Fixed-Point Multiplication

fixed_point_mult.c

// http://theramblingness.com
#include <stdio.h>
#include <stdint.h>

#define Qn 31

int main()
{
    // Variables
    uint32_t scaler = (uint32_t)(1<<Qn);
    int64_t tmp = 0;
    int32_t op1 = 0, op2 = 0;
    int32_t res;
    double res_f;

    double f_val = 0.123456;
    double f_res = f_val*f_val;

    op1 = (int32_t)(f_val*(double)scaler);
    op2 = op1;

    printf("f_val:  %f\n", f_val);
    printf("f_res:  %f\n", f_res);
    printf("Qn:     %u\n", Qn);
    printf("scaler: %u\n", scaler);
    printf("op:     %d\n", op1);

    printf("Fixed-point multiplication: op^2\n");

    // Multiplication
    tmp = (int64_t)op1*(int64_t)op2;

    // Rounding
    tmp = tmp + (int64_t)(1 << Qn);

    // Truncation
    tmp = tmp >> Qn;

    // Discard the upper-half bytes of tmp to get the final result
    res = (int32_t) tmp;

    res_f = (double)res/(double)scaler;

    printf("res:    %d (%f)\n", res, res_f);
    printf("err:    %f\n", res_f - f_res);

    return 0;
}