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1c839dfede
Add new logn(x, n [,eps]) builtin to compute logarithms to base n. Verify that eps arguments (error tolerance arguments that override the default epsilon value) to builtin functions have proper values. Previously the eps argument had little to no value checks for many builtin functions. Document in help files for builtin functions that take eps arguments, the LIMIT range for such eps values.
88 lines
3.1 KiB
Plaintext
88 lines
3.1 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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