1#! /usr/bin/bc -l
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
30# Adjust this number to try ranges above different powers of 10.
31max = 0
32
33n = (1 << max)
34
35# Uncomment this to test the high part of the ranges.
36#n += (1 - (1 >> 10))
37
38n
39
40# Loop from the start number to the next power of 10.
41for (i = n; i < (n$ << 1); i += 1)
42{
43	# This is the lower limit.
44	t1 = sqrt(1/(3*i))
45
46	l = length(i$)/2
47
48	print "i: ", i, "\n"
49	#print "l: ", l, "\n"
50
51	if (l$ != l)
52	{
53		# Limit between 2.4 and 3.
54		limit = 2.7 << (l$ * 2)
55		#print "limit: ", limit, "\n"
56
57		if (i >= limit)
58		{
59			t2 = 1/(i >> (l$)) * 2
60		}
61		else
62		{
63			t2 = 1/(i >> (l$))
64		}
65	}
66	else
67	{
68		# Limit between 3.8-ish and 4.8
69		limit = 4.3 << (l$ * 2 - 1)
70		#print "limit: ", limit, "\n"
71
72		if (i >= limit)
73		{
74			t2 = 1/(i >> (l$ - 1)) * 8
75		}
76		else
77		{
78			t2 = 1/(i >> (l$ - 1)) * 4
79		}
80	}
81
82	# This is the upper limit.
83	t3 = sqrt(5/(3*i))
84
85	# This is true when the guess is in between the limits.
86	good = (t1 < t2 && t2 < t3)
87
88	print t1, " < ", t2, " < ", t3, ": ", good, "\n"
89
90	# Error if we have a problem.
91	if (!good) sqrt(-1)
92}
93
94halt
95