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