example of zero-cost abstraction using the fixed_point library

godbolt_average.cpp

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

// Here's how to use the fixed_point library on Godbolt.org.
// Normally, you'd just add `#include <sg14/fixed_point>`.
#define SG14_GODBOLT_ORG
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/config.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/config.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/cstdint>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/limits>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/type_traits>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/common.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_type.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_arithmetic.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_make.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_named.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_common_type.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_operators.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/bits/fixed_point_extras.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/auxiliary/elastic_integer.h>
#include <https://raw.githubusercontent.com/johnmcfarlane/fixed_point/develop/include/sg14/auxiliary/elastic.h>

using namespace sg14;

// average two nunbers using 15:16 fixed-point arithmetic
// without using a fixed-point library
float average_int(float input1, float input2) {
    // user must scale values by the correct amount
    auto fixed1 = static_cast<int32_t>(input1 * 65536.f);
    auto fixed2 = static_cast<int32_t>(input2 * 65536.f);

    // user must remember to widen the result to avoid overflow
    auto sum = int64_t{fixed1} + fixed2;
  
  	// at least division is simple
    auto avg = sum / 2;

    // user must return value to the original scale
    return avg / 65536.f;
}

// the same function using sg14::elastic_integer
float average_elastic_integer(float input1, float input2) {
    auto fixed1 = elastic_integer<31>{input1 * 65536.f};
    auto fixed2 = elastic_integer<31>{input2 * 65536.f};

    // elastic_integer automatically widens the result
    auto sum = fixed1 + fixed2;
  
  	// showing off: to store 2, you only need a 2-bit integer
    auto avg = sum / elastic_integer<2>{2};

    // but the user must still do all the scaling themselves
    return static_cast<float>(avg) / 65536.f;
}

// the same function using sg14::fixed_point
float average_fixed_point(float input1, float input2) {
    // fixed_point handles scaling
    auto fixed1 = fixed_point<int32_t, -16>{input1};
    auto fixed2 = fixed_point<int32_t, -16>{input2};

    // but it uses int under the hood; user must still widen
    auto sum = fixed_point<int64_t, -16>{fixed1} + fixed2;
  
    // specal function 'divide' is used when we 
    // want to perform integer division on a real number
    auto avg = divide(sum, 2);

    return static_cast<float>(avg);
}

// finally, the composition of fixed_point and elastic_integer
float average_elastic(float input1, float input2) {
    // alias to fixed_point<elastic_integer<31, int>, -16>
    auto elastic1 = elastic<15, 16>{input1};
    auto elastic2 = elastic<15, 16>{input2};

    // concise, safe and zero-cost!
    auto sum = elastic1 + elastic2;
    auto avg = sum / elastic<2>{2};

    return static_cast<float>(avg);
}

Hmm... this doesn't work for me, even after fixing line 20 to include elastic_fixed_point.h instead of elastic.h: https://godbolt.org/g/N04hY7