/* Copyright (C) 2003 Free Software Foundation, Inc.
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/* Copyright (C) 2003 Free Software Foundation, Inc.
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This file is free software; you can redistribute it and/or modify it
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This file is free software; you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by the
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under the terms of the GNU General Public License as published by the
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Free Software Foundation; either version 2, or (at your option) any
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Free Software Foundation; either version 2, or (at your option) any
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later version.
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later version.
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In addition to the permissions in the GNU General Public License, the
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In addition to the permissions in the GNU General Public License, the
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Free Software Foundation gives you unlimited permission to link the
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Free Software Foundation gives you unlimited permission to link the
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compiled version of this file into combinations with other programs,
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compiled version of this file into combinations with other programs,
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and to distribute those combinations without any restriction coming
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and to distribute those combinations without any restriction coming
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from the use of this file. (The General Public License restrictions
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from the use of this file. (The General Public License restrictions
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do apply in other respects; for example, they cover modification of
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do apply in other respects; for example, they cover modification of
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the file, and distribution when not linked into a combine
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the file, and distribution when not linked into a combine
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executable.)
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executable.)
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This file is distributed in the hope that it will be useful, but
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This file is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of
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WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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General Public License for more details.
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General Public License for more details.
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You should have received a copy of the GNU General Public License
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You should have received a copy of the GNU General Public License
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along with this program; see the file COPYING. If not, write to
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along with this program; see the file COPYING. If not, write to
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the Free Software Foundation, 51 Franklin Street, Fifth Floor,
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the Free Software Foundation, 51 Franklin Street, Fifth Floor,
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Boston, MA 02110-1301, USA. */
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Boston, MA 02110-1301, USA. */
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/* Calculate division table for SH5Media integer division
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/* Calculate division table for SH5Media integer division
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Contributed by Joern Rennecke
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Contributed by Joern Rennecke
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joern.rennecke@superh.com */
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joern.rennecke@superh.com */
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#include <stdio.h>
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#include <stdio.h>
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#include <math.h>
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#include <math.h>
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#define BITS 5
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#define BITS 5
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#define N_ENTRIES (1 << BITS)
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#define N_ENTRIES (1 << BITS)
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#define CUTOFF_BITS 20
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#define CUTOFF_BITS 20
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#define BIAS (-330)
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#define BIAS (-330)
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double max_defect = 0.;
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double max_defect = 0.;
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double max_defect_x;
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double max_defect_x;
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double min_defect = 1e9;
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double min_defect = 1e9;
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double min_defect_x;
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double min_defect_x;
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double max_defect2 = 0.;
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double max_defect2 = 0.;
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double max_defect2_x;
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double max_defect2_x;
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double min_defect2 = 0.;
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double min_defect2 = 0.;
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double min_defect2_x;
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double min_defect2_x;
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double min_defect3 = 01e9;
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double min_defect3 = 01e9;
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double min_defect3_x;
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double min_defect3_x;
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int min_defect3_val;
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int min_defect3_val;
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double max_defect3 = 0.;
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double max_defect3 = 0.;
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double max_defect3_x;
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double max_defect3_x;
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int max_defect3_val;
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int max_defect3_val;
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static double note_defect3 (int val, double d2, double y2d, double x)
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static double note_defect3 (int val, double d2, double y2d, double x)
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{
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{
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int cutoff_val = val >> CUTOFF_BITS;
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int cutoff_val = val >> CUTOFF_BITS;
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double cutoff;
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double cutoff;
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double defect;
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double defect;
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if (val < 0)
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if (val < 0)
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cutoff_val++;
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cutoff_val++;
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cutoff = (cutoff_val * (1<<CUTOFF_BITS) - val) * y2d;
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cutoff = (cutoff_val * (1<<CUTOFF_BITS) - val) * y2d;
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defect = cutoff + val * d2;
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defect = cutoff + val * d2;
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if (val < 0)
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if (val < 0)
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defect = - defect;
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defect = - defect;
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if (defect > max_defect3)
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if (defect > max_defect3)
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{
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{
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max_defect3 = defect;
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max_defect3 = defect;
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max_defect3_x = x;
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max_defect3_x = x;
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max_defect3_val = val;
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max_defect3_val = val;
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}
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}
