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.
2025-08-19 01:13:27 +03:00 · 2023-08-31 22:33:41 -07:00
parent 4787199462
commit 1c839dfede
55 changed files with 1092 additions and 199 deletions
--- a/10
+++ b/10
@@ -89,6 +89,16 @@ The following are the changes from calc version 2.14.3.5 to date:
    Setting an invalid epsilon via the epsilon(value) or confiv("epsilon",
    value) triggers an error.  The epsilon value must be: 0 < epsilon < 1.

+    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.
+

 The following are the changes from calc version 2.14.3.4 to 2.14.3.5:

--- a/cal/regress.cal
+++ b/cal/regress.cal
@@ -3007,8 +3007,6 @@ define test_2600()
 			    strcat(str(tnum++), ': log2(2^500) == 500'));
 	vrfy(log2(1/2^23209) == -23209,
 			    strcat(str(tnum++), ': log2(1/2^23209) == -23209'));
-	vrfy(isint(log2(1/2^23209)),
-			    strcat(str(tnum++), ': isint(log2(1/2^23209))'));
 	vrfy(round(log2(127),10) == 6.9886846868,
 	    strcat(str(tnum++),
 		   ': round(log2(127),10) == 6.9886846868'));
@@ -3036,6 +3034,48 @@ define test_2600()
 	vrfy(round(log2(17+0.3i),10) == 4.0876874474+0.0254566819i,
 	    strcat(str(tnum++),
 		   ': round(log2(17+0.3i),10) == 4.0876874474+0.0254566819i'));
+	vrfy(logn(2, 2) == 1,
+			    strcat(str(tnum++), ': logn(2, 2) == 1'));
+	vrfy(logn(4, 2) == 2,
+			    strcat(str(tnum++), ': logn(4, 2) == 2'));
+	vrfy(logn(1024, 2) == 10,
+			    strcat(str(tnum++), ': logn(1024, 2) == 10'));
+	vrfy(logn(2^500, 2) == 500,
+			    strcat(str(tnum++), ': logn(2^500, 2) == 500'));
+	vrfy(logn(1/2^23209, 2) == -23209,
+			    strcat(str(tnum++), ': logn(1/2^23209, 2) == -23209'));
+	vrfy(round(logn(127, 1/13),10) == -1.8886092516,
+	    strcat(str(tnum++),
+		   ': round(logn(127, 1/13),10) == -1.8886092516'));
+	vrfy(round(logn(23209, sqrt(3)),10) == 18.299987206,
+	    strcat(str(tnum++),
+		   ': round(logn(23209, sqrt(3)),10) == 18.299987206'));
+	vrfy(round(logn(2, 42),10) == 0.1854490234,
+	    strcat(str(tnum++),
+		   ': round(logn(2, 42),10) == 0.1854490234'));
+	vrfy(round(logn(1024, 42),10) == 1.8544902342,
+	    strcat(str(tnum++),
+		   ': round(logn(1024, 42),10) == 1.8544902342'));
+	vrfy(round(logn(2^500, 42),10) == 92.7245117077,
+	    strcat(str(tnum++),
+		   ': round(logn(2^500, 42),10) == 92.7245117077'));
+	vrfy(round(logn(1/2^23209, 42),10) == -4304.0863844473,
+	    strcat(str(tnum++),
+		   ': round(logn(1/2^23209, 42),10) == -4304.0863844473'));
+	vrfy(logn(-1, 1i) == 2,
+		   strcat(str(tnum++), ': logn(-1, 1i) == 2'));
+	vrfy(round(logn(22+3i, 3i),10) == 0.984899142-1.2848465788i,
+	    strcat(str(tnum++),
+		   ': round(logn(22+3i, 3i),10) == 0.984899142-1.2848465788i'));
+	vrfy(round(logn(22.2+3.3i, -4-3.3i),10) == 0.5456929478+0.9025545623i,
+	    strcat(str(tnum++),
+		   ': round(logn(22.2+3.3i, -4-3.3i),10) == 0.5456929478+0.9025545623i'));
+	vrfy(round(logn(-127, 7),10) == 2.4894197139+1.6144592571i,
+	    strcat(str(tnum++),
+		   ': round(logn(-127, 7),10) == 2.4894197139+1.6144592571i'));
+	vrfy(round(logn(-127, 7i),10) == 2.2963271277-0.2392040372i,
+	    strcat(str(tnum++),
+		   ': round(logn(-127, 7i),10) == 2.2963271277-0.2392040372i'));
        epsilon(i),;
 	print tnum++: ': epsilon(i),;';

--- a/calcerr.tbl
+++ b/calcerr.tbl
@@ -545,3 +545,8 @@ E_HM2H2		Invalid rounding arg 4 for hm2h
 E_LOG2_1	Bad epsilon argument for log2
 E_LOG2_2	Non-numeric first argument for log2
 E_LOG2_3	Cannot calculate log2 for this value
+E_LOGN_1	Bad epsilon argument for logn
+E_LOGN_2	Non-numeric first argument for logn
+E_LOGN_3	Cannot calculate logn for this value
+E_LOGN_4	Cannot calculate logn for this log base
+E_LOGN_5	Non-numeric second argument for logn
--- a/func.c
+++ b/func.c
--- a/help/abs
+++ b/help/abs
@@ -36,7 +36,7 @@ EXAMPLE
    5 6.40312 6.4031242374

 LIMITS
-    none
+    when x is complex, eps != 0

 LINK LIBRARY
    NUMBER *qqabs(NUMBER *x)
@@ -44,7 +44,7 @@ LINK LIBRARY
 SEE ALSO
    cmp, epsilon, hypot, norm, near, obj

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acos
+++ b/help/acos
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, -1 <= x <= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    1.0472 1.0471975512 1.047197551196598 1.04719755119659774615

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacos(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    asin, atan, asec, acsc, acot, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acosh
+++ b/help/acosh
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, x >= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	nonnegative real

@@ -24,7 +24,7 @@ EXAMPLE
    1.31696 1.3169578969 1.316957896924817 1.31695789692481670862

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacosh(NUMBER *x, NUMBER *eps)
@@ -32,7 +32,7 @@ LINK LIBRARY
 SEE ALSO
    asinh, atanh, asech, acsch, acoth, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acot
+++ b/help/acot
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    0.46365 0.463647609 0.463647609000806 0.46364760900080611621

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacot(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    asin, acos, atan, asec, acsc, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acoth
+++ b/help/acoth
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, with abs(x) > 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -23,7 +23,7 @@ EXAMPLE
    0.54931 0.5493061443 0.549306144334055 0.5493061443340548457

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacoth(NUMBER *x, NUMBER *eps)
@@ -31,7 +31,7 @@ LINK LIBRARY
 SEE ALSO
    asinh, acosh, atanh, asech, acsch, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acsc
+++ b/help/acsc
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, with absolute value >= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    0.5236 0.5235987756 0.523598775598299 0.52359877559829887308

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacsc(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    asin, acos, atan, asec, acot, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/acsch
+++ b/help/acsch
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -23,7 +23,7 @@ EXAMPLE
    0.48121 0.4812118251 0.481211825059603 0.4812118250596034475

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qacsch(NUMBER *x, NUMBER *eps)
@@ -31,7 +31,7 @@ LINK LIBRARY
 SEE ALSO
    asinh, acosh, atanh, asech, acoth, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/arg
+++ b/help/arg
@@ -24,7 +24,7 @@ EXAMPLE
    56.3099 135 -135

 LIMITS
-    none
+    eps != 0

 LINK LIBRARY
    none
--- a/help/asec
+++ b/help/asec
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, with absolute value >= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    1.0472 1.0471975512 1.047197551196598 1.04719755119659774615

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qasec(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    asin, acos, atan, acsc, acot, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/asech
+++ b/help/asech
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, 0 < x <= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -23,7 +23,7 @@ EXAMPLE
    1.31696 1.3169578969 1.316957896924817 1.31695789692481670862

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qasech(NUMBER *x, NUMBER *eps)
@@ -31,7 +31,7 @@ LINK LIBRARY
 SEE ALSO
    asinh, acosh, atanh, acsch, acoth, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/asin
+++ b/help/asin
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real, -1 <= x <= 1
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    0.5236 0.5235987756 0.523598775598299 0.52359877559829887308

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qasin(NUMBER *q, NUMBER *epsilon)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    acos, atan, asec, acsc, acot, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/asinh
+++ b/help/asinh
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -23,7 +23,7 @@ EXAMPLE
    1.44363 1.4436354752 1.44363547517881 1.44363547517881034249

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qasinh(NUMBER *x, NUMBER *eps)
@@ -31,7 +31,7 @@ LINK LIBRARY
 SEE ALSO
    acosh, atanh, asech, acsch, acoth, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/atan
+++ b/help/atan
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    1.10715 1.1071487178 1.107148717794091 1.10714871779409050302

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qatan(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    asin, acos, asec, acsc, acot, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/atan2
+++ b/help/atan2
@@ -28,7 +28,7 @@ EXAMPLE
    0 ~0.52359877559829887307 ~0.31038740713235146535

 LIMITS
-    none
+    eps != 0

 LINK LIBRARY
    NUMBER *qatan2(NUMBER *y, *x, *acc)
@@ -36,7 +36,7 @@ LINK LIBRARY
 SEE ALSO
    acos, asin, atan, cos, epsilon, sin, tan

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/atanh
+++ b/help/atanh
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -23,7 +23,7 @@ EXAMPLE
    0.54931 0.5493061443 0.549306144334055 0.5493061443340548457

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qatanh(NUMBER *x, NUMBER *eps)
@@ -31,7 +31,7 @@ LINK LIBRARY
 SEE ALSO
    asinh, acosh, asech, acsch, acoth, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/config
+++ b/help/config
@@ -1034,7 +1034,7 @@ EXAMPLE
    3.141592653589793238462643383279502884197169399375105820974944592307816406

 LIMITS
-    none
+    0 < epsilon < 1

 LINK LIBRARY
     none
--- a/help/cos
+++ b/help/cos
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -26,7 +26,7 @@ EXAMPLE
    0.5 0 -1

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcos(NUMBER *x, NUMBER *eps)
@@ -35,7 +35,7 @@ LINK LIBRARY
 SEE ALSO
    sin, tan, sec, csc, cot, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/cosh
+++ b/help/cosh
@@ -6,13 +6,13 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

 DESCRIPTION
    Calculate the cosh of x to the nearest or next to nearest multiple of
-    epsilon, with absolute error less than .75 * abs(eps).
+    epsilon, with absolute error less than .75 * eps.

    cosh(x) = (exp(x) + exp(-x))/2

@@ -21,7 +21,7 @@ EXAMPLE
    1.54308 1.5430806348 1.543080634815244 1.54308063481524377848

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcosh(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    sinh, tanh, sech, csch, coth, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/cot
+++ b/help/cot
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real
-    acc		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -19,7 +19,7 @@ EXAMPLE
    0.64209 0.6420926159 0.642092615934331 0.64209261593433070301

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcot(NUMBER *x, NUMBER *eps)
@@ -27,7 +27,7 @@ LINK LIBRARY
 SEE ALSO
    sin, cos, tan, sec, csc, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/coth
+++ b/help/coth
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    1.31304 1.3130352855 1.313035285499331 1.31303528549933130364

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcoth(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    sinh, cosh, tanh, sech, csch, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/csc
+++ b/help/csc
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -19,7 +19,7 @@ EXAMPLE
    1.1884 1.1883951058 1.188395105778121 1.18839510577812121626

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcsc(NUMBER *x, NUMBER *eps)
@@ -27,7 +27,7 @@ LINK LIBRARY
 SEE ALSO
    sin, cos, tan, sec, cot, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/csch
+++ b/help/csch
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -21,7 +21,7 @@ EXAMPLE
    0.85092 0.8509181282 0.850918128239322 0.85091812823932154513

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qcsch(NUMBER *x, NUMBER *eps)
@@ -29,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    sinh, cosh, tanh, sech, coth, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/d2g
+++ b/help/d2g
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		eps value is ignored

    return	number

@@ -32,7 +32,7 @@ SEE ALSO
    d2r, r2d, g2r, r2g, g2d,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/d2r
+++ b/help/d2r
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -27,7 +27,7 @@ EXAMPLE
    0.5 0.5 1

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qpidiv180(NUMBER *eps)
@@ -36,7 +36,7 @@ SEE ALSO
    r2d, g2r, r2g, d2g, g2d,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/epsilon
+++ b/help/epsilon
@@ -5,7 +5,7 @@ SYNOPSIS
    epsilon([eps])

 TYPES
-    eps		real number greater than 0 and less than 1
+    eps		0 < real < 1, defaults to epsilon()

    return	real number greater than 0 and less than 1

@@ -72,7 +72,7 @@ EXAMPLE
    3.141592653589793238462643383279502884197169399375105820974944592307816406

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    void setepsilon(NUMBER *eps)
@@ -81,7 +81,7 @@ LINK LIBRARY
 SEE ALSO
    config, display, fprintf, printf, strprintf

-## Copyright (C) 1999,2018,2021  Landon Curt Noll
+## Copyright (C) 1999,2018,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/exp
+++ b/help/exp
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real or complex
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real or complex

@@ -32,6 +32,7 @@ EXAMPLE

 LIMITS
    x < 693093
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qexp(NUMBER *x, NUMBER *eps)
@@ -40,7 +41,7 @@ LINK LIBRARY
 SEE ALSO
    ln, cosh, sinh, tanh

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/g2d
+++ b/help/g2d
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		eps value is ignored

    return	number

@@ -32,7 +32,7 @@ SEE ALSO
    d2r, r2d, g2r, r2g, d2g,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/g2r
+++ b/help/g2r
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -27,7 +27,7 @@ EXAMPLE
    0.5 0.5 1

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qpidiv200(NUMBER *eps)
@@ -36,7 +36,7 @@ SEE ALSO
    d2r, r2d, r2g, d2g, g2d,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/gd
+++ b/help/gd
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    z		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number or "Log of zero or infinity" error value

@@ -42,7 +42,7 @@ EXAMPLE
    1.42291+0.22751i 1.4229114625+0.2275106584i

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    COMPLEX *c_gd(COMPLEX *x, NUMBER *eps)
@@ -50,7 +50,7 @@ LINK LIBRARY
 SEE ALSO
    agd, exp, ln, sin, sinh, etc.

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/hypot
+++ b/help/hypot
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x, y	real
-    eps		nonzero real
+    eps		nonzero real, defaults to epsilon()

    return	real

@@ -19,7 +19,7 @@ EXAMPLE
    5 3.605551

 LIMITS
-    none
+    eps != 0

 LINK LIBRARY
    NUMBER *qhypot(NUMBER *q1, *q2, *epsilon)
@@ -27,7 +27,7 @@ LINK LIBRARY
 SEE ALSO
    ltol

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/ln
+++ b/help/ln
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real or complex
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real or complex

@@ -25,7 +25,7 @@ EXAMPLE

 LIMITS
    x != 0
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qln(NUMBER *x, NUMBER *eps)
--- a/help/log
+++ b/help/log
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real or complex
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real or complex

@@ -29,7 +29,7 @@ EXAMPLE

 LIMITS
    x != 0
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qlog(NUMBER *x, NUMBER *eps)
@@ -38,7 +38,7 @@ LINK LIBRARY
 SEE ALSO
    ilog, ilogn, ilog10, ilog2, ln, log2, logn

-## Copyright (C) 2006  Landon Curt Noll
+## Copyright (C) 2006,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/log2
+++ b/help/log2
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		nonzero real or complex
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real or complex

@@ -17,7 +17,7 @@ DESCRIPTION
    When x is an integer power of 2, log2(x) will return an integer
    regardless of the value of eps or epsilon().

-    If y is a positive integer, log(x, 2^-y) will usually be correct
+    If y is a positive integer, log2(x, 2^-y) will usually be correct
    to the y-th decimal place.

 EXAMPLE
@@ -41,7 +41,7 @@ EXAMPLE

 LIMITS
    x != 0
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qlog2(NUMBER *x, NUMBER *eps)
--- a/help/logn
+++ b/help/logn
@@ -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)
--- a/help/ltol
+++ b/help/ltol
@@ -7,7 +7,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real
+    eps		nonzero real, defaults to epsilon()

    return	real

@@ -21,6 +21,7 @@ EXAMPLE

 LIMITS
    abs(x) <= 1
+    eps != 0

 LINK LIBRARY
    NUMBER *qlegtoleg(NUMBER *q1, *epsilon, BOOL wantneg)
@@ -28,7 +29,7 @@ LINK LIBRARY
 SEE ALSO
    hypot

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/near
+++ b/help/near
@@ -7,7 +7,7 @@ SYNOPSIS
 TYPES
    x		real
    y		real
-    eps		real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	-1, 0 or 1

@@ -22,7 +22,7 @@ EXAMPLE
    -1 1

 LIMITS
-    eps >= 0
+    0 < eps < 1

 LINK LIBRARY
    FLAG qnear(NUMBER *x, NUMBER *y, NUMBER *eps)
@@ -30,7 +30,7 @@ LINK LIBRARY
 SEE ALSO
    epsilon, abs

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/pi
+++ b/help/pi
@@ -5,7 +5,7 @@ SYNOPSIS
    pi([eps])

 TYPES
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -18,7 +18,7 @@ EXAMPLE
    3.14159 3.1415926536 3.141592653589793 3.14159265358979323846

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qpi(NUMBER *eps)
@@ -26,7 +26,7 @@ LINK LIBRARY
 SEE ALSO
    atan2

-## Copyright (C) 1999-2006  Landon Curt Noll
+## Copyright (C) 1999-2006,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/polar
+++ b/help/polar
@@ -26,7 +26,7 @@ EXAMPLE
    1.41421+1.41421i 2i -1.414215+1.41421i

 LIMITS
-    none
+    eps != 0

 LINK LIBRARY
    COMPLEX *c_polar(NUMBER *r, NUMBER *t, NUMBER *eps);
@@ -34,7 +34,7 @@ LINK LIBRARY
 SEE ALSO
    abs, arg, re, im

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/power
+++ b/help/power
@@ -45,7 +45,7 @@ LIMITS
    except in the case of y = 0; power(0, 0, eps) is the multiple of
    eps nearest 1.

-    eps > 0
+    eps != 0

 LINK LIBRARY
    void powervalue(VALUE *x, VALUE *y, VALUE *eps, VALUE *result)
@@ -55,7 +55,7 @@ LINK LIBRARY
 SEE ALSO
    root

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/r2d
+++ b/help/r2d
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -25,7 +25,7 @@ EXAMPLE
    180+~229.18311805232928350739i 60+180, 36+900i

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qpidiv180(NUMBER *eps)
@@ -34,7 +34,7 @@ SEE ALSO
    d2r, g2r, r2g, d2g, g2d,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/r2g
+++ b/help/r2g
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -25,7 +25,7 @@ EXAMPLE
    200+~254.64790894703253723043i 50+200i 40+1000i

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qpidiv200(NUMBER *eps)
@@ -34,7 +34,7 @@ SEE ALSO
    d2r, r2d, g2r, d2g, g2d,
    sin, cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 2021  Landon Curt Noll
+## Copyright (C) 2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/root
+++ b/help/root
@@ -42,7 +42,7 @@ EXAMPLE

 LIMITS
    n >= 0
-    eps > 0
+    eps != 0

 LINK LIBRARY
    void rootvalue(VALUE *x, VALUE *n, VALUE *eps, VALUE *result)
@@ -52,7 +52,7 @@ LINK LIBRARY
 SEE ALSO
    power

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/sec
+++ b/help/sec
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -20,7 +20,7 @@ EXAMPLE

 LIMITS
    unlike sin and cos, x must be real
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qsec(NUMBER *x, NUMBER *eps)
@@ -28,7 +28,7 @@ LINK LIBRARY
 SEE ALSO
    sin, cos, tan, csc, cot, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/sech
+++ b/help/sech
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -22,7 +22,7 @@ EXAMPLE

 LIMITS
    unlike sin and cos, x must be real
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qsech(NUMBER *x, NUMBER *eps)
@@ -30,7 +30,7 @@ LINK LIBRARY
 SEE ALSO
    sinh, cosh, tanh, csch, coth, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/sin
+++ b/help/sin
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		number (real or complex)
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	number

@@ -26,7 +26,7 @@ EXAMPLE
    0.5 1 0

 LIMITS
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qsin(NUMBER *x, NUMBER *eps)
@@ -35,7 +35,7 @@ LINK LIBRARY
 SEE ALSO
    cos, tan, sec, csc, cot, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/sinh
+++ b/help/sinh
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -22,7 +22,7 @@ EXAMPLE

 LIMITS
    unlike sin and cos, x must be real
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qsinh(NUMBER *x, NUMBER *eps)
@@ -30,7 +30,7 @@ LINK LIBRARY
 SEE ALSO
    cosh, tanh, sech, csch, coth, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/sqrt
+++ b/help/sqrt
@@ -15,7 +15,7 @@ TYPES
    For other argument types:

    x		real or complex
-    eps		nonzero real
+    eps		0 < real < 1, defaults to epsilon()
    z		integer

    return	real or complex
@@ -119,7 +119,7 @@ EXAMPLE
    0 0.0002

 LIMITS
-    none
+    0 < eps < 1

 LINK LIBRARY
    COMPLEX *c_sqrt(COMPLEX *x, NUMBER *ep, long z)
@@ -130,7 +130,7 @@ LINK LIBRARY
 SEE ALSO
   appr, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/tan
+++ b/help/tan
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -20,7 +20,7 @@ EXAMPLE

 LIMITS
    unlike sin and cos, x must be real
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qtan(NUMBER *x, NUMBER *eps)
@@ -28,7 +28,7 @@ LINK LIBRARY
 SEE ALSO
    sin, cos, sec, csc, cot, epsilon

-## Copyright (C) 1999  Landon Curt Noll
+## Copyright (C) 1999,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/help/tanh
+++ b/help/tanh
@@ -6,7 +6,7 @@ SYNOPSIS

 TYPES
    x		real
-    eps		nonzero real, defaults to epsilon()
+    eps		0 < real < 1, defaults to epsilon()

    return	real

@@ -22,7 +22,7 @@ EXAMPLE

 LIMITS
    unlike sin and cos, x must be real
-    eps > 0
+    0 < eps < 1

 LINK LIBRARY
    NUMBER *qtanh(NUMBER *x, NUMBER *eps)
@@ -30,7 +30,7 @@ LINK LIBRARY
 SEE ALSO
    sinh, cosh, sech, csch, coth, epsilon

-## Copyright (C) 1999,2021  Landon Curt Noll
+## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
 ## Calc is open software; you can redistribute it and/or modify it under
 ## the terms of the version 2.1 of the GNU Lesser General Public License
--- a/qmath.h
+++ b/qmath.h
@@ -189,6 +189,7 @@ E_FUNC NUMBER *qexp(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qln(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qlog(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qlog2(NUMBER *q, NUMBER *epsilon);
+E_FUNC NUMBER *qlogn(NUMBER *q, NUMBER *n, NUMBER *epsilon);
 E_FUNC NUMBER *qtan(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qsec(NUMBER *q, NUMBER *epsilon);
 E_FUNC NUMBER *qcot(NUMBER *q, NUMBER *epsilon);
--- a/qtrans.c
+++ b/qtrans.c
@@ -49,6 +49,8 @@ STATIC NUMBER *ln_10 = NULL;
 STATIC NUMBER *ln_10_epsilon = NULL;
 STATIC NUMBER *ln_2 = NULL;
 STATIC NUMBER *ln_2_epsilon = NULL;
+STATIC NUMBER *ln_n = NULL;
+STATIC NUMBER *ln_n_epsilon = NULL;

 /*
 * cache pi
@@ -1049,10 +1051,14 @@ qln(NUMBER *q, NUMBER *epsilon)
 	NUMBER *qtmp, *res;
 	bool neg;

-	if (qiszero(q) || qiszero(epsilon)) {
+	if (qiszero(q)) {
 		math_error("logarithm of 0");
 		not_reached();
 	}
+	if (qiszero(epsilon)) {
+		math_error("Zero epsilon value for ln");
+		not_reached();
+	}
 	if (qisunit(q))
 		return qlink(&_qzero_);
 	q = qqabs(q);			/* Ignore sign of q */
@@ -1161,10 +1167,14 @@ qlog(NUMBER *q, NUMBER *epsilon)
 	NUMBER *ret;			/* base 10 logarithm of x */

 	/* firewall */
-	if (qiszero(q) || qiszero(epsilon)) {
+	if (qiszero(q)) {
 		math_error("logarithm of 0");
 		not_reached();
 	}
+	if (qiszero(epsilon)) {
+		math_error("Zero epsilon value for log");
+		not_reached();
+	}

 	/*
 	 * shortcut for small integer powers of 10
@@ -1238,10 +1248,14 @@ qlog2(NUMBER *q, NUMBER *epsilon)
 	NUMBER *ret;			/* base 2 logarithm of x */

 	/* firewall */
-	if (qiszero(q) || qiszero(epsilon)) {
+	if (qiszero(q)) {
 		math_error("logarithm of 0");
 		not_reached();
 	}
+	if (qiszero(epsilon)) {
+		math_error("Zero epsilon value for log2");
+		not_reached();
+	}

 	/*
 	 * special case: q is integer power of 2
@@ -1256,7 +1270,7 @@ qlog2(NUMBER *q, NUMBER *epsilon)
 	 * compute ln(c) first
 	 */
 	ln_q = qln(q, epsilon);
-	/* quick return for log(1) == 0 */
+	/* quick return for ln(1) == 0 */
 	if (qiszero(ln_q)) {
 		return ln_q;
 	}
@@ -1295,6 +1309,89 @@ qlog2(NUMBER *q, NUMBER *epsilon)
 }


+/*
+ * Calculate the base n logarithm
+ *
+ *	logn(q, n) = ln(q) / ln(n)
+ */
+NUMBER *
+qlogn(NUMBER *q, NUMBER *n, NUMBER *epsilon)
+{
+	int need_new_ln_n = true;	/* false => use cached ln_n value */
+	NUMBER *ln_q;			/* ln(x) */
+	NUMBER *ret;			/* base 2 logarithm of x */
+
+	/* firewall */
+	if (qiszero(q)) {
+		math_error("logarithm of 0");
+		not_reached();
+	}
+	if (qiszero(epsilon)) {
+		math_error("Zero epsilon value for logn");
+		not_reached();
+	}
+	if (qiszero(n)) {
+		math_error("invalid logarithm base of 0 for logn");
+		not_reached();
+	}
+	if (qisone(n)) {
+		math_error("invalid logarithm base of 1 for logn");
+		not_reached();
+	}
+
+	/*
+	 * special case: q is integer power of 2
+	 */
+	ret = qalloc();
+	if (qispowerof2(q, &ret)) {
+		return ret;
+	}
+	/* XXX - deal with n is integer power of 2 - XXX */
+	qfree(ret);
+
+	/*
+	 * compute ln(q) first
+	 */
+	ln_q = qln(q, epsilon);
+	/* quick return for ln(1) == 0 */
+	if (qiszero(ln_q)) {
+		return ln_q;
+	}
+
+	/*
+	 * save epsilon for ln(n) if needed
+	 */
+	if (ln_n_epsilon == NULL) {
+		/* first time call */
+		ln_n_epsilon = qcopy(epsilon);
+	} else if (qcmp(ln_n_epsilon, epsilon) == true) {
+		/* replaced cached value with epsilon arg */
+		qfree(ln_n_epsilon);
+		ln_n_epsilon = qcopy(epsilon);
+	} else if (ln_n != NULL) {
+		/* the previously computed ln(2) is OK to use */
+		need_new_ln_n = false;
+	}
+
+	/*
+	 * compute ln(n) if needed
+	 */
+	if (need_new_ln_n == true) {
+		if (ln_n != NULL) {
+			qfree(ln_n);
+		}
+		ln_n = qln(&_qtwo_, ln_n_epsilon);
+	}
+
+	/*
+	 * return ln(q) / ln(2)
+	 */
+	ret = qqdiv(ln_q, ln_n);
+	qfree(ln_q);
+	return ret;
+}
+
+
 /*
 * Calculate the result of raising one number to the power of another.
 * The result is calculated to the nearest or next to nearest multiple of