js/src/fdlibm/e_hypot.c

   1 /* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
   2  *
   3  * ***** BEGIN LICENSE BLOCK *****
   4  * Version: MPL 1.1/GPL 2.0/LGPL 2.1
   5  *
   6  * The contents of this file are subject to the Mozilla Public License Version
   7  * 1.1 (the "License"); you may not use this file except in compliance with
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   9  * http://www.mozilla.org/MPL/
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  12  * WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
  13  * for the specific language governing rights and limitations under the
  14  * License.
  15  *
  16  * The Original Code is Mozilla Communicator client code, released
  17  * March 31, 1998.
  18  *
  19  * The Initial Developer of the Original Code is
  20  * Sun Microsystems, Inc.
  21  * Portions created by the Initial Developer are Copyright (C) 1998
  22  * the Initial Developer. All Rights Reserved.
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  38  * ***** END LICENSE BLOCK ***** */
  39
  40 /* @(#)e_hypot.c 1.3 95/01/18 */
  41 /*
  42  * ====================================================
  43  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
  44  *
  45  * Developed at SunSoft, a Sun Microsystems, Inc. business.
  46  * Permission to use, copy, modify, and distribute this
  47  * software is freely granted, provided that this notice
  48  * is preserved.
  49  * ====================================================
  50  */
  51
  52 /* __ieee754_hypot(x,y)
  53  *
  54  * Method :
  55  *      If (assume round-to-nearest) z=x*x+y*y
  56  *      has error less than sqrt(2)/2 ulp, than
  57  *      sqrt(z) has error less than 1 ulp (exercise).
  58  *
  59  *      So, compute sqrt(x*x+y*y) with some care as
  60  *      follows to get the error below 1 ulp:
  61  *
  62  *      Assume x>y>0;
  63  *      (if possible, set rounding to round-to-nearest)
  64  *      1. if x > 2y  use
  65  *              x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y
  66  *      where x1 = x with lower 32 bits cleared, x2 = x-x1; else
  67  *      2. if x <= 2y use
  68  *              t1*y1+((x-y)*(x-y)+(t1*y2+t2*y))
  69  *      where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1,
  70  *      y1= y with lower 32 bits chopped, y2 = y-y1.
  71  *
  72  *      NOTE: scaling may be necessary if some argument is too
  73  *            large or too tiny
  74  *
  75  * Special cases:
  76  *      hypot(x,y) is INF if x or y is +INF or -INF; else
  77  *      hypot(x,y) is NAN if x or y is NAN.
  78  *
  79  * Accuracy:
  80  *      hypot(x,y) returns sqrt(x^2+y^2) with error less
  81  *      than 1 ulps (units in the last place)
  82  */
  83
  84 #include "fdlibm.h"
  85
  86 #ifdef __STDC__
  87         double __ieee754_hypot(double x, double y)
  88 #else
  89         double __ieee754_hypot(x,y)
  90         double x, y;
  91 #endif
  92 {
  93         fd_twoints ux, uy;
  94         double a=x,b=y,t1,t2,y1,y2,w;
  95         int j,k,ha,hb;
  96
  97         ux.d = x; uy.d = y;
  98         ha = __HI(ux)&0x7fffffff;       /* high word of  x */
  99         hb = __HI(uy)&0x7fffffff;       /* high word of  y */
 100         if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;}
 101         ux.d = a; uy.d = b;
 102         __HI(ux) = ha;  /* a <- |a| */
 103         __HI(uy) = hb;  /* b <- |b| */
 104         a = ux.d; b = uy.d;
 105         if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */
 106         k=0;
 107         if(ha > 0x5f300000) {   /* a>2**500 */
 108            if(ha >= 0x7ff00000) {       /* Inf or NaN */
 109                w = a+b;                 /* for sNaN */
 110                ux.d = a; uy.d = b;
 111                if(((ha&0xfffff)|__LO(ux))==0) w = a;
 112                if(((hb^0x7ff00000)|__LO(uy))==0) w = b;
 113                return w;
 114            }
 115            /* scale a and b by 2**-600 */
 116            ha -= 0x25800000; hb -= 0x25800000;  k += 600;
 117            ux.d = a; uy.d = b;
 118            __HI(ux) = ha;
 119            __HI(uy) = hb;
 120            a = ux.d; b = uy.d;
 121         }
 122         if(hb < 0x20b00000) {   /* b < 2**-500 */
 123             if(hb <= 0x000fffff) {      /* subnormal b or 0 */
 124                 uy.d = b;
 125                 if((hb|(__LO(uy)))==0) return a;
 126                 t1=0;
 127                 ux.d = t1;
 128                 __HI(ux) = 0x7fd00000;  /* t1=2^1022 */
 129                 t1 = ux.d;
 130                 b *= t1;
 131                 a *= t1;
 132                 k -= 1022;
 133             } else {            /* scale a and b by 2^600 */
 134                 ha += 0x25800000;       /* a *= 2^600 */
 135                 hb += 0x25800000;       /* b *= 2^600 */
 136                 k -= 600;
 137                 ux.d = a; uy.d = b;
 138                 __HI(ux) = ha;
 139                 __HI(uy) = hb;
 140                 a = ux.d; b = uy.d;
 141             }
 142         }
 143     /* medium size a and b */
 144         w = a-b;
 145         if (w>b) {
 146             t1 = 0;
 147             ux.d = t1;
 148             __HI(ux) = ha;
 149             t1 = ux.d;
 150             t2 = a-t1;
 151             w  = fd_sqrt(t1*t1-(b*(-b)-t2*(a+t1)));
 152         } else {
 153             a  = a+a;
 154             y1 = 0;
 155             ux.d = y1;
 156             __HI(ux) = hb;
 157             y1 = ux.d;
 158             y2 = b - y1;
 159             t1 = 0;
 160             ux.d = t1;
 161             __HI(ux) = ha+0x00100000;
 162             t1 = ux.d;
 163             t2 = a - t1;
 164             w  = fd_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b)));
 165         }
 166         if(k!=0) {
 167             t1 = 1.0;
 168             ux.d = t1;
 169             __HI(ux) += (k<<20);
 170             t1 = ux.d;
 171             return t1*w;
 172         } else return w;
 173 }