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141 lines
4.9 KiB
C
141 lines
4.9 KiB
C
/*
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* IBM Accurate Mathematical Library
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* written by International Business Machines Corp.
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* Copyright (C) 2001-2013 Free Software Foundation, Inc.
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU Lesser General Public License as published by
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* the Free Software Foundation; either version 2.1 of the License, or
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* (at your option) any later version.
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*
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* This program is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU Lesser General Public License for more details.
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*
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* You should have received a copy of the GNU Lesser General Public License
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* along with this program; if not, see <http://www.gnu.org/licenses/>.
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*/
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/*********************************************************************/
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/* MODULE_NAME: uroot.c */
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/* */
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/* FUNCTION: usqrt */
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/* */
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/* FILES NEEDED: dla.h endian.h mydefs.h uroot.h */
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/* uroot.tbl */
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/* */
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/* An ultimate sqrt routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of square */
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/* root of x. */
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/* Assumption: Machine arithmetic operations are performed in */
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/* round to nearest mode of IEEE 754 standard. */
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/* */
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/*********************************************************************/
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#include "endian.h"
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#include "mydefs.h"
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#include <dla.h>
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#include "MathLib.h"
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#include "root.tbl"
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#include <math_private.h>
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/*********************************************************************/
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/* An ultimate sqrt routine. Given an IEEE double machine number x */
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/* it computes the correctly rounded (to nearest) value of square */
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/* root of x. */
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/*********************************************************************/
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double
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__ieee754_sqrt (double x)
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{
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#include "uroot.h"
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static const double
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rt0 = 9.99999999859990725855365213134618E-01,
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rt1 = 4.99999999495955425917856814202739E-01,
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rt2 = 3.75017500867345182581453026130850E-01,
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rt3 = 3.12523626554518656309172508769531E-01;
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static const double big = 134217728.0;
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double y, t, del, res, res1, hy, z, zz, p, hx, tx, ty, s;
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mynumber a, c = { { 0, 0 } };
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int4 k;
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a.x = x;
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k = a.i[HIGH_HALF];
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a.i[HIGH_HALF] = (k & 0x001fffff) | 0x3fe00000;
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t = inroot[(k & 0x001fffff) >> 14];
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s = a.x;
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/*----------------- 2^-1022 <= | x |< 2^1024 -----------------*/
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if (k > 0x000fffff && k < 0x7ff00000)
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{
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int rm = fegetround ();
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fenv_t env;
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libc_feholdexcept_setround (&env, FE_TONEAREST);
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double ret;
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y = 1.0 - t * (t * s);
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t = t * (rt0 + y * (rt1 + y * (rt2 + y * rt3)));
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c.i[HIGH_HALF] = 0x20000000 + ((k & 0x7fe00000) >> 1);
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y = t * s;
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hy = (y + big) - big;
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del = 0.5 * t * ((s - hy * hy) - (y - hy) * (y + hy));
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res = y + del;
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if (res == (res + 1.002 * ((y - res) + del)))
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ret = res * c.x;
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else
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{
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res1 = res + 1.5 * ((y - res) + del);
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EMULV (res, res1, z, zz, p, hx, tx, hy, ty); /* (z+zz)=res*res1 */
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res = ((((z - s) + zz) < 0) ? max (res, res1) :
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min (res, res1));
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ret = res * c.x;
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}
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math_force_eval (ret);
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libc_fesetenv (&env);
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double dret = x / ret;
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if (dret != ret)
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{
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double force_inexact = 1.0 / 3.0;
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math_force_eval (force_inexact);
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/* The square root is inexact, ret is the round-to-nearest
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value which may need adjusting for other rounding
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modes. */
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switch (rm)
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{
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#ifdef FE_UPWARD
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case FE_UPWARD:
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if (dret > ret)
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ret = (res + 0x1p-1022) * c.x;
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break;
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#endif
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#ifdef FE_DOWNWARD
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case FE_DOWNWARD:
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#endif
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#ifdef FE_TOWARDZERO
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case FE_TOWARDZERO:
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#endif
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#if defined FE_DOWNWARD || defined FE_TOWARDZERO
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if (dret < ret)
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ret = (res - 0x1p-1022) * c.x;
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break;
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#endif
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default:
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break;
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}
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}
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/* Otherwise (x / ret == ret), either the square root was exact or
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the division was inexact. */
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return ret;
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}
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else
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{
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if ((k & 0x7ff00000) == 0x7ff00000)
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return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
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if (x == 0)
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return x; /* sqrt(+0)=+0, sqrt(-0)=-0 */
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if (k < 0)
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return (x - x) / (x - x); /* sqrt(-ve)=sNaN */
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return tm256.x * __ieee754_sqrt (x * t512.x);
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}
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}
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strong_alias (__ieee754_sqrt, __sqrt_finite)
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