*
* Program that computes \f$a^b\f$ in \f$O(logN)\f$ time.
* It is based on formula that:
* 1. if \f$b\f$ is even:
* \f$a^b = a^\frac{b}{2} \cdot a^\frac{b}{2} = {a^\frac{b}{2}}^2\f$
* 2. if \f$b\f$ is odd: \f$a^b = a^\frac{b-1}{2}
* \cdot a^\frac{b-1}{2} \cdot a = {a^\frac{b-1}{2}}^2 \cdot a\f$
*
* We can compute \f$a^b\f$ recursively using above algorithm.
*/
#include <cassert>
#include <cmath>
@@ -41,7 +42,7 @@ double fast_power_recursive(T a, T b) {
/**
Same algorithm with little different formula.
It still calculates in O(logN)
It still calculates in \f$O(\log N)\f$
*/
template <typename T>
double fast_power_linear(T a, T b) {
@@ -57,6 +58,9 @@ double fast_power_linear(T a, T b) {
return result;
}
/**
* Main function
*/
int main() {
std::srand(std::time(nullptr));
std::ios_base::sync_with_stdio(false);