1#! /usr/bin/bc
2#
3# SPDX-License-Identifier: BSD-2-Clause
4#
5# Copyright (c) 2018-2023 Gavin D. Howard and contributors.
6#
7# Redistribution and use in source and binary forms, with or without
8# modification, are permitted provided that the following conditions are met:
9#
10# * Redistributions of source code must retain the above copyright notice, this
11#   list of conditions and the following disclaimer.
12#
13# * Redistributions in binary form must reproduce the above copyright notice,
14#   this list of conditions and the following disclaimer in the documentation
15#   and/or other materials provided with the distribution.
16#
17# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
18# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
21# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
22# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
23# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
24# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
25# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
26# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
27# POSSIBILITY OF SUCH DAMAGE.
28#
29
30scale = 20
31
32# Adjust this number to try ranges below different powers of 10.
33shift = 4
34
35# Adjust this to try extra digits. For example, a value of one means that one
36# digit is checked (such as 0.09 through 0.01), a value of two means that two
37# digits are checked (0.090 through 0.010), etc.
38max = shift + 2
39
40n = (9 >> shift)
41inc = (1 >> max)
42stop = (1 >> shift)
43
44# Uncomment this to test the high part of the ranges.
45#n += (1 - (1 >> max + 5)) >> shift
46
47for (i = n; i >= stop; i -= inc)
48{
49	# This is the lower limit.
50	t1 = sqrt(1/(3*i))
51
52	# Start with the inverse.
53	t2 = (1/i)
54
55	# And take half its length of course.
56	l = length(t2$)/2
57
58	temp = i
59	odd = 0
60
61	# We go by powers of 10 below, but there is a degenerate case: an exact
62	# power of 10, for which length() will return one digit more. So we check
63	# for that and fix it.
64	while (temp < 1)
65	{
66		temp <<= 1
67		odd = !odd
68	}
69
70	if (temp == 1)
71	{
72		odd = !odd
73	}
74
75	print "i:  ", i, "\n"
76	print "t2: ", t2, "\n"
77	#print "l:  ", l, "\n"
78	print "odd: ", odd, "\n"
79
80	if (odd)
81	{
82		# Limit between 6 and 7.5.
83		limit1 = 6.7 >> (l$ * 2 + 1)
84
85		# Limit between 1.5 and 1.83-ish.
86		limit2 = 1.7 >> (l$ * 2 + 1)
87		print "limit1: ", limit1, "\n"
88		print "limit2: ", limit2, "\n"
89
90		if (i >= limit1)
91		{
92			t2 = (t2 >> l$)
93		}
94		else if (i >= limit2)
95		{
96			t2 = (t2 >> l$) / 2
97		}
98		else
99		{
100			t2 = (t2 >> l$) / 4
101		}
102	}
103	else
104	{
105		# Limit between 2.4 and 3.
106		limit = 2.7 >> (l$ * 2)
107		print "limit: ", limit, "\n"
108
109		if (i >= limit)
110		{
111			t2 = (t2 >> l$) * 2
112		}
113		else
114		{
115			t2 = (t2 >> l$)
116		}
117	}
118	#t2 = 1
119	t3 = sqrt(5/(3*i))
120	good = (t1 < t2 && t2 < t3)
121
122	print t1, " < ", t2, " < ", t3, ": ", good, "\n\n"
123	if (!good) sqrt(-1)
124}
125
126halt
127