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  * ########################################################################
   9  *
  10  *  This program is free software; you can distribute it and/or modify it
  11  *  under the terms of the GNU General Public License (Version 2) as
  12  *  published by the Free Software Foundation.
  13  *
  14  *  This program is distributed in the hope it will be useful, but WITHOUT
  15  *  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  16  *  FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  17  *  for more details.
  18  *
  19  *  You should have received a copy of the GNU General Public License along
  20  *  with this program; if not, write to the Free Software Foundation, Inc.,
  21  *  59 Temple Place - Suite 330, Boston MA 02111-1307, USA.
  22  *
  23  * ########################################################################
  24  */
  25
  26
  27 #include "ieee754dp.h"
  28
  29 static const unsigned table[] = {
  30         0, 1204, 3062, 5746, 9193, 13348, 18162, 23592,
  31         29598, 36145, 43202, 50740, 58733, 67158, 75992,
  32         85215, 83599, 71378, 60428, 50647, 41945, 34246,
  33         27478, 21581, 16499, 12183, 8588, 5674, 3403,
  34         1742, 661, 130
  35 };
  36
  37 ieee754dp ieee754dp_sqrt(ieee754dp x)
  38 {
  39         struct _ieee754_csr oldcsr;
  40         ieee754dp y, z, t;
  41         unsigned scalx, yh;
  42         COMPXDP;
  43
  44         EXPLODEXDP;
  45         CLEARCX;
  46         FLUSHXDP;
  47
  48         /* x == INF or NAN? */
  49         switch (xc) {
  50         case IEEE754_CLASS_QNAN:
  51                 /* sqrt(Nan) = Nan */
  52                 return ieee754dp_nanxcpt(x, "sqrt");
  53         case IEEE754_CLASS_SNAN:
  54                 SETCX(IEEE754_INVALID_OPERATION);
  55                 return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  56         case IEEE754_CLASS_ZERO:
  57                 /* sqrt(0) = 0 */
  58                 return x;
  59         case IEEE754_CLASS_INF:
  60                 if (xs) {
  61                         /* sqrt(-Inf) = Nan */
  62                         SETCX(IEEE754_INVALID_OPERATION);
  63                         return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  64                 }
  65                 /* sqrt(+Inf) = Inf */
  66                 return x;
  67         case IEEE754_CLASS_DNORM:
  68                 DPDNORMX;
  69                 /* fall through */
  70         case IEEE754_CLASS_NORM:
  71                 if (xs) {
  72                         /* sqrt(-x) = Nan */
  73                         SETCX(IEEE754_INVALID_OPERATION);
  74                         return ieee754dp_nanxcpt(ieee754dp_indef(), "sqrt");
  75                 }
  76                 break;
  77         }
  78
  79         /* save old csr; switch off INX enable & flag; set RN rounding */
  80         oldcsr = ieee754_csr;
  81         ieee754_csr.mx &= ~IEEE754_INEXACT;
  82         ieee754_csr.sx &= ~IEEE754_INEXACT;
  83         ieee754_csr.rm = IEEE754_RN;
  84
  85         /* adjust exponent to prevent overflow */
  86         scalx = 0;
  87         if (xe > 512) {         /* x > 2**-512? */
  88                 xe -= 512;      /* x = x / 2**512 */
  89                 scalx += 256;
  90         } else if (xe < -512) { /* x < 2**-512? */
  91                 xe += 512;      /* x = x * 2**512 */
  92                 scalx -= 256;
  93         }
  94
  95         y = x = builddp(0, xe + DP_EBIAS, xm & ~DP_HIDDEN_BIT);
  96
  97         /* magic initial approximation to almost 8 sig. bits */
  98         yh = y.bits >> 32;
  99         yh = (yh >> 1) + 0x1ff80000;
 100         yh = yh - table[(yh >> 15) & 31];
 101         y.bits = ((u64) yh << 32) | (y.bits & 0xffffffff);
 102
 103         /* Heron's rule once with correction to improve to ~18 sig. bits */
 104         /* t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; */
 105         t = ieee754dp_div(x, y);
 106         y = ieee754dp_add(y, t);
 107         y.bits -= 0x0010000600000000LL;
 108         y.bits &= 0xffffffff00000000LL;
 109
 110         /* triple to almost 56 sig. bits: y ~= sqrt(x) to within 1 ulp */
 111         /* t=y*y; z=t;  pt[n0]+=0x00100000; t+=z; z=(x-z)*y; */
 112         z = t = ieee754dp_mul(y, y);
 113         t.parts.bexp += 0x001;
 114         t = ieee754dp_add(t, z);
 115         z = ieee754dp_mul(ieee754dp_sub(x, z), y);
 116
 117         /* t=z/(t+x) ;  pt[n0]+=0x00100000; y+=t; */
 118         t = ieee754dp_div(z, ieee754dp_add(t, x));
 119         t.parts.bexp += 0x001;
 120         y = ieee754dp_add(y, t);
 121
 122         /* twiddle last bit to force y correctly rounded */
 123
 124         /* set RZ, clear INEX flag */
 125         ieee754_csr.rm = IEEE754_RZ;
 126         ieee754_csr.sx &= ~IEEE754_INEXACT;
 127
 128         /* t=x/y; ...chopped quotient, possibly inexact */
 129         t = ieee754dp_div(x, y);
 130
 131         if (ieee754_csr.sx & IEEE754_INEXACT || t.bits != y.bits) {
 132
 133                 if (!(ieee754_csr.sx & IEEE754_INEXACT))
 134                         /* t = t-ulp */
 135                         t.bits -= 1;
 136
 137                 /* add inexact to result status */
 138                 oldcsr.cx |= IEEE754_INEXACT;
 139                 oldcsr.sx |= IEEE754_INEXACT;
 140
 141                 switch (oldcsr.rm) {
 142                 case IEEE754_RP:
 143                         y.bits += 1;
 144                         /* drop through */
 145                 case IEEE754_RN:
 146                         t.bits += 1;
 147                         break;
 148                 }
 149
 150                 /* y=y+t; ...chopped sum */
 151                 y = ieee754dp_add(y, t);
 152
 153                 /* adjust scalx for correctly rounded sqrt(x) */
 154                 scalx -= 1;
 155         }
 156
 157         /* py[n0]=py[n0]+scalx; ...scale back y */
 158         y.parts.bexp += scalx;
 159
 160         /* restore rounding mode, possibly set inexact */
 161         ieee754_csr = oldcsr;
 162
 163         return y;
 164 }