convert ASCII TABs to ASCII SPACEs

Converted all ASCII tabs to ASCII spaces using a 8 character tab stop, for all files, except for all Makefiles (plus rpm.mk). The `git diff -w` reports no changes.
2025-08-19 01:13:27 +03:00 · 2024-07-11 22:03:52 -07:00
parent fe9cefe6ef
commit db77e29a23
631 changed files with 90607 additions and 90600 deletions
--- a/help/abs
+++ b/help/abs
@@ -11,11 +11,11 @@ TYPES

    For non-object x and eps:

-    x		number (real or complex)
-    eps		ignored if x is real, nonzero real for complex x,
-		defaults to epsilon().
+    x           number (real or complex)
+    eps         ignored if x is real, nonzero real for complex x,
+                defaults to epsilon().

-    return	non-negative real
+    return      non-negative real

 DESCRIPTION
    If x is real, returns the absolute value of x, i.e. x if x >= 0,
@@ -52,7 +52,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -60,8 +60,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:22
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:22
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/access
+++ b/help/access
@@ -5,10 +5,10 @@ SYNOPSIS
    access(name [, mode])

 TYPES
-    name	string
-    mode	integer or string containing only 'r', 'w', 'x' characters
+    name        string
+    mode        integer or string containing only 'r', 'w', 'x' characters

-    return	null value or error
+    return      null value or error

 DESCRIPTION
    access(name) or access(name, 0) or access(name, "") returns the null
@@ -25,18 +25,18 @@ EXAMPLE

    ; !rm -f junk
    ; access("junk")
-	System error 2
+        System error 2
    ; strerror(.)
-	"No such file or directory"
+        "No such file or directory"
    ; f = fopen("junk", "w")
    ; access("junk")
    ; fputs(f, "Alpha")
    ; fclose(f)
    ; !chmod u-w junk
    ; access("junk", "w")
-	System error 13
+        System error 13
    ; strerror(.)
-	"Permission denied"
+        "Permission denied"

 LIMITS
    There may be implementation-dependent limits inherited from the
@@ -56,7 +56,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -64,8 +64,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1996/04/30 03:36:20
-## File existed as early as:	1996
+## Under source code control:   1996/04/30 03:36:20
+## File existed as early as:    1996
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acos
+++ b/help/acos
@@ -5,10 +5,10 @@ SYNOPSIS
    acos(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric cosine of x to a multiple of eps with error less in
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:23
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:23
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acosh
+++ b/help/acosh
@@ -5,10 +5,10 @@ SYNOPSIS
    acosh(x [,eps])

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

-    return	nonnegative real
+    return      nonnegative real

 DESCRIPTION
    Returns the acosh of x to a multiple of eps with error less in
@@ -17,7 +17,7 @@ DESCRIPTION
    acosh(x) is the nonnegative real number v for which cosh(v) = x.
    It is given by

-		 acosh(x) = ln(x + sqrt(x^2 - 1))
+                 acosh(x) = ln(x + sqrt(x^2 - 1))

 EXAMPLE
    ; print acosh(2, 1e-5), acosh(2, 1e-10), acosh(2, 1e-15), acosh(2, 1e-20)
@@ -42,7 +42,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -50,8 +50,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:24
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:24
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acot
+++ b/help/acot
@@ -5,10 +5,10 @@ SYNOPSIS
    acot(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric cotangent of x to a multiple of eps with error less in
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acoth
+++ b/help/acoth
@@ -5,10 +5,10 @@ SYNOPSIS
    acoth(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the acoth of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    acoth(x) is the real number v for which coth(v) = x.
    It is given by
-		acoth(x) = ln((x + 1)/(x - 1))/2
+                acoth(x) = ln((x + 1)/(x - 1))/2

