Fixed-point multiplication and division

fixed_point_mul_div.c

// http://theramblingness.com

#include <stdio.h>
#include <stdint.h>

#define Qn 15    // Q-format

// These types should be defined according to CPU bitness
#define FXPLONG     int64_t
#define FXPSHORT    int32_t

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

    double f_op1 = 0.654321;
    double f_op2 = 0.123456;
    double f_mul_res = f_op2*f_op2;
    double f_div_res = f_op1/f_op2;

    printf("f_op1:     %f\n", f_op1);
    printf("f_op2:     %f\n", f_op2);
    printf("f_mul_res: %f\n", f_mul_res);
    printf("f_div_res: %f\n", f_div_res);
    printf("Qn:        %u\n", Qn);
    printf("scaler:    %u\n", scaler);

    printf(" -- Fixed-point multiplication: (op2)^2\n");

    op2 = (FXPSHORT)(f_op2*(double)scaler);
    op1 = op2;
    printf("op1:       %d\n", op1);
    printf("op2:       %d\n", op2);

    // Multiplication
    // (the cast may also be applied to each operand individually)
    tmp = (FXPLONG)op1*(FXPLONG)op2;
    // Rounding
    tmp = tmp + (FXPLONG)(1 << Qn);
    // Truncation
    tmp = tmp >> Qn;
    // Discard the upper-half bytes of tmp to get the final result
    res = (FXPSHORT) tmp;

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

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

    printf(" -- Fixed-point division: op1/op2\n");

    op1 = (FXPSHORT)(f_op1*(double)scaler);
    op2 = (FXPSHORT)(f_op2*(double)scaler);

    printf("op1:       %08X %d (%f)\n", op1, op1, f_op1);
    printf("op2:       %08X %d (%f)\n", op2, op2, f_op2);

    // Convert dividend to Q(2*n) format
    tmp = ((FXPLONG)op1 << Qn);
    // Round by summing half the divisor
    tmp += op2 >> 1;
    // Division
    tmp /= (FXPLONG)(op2);

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

    printf("res:       %08X %d (%f)\n", res, res, res_f);
    printf("err:       %f\n", res_f - f_div_res);

    return 0;
}