xref: /freebsd-src/contrib/bc/scripts/sqrt_frac_guess.bc (revision a970610a3af63b3f4df5b69d91c6b4093a00ed8f)

#! /usr/bin/bc
#
# SPDX-License-Identifier: BSD-2-Clause
#
# Copyright (c) 2018-2024 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