| /* Copyright (C) 2003-2020 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); |
| } |