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if (defect < min_defect3)
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if (defect < min_defect3)
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{
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{
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min_defect3 = defect;
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min_defect3 = defect;
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min_defect3_x = x;
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min_defect3_x = x;
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min_defect3_val = val;
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min_defect3_val = val;
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}
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}
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}
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}
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/* This function assumes 32 bit integers. */
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/* This function assumes 32 bit integers. */
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static double
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static double
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calc_defect (double x, int constant, int factor)
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calc_defect (double x, int constant, int factor)
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{
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{
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double y0 = (constant - (int) floor ((x * factor * 64.))) / 16384.;
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double y0 = (constant - (int) floor ((x * factor * 64.))) / 16384.;
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double y1 = 2 * y0 -y0 * y0 * (x + BIAS / (1.*(1LL<<30)));
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double y1 = 2 * y0 -y0 * y0 * (x + BIAS / (1.*(1LL<<30)));
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double y2d0, y2d;
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double y2d0, y2d;
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int y2d1;
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int y2d1;
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double d, d2;
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double d, d2;
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y1 = floor (y1 * (1024 * 1024 * 1024)) / (1024 * 1024 * 1024);
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y1 = floor (y1 * (1024 * 1024 * 1024)) / (1024 * 1024 * 1024);
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d = y1 - 1 / x;
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d = y1 - 1 / x;
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if (d > max_defect)
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if (d > max_defect)
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{
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{
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max_defect = d;
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max_defect = d;
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max_defect_x = x;
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max_defect_x = x;
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}
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}
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if (d < min_defect)
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if (d < min_defect)
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{
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{
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min_defect = d;
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min_defect = d;
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min_defect_x = x;
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min_defect_x = x;
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}
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}
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y2d0 = floor (y1 * x * (1LL << 60-16));
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y2d0 = floor (y1 * x * (1LL << 60-16));
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y2d1 = (int) (long long) y2d0;
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y2d1 = (int) (long long) y2d0;
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y2d = - floor ((y1 - y0 / (1<<30-14)) * y2d1) / (1LL<<44);
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y2d = - floor ((y1 - y0 / (1<<30-14)) * y2d1) / (1LL<<44);
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d2 = y1 + y2d - 1/x;
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d2 = y1 + y2d - 1/x;
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if (d2 > max_defect2)
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if (d2 > max_defect2)
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{
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{
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max_defect2 = d2;
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max_defect2 = d2;
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max_defect2_x = x;
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max_defect2_x = x;
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}
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}
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if (d2 < min_defect2)
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if (d2 < min_defect2)
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{
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{
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min_defect2 = d2;
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min_defect2 = d2;
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min_defect2_x = x;
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min_defect2_x = x;
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}
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}
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/* zero times anything is trivially zero. */
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/* zero times anything is trivially zero. */
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note_defect3 ((1 << CUTOFF_BITS) - 1, d2, y2d, x);
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note_defect3 ((1 << CUTOFF_BITS) - 1, d2, y2d, x);
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note_defect3 (1 << CUTOFF_BITS, d2, y2d, x);
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note_defect3 (1 << CUTOFF_BITS, d2, y2d, x);
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note_defect3 ((1U << 31) - (1 << CUTOFF_BITS), d2, y2d, x);
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note_defect3 ((1U << 31) - (1 << CUTOFF_BITS), d2, y2d, x);
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note_defect3 ((1U << 31) - 1, d2, y2d, x);
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note_defect3 ((1U << 31) - 1, d2, y2d, x);
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note_defect3 (-1, d2, y2d, x);
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note_defect3 (-1, d2, y2d, x);
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note_defect3 (-(1 << CUTOFF_BITS), d2, y2d, x);
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note_defect3 (-(1 << CUTOFF_BITS), d2, y2d, x);
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note_defect3 ((1U << 31) - (1 << CUTOFF_BITS) + 1, d2, y2d, x);
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note_defect3 ((1U << 31) - (1 << CUTOFF_BITS) + 1, d2, y2d, x);
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note_defect3 (-(1U << 31), d2, y2d, x);
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note_defect3 (-(1U << 31), d2, y2d, x);
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return d;
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return d;
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}
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}
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int
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int
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main ()
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main ()
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{
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{
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int i;
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int i;
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unsigned char factors[N_ENTRIES];
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unsigned char factors[N_ENTRIES];
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short constants[N_ENTRIES];
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short constants[N_ENTRIES];
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int steps = N_ENTRIES / 2;
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int steps = N_ENTRIES / 2;
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double step = 1. / steps;
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double step = 1. / steps;
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double eps30 = 1. / (1024 * 1024 * 1024);
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double eps30 = 1. / (1024 * 1024 * 1024);
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for (i = 0; i < N_ENTRIES; i++)
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for (i = 0; i < N_ENTRIES; i++)
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{
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{
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double x_low = (i < steps ? 1. : -3.) + i * step;
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double x_low = (i < steps ? 1. : -3.) + i * step;
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double x_high = x_low + step - eps30;
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double x_high = x_low + step - eps30;
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double x_med;
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double x_med;
