[英]Fastest way to get square root in float value
I am trying to find a fastest way to make square root of any float number in C++. I am using this type of function in a huge particles movement calculation like calculation distance between two particle, we need a square root etc. So If any suggestion it will be very helpful.我正在尝试找到一种最快的方法来计算 C++ 中任何浮点数的平方根。我正在使用这种类型的 function 进行巨大的粒子运动计算,例如计算两个粒子之间的距离,我们需要一个平方根等。所以如果有任何建议这将非常有帮助。 I have tried and below is my code我试过了,下面是我的代码
#include <math.h>
#include <iostream>
#include <chrono>
using namespace std;
using namespace std::chrono;
#define CHECK_RANGE 100
inline float msqrt(float a)
{
int i;
for (i = 0;i * i <= a;i++);
float lb = i - 1; //lower bound
if (lb * lb == a)
return lb;
float ub = lb + 1; // upper bound
float pub = ub; // previous upper bound
for (int j = 0;j <= 20;j++)
{
float ub2 = ub * ub;
if (ub2 > a)
{
pub = ub;
ub = (lb + ub) / 2; // mid value of lower and upper bound
}
else
{
lb = ub;
ub = pub;
}
}
return ub;
}
void check_msqrt()
{
for (size_t i = 0; i < CHECK_RANGE; i++)
{
msqrt(i);
}
}
void check_sqrt()
{
for (size_t i = 0; i < CHECK_RANGE; i++)
{
sqrt(i);
}
}
int main()
{
auto start1 = high_resolution_clock::now();
check_msqrt();
auto stop1 = high_resolution_clock::now();
auto duration1 = duration_cast<microseconds>(stop1 - start1);
cout << "Time for check_msqrt = " << duration1.count() << " micro secs\n";
auto start2 = high_resolution_clock::now();
check_sqrt();
auto stop2 = high_resolution_clock::now();
auto duration2 = duration_cast<microseconds>(stop2 - start2);
cout << "Time for check_sqrt = " << duration2.count() << " micro secs";
//cout << msqrt(3);
return 0;
}
output of above code showing the implemented method 4 times more slow than sqrt of math.h file.上面代码的 output 显示实现的方法比 math.h 文件的 sqrt 慢 4 倍。 I need faster than math.h version.我需要比 math.h 更快的版本。
In short, I do not think it is possible to implement something generally faster than the standard library version of sqrt
.简而言之,我认为不可能比sqrt
的标准库版本更快地实现某些东西。
Performance is a very important parameter when implementing standard library functions and it is fair to assume that such a commonly used function as sqrt
is optimized as much as possible.在实现标准库函数时,性能是一个非常重要的参数,可以公平地假设像sqrt
这样常用的 function 是尽可能优化的。
Beating the standard library function would require a special case, such as:击败标准库 function 需要特殊情况,例如:
Here's another alternative to binary search.这是二进制搜索的另一种选择。 It may not be as fast as std::sqrt
, haven't tested it.它可能不如std::sqrt
快,还没有测试过。 But it will definitely be faster than your binary search.但它肯定会比你的二进制搜索更快。
auto
Sqrt(float x)
{
using F = decltype(x);
if (x == 0 || x == INFINITY || isnan(x))
return x;
if (x < 0)
return F{NAN};
int e;
x = std::frexp(x, &e);
if (e % 2 != 0)
{
++e;
x /= 2;
}
auto y = (F{-160}/567*x + F{2'848}/2'835)*x + F{155}/567;
y = (y + x/y)/2;
y = (y + x/y)/2;
return std::ldexp(y, e/2);
}
After getting +/-0, nan, inf, and negatives out of the way, it works by decomposing the float
into a mantissa in the range of [ 1 / 4 , 1) times 2 e where e
is an even integer. The answer is then sqrt(mantissa)* 2 e / 2 .在排除了 +/-0、nan、inf 和负数之后,它通过将float
分解为 [ 1 / 4 , 1) 乘以 2 e范围内的尾数来工作,其中e
是偶数 integer。答案然后是 sqrt(mantissa)* 2 e / 2 。
Finding the sqrt of the mantissa can be guessed at with a least squares quadratic curve fit in the range [ 1 / 4 , 1].可以使用范围 [ 1 / 4 , 1] 内的最小二乘二次曲线来猜测找到尾数的平方根。 Then that good guess is refined by two iterations of Newton–Raphson.然后这个好的猜测通过牛顿-拉夫森的两次迭代得到改进。 This will get you within 1 ulp of the correctly rounded result.这将使您在正确舍入结果的 1 ulp范围内。 A good std::sqrt
will typically get that last bit correct.好的std::sqrt
通常会使最后一位正确。
I have also tried with the algorithm mention in https://en.wikipedia.org/wiki/Fast_inverse_square_root , but not found desired result, please check我也尝试过https://en.wikipedia.org/wiki/Fast_inverse_square_root中提到的算法,但没有找到想要的结果,请检查
#include <math.h>
#include <iostream>
#include <chrono>
#include <bit>
#include <limits>
#include <cstdint>
using namespace std;
using namespace std::chrono;
#define CHECK_RANGE 10000
inline float msqrt(float a)
{
int i;
for (i = 0;i * i <= a;i++);
float lb = i - 1; //lower bound
if (lb * lb == a)
return lb;
float ub = lb + 1; // upper bound
float pub = ub; // previous upper bound
for (int j = 0;j <= 20;j++)
{
float ub2 = ub * ub;
if (ub2 > a)
{
pub = ub;
ub = (lb + ub) / 2; // mid value of lower and upper bound
}
else
{
lb = ub;
ub = pub;
}
}
return ub;
}
/* mentioned here -> https://en.wikipedia.org/wiki/Fast_inverse_square_root */
inline float Q_sqrt(float number)
{
union Conv {
float f;
uint32_t i;
};
Conv conv;
conv.f= number;
conv.i = 0x5f3759df - (conv.i >> 1);
conv.f *= 1.5F - (number * 0.5F * conv.f * conv.f);
return 1/conv.f;
}
void check_Qsqrt()
{
for (size_t i = 0; i < CHECK_RANGE; i++)
{
Q_sqrt(i);
}
}
void check_msqrt()
{
for (size_t i = 0; i < CHECK_RANGE; i++)
{
msqrt(i);
}
}
void check_sqrt()
{
for (size_t i = 0; i < CHECK_RANGE; i++)
{
sqrt(i);
}
}
int main()
{
auto start1 = high_resolution_clock::now();
check_msqrt();
auto stop1 = high_resolution_clock::now();
auto duration1 = duration_cast<microseconds>(stop1 - start1);
cout << "Time for check_msqrt = " << duration1.count() << " micro secs\n";
auto start2 = high_resolution_clock::now();
check_sqrt();
auto stop2 = high_resolution_clock::now();
auto duration2 = duration_cast<microseconds>(stop2 - start2);
cout << "Time for check_sqrt = " << duration2.count() << " micro secs\n";
auto start3 = high_resolution_clock::now();
check_Qsqrt();
auto stop3 = high_resolution_clock::now();
auto duration3 = duration_cast<microseconds>(stop3 - start3);
cout << "Time for check_Qsqrt = " << duration3.count() << " micro secs\n";
//cout << Q_sqrt(3);
//cout << sqrt(3);
//cout << msqrt(3);
return 0;
}
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