 EXAMPLE
    ; print acoth(2, 1e-5), acoth(2, 1e-10), acoth(2, 1e-15), acoth(2, 1e-20)
@@ -41,7 +41,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -49,8 +49,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:01
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:01
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acovercos
+++ b/help/acovercos
@@ -5,10 +5,10 @@ SYNOPSIS
    acovercos(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the inverse coversed trigonometric cosine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called acvc, or arccovercos, is equivalent to:

-	acovercos(x) = asin(x - 1)
+        acovercos(x) = asin(x - 1)

 EXAMPLE
    ; print acovercos(0), acovercos(0.5), acovercos(1)
@@ -60,14 +60,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -77,7 +77,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -85,8 +85,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/05 23:30:08
-## File existed as early as:	2023
+## Under source code control:   2023/09/05 23:30:08
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acoversin
+++ b/help/acoversin
@@ -5,10 +5,10 @@ SYNOPSIS
    acoversin(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the inverse coversed trigonometric sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called acovers, or acvs, or arccoversin, is equivalent to:

-	acoversin(x) = asin(1 - x)
+        acoversin(x) = asin(1 - x)

 EXAMPLE
    ; print acoversin(0), acoversin(0.5), acoversin(1)
@@ -60,14 +60,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -77,7 +77,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -85,8 +85,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/08/31 23:07:08
-## File existed as early as:	2023
+## Under source code control:   2023/08/31 23:07:08
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acrd
+++ b/help/acrd
@@ -5,10 +5,10 @@ SYNOPSIS
    acrd(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate angle of unit circle chord of length x to a multiple of eps with error less in
@@ -19,7 +19,7 @@ DESCRIPTION

    This function is sometimes called chord, is equivalent to:

-	acrd(x) = 2 * asin(x / 2)
+        acrd(x) = 2 * asin(x / 2)

 EXAMPLE
    ; print acrd(1/2), acrd(5/7), acrd(42/7)
@@ -57,14 +57,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -74,7 +74,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -82,8 +82,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/10/02 16:49:42
-## File existed as early as:	2023
+## Under source code control:   2023/10/02 16:49:42
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acsc
+++ b/help/acsc
@@ -5,10 +5,10 @@ SYNOPSIS
    acsc(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric cosecant of x to a multiple of eps with error less in
@@ -64,14 +64,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -81,7 +81,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -89,8 +89,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/acsch
+++ b/help/acsch
@@ -5,10 +5,10 @@ SYNOPSIS
    acsch(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the acsch of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    acsch(x) is the real number v for which csch(v) = x.  It is given by

-		acsch(x) = ln((1 + sqrt(1 + x^2))/x)
+                acsch(x) = ln((1 + sqrt(1 + x^2))/x)

 EXAMPLE
    ; print acsch(2, 1e-5), acsch(2, 1e-10), acsch(2, 1e-15), acsch(2, 1e-20)
@@ -41,7 +41,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -49,8 +49,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:01
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:01
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/address
+++ b/help/address
@@ -5,9 +5,9 @@ SYNOPSIS
    &X

 TYPES
-    X		expression specifying an octet, lvalue, string or number
+    X           expression specifying an octet, lvalue, string or number

-    return	pointer
+    return      pointer

 DESCRIPTION
    &X returns the address at which information for determining the current
@@ -20,7 +20,7 @@ DESCRIPTION
    otherwise accessing, such a vacated address may be catastrophic.

    An octet is normally expressed by B[i] where B is a block and
-    0 <= i < sizeof(B).	 &B[i] then returns the address at which this
+    0 <= i < sizeof(B).  &B[i] then returns the address at which this
    octet is located until the block is freed or relocated.  Freeing
    of an unnamed block B occurs when a new value is assigned to B or
    when B ceases to exist; a named block B is freed by blkfree(B).
@@ -38,7 +38,7 @@ DESCRIPTION
    &X with that component or element depends only on the continued existence
    of the matrix or object.  For example, after

-	; mat A[3]
+        ; mat A[3]

    the addresses &A[0], &A[1], &A[2] locate the three elements
    of the matrix specified by A until another value is assigned to A, etc.
@@ -60,15 +60,15 @@ DESCRIPTION
    results refer to octets in the same block or existing components of the
    same matrix or object.  For example, immediately after

-	; mat A[10]
-	; p = &A[5]
+        ; mat A[10]
+        ; p = &A[5]

    it is permitted to use expressions like p + 4, p - 5, p++ .

    Strings defined literally have fixed addresses, e.g., after

-	; p = &"abc"
-	; A = "abc"
+        ; p = &"abc"
+        ; A = "abc"

    the address &*A of the value of A will be equal to p.

@@ -78,7 +78,7 @@ DESCRIPTION
    be usable only while the variables retain these defined values.
    For example, after

-	; B = C = strcat("a", "bc");
+        ; B = C = strcat("a", "bc");

    &*B and &*C will be different.  If p is defined by p = &*B, p should
    not be used after a new value is assigned to B, or B ceases to exist,
@@ -91,12 +91,12 @@ DESCRIPTION
    so long as the number remains associated with at least one function or
    lvalue.  For example, after

-	; x = 27;
-	; y = 3 * 9;
-	; define f(a) = 27 + a;
+        ; x = 27;
+        ; y = 3 * 9;
+        ; define f(a) = 27 + a;

    the three occurrences of 27 have the same address which may be displayed
-    by any of &27, &*x, &*y and &f(0).	If x and y are assigned
+    by any of &27, &*x, &*y and &f(0).  If x and y are assigned
    other values and f is redefined or undefined and the 27 has not been
    stored elsewhere (e.g. as the "old value" or in another function
    definition or as an element in an association), the address assigned at
@@ -105,17 +105,17 @@ DESCRIPTION

    When a function returns a number value, that number value is usually
    placed at a newly allocated address, even if an equal number is stored
-    elsewhere.	For example calls to f(a), as defined above, with the same
+    elsewhere.  For example calls to f(a), as defined above, with the same
    non-zero value for a will be assigned to different addresses as can be
    seen from printing &*A, &*B, &*C after

-	; A = f(2); B = f(2); C = f(2);
+        ; A = f(2); B = f(2); C = f(2);

    (the case of f(0) is exceptional since 27 + 0 simply copies the 27
    rather than creating a new number value).  Here it is clearly more
    efficient to use

-	; A = B = C = f(2);
+        ; A = B = C = f(2);

    which, not only performs the addition in f() only once, but stores the
    number values for A, B and C at the same address.
@@ -168,7 +168,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -176,8 +176,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/09/06 20:03:34
-## File existed as early as:	1997
+## Under source code control:   1997/09/06 20:03:34
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/aexcsc
+++ b/help/aexcsc
@@ -5,10 +5,10 @@ SYNOPSIS
    aexcsc(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse exterior trigonometric cscant of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called arcexcsc, is equivalent to:

-	aexcsc(x) = acsc(x + 1)
+        aexcsc(x) = acsc(x + 1)

 EXAMPLE
    ; print aexcsc(0), aexcsc(0.5), aexcsc(1)
@@ -66,14 +66,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -83,7 +83,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -91,8 +91,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/30 23:22:21
-## File existed as early as:	2023
+## Under source code control:   2023/09/30 23:22:21
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/aexsec
+++ b/help/aexsec
@@ -5,10 +5,10 @@ SYNOPSIS
    aexsec(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric secant of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called arcexsec, is equivalent to:

-	aexsec(x) = asec(x + 1)
+        aexsec(x) = asec(x + 1)

 EXAMPLE
    ; print aexsec(0), aexsec(0.5), aexsec(1)
@@ -63,14 +63,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -80,7 +80,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -88,8 +88,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/10/01 00:20:20
-## File existed as early as:	2023
+## Under source code control:   2023/10/01 00:20:20
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/agd
+++ b/help/agd
@@ -5,10 +5,10 @@ SYNOPSIS
    agd(z [,eps])

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

-    return	number or infinite error value
+    return      number or infinite error value

 DESCRIPTION
    Calculate the inverse Gudermannian of z to a multiple of eps with
@@ -19,11 +19,11 @@ DESCRIPTION
    agd(z) is usually defined initially for real z with abs(z) < pi/2 by
    one of the formulae

-		 agd(z) = ln(sec(z) + tan(z))
+                 agd(z) = ln(sec(z) + tan(z))

-			= 2 * atanh(tan(z/2))
+                        = 2 * atanh(tan(z/2))

-			= asinh(tan(z)),
+                        = asinh(tan(z)),

    or as the integral from 0 to z of (1/cos(t))dt.  For complex z, the
    principal branch, approximated by gd(z, eps), has cuts along the real
@@ -31,7 +31,7 @@ DESCRIPTION

    If z = x + i * y and abs(x) < pi/2, agd(z) is given by

-	agd(z) = atanh(sin(x)/cosh(y)) + i * atan(sinh(y)/cos(x)>
+        agd(z) = atanh(sin(x)/cosh(y)) + i * atan(sinh(y)/cos(x)>

 EXAMPLE
    ; print agd(1, 1e-5), agd(1, 1e-10), agd(1, 1e-15)
@@ -63,7 +63,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -71,8 +71,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/09/06 20:03:34
-## File existed as early as:	1997
+## Under source code control:   1997/09/06 20:03:34
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ahacovercos
+++ b/help/ahacovercos
@@ -5,10 +5,10 @@ SYNOPSIS
    ahacovercos(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the inverse half coversed trigonometric cosine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called ahacvc, or archacovercos, or archacovercosine, is equivalent to:

-	ahacovercos(x) = asin(2*x - 1)
+        ahacovercos(x) = asin(2*x - 1)

 EXAMPLE
    ; print ahacovercos(0), ahacovercos(0.5), ahacovercos(1)
@@ -63,14 +63,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -80,7 +80,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -88,8 +88,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/24 11:16:08
-## File existed as early as:	2023
+## Under source code control:   2023/09/24 11:16:08
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ahacoversin
+++ b/help/ahacoversin
@@ -5,10 +5,10 @@ SYNOPSIS
    ahacoversin(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the inverse half coversed trigonometric sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called ahacovers, or ahacvs, or archacoversin, is equivalent to:

-	ahacoversin(x) = asin(1 - 2*x)
+        ahacoversin(x) = asin(1 - 2*x)

 EXAMPLE
    ; print ahacoversin(0), ahacoversin(0.5), ahacoversin(1)
@@ -63,14 +63,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -80,7 +80,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -88,8 +88,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/24 11:17:28
-## File existed as early as:	2023
+## Under source code control:   2023/09/24 11:17:28
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ahavercos
+++ b/help/ahavercos
@@ -5,10 +5,10 @@ SYNOPSIS
    ahavercos(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse half versed trigonometric cosine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called ahaverc, or archavercos, or archavercosine, is equivalent to:

-	ahavercos(x) = acos(2*x - 1)
+        ahavercos(x) = acos(2*x - 1)

 EXAMPLE
    ; print ahavercos(0), ahavercos(0.5), ahavercos(1)
@@ -64,14 +64,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -81,7 +81,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -89,8 +89,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/24 11:18:04
-## File existed as early as:	2023
+## Under source code control:   2023/09/24 11:18:04
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ahaversin
+++ b/help/ahaversin
@@ -5,10 +5,10 @@ SYNOPSIS
    ahaversin(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse half versed trigonometric sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called ahavers, or archaversin, is equivalent to:

-	ahaversin(x) = acos(1 - 2*x)
+        ahaversin(x) = acos(1 - 2*x)

 EXAMPLE
    ; print ahaversin(0), ahaversin(0.5), ahaversin(1)
@@ -64,14 +64,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -81,7 +81,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -89,8 +89,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/24 11:19:54
-## File existed as early as:	2023
+## Under source code control:   2023/09/24 11:19:54
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/append
+++ b/help/append
@@ -5,10 +5,10 @@ SYNOPSIS
    append(x, y_0, y_1, ...)

 TYPES
-    x		lvalue whose value is a list
-    y_0, ...	any
+    x           lvalue whose value is a list
+    y_0, ...    any

-    return	null value
+    return      null value

 DESCRIPTION
    If after evaluation of y_0, y_1, ..., x is a list with contents
@@ -68,7 +68,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -76,8 +76,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 03:13:17
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 03:13:17
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/appr
+++ b/help/appr
@@ -5,11 +5,11 @@ SYNOPSIS
    appr(x [,y [,z]])

 TYPES
-    x		real, complex, matrix, list
-    y		real
-    z		integer
+    x           real, complex, matrix, list
+    y           real
+    z           integer

-    return	same type as x except that complex x may return a real number
+    return      same type as x except that complex x may return a real number

 DESCRIPTION
    Return the approximate value of x as specified by a specific error
@@ -24,77 +24,77 @@ DESCRIPTION
    In the following it is assumed y is nonzero and x is not a multiple of y.
    For real x:

-	appr(x,y,z) is either the nearest multiple of y greater
-	than x or the nearest multiple of y less than x.  Thus, if
-	we write a = appr(x,y,z) and r = x - a, then a/y is an integer
-	and abs(r) < abs(y).  If r > 0, we say x has been "rounded down"
-	to a; if r < 0, the rounding is "up".  For particular x and y,
-	whether the rounding is down or up is determined by z.
+        appr(x,y,z) is either the nearest multiple of y greater
+        than x or the nearest multiple of y less than x.  Thus, if
+        we write a = appr(x,y,z) and r = x - a, then a/y is an integer
+        and abs(r) < abs(y).  If r > 0, we say x has been "rounded down"
+        to a; if r < 0, the rounding is "up".  For particular x and y,
+        whether the rounding is down or up is determined by z.

-	Only the 5 lowest bits of z are used, so we may assume z has been
-	replaced by its value modulo 32.  The type of rounding depends on
-	z as follows:
+        Only the 5 lowest bits of z are used, so we may assume z has been
+        replaced by its value modulo 32.  The type of rounding depends on
+        z as follows:

-	z = 0	round down or up according as y is positive or negative,
-		sgn(r) = sgn(y)
+        z = 0   round down or up according as y is positive or negative,
+                sgn(r) = sgn(y)

-	z = 1	round up or down according as y is positive or negative,
-		sgn(r) = -sgn(y)
+        z = 1   round up or down according as y is positive or negative,
+                sgn(r) = -sgn(y)

-	z = 2	round towards zero, sgn(r) = sgn(x)
+        z = 2   round towards zero, sgn(r) = sgn(x)

-	z = 3	round away from zero, sgn(r) = -sgn(x)
+        z = 3   round away from zero, sgn(r) = -sgn(x)

-	z = 4	round down, r > 0
+        z = 4   round down, r > 0

-	z = 5	round up, r < 0
+        z = 5   round up, r < 0

-	z = 6	round towards or from zero according as y is positive or
-		negative, sgn(r) = sgn(x/y)
+        z = 6   round towards or from zero according as y is positive or
+                negative, sgn(r) = sgn(x/y)

-	z = 7	round from or towards zero according as y is positive or
-		negative, sgn(r) = -sgn(x/y)
+        z = 7   round from or towards zero according as y is positive or
+                negative, sgn(r) = -sgn(x/y)

-	z = 8	a/y is even
+        z = 8   a/y is even

-	z = 9	a/y is odd
+        z = 9   a/y is odd

-	z = 10	a/y is even or odd according as x/y is positive or negative
+        z = 10  a/y is even or odd according as x/y is positive or negative

-	z = 11	a/y is odd or even according as x/y is positive or negative
+        z = 11  a/y is odd or even according as x/y is positive or negative

-	z = 12	a/y is even or odd according as y is positive or negative
+        z = 12  a/y is even or odd according as y is positive or negative

-	z = 13	a/y is odd or even according as y is positive or negative
+        z = 13  a/y is odd or even according as y is positive or negative

-	z = 14	a/y is even or odd according as x is positive or negative
+        z = 14  a/y is even or odd according as x is positive or negative

-	z = 15	a/y is odd or even according as x is positive or negative
+        z = 15  a/y is odd or even according as x is positive or negative

-	z = 16 to 31	abs(r) <= abs(y)/2; if there is a unique multiple
-		of y that is nearest x, appr(x,y,z) is that multiple of y
-		and then abs(r) < abs(y)/2.  If x is midway between
-		successive multiples of y, then abs(r) = abs(y)/2 and
-		the value of a is as given by appr(x, y, z-16).
+        z = 16 to 31    abs(r) <= abs(y)/2; if there is a unique multiple
+                of y that is nearest x, appr(x,y,z) is that multiple of y
+                and then abs(r) < abs(y)/2.  If x is midway between
+                successive multiples of y, then abs(r) = abs(y)/2 and
+                the value of a is as given by appr(x, y, z-16).

    Matrix or List x:

-	appr(x,y,z) returns the matrix or list indexed in the same way as x,
-	in which each element t has been replaced by appr(t,y,z).
+        appr(x,y,z) returns the matrix or list indexed in the same way as x,
+        in which each element t has been replaced by appr(t,y,z).

    Complex x:

-	Returns	 appr(re(x), y, z) + appr(im(x), y, z) * 1i
+        Returns  appr(re(x), y, z) + appr(im(x), y, z) * 1i

 PROPERTIES
-	If appr(x,y,z) != x, then abs(x - appr(x,y,z)) < abs(y).
+        If appr(x,y,z) != x, then abs(x - appr(x,y,z)) < abs(y).

-	If appr(x,y,z) != x and 16 <= z <= 31, abs(x - appr(x,y,z)) <= abs(y)/2.
+        If appr(x,y,z) != x and 16 <= z <= 31, abs(x - appr(x,y,z)) <= abs(y)/2.

-	For z = 0, 1, 4, 5, 16, 17, 20 or 21, and any integer n,
-		appr(x + n*y, y, z) = appr(x, y, z) + n * y.
+        For z = 0, 1, 4, 5, 16, 17, 20 or 21, and any integer n,
+                appr(x + n*y, y, z) = appr(x, y, z) + n * y.

-	If y is nonzero, appr(x,y,8)/y = an odd integer n only if x = n * y.
+        If y is nonzero, appr(x,y,8)/y = an odd integer n only if x = n * y.

 EXAMPLE
    ; print appr(-5.44,0.1,0), appr(5.44,0.1,0), appr(5.7,1,0), appr(-5.7,1,0)
@@ -159,7 +159,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -167,8 +167,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/25 17:18:21
-## File existed as early as:	1994
+## Under source code control:   1994/09/25 17:18:21
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/archive
+++ b/help/archive
@@ -2,11 +2,11 @@ Where to get the latest versions of calc

    Official calc source is maintained on GitHub:

-	https://github.com/lcn2/calc
+        https://github.com/lcn2/calc

    Calc releases may be found as GitHub tagged releases:

-	https://github.com/lcn2/calc/releases?page=2
+        https://github.com/lcn2/calc/releases?page=2

     At the bottom of a given release is a "> Assets" that may
     be opened to reveal down-loadable files such as source
@@ -14,7 +14,7 @@ Where to get the latest versions of calc

    Landon Noll also maintains a calc home page at:

-	    http://www.isthe.com/chongo/tech/comp/calc/
+            http://www.isthe.com/chongo/tech/comp/calc/

 Landon Curt Noll
 http://www.isthe.com/chongo/
@@ -29,7 +29,7 @@ chongo <was here> /\../\
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -37,8 +37,8 @@ chongo <was here> /\../\
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1996/06/13 02:51:48
-## File existed as early as:	1996
+## Under source code control:   1996/06/13 02:51:48
+## File existed as early as:    1996
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/arg
+++ b/help/arg
@@ -5,10 +5,10 @@ SYNOPSIS
    arg(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the argument of x to the nearest or next to nearest multiple of
@@ -40,7 +40,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -48,8 +48,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/25 20:22:31
-## File existed as early as:	1994
+## Under source code control:   1994/09/25 20:22:31
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/argv
+++ b/help/argv
@@ -5,9 +5,9 @@ SYNOPSIS
    argv([n])

 TYPES
-    n		nonnegative integer
+    n           nonnegative integer

-    return	any
+    return      any

 DESCRIPTION
    Without args, this builtin returns the number of calc command line
@@ -22,16 +22,16 @@ DESCRIPTION
    assuming the calc is located in /usr/local/bin/calc, the first
    line of a calc script would be:

-	#!/usr/local/bin/calc -f
-	...
+        #!/usr/local/bin/calc -f
+        ...

    then argv(0) will refer to the filename of the script.

    As it is common to use -q in a calc script, and using that same
    /usr/local/bin/calc location:

-	#!/usr/local/bin/calc -q -f
-	...
+        #!/usr/local/bin/calc -q -f
+        ...

    and again, argv(0) will refer to the filename of the script.

@@ -43,14 +43,14 @@ DESCRIPTION
    However, if calc is invoked with -s, all non-dashed options will
    be left as unevaluated strings.  Thus:

-	calc -i 2+2
+        calc -i 2+2

    will cause calc to print 4 and enter interactive mode.  In this case
    argv() will return 1.

    On the other hand:

-	calc -i -s 2+2
+        calc -i -s 2+2

    will cause calc to interactive mode.  The argv() builtin will return 2
    and argv(1) will return the string "2+2".
@@ -84,7 +84,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -92,8 +92,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1999/11/23 19:45:05
-## File existed as early as:	1999
+## Under source code control:   1999/11/23 19:45:05
+## File existed as early as:    1999
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/arrow
+++ b/help/arrow
@@ -1,14 +1,14 @@
 SYMBOL and NAME
-    ->	- arrow operator
+    ->  - arrow operator

 SYNOPSIS
    p -> X

 TYPES
-    p		pointer to an lvalue
-    X		identifier
+    p           pointer to an lvalue
+    X           identifier

-    return	lvalue
+    return      lvalue

 DESCRIPTION
    p->X returns the same as (*p).X.  Thus the current value of *p is
@@ -28,17 +28,17 @@ EXAMPLE
    ; p = &A
    ; p->one = 1; p->two = 2
    ; A
-	obj pair {1, 2}
+        obj pair {1, 2}

    ; A->two = &B
    ; p->one = 3; p->two = 4

    ; *p
-	    obj pair {3, 4}
+            obj pair {3, 4}

    ; B = {5,6}
    ; *p->two
-	    4
+            4

 LIMITS
    none
@@ -57,7 +57,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -65,8 +65,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/09/06 20:03:34
-## File existed as early as:	1997
+## Under source code control:   1997/09/06 20:03:34
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/asec
+++ b/help/asec
@@ -5,10 +5,10 @@ SYNOPSIS
    asec(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric secant of x to a multiple of eps with error less in
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/asech
+++ b/help/asech
@@ -5,10 +5,10 @@ SYNOPSIS
    asech(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the asech of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    asech(x) is the real number v for which sech(v) = x.  It is given by

