divtab.c

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/* Copyright (C) 2003 Free Software Foundation, Inc.

This file is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version.

In addition to the permissions in the GNU General Public License, the
Free Software Foundation gives you unlimited permission to link the
compiled version of this file into combinations with other programs,
and to distribute those combinations without any restriction coming
from the use of this file.  (The General Public License restrictions
do apply in other respects; for example, they cover modification of
the file, and distribution when not linked into a combine
executable.)

This file is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with this program; see the file COPYING.  If not, write to
the Free Software Foundation, 51 Franklin Street, Fifth Floor,
Boston, MA 02110-1301, USA.  */

/* Calculate division table for SH5Media integer division
   Contributed by Joern Rennecke
   [e-mail]  */

#include <stdio.h>
#include <math.h>

#define BITS 5
#define N_ENTRIES (1 << BITS)
#define CUTOFF_BITS 20

#define BIAS (-330)

double max_defect = 0.;
double max_defect_x;

double min_defect = 1e9;
double min_defect_x;

double max_defect2 = 0.;
double max_defect2_x;

double min_defect2 = 0.;
double min_defect2_x;

double min_defect3 = 01e9;
double min_defect3_x;
int min_defect3_val;

double max_defect3 = 0.;
double max_defect3_x;
int max_defect3_val;

static double note_defect3 (int val, double d2, double y2d, double x)
{
  int cutoff_val = val >> CUTOFF_BITS;
  double cutoff;
  double defect;

  if (val < 0)
    cutoff_val++;
  cutoff = (cutoff_val * (1<<CUTOFF_BITS) - val) * y2d;
  defect = cutoff + val * d2;
  if (val < 0)
    defect = - defect;
  if (defect > max_defect3)
    {
      max_defect3 = defect;
      max_defect3_x = x;
      max_defect3_val = val;
    }
  if (defect < min_defect3)
    {
      min_defect3 = defect;
      min_defect3_x = x;
      min_defect3_val = val;
    }
}

/* This function assumes 32 bit integers.  */
static double
calc_defect (double x, int constant, int factor)
{
  double y0 = (constant - (int) floor ((x * factor * 64.))) / 16384.;
  double y1 = 2 * y0 -y0 * y0 * (x + BIAS / (1.*(1LL<<30)));
  double y2d0, y2d;
  int y2d1;
  double d, d2;

  y1 = floor (y1 * (1024 * 1024 * 1024)) / (1024 * 1024 * 1024);
  d = y1 - 1 / x;
  if (d > max_defect)
    {
      max_defect = d;
      max_defect_x = x;
    }
  if (d < min_defect)
    {
      min_defect = d;
      min_defect_x = x;
    }
  y2d0 = floor (y1 * x * (1LL << 60-16));
  y2d1 = (int) (long long) y2d0;
  y2d = - floor ((y1 - y0 / (1<<30-14)) * y2d1) / (1LL<<44);
  d2 = y1 + y2d - 1/x;
  if (d2 > max_defect2)
    {
      max_defect2 = d2;
      max_defect2_x = x;
    }
  if (d2 < min_defect2)
    {
      min_defect2 = d2;
      min_defect2_x = x;
    }
  /* zero times anything is trivially zero.  */
  note_defect3 ((1 << CUTOFF_BITS) - 1, d2, y2d, x);
  note_defect3 (1 << CUTOFF_BITS, d2, y2d, x);
  note_defect3 ((1U << 31) - (1 << CUTOFF_BITS), d2, y2d, x);
  note_defect3 ((1U << 31) - 1, d2, y2d, x);
  note_defect3 (-1, d2, y2d, x);
  note_defect3 (-(1 << CUTOFF_BITS), d2, y2d, x);
  note_defect3 ((1U << 31) - (1 << CUTOFF_BITS) + 1, d2, y2d, x);
  note_defect3 (-(1U << 31), d2, y2d, x);
  return d;
}

int
main ()
{
  int i;
  unsigned char factors[N_ENTRIES];
  short constants[N_ENTRIES];
  int steps = N_ENTRIES / 2;
  double step = 1. / steps;
  double eps30 = 1. / (1024 * 1024 * 1024);

  for (i = 0; i < N_ENTRIES; i++)
    {
      double x_low = (i < steps ? 1. : -3.) + i * step;
      double x_high = x_low + step - eps30;
      double x_med;
      int factor, constant;
      double low_defect, med_defect, high_defect, max_defect;

      factor = (1./x_low- 1./x_high) / step * 256. + 0.5;
      if (factor == 256)
	factor = 255;
      factors[i] = factor;
      /* Use minimum of error function for x_med.  */
      x_med = sqrt (256./factor);
      if (x_low < 0)
	x_med = - x_med;
      low_defect = 1. / x_low + x_low * factor / 256.;
      high_defect = 1. / x_high + x_high * factor / 256.;
      med_defect = 1. / x_med + x_med * factor / 256.;
      max_defect
	= ((low_defect > high_defect) ^ (x_med < 0)) ? low_defect : high_defect;
      constant = (med_defect + max_defect) * 0.5 * 16384. + 0.5;
      if (constant < -32768 || constant > 32767)
	abort ();
      constants[i] = constant;
      calc_defect (x_low, constant, factor);
      calc_defect (x_med, constant, factor);
      calc_defect (x_high, constant, factor);
    }
    printf ("/* This table has been generated by divtab.c .\n");
    printf ("Defects for bias %d:\n", BIAS);
    printf ("   Max defect: %e at %e\n", max_defect, max_defect_x);
    printf ("   Min defect: %e at %e\n", min_defect, min_defect_x);
    printf ("   Max 2nd step defect: %e at %e\n", max_defect2, max_defect2_x);
    printf ("   Min 2nd step defect: %e at %e\n", min_defect2, min_defect2_x);
    printf ("   Max div defect: %e at %d:%e\n", max_defect3, max_defect3_val, max_defect3_x);
    printf ("   Min div defect: %e at %d:%e\n", min_defect3, min_defect3_val, min_defect3_x);
    printf ("   Defect at 1: %e\n",
	    calc_defect (1., constants[0], factors[0]));
    printf ("   Defect at -2: %e */\n",
	    calc_defect (-2., constants[steps], factors[steps]));
    printf ("\t.section\t.rodata\n");
    printf ("\t.balign 2\n");
    printf ("/* negative division constants */\n");
    for (i = steps; i < 2 * steps; i++)
      printf ("\t.word\t%d\n", constants[i]);
    printf ("/* negative division factors */\n");
    for (i = steps; i < 2*steps; i++)
      printf ("\t.byte\t%d\n", factors[i]);
    printf ("\t.skip %d\n", steps);
    printf ("\t.global	GLOBAL(div_table):\n");
    printf ("GLOBAL(div_table):\n");
    printf ("\t.skip %d\n", steps);
    printf ("/* positive division factors */\n");
    for (i = 0; i < steps; i++)
      printf ("\t.byte\t%d\n", factors[i]);
    printf ("/* positive division constants */\n");
    for (i = 0; i < steps; i++)
      printf ("\t.word\t%d\n", constants[i]);
  exit (0);
}