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add logn and error checking for invalue eps and epsilon values

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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.
This commit is contained in:
Landon Curt Noll
2023-08-31 22:33:41 -07:00
parent 4787199462
commit 1c839dfede
55 changed files with 1092 additions and 199 deletions
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39
help/logn
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@@ -7,7 +7,7 @@ SYNOPSIS
TYPES
x nonzero real or complex
n nonzero real or complex
eps nonzero real, defaults to epsilon()
eps 0 < real < 1, defaults to epsilon()
return real or complex
@@ -17,26 +17,45 @@ DESCRIPTION
The base, n, must not be 0 nor 1.
If y is a positive integer, log(x, n^-y) will usually be correct
When x = 2^a is an integer power of 2 and when n = 2^b is an
integer power of 2, then log2(x, n) will return a/b
regardless of the value of eps or epsilon().
If y is a positive integer, logn(x, n, m^-y) will usually be correct
to the y-th decimal place.
EXAMPLE
; print logn(15.625, 2.5), logn(15.625, 2.5, 1e-25)
~3.00000000000000000001 3
; print logn(2, 2), logn(4, 2), logn(1024, 2), logn(2^500, 2), logn(1/2^23209, 2)
1 2 10 500 -23209
; print logn(127, 1/13), log(23209, sqrt(3)), logn(2^17-19, 17)
~-1.88860925162778125111 6 ~4.15900804831225415076
; print logn(2, 42), logn(1024, 42), logn(2^500, 42), logn(1/2^23209, 42)
0.18544902341536890054 1.85449023415368900542 92.72451170768445027095 -4304.08638444729681267682
; print logn(127, 1/13), logn(23209, sqrt(3)), logn(2^17-19, 17)
-1.88860925162778125111 18.29998720595030380546 4.15900804831225415076
; print logn(-1, 1i), logn(2+3i, 3i+2), logn(2+3i, 3i)
2 1 ~0.80360095345990217753-~0.25441159318835790311i
2 1 0.80360095345990217753-0.25441159318835790311i
; print logn(22+3i, 3i, 1e-50)
~0.98489914201047045408-~1.28484657882287682702i
; print logn(22+3i, 3i), logn(22+3i, 3i, 1e-50)
0.98489914201047045409-1.28484657882287682702i 0.98489914201047045408-1.28484657882287682702i
; print logn(-127, 7), logn(-127i, 7i)
2.48941971386002223933+1.61445925708078115429i 1.11272593230445294959-1.70545496954177392315i
; print logn(2+3i, 4), logn(-2+3i, 4i)
0.92510992953527304010+0.70893581537286099830i 1.17764179178059522911+0.22287007593665359808i
; print logn(2-3i, 4), logn(-2-3i, 4i)
0.92510992953527304010-0.70893581537286099830i -0.36752510241663632776-1.14080522421220596732i
; print logn(17+0.3i, 17, 1e-75), logn(-17-0.3i, 17i, 1e-75)
1.00005495001021376506+0.00622799102938744640i 0.29734185630294053511-1.26746929577868497155i
LIMITS
x != 0
n != 0 && n != 1
eps > 0
0 < eps < 1
LINK LIBRARY
NUMBER *qlogn(NUMBER *x, NUMBER *n, NUMBER *eps)