sqrt-c.asm (Motorola DSP Developer's Kit)

[ Y ] = mot###_sqrt( X )

Description

This function returns the square root of the complex input vector

Input/Output

Input: Vector X (includes the real part Xr, and the imaginary part Xi)

Output: Vector Y (includes the real part Yr, and the imaginary part Yi)

Algorithm

sqrt(a+bi) = [sqrt(sqrt(a^2+b^2))]*[cos(angle(a+bi)/
2)+i*sin(angle(a+bi)/2)]

To implement it in fix point dsp, we change this to

sqrt(a+bi) = sqrt(sqrt((a^2+b^2)/2))]*[cos(angle(a+bi)/
2)+i*sin(angle(a+bi)/2)] * [power(2,.25)]

For the ANGLE-C.ASM algorithm, please refer to angle-c.asm. The following describes how to calculate SIN and COS

Use the CORDIC algorithm

for (i=0; i < fracbits; i++)
    {
        atan_tab[i] = atan(pow(2,double(-i)))/4;
    }

          K = 0.30362641811371;
          X = x = K;
          Y = y = 0;
          Z = z = angle;

          Z = z = x>>2 ;

/* Circular Function */
          for (i = 0; i < fracbits; ++i)
         {
            x = X >> i;
            y = Y >> i;
            z = atan[i];

          if (Z >= 0)
         {
             X -= y;
              Y += x;
              Z -= z;
           }
            else
           {
              X += y;
              Y -= x;
              Z += z;
           }
         }
          X = X << 1;    //cos(angle)
          Y = Y << 1;    //sin(angle)

          return X and Y;

Memory & Register

Memory allocation:

X memory:

Label IN stores the start address of the input of vector X

Label IN_REAL stores the start address of the real data of the input vector

Label IN_IMAG stores the start address of the complex (imaginary) data of the input vector

Label OUTREAL stores the start address of the real data of the output vector

Y memory:

Label OUTIMAG stores the start address of the imaginary data of the output vector

Label XYZ stores the start address of variables X,Y, i

X0 is x, as defined in CORDIC algorithm above

X1 is y, as defined in CORDIC algorithm above

Y1 is z, as defined in CORDIC algorithm above

B is Z, as defined in CORDIC algorithm above

R6 stores the address of the number of items in the input array

R3 stores the address of the atan table,

R0 and R5 are used for IN(OUT)

R7is used for the start address of label XYZ

R2 is used for number of fraction bits+1 (56300--22, 56600--14)

R1 is used as the current loop number

Y0 is mainly used as the shift number register (i.e., 'i' - see CORDIC algorithm above)

N7 = 1. Use N7 rather than '1' to make a parallel move possible

Status Register

The assembly function sqrt-c.asm does not explicitly set any status registers/bits during the function execution.

Data Size Limit

The length of vector X can't be larger than the continuous available data memory size.

Data Range Limit

The value of input vector X must be between -1.0 and +1.0.

Precision

In the case of DSP563, precision is 14 bits.

In the case of DSP566, precision is 15 bits.

sqrt-pr.asm sum-r.asm