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calc/help/ln
Landon Curt Noll 1c839dfede add logn and error checking for invalue eps and epsilon values
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.
2023-08-31 22:33:41 -07:00

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NAME
ln - logarithm function
SYNOPSIS
ln(x [,eps])
TYPES
x nonzero real or complex
eps 0 < real < 1, defaults to epsilon()
return real or complex
DESCRIPTION
Approximate the natural logarithm function of x by a multiple of
epsilon, the error having absolute value less than 0.75 * eps.
If n is a positive integer, ln(x, 10^-n) will usually be correct
to the n-th decimal place.
EXAMPLE
; print ln(10, 1e-5), ln(10, 1e-10), ln(10, 1e-15), ln(10, 1e-20)
2.30259 2.302585093 2.302585092994046 2.30258509299404568402
; print ln(2+3i, 1e-5), ln(2+3i, 1e-10)
1.28247+0.98279i 1.2824746787+0.9827937232i
LIMITS
x != 0
0 < eps < 1
LINK LIBRARY
NUMBER *qln(NUMBER *x, NUMBER *eps)
COMPLEX *c_ln(COMPLEX *x, NUMBER *eps)
SEE ALSO
acosh, asinh, atanh, exp, ilog, ilogn, ilog10, ilog2, log, log2, logn
## Copyright (C) 1999,2021,2023 Landon Curt Noll
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## Under source code control: 1995/10/11 04:41:26
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