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1 | /* Copyright (C) 2003 Free Software Foundation, Inc. |
2 | ||
3 | This file is free software; you can redistribute it and/or modify it | |
4 | under the terms of the GNU General Public License as published by the | |
5 | Free Software Foundation; either version 2, or (at your option) any | |
6 | later version. | |
7 | ||
8 | In addition to the permissions in the GNU General Public License, the | |
9 | Free Software Foundation gives you unlimited permission to link the | |
10 | compiled version of this file into combinations with other programs, | |
11 | and to distribute those combinations without any restriction coming | |
12 | from the use of this file. (The General Public License restrictions | |
13 | do apply in other respects; for example, they cover modification of | |
14 | the file, and distribution when not linked into a combine | |
15 | executable.) | |
16 | ||
17 | This file is distributed in the hope that it will be useful, but | |
18 | WITHOUT ANY WARRANTY; without even the implied warranty of | |
19 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
20 | General Public License for more details. | |
21 | ||
22 | You should have received a copy of the GNU General Public License | |
23 | along with this program; see the file COPYING. If not, write to | |
24 | the Free Software Foundation, 59 Temple Place - Suite 330, | |
25 | Boston, MA 02111-1307, USA. */ | |
26 | ||
27 | /* Calculate division table for SH5Media integer division | |
28 | Contributed by Joern Rernnecke | |
29 | joern.rennecke@superh.com */ | |
30 | ||
31 | #include <stdio.h> | |
32 | #include <math.h> | |
33 | ||
34 | #define BITS 5 | |
35 | #define N_ENTRIES (1 << BITS) | |
36 | #define CUTOFF_BITS 20 | |
37 | ||
38 | #define BIAS (-330) | |
39 | ||
40 | double max_defect = 0.; | |
41 | double max_defect_x; | |
42 | ||
43 | double min_defect = 1e9; | |
44 | double min_defect_x; | |
45 | ||
46 | double max_defect2 = 0.; | |
47 | double max_defect2_x; | |
48 | ||
49 | double min_defect2 = 0.; | |
50 | double min_defect2_x; | |
51 | ||
52 | double min_defect3 = 01e9; | |
53 | double min_defect3_x; | |
54 | int min_defect3_val; | |
55 | ||
56 | double max_defect3 = 0.; | |
57 | double max_defect3_x; | |
58 | int max_defect3_val; | |
59 | ||
60 | static double note_defect3 (int val, double d2, double y2d, double x) | |
61 | { | |
62 | int cutoff_val = val >> CUTOFF_BITS; | |
63 | double cutoff; | |
64 | double defect; | |
65 | ||
66 | if (val < 0) | |
67 | cutoff_val++; | |
68 | cutoff = (cutoff_val * (1<<CUTOFF_BITS) - val) * y2d; | |
69 | defect = cutoff + val * d2; | |
70 | if (val < 0) | |
71 | defect = - defect; | |
72 | if (defect > max_defect3) | |
73 | { | |
74 | max_defect3 = defect; | |
75 | max_defect3_x = x; | |
76 | max_defect3_val = val; | |
77 | } | |
78 | if (defect < min_defect3) | |
79 | { | |
80 | min_defect3 = defect; | |
81 | min_defect3_x = x; | |
82 | min_defect3_val = val; | |
83 | } | |
84 | } | |
85 | ||
86 | /* This function assumes 32 bit integers. */ | |
87 | static double | |
88 | calc_defect (double x, int constant, int factor) | |
89 | { | |
90 | double y0 = (constant - (int) floor ((x * factor * 64.))) / 16384.; | |
91 | double y1 = 2 * y0 -y0 * y0 * (x + BIAS / (1.*(1LL<<30))); | |
92 | double y2d0, y2d; | |
93 | int y2d1; | |
94 | double d, d2; | |
95 | ||
96 | y1 = floor (y1 * (1024 * 1024 * 1024)) / (1024 * 1024 * 1024); | |
97 | d = y1 - 1 / x; | |
98 | if (d > max_defect) | |
99 | { | |
100 | max_defect = d; | |
101 | max_defect_x = x; | |
102 | } | |
103 | if (d < min_defect) | |
104 | { | |
105 | min_defect = d; | |
106 | min_defect_x = x; | |
107 | } | |
108 | y2d0 = floor (y1 * x * (1LL << 60-16)); | |
109 | y2d1 = (int) (long long) y2d0; | |
110 | y2d = - floor ((y1 - y0 / (1<<30-14)) * y2d1) / (1LL<<44); | |
111 | d2 = y1 + y2d - 1/x; | |
112 | if (d2 > max_defect2) | |
113 | { | |
