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  *
   8  *  This program is free software; you can distribute it and/or modify it
   9  *  under the terms of the GNU General Public License (Version 2) as
  10  *  published by the Free Software Foundation.
  11  *
  12  *  This program is distributed in the hope 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  *  for more details.
  16  *
  17  *  You should have received a copy of the GNU General Public License along
  18  *  with this program; if not, write to the Free Software Foundation, Inc.,
  19  *  51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA.
  20  */
  21
  22 #include "ieee754dp.h"
  23
  24 static const unsigned table[] = {
  25         0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
  26         29598, 36145, 43202, 50740, 58733, 67158, 75992,
  27         85215, 83599, 71378, 60428, 50647, 41945, 34246,
  28         27478, 21581, 16499, 12183, 8588, 5674, 3403,
  29         1742, 661, 130
  30 };
  31
  32 union ieee754dp ieee754dp_sqrt(union ieee754dp x)
  33 {
  34         struct _ieee754_csr oldcsr;
  35         union ieee754dp y, z, t;
  36         unsigned scalx, yh;
  37         COMPXDP;
  38
  39         EXPLODEXDP;
  40         ieee754_clearcx();
  41         FLUSHXDP;
  42
  43         /* x == INF or NAN? */
  44         switch (xc) {
  45         case IEEE754_CLASS_SNAN:
  46                 return ieee754dp_nanxcpt(x);
  47
  48         case IEEE754_CLASS_QNAN:
  49                 /* sqrt(Nan) = Nan */
  50                 return x;
  51
  52         case IEEE754_CLASS_ZERO:
  53                 /* sqrt(0) = 0 */
  54                 return x;
  55
  56         case IEEE754_CLASS_INF:
  57                 if (xs) {
  58                         /* sqrt(-Inf) = Nan */
  59                         ieee754_setcx(IEEE754_INVALID_OPERATION);
  60                         return ieee754dp_indef();
  61                 }
  62                 /* sqrt(+Inf) = Inf */
  63                 return x;
  64
  65         case IEEE754_CLASS_DNORM:
  66                 DPDNORMX;
  67                 /* fall through */
  68
  69         case IEEE754_CLASS_NORM:
  70                 if (xs) {
  71                         /* sqrt(-x) = Nan */
  72                         ieee754_setcx(IEEE754_INVALID_OPERATION);
  73                         return ieee754dp_indef();
  74                 }
  75                 break;
  76         }
  77
  78         /* save old csr; switch off INX enable & flag; set RN rounding */
  79         oldcsr = ieee754_csr;
  80         ieee754_csr.mx &= ~IEEE754_INEXACT;
  81         ieee754_csr.sx &= ~IEEE754_INEXACT;
  82         ieee754_csr.rm = FPU_CSR_RN;
  83
  84         /* adjust exponent to prevent overflow */
  85         scalx = 0;
  86         if (xe > 512) {         /* x > 2**-512? */
  87                 xe -= 512;      /* x = x / 2**512 */
  88                 scalx += 256;
  89         } else if (xe < -512) { /* x < 2**-512? */
  90                 xe += 512;      /* x = x * 2**512 */
  91                 scalx -= 256;
  92         }
  93
  94         y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
  95
  96         /* magic initial approximation to almost 8 sig. bits */
  97         yh = y.bits >> 32;
  98         yh = (yh >> 1) + 0x1ff80000;
  99         yh = yh - table[(yh >> 15) & 31];
 100         y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
 101
 102         /* Heron's rule once with correction to improve to ~18 sig. bits */
 103         /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
 104         t = ieee754dp_div(x, y);
 105         y = ieee754dp_add(y, t);
 106         y.bits -= 0x0010000600000000LL;
 107         y.bits &= 0xffffffff00000000LL;
 108
 109         /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
 110         /* t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
 111         z = t = ieee754dp_mul(y, y);
 112         t.bexp += 0x001;
 113         t = ieee754dp_add(t, z);
 114         z = ieee754dp_mul(ieee754dp_sub(x, z), y);
 115
 116         /* t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t; */
 117         t = ieee754dp_div(z, ieee754dp_add(t, x));
 118         t.bexp += 0x001;
 119         y = ieee754dp_add(y, t);
 120
 121         /* twiddle last bit to force y correctly rounded */
 122
 123         /* set RZ, clear INEX flag */
 124         ieee754_csr.rm = FPU_CSR_RZ;
 125         ieee754_csr.sx &= ~IEEE754_INEXACT;
 126
 127         /* t=x/y; ...chopped quotient, possibly inexact */
 128         t = ieee754dp_div(x, y);
 129
 130         if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
 131
 132                 if (!(ieee754_csr.sx & IEEE754_INEXACT))
 133                         /* t = t-ulp */
 134                         t.bits -= 1;
 135
 136                 /* add inexact to result status */
 137                 oldcsr.cx |= IEEE754_INEXACT;
 138                 oldcsr.sx |= IEEE754_INEXACT;
 139
 140                 switch (oldcsr.rm) {
 141                 case FPU_CSR_RU:
 142                         y.bits += 1;
 143                         /* drop through */
 144                 case FPU_CSR_RN:
 145                         t.bits += 1;
 146                         break;
 147                 }
 148
 149                 /* y=y+t; ...chopped sum */
 150                 y = ieee754dp_add(y, t);
 151
 152                 /* adjust scalx for correctly rounded sqrt(x) */
 153                 scalx -= 1;
 154         }
 155
 156         /* py[n0]=py[n0]+scalx; ...scale back y */
 157         y.bexp += scalx;
 158
 159         /* restore rounding mode, possibly set inexact */
 160         ieee754_csr = oldcsr;
 161
 162         return y;
 163 }