complex Sqrtz(complex z) /* rz = sqrt( z) */
{
complex rz;
double r,th,abz;
abz = Magz( z);
if( abz == INFINITY){
rz = InfSetofComplex();
return rz;
}
if( z.x == 0.0 && z.y == 0.0){
rz = ZeroSetofComplex();
return rz;
}
if( z.y == 0.0){
if( z.x > 0.0) rz = MakeComplex( sqrt( z.x), 0.0);
else rz = MakeComplex( 0.0, sqrt( fabs( z.x)));
} else{
r = Magz( z);
th = Argz( z) / 2;
rz.x = sign( cos( th)) * sqrt( ( r + z.x)/2);
rz.y = sign( sin( th)) * sqrt( ( r - z.x)/2);
}
return rz;
} /* end. Sqrtz */
complex tanz(complex z) /* rz = tan( z) */
{
complex rz;
complex s,c;
if( z.x == 0.0 && z.y == 0.0){
rz = ZeroSetofComplex();
return rz;
}
if( z.x != 0.0 && z.y == 0.0){
rz = MakeComplex( tan( z.x), 0.0);
return rz;
}
if( z.x == 0.0 && z.y != 0.0){
rz = MakeComplex( 0.0, tanh( z.y));
return rz;
}
if( z.x != 0.0 && z.y != 0.0){
s = sinz( z);
c = cosz( z);
TRY {
rz = Divz( s, c);
return rz;
}
CATCH (EX_DIVZ) {
rz = NaNSetofComplex();
THROW (EX_TANZ);
return rz;
}
ENDTRY;
}
complex Divz(complex z1, complex z2) /* rz = z1 / z2 */
{
complex rz;
double abx2,aby2,abz1,abz2,s,temp;
abz1 = Magz(z1); abz2 = Magz(z2);
abx2 = fabs(z2.x); aby2 = fabs(z2.y);
if( abz2 == 0.0){
if( abz1 == 0.0 || abz1 == INFINITY){
rz = NaNSetofComplex();
THROW (EX_DIVZ);
return rz;
} /* in case of 0/0 or Inf/0 */
else{
rz = InfSetofComplex();
return rz;
} /* in case of z/0 */
}
if( abz2 == INFINITY){
if( abz1 == 0.0 || abz1 == INFINITY){
rz = NaNSetofComplex();
THROW (EX_DIVZ);
return rz;
} /* in case of 0/Inf or Inf/Inf */
else{
rz = ZeroSetofComplex();
return rz;
} /* in case of 0/z */
}
if( z1.x != 0.0 && z1.y == 0.0 && z2.x != 0.0 && z2.y == 0.0){
rz = MakeComplex( z1.x / z2.x, 0.0);
return rz;
}
if( z1.x == 0.0 && z1.y != 0.0 && z2.x == 0.0 && z2.y != 0.0){
rz = MakeComplex( z1.y / z2.y, 0.0);
return rz;
}
else{
if( abx2 >= aby2){
temp = z2.y / z2.x;
s = z2.x + z2.y * temp;
rz.x = ( z1.x + z1.y * temp ) / s;
rz.y = ( -z1.x * temp + z1.y ) / s;
}
else{
temp = z2.x / z2.y;
s = z2.x * temp + z2.y;
rz.x = ( z1.x * temp + z1.y ) / s;
rz.y = ( -z1.x + z1.y * temp ) / s;
}
} return rz;
} /* end. Divz */
// W^n_N = exp(-i2pin/N)
// = cos(2 pi n/N) - isin(2 pi n/N)
static inline osk_complex_t twiddle(int n, int Nin)
{
float theta = (float)(2.0f*M_PI*n / Nin);
return MakeComplex((float)cos(theta), (float)-sin(theta));
}