114 | max_defect2 = d2; | |
115 | max_defect2_x = x; | |
116 | } | |
117 | if (d2 < min_defect2) | |
118 | { | |
119 | min_defect2 = d2; | |
120 | min_defect2_x = x; | |
121 | } | |
122 | /* zero times anything is trivially zero. */ | |
123 | note_defect3 ((1 << CUTOFF_BITS) - 1, d2, y2d, x); | |
124 | note_defect3 (1 << CUTOFF_BITS, d2, y2d, x); | |
125 | note_defect3 ((1U << 31) - (1 << CUTOFF_BITS), d2, y2d, x); | |
126 | note_defect3 ((1U << 31) - 1, d2, y2d, x); | |
127 | note_defect3 (-1, d2, y2d, x); | |
128 | note_defect3 (-(1 << CUTOFF_BITS), d2, y2d, x); | |
129 | note_defect3 ((1U << 31) - (1 << CUTOFF_BITS) + 1, d2, y2d, x); | |
130 | note_defect3 (-(1U << 31), d2, y2d, x); | |
131 | return d; | |
132 | } | |
133 | ||
134 | int | |
135 | main () | |
136 | { | |
137 | int i; | |
138 | unsigned char factors[N_ENTRIES]; | |
139 | short constants[N_ENTRIES]; | |
140 | int steps = N_ENTRIES / 2; | |
141 | double step = 1. / steps; | |
142 | double eps30 = 1. / (1024 * 1024 * 1024); | |
143 | ||
144 | for (i = 0; i < N_ENTRIES; i++) | |
145 | { | |
146 | double x_low = (i < steps ? 1. : -3.) + i * step; | |
147 | double x_high = x_low + step - eps30; | |
148 | double x_med; | |
149 | int factor, constant; | |
150 | double low_defect, med_defect, high_defect, max_defect; | |
151 | ||
152 | factor = (1./x_low- 1./x_high) / step * 256. + 0.5; | |
153 | if (factor == 256) | |
154 | factor = 255; | |
155 | factors[i] = factor; | |
156 | /* Use minimum of error function for x_med. */ | |
157 | x_med = sqrt (256./factor); | |
158 | if (x_low < 0) | |
159 | x_med = - x_med; | |
160 | low_defect = 1. / x_low + x_low * factor / 256.; | |
161 | high_defect = 1. / x_high + x_high * factor / 256.; | |
162 | med_defect = 1. / x_med + x_med * factor / 256.; | |
163 | max_defect | |
164 | = ((low_defect > high_defect) ^ (x_med < 0)) ? low_defect : high_defect; | |
165 | constant = (med_defect + max_defect) * 0.5 * 16384. + 0.5; | |
166 | if (constant < -32768 || constant > 32767) | |
167 | abort (); | |
168 | constants[i] = constant; | |
169 | calc_defect (x_low, constant, factor); | |
170 | calc_defect (x_med, constant, factor); | |
171 | calc_defect (x_high, constant, factor); | |
172 | } | |
173 | printf ("/* This table has been generated by divtab.c .\n"); | |
174 | printf ("Defects for bias %d:\n", BIAS); | |
175 | printf (" Max defect: %e at %e\n", max_defect, max_defect_x); | |
176 | printf (" Min defect: %e at %e\n", min_defect, min_defect_x); | |
177 | printf (" Max 2nd step defect: %e at %e\n", max_defect2, max_defect2_x); | |
178 | printf (" Min 2nd step defect: %e at %e\n", min_defect2, min_defect2_x); | |
179 | printf (" Max div defect: %e at %d:%e\n", max_defect3, max_defect3_val, max_defect3_x); | |
180 | printf (" Min div defect: %e at %d:%e\n", min_defect3, min_defect3_val, min_defect3_x); | |
181 | printf (" Defect at 1: %e\n", | |
182 | calc_defect (1., constants[0], factors[0])); | |
183 | printf (" Defect at -2: %e */\n", | |
184 | calc_defect (-2., constants[steps], factors[steps])); | |
185 | printf ("\t.section\t.rodata\n"); | |
186 | printf ("\t.balign 2\n"); | |
187 | printf ("/* negative division constants */\n"); | |
188 | for (i = steps; i < 2 * steps; i++) | |
189 | printf ("\t.word\t%d\n", constants[i]); | |
190 | printf ("/* negative division factors */\n"); | |
191 | for (i = steps; i < 2*steps; i++) | |
192 | printf ("\t.byte\t%d\n", factors[i]); | |
193 | printf ("\t.skip %d\n", steps); | |
194 | printf ("\t.global GLOBAL(div_table):\n"); | |
195 | printf ("GLOBAL(div_table):\n"); | |
196 | printf ("\t.skip %d\n", steps); | |
197 | printf ("/* positive division factors */\n"); | |
198 | for (i = 0; i < steps; i++) | |
199 | printf ("\t.byte\t%d\n", factors[i]); | |
200 | printf ("/* positive division constants */\n"); | |
201 | for (i = 0; i < steps; i++) | |
202 | printf ("\t.word\t%d\n", constants[i]); | |
203 | exit (0); | |
204 | } |