10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak csqrt = __csqrt
  31 
  32 /* INDENT OFF */
  33 /*
  34  * dcomplex csqrt(dcomplex z);
  35  *
  36  *                                         2    2    2
  37  * Let w=r+i*s = sqrt(x+iy). Then (r + i s)  = r  - s  + i 2sr = x + i y.
  38  *
  39  * Hence x = r*r-s*s, y = 2sr.
  40  *
  41  * Note that x*x+y*y = (s*s+r*r)**2. Thus, we have
  42  *                        ________
  43  *            2    2     / 2    2
  44  *      (1) r  + s  = \/ x  + y  ,
  45  *
  46  *            2    2
  47  *       (2) r  - s  = x
  48  *
  49  *      (3) 2sr = y.
  50  *

  10  * See the License for the specific language governing permissions
  11  * and limitations under the License.
  12  *
  13  * When distributing Covered Code, include this CDDL HEADER in each
  14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
  15  * If applicable, add the following below this CDDL HEADER, with the
  16  * fields enclosed by brackets "[]" replaced with your own identifying
  17  * information: Portions Copyright [yyyy] [name of copyright owner]
  18  *
  19  * CDDL HEADER END
  20  */
  21 
  22 /*
  23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
  24  */
  25 /*
  26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
  27  * Use is subject to license terms.
  28  */
  29 
  30 #pragma weak __csqrt = csqrt
  31 
  32 /* INDENT OFF */
  33 /*
  34  * dcomplex csqrt(dcomplex z);
  35  *
  36  *                                         2    2    2
  37  * Let w=r+i*s = sqrt(x+iy). Then (r + i s)  = r  - s  + i 2sr = x + i y.
  38  *
  39  * Hence x = r*r-s*s, y = 2sr.
  40  *
  41  * Note that x*x+y*y = (s*s+r*r)**2. Thus, we have
  42  *                        ________
  43  *            2    2     / 2    2
  44  *      (1) r  + s  = \/ x  + y  ,
  45  *
  46  *            2    2
  47  *       (2) r  - s  = x
  48  *
  49  *      (3) 2sr = y.
  50  *