sqrt_int_guess.bc

#! /usr/bin/bc -l
#
# SPDX-License-Identifier: BSD-2-Clause
#
# Copyright (c) 2018-2025 Gavin D. Howard and contributors.
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# Adjust this number to try ranges above different powers of 10.
max = 0

n = (1 << max)

# Uncomment this to test the high part of the ranges.
#n += (1 - (1 >> 10))

n

# Loop from the start number to the next power of 10.
for (i = n; i < (n$ << 1); i += 1)
{
	# This is the lower limit.
	t1 = sqrt(1/(3*i))

	l = length(i$)/2

	print "i: ", i, "\n"
	#print "l: ", l, "\n"

	if (l$ != l)
	{
		# Limit between 2.4 and 3.
		limit = 2.7 << (l$ * 2)
		#print "limit: ", limit, "\n"

		if (i >= limit)
		{
			t2 = 1/(i >> (l$)) * 2
		}
		else
		{
			t2 = 1/(i >> (l$))
		}
	}
	else
	{
		# Limit between 3.8-ish and 4.8
		limit = 4.3 << (l$ * 2 - 1)
		#print "limit: ", limit, "\n"

		if (i >= limit)
		{
			t2 = 1/(i >> (l$ - 1)) * 8
		}
		else
		{
			t2 = 1/(i >> (l$ - 1)) * 4
		}
	}

	# This is the upper limit.
	t3 = sqrt(5/(3*i))

	# This is true when the guess is in between the limits.
	good = (t1 < t2 && t2 < t3)

	print t1, " < ", t2, " < ", t3, ": ", good, "\n"

	# Error if we have a problem.
	if (!good) sqrt(-1)
}

halt