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88 lines
3.2 KiB
Plaintext
88 lines
3.2 KiB
Plaintext
NAME
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logn - base n logarithm
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SYNOPSIS
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logn(x, n [,eps])
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TYPES
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x nonzero real or complex
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n nonzero real or complex
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eps 0 < real < 1, defaults to epsilon()
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return real or complex
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DESCRIPTION
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Approximate the base n logarithm function of x by a multiple of
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epsilon, the error having absolute value less than 0.75 * eps.
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The base, n, must not be 0 nor 1.
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When x = 2^a is an integer power of 2 and when n = 2^b is an
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integer power of 2, then log2(x, n) will return a/b
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regardless of the value of eps or epsilon().
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If y is a positive integer, logn(x, n, m^-y) will usually be correct
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to the y-th decimal place.
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EXAMPLE
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; print logn(2, 2), logn(4, 2), logn(1024, 2), logn(2^500, 2), logn(1/2^23209, 2)
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1 2 10 500 -23209
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; print logn(2, 42), logn(1024, 42), logn(2^500, 42), logn(1/2^23209, 42)
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0.18544902341536890054 1.85449023415368900542 92.72451170768445027095 -4304.08638444729681267682
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; print logn(127, 1/13), logn(23209, sqrt(3)), logn(2^17-19, 17)
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-1.88860925162778125111 18.29998720595030380546 4.15900804831225415076
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; print logn(-1, 1i), logn(2+3i, 3i+2), logn(2+3i, 3i)
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2 1 0.80360095345990217753-0.25441159318835790311i
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; print logn(22+3i, 3i), logn(22+3i, 3i, 1e-50)
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0.98489914201047045409-1.28484657882287682702i 0.98489914201047045408-1.28484657882287682702i
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; print logn(-127, 7), logn(-127i, 7i)
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2.48941971386002223933+1.61445925708078115429i 1.11272593230445294959-1.70545496954177392315i
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; print logn(2+3i, 4), logn(-2+3i, 4i)
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0.92510992953527304010+0.70893581537286099830i 1.17764179178059522911+0.22287007593665359808i
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; print logn(2-3i, 4), logn(-2-3i, 4i)
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0.92510992953527304010-0.70893581537286099830i -0.36752510241663632776-1.14080522421220596732i
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; print logn(17+0.3i, 17, 1e-75), logn(-17-0.3i, 17i, 1e-75)
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1.00005495001021376506+0.00622799102938744640i 0.29734185630294053511-1.26746929577868497155i
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LIMITS
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x != 0
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n != 0 && n != 1
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qlogn(NUMBER *x, NUMBER *n, NUMBER *eps)
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COMPLEX *c_logn(COMPLEX *x, COMPLEX *n, NUMBER *eps)
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SEE ALSO
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ilog, ilogn, ilog10, ilog2, ln, log, log2
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## Copyright (C) 2023 Landon Curt Noll
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##
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## Calc is open software; you can redistribute it and/or modify it under
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## the terms of the version 2.1 of the GNU Lesser General Public License
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## as published by the Free Software Foundation.
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##
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## Calc is distributed in the hope that it will be useful, but WITHOUT
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## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
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## Public License for more details.
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##
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## A copy of version 2.1 of the GNU Lesser General Public License is
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## distributed with calc under the filename COPYING-LGPL. You should have
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## received a copy with calc; if not, write to Free Software Foundation, Inc.
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## 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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##
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## Under source code control: 2023/08/19 09:14:04
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## File existed as early as: 2023
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##
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## chongo <was here> /\oo/\ http://www.isthe.com/chongo/
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## Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
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