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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.
76 lines
2.5 KiB
Plaintext
76 lines
2.5 KiB
Plaintext
NAME
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root - root of a number
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SYNOPSIS
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root(x, n, [, eps])
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TYPES
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x number
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n positive integer
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eps nonzero real, defaults to epsilon()
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return real number
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DESCRIPTION
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For real x and positive integer n, n being odd if x is negative,
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root(x,n,eps) returns a multiple of eps differing from the
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real n-th root of x (nonnegative if x is positive) by less than
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0.75 eps, usually by less than 0.5 eps. If the n-th root of
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x is a multiple of eps, it will be returned exactly.
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For complex x and positive integer n, or negative x with positive even
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n, root(x, n, eps) returns a real or complex numbers whose real
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and imaginary parts are multiples of eps differing from the real
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and imaginary parts of the principal n-th root of x by less than
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0.75 eps, usually by less than 0.5 eps.
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For negative x and odd n, the principal n-th root of x may be
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obtained by using power(x, 1/n, eps).
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EXAMPLE
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; print root(7, 4, 1e-5), root(7, 4, 1e-10), root(7, 4, 1e-15)
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1.62658 1.6265765617 1.626576561697786
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; print root(1+3i, 3, 1e-5), root(1 + 3i, 3, 1e-10)
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1.34241+0.59361i 1.3424077452+0.5936127825i
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; print root(-8, 3, 1e-5), root(-8, 34, 1e-5)
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-2 ~1.05853505050032399594+~0.09807874962631613016i
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; print root(1i, 100, 1e-20)
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0.99987663248166059864+0.01570731731182067575i
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LIMITS
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n >= 0
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eps != 0
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LINK LIBRARY
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void rootvalue(VALUE *x, VALUE *n, VALUE *eps, VALUE *result)
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NUMBER *qroot(NUMBER *x, NUMBER *n, NUMBER *eps)
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COMPLEX *c_root(COMPLEX *x, NUMBER *n, NUMBER *eps)
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SEE ALSO
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power
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## Copyright (C) 1999,2021,2023 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: 1995/10/25 04:03:46
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## File existed as early as: 1995
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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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