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int factor, constant;
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int factor, constant;
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double low_defect, med_defect, high_defect, max_defect;
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double low_defect, med_defect, high_defect, max_defect;
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factor = (1./x_low- 1./x_high) / step * 256. + 0.5;
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factor = (1./x_low- 1./x_high) / step * 256. + 0.5;
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if (factor == 256)
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if (factor == 256)
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factor = 255;
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factor = 255;
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factors[i] = factor;
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factors[i] = factor;
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/* Use minimum of error function for x_med. */
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/* Use minimum of error function for x_med. */
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x_med = sqrt (256./factor);
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x_med = sqrt (256./factor);
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if (x_low < 0)
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if (x_low < 0)
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x_med = - x_med;
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x_med = - x_med;
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low_defect = 1. / x_low + x_low * factor / 256.;
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low_defect = 1. / x_low + x_low * factor / 256.;
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high_defect = 1. / x_high + x_high * factor / 256.;
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high_defect = 1. / x_high + x_high * factor / 256.;
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med_defect = 1. / x_med + x_med * factor / 256.;
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med_defect = 1. / x_med + x_med * factor / 256.;
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max_defect
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max_defect
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= ((low_defect > high_defect) ^ (x_med < 0)) ? low_defect : high_defect;
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= ((low_defect > high_defect) ^ (x_med < 0)) ? low_defect : high_defect;
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constant = (med_defect + max_defect) * 0.5 * 16384. + 0.5;
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constant = (med_defect + max_defect) * 0.5 * 16384. + 0.5;
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if (constant < -32768 || constant > 32767)
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if (constant < -32768 || constant > 32767)
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abort ();
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abort ();
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constants[i] = constant;
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constants[i] = constant;
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calc_defect (x_low, constant, factor);
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calc_defect (x_low, constant, factor);
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calc_defect (x_med, constant, factor);
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calc_defect (x_med, constant, factor);
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calc_defect (x_high, constant, factor);
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calc_defect (x_high, constant, factor);
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}
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}
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printf ("/* This table has been generated by divtab.c .\n");
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printf ("/* This table has been generated by divtab.c .\n");
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printf ("Defects for bias %d:\n", BIAS);
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printf ("Defects for bias %d:\n", BIAS);
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printf (" Max defect: %e at %e\n", max_defect, max_defect_x);
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printf (" Max defect: %e at %e\n", max_defect, max_defect_x);
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printf (" Min defect: %e at %e\n", min_defect, min_defect_x);
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printf (" Min defect: %e at %e\n", min_defect, min_defect_x);
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printf (" Max 2nd step defect: %e at %e\n", max_defect2, max_defect2_x);
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printf (" Max 2nd step defect: %e at %e\n", max_defect2, max_defect2_x);
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printf (" Min 2nd step defect: %e at %e\n", min_defect2, min_defect2_x);
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printf (" Min 2nd step defect: %e at %e\n", min_defect2, min_defect2_x);
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printf (" Max div defect: %e at %d:%e\n", max_defect3, max_defect3_val, max_defect3_x);
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printf (" Max div defect: %e at %d:%e\n", max_defect3, max_defect3_val, max_defect3_x);
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printf (" Min div defect: %e at %d:%e\n", min_defect3, min_defect3_val, min_defect3_x);
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printf (" Min div defect: %e at %d:%e\n", min_defect3, min_defect3_val, min_defect3_x);
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printf (" Defect at 1: %e\n",
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printf (" Defect at 1: %e\n",
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calc_defect (1., constants[0], factors[0]));
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calc_defect (1., constants[0], factors[0]));
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printf (" Defect at -2: %e */\n",
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printf (" Defect at -2: %e */\n",
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calc_defect (-2., constants[steps], factors[steps]));
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calc_defect (-2., constants[steps], factors[steps]));
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printf ("\t.section\t.rodata\n");
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printf ("\t.section\t.rodata\n");
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printf ("\t.balign 2\n");
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printf ("\t.balign 2\n");
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printf ("/* negative division constants */\n");
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printf ("/* negative division constants */\n");
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for (i = steps; i < 2 * steps; i++)
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for (i = steps; i < 2 * steps; i++)
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printf ("\t.word\t%d\n", constants[i]);
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printf ("\t.word\t%d\n", constants[i]);
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printf ("/* negative division factors */\n");
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printf ("/* negative division factors */\n");
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for (i = steps; i < 2*steps; i++)
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for (i = steps; i < 2*steps; i++)
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printf ("\t.byte\t%d\n", factors[i]);
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printf ("\t.byte\t%d\n", factors[i]);
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printf ("\t.skip %d\n", steps);
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printf ("\t.skip %d\n", steps);
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printf ("\t.global GLOBAL(div_table):\n");
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printf ("\t.global GLOBAL(div_table):\n");
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printf ("GLOBAL(div_table):\n");
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printf ("GLOBAL(div_table):\n");
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printf ("\t.skip %d\n", steps);
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printf ("\t.skip %d\n", steps);
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printf ("/* positive division factors */\n");
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printf ("/* positive division factors */\n");
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for (i = 0; i < steps; i++)
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for (i = 0; i < steps; i++)
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printf ("\t.byte\t%d\n", factors[i]);
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printf ("\t.byte\t%d\n", factors[i]);
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printf ("/* positive division constants */\n");
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printf ("/* positive division constants */\n");
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for (i = 0; i < steps; i++)
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for (i = 0; i < steps; i++)
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printf ("\t.word\t%d\n", constants[i]);
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printf ("\t.word\t%d\n", constants[i]);
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exit (0);
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exit (0);
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}
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}
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