1 

     2 /*

     3  * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.

     4  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

     5  *

     6  * This code is free software; you can redistribute it and/or modify it

     7  * under the terms of the GNU General Public License version 2 only, as

     8  * published by the Free Software Foundation.  Oracle designates this

     9  * particular file as subject to the "Classpath" exception as provided

    10  * by Oracle in the LICENSE file that accompanied this code.

    11  *

    12  * This code is distributed in the hope that it will be useful, but WITHOUT

    13  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

    14  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

    15  * version 2 for more details (a copy is included in the LICENSE file that

    16  * accompanied this code).

    17  *

    18  * You should have received a copy of the GNU General Public License version

    19  * 2 along with this work; if not, write to the Free Software Foundation,

    20  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

    21  *

    22  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

    23  * or visit www.oracle.com if you need additional information or have any

    24  * questions.

    25  */

    26 

    27 /* __ieee754_hypot(x,y)

    28  *

    29  * Method :

    30  *      If (assume round-to-nearest) z=x*x+y*y

    31  *      has error less than sqrt(2)/2 ulp, than

    32  *      sqrt(z) has error less than 1 ulp (exercise).

    33  *

    34  *      So, compute sqrt(x*x+y*y) with some care as

    35  *      follows to get the error below 1 ulp:

    36  *

    37  *      Assume x>y>0;

    38  *      (if possible, set rounding to round-to-nearest)

    39  *      1. if x > 2y  use

    40  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y

    41  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else

    42  *      2. if x <= 2y use

    43  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))

    44  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,

    45  *      y1= y with lower 32 bits chopped, y2 = y-y1.

    46  *

    47  *      NOTE: scaling may be necessary if some argument is too

    48  *            large or too tiny

    49  *

    50  * Special cases:

    51  *      hypot(x,y) is INF if x or y is +INF or -INF; else

    52  *      hypot(x,y) is NAN if x or y is NAN.

    53  *

    54  * Accuracy:

    55  *      hypot(x,y) returns sqrt(x^2+y^2) with error less

    56  *      than 1 ulps (units in the last place)

    57  */

    58 

    59 #include "fdlibm.h"

    60 

    61 #ifdef __STDC__

    62         double __ieee754_hypot(double x, double y)

    63 #else

    64         double __ieee754_hypot(x,y)

    65         double x, y;

    66 #endif

    67 {

    68         double a=x,b=y,t1,t2,y1,y2,w;

    69         int j,k,ha,hb;

    70 

    71         ha = __HI(x)&0x7fffffff;        /* high word of  x */

    72         hb = __HI(y)&0x7fffffff;        /* high word of  y */

    73         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}

    74         __HI(a) = ha;   /* a <- |a| */

    75         __HI(b) = hb;   /* b <- |b| */

    76         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */

    77         k=0;

    78         if(ha > 0x5f300000) {   /* a>2**500 */

    79            if(ha >= 0x7ff00000) {       /* Inf or NaN */

    80                w = a+b;                 /* for sNaN */

    81                if(((ha&0xfffff)|__LO(a))==0) w = a;

    82                if(((hb^0x7ff00000)|__LO(b))==0) w = b;

    83                return w;

    84            }

    85            /* scale a and b by 2**-600 */

    86            ha -= 0x25800000; hb -= 0x25800000;  k += 600;

    87            __HI(a) = ha;

    88            __HI(b) = hb;

    89         }

    90         if(hb < 0x20b00000) {   /* b < 2**-500 */

    91             if(hb <= 0x000fffff) {      /* subnormal b or 0 */

    92                 if((hb|(__LO(b)))==0) return a;

    93                 t1=0;

    94                 __HI(t1) = 0x7fd00000;  /* t1=2^1022 */

    95                 b *= t1;

    96                 a *= t1;

    97                 k -= 1022;

    98             } else {            /* scale a and b by 2^600 */

    99                 ha += 0x25800000;       /* a *= 2^600 */

   100                 hb += 0x25800000;       /* b *= 2^600 */

   101                 k -= 600;

   102                 __HI(a) = ha;

   103                 __HI(b) = hb;

   104             }

   105         }

   106     /* medium size a and b */

   107         w = a-b;

   108         if (w>b) {

   109             t1 = 0;

   110             __HI(t1) = ha;

   111             t2 = a-t1;

   112             w  = sqrt(t1*t1-(b*(-b)-t2*(a+t1)));

   113         } else {

   114             a  = a+a;

   115             y1 = 0;

   116             __HI(y1) = hb;

   117             y2 = b - y1;

   118             t1 = 0;

   119             __HI(t1) = ha+0x00100000;

   120             t2 = a - t1;

   121             w  = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));

   122         }

   123         if(k!=0) {

   124             t1 = 1.0;

   125             __HI(t1) += (k<<20);

   126             return t1*w;

   127         } else return w;

   128 }