example of zero-cost abstraction using the fixed_point library

godbold_square.cpp

// Signed 15:16 Fixed-Point Square Function Using sg14::elastic

#include <https://gist.githubusercontent.com/johnmcfarlane/23b8bc5fefb77d482306c5bc837b5df1/raw/ed6cdfc3de42ae3c140bbbdd0ce5b8bc131d1f02/fixed_point.h>

using namespace sg14;

// square a nunber using 15:16 fixed-point arithmetic
// without using a fixed-point library
float square_int(float input) {
    // user must scale values by the correct amount
	auto fixed = static_cast<int32_t>(input * 65536.f);
  
    // user must remember to widen the result to avoid overflow
	auto prod = int64_t{fixed} * fixed;
  
    // user must remember that the scale also was squared
    return prod / 4294967296.f;
}

// the same function using sg14::elastic_integer
float square_elastic_integer(float input) {
	auto fixed = elastic_integer<31>{input * 65536.f};

    // elastic_integer automatically widens the result
	auto prod = fixed * fixed;

    // but the user must still do all the scaling themselves
	return static_cast<float>(prod) / 4294967296.f;
}

// the same function using sg14::fixed_point
float square_fixed_point(float input) {
    // fixed_point handles scaling
	auto fixed = fixed_point<int32_t, -16>{input};

    // but it uses int under the hood; user must still widen
	auto prod = fixed_point<int64_t, -16>{fixed} * fixed;

	return static_cast<float>(prod);
}

// finally, the composition of fixed_point and elastic_integer
float square_elastic(float input) {
  	// alias to fixed_point<elastic_integer<31, int>, -16>
	auto fixed = elastic_fixed_point<15, 16>{input};

    // concise, safe and zero-cost!
	auto prod = fixed * fixed;

	return static_cast<float>(prod);
}