/* Copyright (C) 2003-2021 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 3, or (at your option) any | |

later version. | |

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. | |

Under Section 7 of GPL version 3, you are granted additional | |

permissions described in the GCC Runtime Library Exception, version | |

3.1, as published by the Free Software Foundation. | |

You should have received a copy of the GNU General Public License and | |

a copy of the GCC Runtime Library Exception along with this program; | |

see the files COPYING3 and COPYING.RUNTIME respectively. If not, see | |

<http://www.gnu.org/licenses/>. */ | |

/* Calculate division table for SH5Media integer division | |

Contributed by Joern Rennecke | |

joern.rennecke@superh.com */ | |

#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); | |

} |