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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.
74 lines
2.4 KiB
Plaintext
74 lines
2.4 KiB
Plaintext
NAME
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log2 - base 10 logarithm
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SYNOPSIS
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log2(x [,eps])
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TYPES
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x 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 2 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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When x is an integer power of 2, log2(x) will return an integer
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regardless of the value of eps or epsilon().
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If y is a positive integer, log2(x, 2^-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 log2(2), log2(4), log2(1024), log2(2^500), log2(1/2^23209)
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1 2 10 500 -23209
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; print log2(127), log2(23209), log2(2^17-19)
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6.98868468677216585326 14.50239674255407864468 16.99979085393743521984
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; print log2(-127)
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6.98868468677216585326+4.53236014182719380961i
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; print log2(2+3i), log2(-2+3i)
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1.85021985907054608020+1.41787163074572199658i 1.85021985907054608020+3.11448851108147181304i
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; print log2(2-3i), log2(-2-3i)
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1.85021985907054608020-1.41787163074572199658i 1.85021985907054608020-3.11448851108147181304i
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; print log2(17+0.3i, 1e-75), log2(-17-0.3i, 1e-75)
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4.08768744737521449955+0.02545668190826163773i 4.08768744737521449955-4.50690345991893217190i
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LIMITS
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x != 0
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0 < eps < 1
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LINK LIBRARY
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NUMBER *qlog2(NUMBER *x, NUMBER *eps)
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COMPLEX *c_log2(COMPLEX *x, NUMBER *eps)
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SEE ALSO
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ilog, ilogn, ilog10, ilog2, ln, log, logn
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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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