arch/mips/math-emu/dp_sqrt.c

   1 /* IEEE754 floating point arithmetic
   2  * double precision square root
   3  */
   4 /*
   5  * MIPS floating point support
   6  * Copyright (C) 1994-2000 Algorithmics Ltd.
   7  * http://www.algor.co.uk
   8  *
   9  * ########################################################################
  10  *
  11  *  This program is free software; you can distribute it and/or modify it
  12  *  under the terms of the GNU General Public License (Version 2) as
  13  *  published by the Free Software Foundation.
  14  *
  15  *  This program is distributed in the hope it will be useful, but WITHOUT
  16  *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  17  *  FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  18  *  for more details.
  19  *
  20  *  You should have received a copy of the GNU General Public License along
  21  *  with this program; if not, write to the Free Software Foundation, Inc.,
  22  *  59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
  23  *
  24  * ########################################################################
  25  */
  26
  27
  28 #include "ieee754dp.h"
  29
  30 static const unsigned table[] = {
  31         0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
  32         29598, 36145, 43202, 50740, 58733, 67158, 75992,
  33         85215, 83599, 71378, 60428, 50647, 41945, 34246,
  34         27478, 21581, 16499, 12183, 8588, 5674, 3403,
  35         1742, 661, 130
  36 };
  37
  38 ieee754dp ieee754dp_sqrt(ieee754dp x)
  39 {
  40         struct ieee754_csr oldcsr;
  41         ieee754dp y, z, t;
  42         unsigned scalx, yh;
  43         COMPXDP;
  44
  45         EXPLODEXDP;
  46         CLEARCX;
  47         FLUSHXDP;
  48
  49         /* x == INF or NAN? */
  50         switch (xc) {
  51         case IEEE754_CLASS_QNAN:
  52                 /* sqrt(Nan) = Nan */
  53                 return ieee754dp_nanxcpt(x, "sqrt");
  54         case IEEE754_CLASS_SNAN:
  55                 SETCX(IEEE754_INVALID_OPERATION);
  56                 return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  57         case IEEE754_CLASS_ZERO:
  58                 /* sqrt(0) = 0 */
  59                 return x;
  60         case IEEE754_CLASS_INF:
  61                 if (xs) {
  62                         /* sqrt(-Inf) = Nan */
  63                         SETCX(IEEE754_INVALID_OPERATION);
  64                         return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  65                 }
  66                 /* sqrt(+Inf) = Inf */
  67                 return x;
  68         case IEEE754_CLASS_DNORM:
  69                 DPDNORMX;
  70                 /* fall through */
  71         case IEEE754_CLASS_NORM:
  72                 if (xs) {
  73                         /* sqrt(-x) = Nan */
  74                         SETCX(IEEE754_INVALID_OPERATION);
  75                         return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  76                 }
  77                 break;
  78         }
  79
  80         /* save old csr; switch off INX enable & flag; set RN rounding */
  81         oldcsr = ieee754_csr;
  82         ieee754_csr.mx &= ~IEEE754_INEXACT;
  83         ieee754_csr.sx &= ~IEEE754_INEXACT;
  84         ieee754_csr.rm = IEEE754_RN;
  85
  86         /* adjust exponent to prevent overflow */
  87         scalx = 0;
  88         if (xe > 512) {         /* x > 2**-512? */
  89                 xe -= 512;      /* x = x / 2**512 */
  90                 scalx += 256;
  91         } else if (xe < -512) { /* x < 2**-512? */
  92                 xe += 512;      /* x = x * 2**512 */
  93                 scalx -= 256;
  94         }
  95
  96         y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
  97
  98         /* magic initial approximation to almost 8 sig. bits */
  99         yh = y.bits >> 32;
 100         yh = (yh >> 1) + 0x1ff80000;
 101         yh = yh - table[(yh >> 15) & 31];
 102         y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
 103
 104         /* Heron's rule once with correction to improve to ~18 sig. bits */
 105         /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
 106         t = ieee754dp_div(x, y);
 107         y = ieee754dp_add(y, t);
 108         y.bits -= 0x0010000600000000LL;
 109         y.bits &= 0xffffffff00000000LL;
 110
 111         /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
 112         /* t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
 113         z = t = ieee754dp_mul(y, y);
 114         t.parts.bexp += 0x001;
 115         t = ieee754dp_add(t, z);
 116         z = ieee754dp_mul(ieee754dp_sub(x, z), y);
 117
 118         /* t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t; */
 119         t = ieee754dp_div(z, ieee754dp_add(t, x));
 120         t.parts.bexp += 0x001;
 121         y = ieee754dp_add(y, t);
 122
 123         /* twiddle last bit to force y correctly rounded */
 124
 125         /* set RZ, clear INEX flag */
 126         ieee754_csr.rm = IEEE754_RZ;
 127         ieee754_csr.sx &= ~IEEE754_INEXACT;
 128
 129         /* t=x/y; ...chopped quotient, possibly inexact */
 130         t = ieee754dp_div(x, y);
 131
 132         if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
 133
 134                 if (!(ieee754_csr.sx & IEEE754_INEXACT))
 135                         /* t = t-ulp */
 136                         t.bits -= 1;
 137
 138                 /* add inexact to result status */
 139                 oldcsr.cx |= IEEE754_INEXACT;
 140                 oldcsr.sx |= IEEE754_INEXACT;
 141
 142                 switch (oldcsr.rm) {
 143                 case IEEE754_RP:
 144                         y.bits += 1;
 145                         /* drop through */
 146                 case IEEE754_RN:
 147                         t.bits += 1;
 148                         break;
 149                 }
 150
 151                 /* y=y+t; ...chopped sum */
 152                 y = ieee754dp_add(y, t);
 153
 154                 /* adjust scalx for correctly rounded sqrt(x) */
 155                 scalx -= 1;
 156         }
 157
 158         /* py[n0]=py[n0]+scalx; ...scale back y */
 159         y.parts.bexp += scalx;
 160
 161         /* restore rounding mode, possibly set inexact */
 162         ieee754_csr = oldcsr;
 163
 164         return y;
 165 }