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 /* 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 . */ /* Calculate division table for SH5Media integer division Contributed by Joern Rennecke joern.rennecke@superh.com */ #include #include #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< 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, factors)); 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); }