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 hypotl = __hypotl
  31 
  32 /*
  33  * hypotl(x,y)
  34  * Method :
  35  *      If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
  36  *      error less than 1 ulp.
  37  *      So, compute sqrt(x*x+y*y) with some care as follows:
  38  *      Assume x>y>0;
  39  *      1. save and set rounding to round-to-nearest
  40  *      2. if x > 2y  use
  41  *              x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
  42  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  43  *      3. if x <= 2y use
  44  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  45  *      where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
  46  *      lower 32 bits cleared, y2 = y-y1.
  47  *
  48  *      NOTE: DO NOT remove parenthsis!
  49  *
  50  * Special cases:

  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 __hypotl = hypotl
  31 
  32 /*
  33  * hypotl(x,y)
  34  * Method :
  35  *      If z=x*x+y*y has error less than sqrt(2)/2 ulp than sqrt(z) has
  36  *      error less than 1 ulp.
  37  *      So, compute sqrt(x*x+y*y) with some care as follows:
  38  *      Assume x>y>0;
  39  *      1. save and set rounding to round-to-nearest
  40  *      2. if x > 2y  use
  41  *              x1*x1+(y*y+(x2*(x+x2))) for x*x+y*y
  42  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  43  *      3. if x <= 2y use
  44  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  45  *      where t1 = 2x with lower 64 bits cleared, t2 = 2x-t1, y1= y with
  46  *      lower 32 bits cleared, y2 = y-y1.
  47  *
  48  *      NOTE: DO NOT remove parenthsis!
  49  *
  50  * Special cases: