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 * 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
  30static 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
  38ieee754dp 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}
 166