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#! /usr/bin/bc
#
# SPDX-License-Identifier: BSD-2-Clause
#
# Copyright (c) 2018-2023 Gavin D. Howard and contributors.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are met:
#
# * Redistributions of source code must retain the above copyright notice, this
# list of conditions and the following disclaimer.
#
# * Redistributions in binary form must reproduce the above copyright notice,
# this list of conditions and the following disclaimer in the documentation
# and/or other materials provided with the distribution.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
#
scale = 20
# Adjust this number to try ranges below different powers of 10.
shift = 4
# Adjust this to try extra digits. For example, a value of one means that one
# digit is checked (such as 0.09 through 0.01), a value of two means that two
# digits are checked (0.090 through 0.010), etc.
max = shift + 2
n = (9 >> shift)
inc = (1 >> max)
stop = (1 >> shift)
# Uncomment this to test the high part of the ranges.
#n += (1 - (1 >> max + 5)) >> shift
for (i = n; i >= stop; i -= inc)
{
# This is the lower limit.
t1 = sqrt(1/(3*i))
# Start with the inverse.
t2 = (1/i)
# And take half its length of course.
l = length(t2$)/2
temp = i
odd = 0
# We go by powers of 10 below, but there is a degenerate case: an exact
# power of 10, for which length() will return one digit more. So we check
# for that and fix it.
while (temp < 1)
{
temp <<= 1
odd = !odd
}
if (temp == 1)
{
odd = !odd
}
print "i: ", i, "\n"
print "t2: ", t2, "\n"
#print "l: ", l, "\n"
print "odd: ", odd, "\n"
if (odd)
{
# Limit between 6 and 7.5.
limit1 = 6.7 >> (l$ * 2 + 1)
# Limit between 1.5 and 1.83-ish.
limit2 = 1.7 >> (l$ * 2 + 1)
print "limit1: ", limit1, "\n"
print "limit2: ", limit2, "\n"
if (i >= limit1)
{
t2 = (t2 >> l$)
}
else if (i >= limit2)
{
t2 = (t2 >> l$) / 2
}
else
{
t2 = (t2 >> l$) / 4
}
}
else
{
# Limit between 2.4 and 3.
limit = 2.7 >> (l$ * 2)
print "limit: ", limit, "\n"
if (i >= limit)
{
t2 = (t2 >> l$) * 2
}
else
{
t2 = (t2 >> l$)
}
}
#t2 = 1
t3 = sqrt(5/(3*i))
good = (t1 < t2 && t2 < t3)
print t1, " < ", t2, " < ", t3, ": ", good, "\n\n"
if (!good) sqrt(-1)
}
halt
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