LXR linux/arch/mips/math-emu/dp

   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
  29static 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
  37ieee754dp 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}
 165