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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.
79 lines
2.6 KiB
Plaintext
79 lines
2.6 KiB
Plaintext
NAME
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power - evaluate a numerical power to specified accuracy
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SYNOPSIS
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power(x, y, [, eps])
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TYPES
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x number
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y number
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eps nonzero real, defaults to epsilon()
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return number
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DESCRIPTION
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For real or complex x and y, power(x,y,eps) returns a real or
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complex number for which the real and imaginary parts are multiples
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of epsilon differing from the true real and imaginary parts of the
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principal y-th power of x by less than 0.75 * abs(eps), usually by
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less than 0.5 * abs(eps). If the principal y-th power of x is a
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multiple of eps, it will be returned exactly.
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If y is a large integer but x^y is not large, and accuracy
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represented by eps is all that is required, power(x,y,eps) may be
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considerably faster than appr(x^y, eps, 24), the difference between
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the two results being probably at most abs(eps).
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EXAMPLE
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; print power(1.2345, 10, 1e-5), power(1.2345, 10, 1e-10)
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8.22074 8.2207405646
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; print power(1+3i, 3, 1e-5), power(1 + 3i, 2+ 1i, 1e-5)
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-26-18i -2.50593-1.39445i
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; print power(1+ 1e-30, 1e30, 1e-20)
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2.71828182845904523536
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; print power(1i, 1i, 1e-20)
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0.20787957635076190855
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; print power(exp(1, 1e-20), pi(1e-20) * 1i/2, 1e-20)
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1i
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LIMITS
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If x = 0, y in power(x,y,eps) has to have positive real part,
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except in the case of y = 0; power(0, 0, eps) is the multiple of
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eps nearest 1.
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eps != 0
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LINK LIBRARY
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void powervalue(VALUE *x, VALUE *y, VALUE *eps, VALUE *result)
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NUMBER *qpower(NUMBER *x, NUMBER *y, NUMBER *eps)
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COMPLEX *c_power(COMPLEX *x, COMPLEX *y, NUMBER *eps)
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SEE ALSO
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root
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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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