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blog:2024-04-01_share_q_format_number_in_c



2024-04-01 Share: Q Format Number in C

  • Here is an article that describes the Q format number in C

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  • Q15
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    #include <stdio.h>
    #include <math.h>
    /*
    Q表示    S表示    十進制數表示範圍
    Q15    S0.15    -1≤x≤0.9999695
    Q14    S1.14    -2≤x≤1.9999390
    Q13    S2.13    -4≤x≤3.9998779
    Q12    S3.12    -8≤x≤7.9997559
    Q11    S4.11    -16≤x≤15.9995117
    Q10    S5.10    -32≤x≤31.9990234
    Q9    S6.9    -64≤x≤63.9980469
    Q8    S7.8    -128≤x≤127.9960938
    Q7    S8.7    -256≤x≤255.9921875
    Q6    S9.6    -512≤x≤511.9804375
    Q5    S10.5    -1024≤x≤1023.96875
    Q4    S11.4    -2048≤x≤2047.9375
    Q3    S12.3    -4096≤x≤4095.875
    Q2    S13.2    -8192≤x≤8191.75
    Q1    S14.1    -16384≤x≤16383.5
    Q0    S15.0    -32768≤x≤32767
    */
     
    #define Q14(X) ((X < 0.0) ? (int)(16384*(X) - 0.5) : (int)(16384*(X) + 0.5))
    #define Q0(x) ( (x)<0 ? ((int) (1.0*(x) - 0.5)) : (min(32767,(int) ((32767.0/32768.0)*(x) + 0.5))))
    #define Q1(x) ( (x)<0 ? ((int) (2.0*(x) - 0.5)) : (min(32767,(int) ((32767.0/16384.0)*(x) + 0.5))))
    #define Q2(x) ( (x)<0 ? ((int) (4.0*(x) - 0.5)) : (min(32767,(int) ((32767.0/8192.0)*(x) + 0.5))))
    #define Q13(x) ( (x)<0 ? ((int) (8192.0*(x) - 0.5)) : (min(32767,(int) ((32767.0/4.0)*(x) + 0.5))))
    // #define Q14(x) ( (x)<0 ? ((int) (16384.0*(x) - 0.5)) : (min(32767,(int) ((32767.0/2.0)*(x) + 0.5))))
    #define Q15(x) ( ((x)<(0.0)) ? ((int) (32768.0*(x) - 0.5)) : (min(32767,(int) (32767.0*(x) + 0.5))))
     
    #define min(a,b)  (((a) < (b)) ? (a) : (b))
     
    double power(double base, int n)
    {
        int i;
        double pow = 1.0;
     
        for (i = 1; i <= n; i++) {
            pow = pow * base;
        }
     
        return pow;
    }
     
    double QFormatIntegerToFloat(const int x,
                                 const int n)
    {
        return (((double)x) / ((double)(1 << n)));
    }
     
    short FloatToQFormatInteger(const double x,
                                const int m,
                                const int n)
    {
        return (((x) < (0.0)) ? ((int)(power(2, n) * (x) - 0.5)) : (min(32767, (int)((32767.0 / (power(2, m))) * (x) + 0.5))));
    }
     
    int main(int argc, char* argv[])
    {
        // Q14    S1.14    -2≤x≤1.9999390
        short s = FloatToQFormatInteger(-2.0, 1, 14);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 14));
     
        s = FloatToQFormatInteger(2.0, 1, 14);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 14));
     
        // Q9
        s = FloatToQFormatInteger(-64, 6, 9);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 9));
     
        s = FloatToQFormatInteger(64, 6, 9);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 9));
     
        // Q15    S0.15    -1≤x≤0.9999695
        s = FloatToQFormatInteger(-1.0, 0, 15);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 15));
     
        s = FloatToQFormatInteger(1.0, 0, 15);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 15));
     
     
        // Q0    S15.0    -32768≤x≤32767
        s = FloatToQFormatInteger(-32768, 15, 0);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 0));
     
        s = FloatToQFormatInteger(32767, 15, 0);
        printf("%x, %f\n", s, QFormatIntegerToFloat(s, 0));
     
        return 0;
    }
  • Q31
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    #include <stdio.h>
     
    double QFormatIntegerToFloat(const int x,
                                 const int n)
     
    {
        return (((double)x) / ((double)(1 << n)));
    }
     
    int FloatToQFormatInteger(const double x,
                              const int m,
                              const int n)
     
    {
        int   i;
        int   y;
        int   mask = 0;
     
        y = (int)(x * ((double)(1 << n)));  // Generate the integer number in m.n format
     
        for (i = 0; i < (m + n);
             i++) {     // Calculate the mask to ensure we return the correct number of valid bits
            mask = (mask << 1) + 1;
        }
     
        return (y & mask);
    }
     
    int MpyQFormatInteger(const int x,
                          const int y,
                          const int n)
     
    {
        long long tmp;
        tmp = ((long long)x * (long long)y) >> n;
        return ((int)tmp);
    }
     
     
    int main()
    {
        int         a, b, c, d, e;
     
     
        printf("%f = 0x%x\n",  2.0 , FloatToQFormatInteger(2.0 , 8, 24));
        printf("%f = 0x%x\n",  1.5 , FloatToQFormatInteger(1.5 , 8, 24));
        printf("%f = 0x%x\n",  0.5 , FloatToQFormatInteger(0.5 , 8, 24));
        printf("%f = 0x%x\n",  0.25, FloatToQFormatInteger(0.25, 8, 24));
        printf("%f = 0x%x\n",  0.75, FloatToQFormatInteger(0.75, 8, 24));
        printf("\n");
     
    #if 1
        a = FloatToQFormatInteger(2.0, 8, 24);
        printf("Result = 0x%x : %f\n", a, QFormatIntegerToFloat(a , 24));
        b = FloatToQFormatInteger(1.5, 8, 24);
        printf("Result = 0x%x : %f\n", b, QFormatIntegerToFloat(b , 24));
        c = FloatToQFormatInteger(0.5, 8, 24);
        printf("Result = 0x%x : %f\n", c, QFormatIntegerToFloat(c , 24));
        d = FloatToQFormatInteger(0.25, 8, 24);
        printf("Result = 0x%x : %f\n", d, QFormatIntegerToFloat(d , 24));
        e = FloatToQFormatInteger(0.75, 8, 24);
        printf("Result = 0x%x : %f\n", e, QFormatIntegerToFloat(e , 24));
     
    #else
        a = FloatToQFormatInteger(0.75, 8, 24);
        b = FloatToQFormatInteger(2.0 , 8, 24);
        c = MpyQFormatInteger(a, b, 24);
     
        printf("Result = 0x%x : %f\n", c, QFormatIntegerToFloat(c , 24));
     
        d = FloatToQFormatInteger(0.5 , 8, 24);
        e = MpyQFormatInteger(c, d, 24);
     
        printf("Result = 0x%x : %f\n", e, QFormatIntegerToFloat(e , 24));
    #endif
     
        return (0);
    }
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blog/2024-04-01_share_q_format_number_in_c.txt · Last modified: 2024/04/01 14:58 (external edit)

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