void
bn_cx_sqrt(bn_complex_t *op, const bn_complex_t *ip)
{
const fastf_t re = ip->re;
const fastf_t im = ip->im;
/* special cases are not necessary; they are here for speed */
if (ZERO(re)) {
if (ZERO(im)) {
op->re = op->im = 0.0;
} else if (im > 0.0) {
op->re = op->im = sqrt(im * 0.5);
} else {
/* ip->im < 0.0 */
op->re = -(op->im = sqrt(im * -0.5));
}
} else if (ZERO(im)) {
if (re > 0.0) {
op->re = sqrt(re);
op->im = 0.0;
} else {
/* ip->re < 0.0 */
op->im = sqrt(-re);
op->re = 0.0;
}
} else {
fastf_t ampl, temp;
/* no shortcuts */
ampl = bn_cx_ampl(ip);
if ((temp = (ampl - re) * 0.5) < 0.0) {
/* This case happens rather often, when the hypot() in
* bn_cx_ampl() returns an ampl ever so slightly smaller
* than ip->re. This can easily happen when ip->re ~=
* 10**20. Just ignore the imaginary part.
*/
op->im = 0.0;
} else {
op->im = sqrt(temp);
}
if ((temp = (ampl + re) * 0.5) < 0.0) {
op->re = 0.0;
} else {
if (im > 0.0) {
op->re = sqrt(temp);
} else {
/* ip->im < 0.0 */
op->re = -sqrt(temp);
}
}
}
}
/**
* B N _ C X _ S Q R T
*@brief
* Compute square root of complex number
*
* bn_cx_sqrt( &out, &c ) replaces out by sqrt(c)
*
* Note: This is a double-valued function; the result of
* bn_cx_sqrt() always has nonnegative imaginary part.
*/
void
bn_cx_sqrt(bn_complex_t *op, register const bn_complex_t *ip)
{
register fastf_t ampl, temp;
/* record signs of original real & imaginary parts */
register int re_sign;
register int im_sign;
/* special cases are not necessary; they are here for speed */
im_sign = SIGN( ip->im );
if ( (re_sign = SIGN(ip->re)) == 0 ) {
if ( im_sign == 0 )
op->re = op->im = 0;
else if ( im_sign > 0 )
op->re = op->im = sqrt( ip->im * 0.5 );
else /* im_sign < 0 */
op->re = -(op->im = sqrt( ip->im * -0.5 ));
} else if ( im_sign == 0 ) {
if ( re_sign > 0 ) {
op->re = sqrt( ip->re );
op->im = 0.0;
} else {
/* re_sign < 0 */
op->im = sqrt( -ip->re );
op->re = 0.0;
}
} else {
/* no shortcuts */
ampl = bn_cx_ampl( ip );
if ( (temp = (ampl - ip->re) * 0.5) < 0.0 ) {
/* This case happens rather often, when the
* hypot() in bn_cx_ampl() returns an ampl ever so
* slightly smaller than ip->re. This can easily
* happen when ip->re ~= 10**20.
* Just ignore the imaginary part.
*/
op->im = 0;
} else
op->im = sqrt( temp );
if ( (temp = (ampl + ip->re) * 0.5) < 0.0 ) {
op->re = 0.0;
} else {
if ( im_sign > 0 )
op->re = sqrt(temp);
else /* im_sign < 0 */
op->re = -sqrt(temp);
}
}
}