-		asech(x) = ln((1 + sqrt(1 - x^2))/x)
+                asech(x) = ln((1 + sqrt(1 - x^2))/x)

 EXAMPLE
    ; print asech(.5,1e-5), asech(.5,1e-10), asech(.5,1e-15), asech(.5,1e-20)
@@ -41,7 +41,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -49,8 +49,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/asin
+++ b/help/asin
@@ -5,10 +5,10 @@ SYNOPSIS
    asin(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric sine of x to a multiple of eps with error less in
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:24
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:24
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/asinh
+++ b/help/asinh
@@ -5,10 +5,10 @@ SYNOPSIS
    asinh(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the asinh of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    asinh(x) is the real number v for which sinh(v) = x.  It is given by

-		asinh(x) = ln(x + sqrt(1 + x^2))
+                asinh(x) = ln(x + sqrt(1 + x^2))

 EXAMPLE
    ; print asinh(2, 1e-5), asinh(2, 1e-10), asinh(2, 1e-15), asinh(2, 1e-20)
@@ -41,7 +41,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -49,8 +49,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:25
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:25
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/assign
+++ b/help/assign
@@ -6,14 +6,14 @@ SYNOPSIS
    a = {e_1, e_2, ...[ { ... } ] }

 TYPES
-    a			lvalue, current value a structure in { } case
+    a                   lvalue, current value a structure in { } case

-    b			expression
+    b                   expression

-    e_0, e_1, ...	expressions, blanks, or initializer lists
+    e_0, e_1, ...       expressions, blanks, or initializer lists


-    return		lvalue (a)
+    return              lvalue (a)

 DESCRIPTION
    Here an lvalue is either a simple variable specified by an identifier,
@@ -22,7 +22,7 @@ DESCRIPTION

    An initializer list is a comma-separated list enclosed in braces as in

-		{e_0, e_1, ... }
+                {e_0, e_1, ... }

    where each e_i is an expression, blank or initializer list.

@@ -44,7 +44,7 @@ DESCRIPTION
    In simple assignments, = associates from right to left so that, for
    example,

-		a = b = c
+                a = b = c

    has the effect of a = (b = c) and results in assigning the value of c
    to both a and b.  The expression (a = b) = c is acceptable, but has the
@@ -54,7 +54,7 @@ DESCRIPTION
    In initializations, = { ...} associates from left to right so that,
    for example,

-		a = {e_0, ... } = {v_0, ...}
+                a = {e_0, ... } = {v_0, ...}

    first assigns e_0, ... to the elements of a, and then assigns v_0, ...
    to the result.
@@ -66,10 +66,10 @@ DESCRIPTION
    that of A[0] = A[1].

    If, in execution of a = b, a is changed by the evaluation of b, the
-    value of b may be stored in an unintended or inaccessible location.	 For
+    value of b may be stored in an unintended or inaccessible location.  For
    example,
-		mat A[2]= {1,2};
-		A[0] = (A = 3);
+                mat A[2]= {1,2};
+                A[0] = (A = 3);

    results in the value 3 being stored not only as the new value for A
    but also at the now unnamed location earlier used for A[0].
@@ -87,8 +87,8 @@ EXAMPLE
    ; print A[1]

    list (2 elements, 2 nonzero):
-	[[0]] = 6
-	[[1]] = 3
+        [[0]] = 6
+        [[1]] = 3

    ; print A[2]
    obj point {7, 5}
@@ -104,8 +104,8 @@ EXAMPLE
    print A[1]

    list (2 elements, 2 nonzero):
-	[[0]] = 2
-	[[1]] = 3
+        [[0]] = 2
+        [[1]] = 3

 LIMITS
    none
@@ -124,7 +124,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -132,8 +132,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/05/11 21:03:23
-## File existed as early as:	1995
+## Under source code control:   1995/05/11 21:03:23
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/assoc
+++ b/help/assoc
@@ -5,7 +5,7 @@ SYNOPSIS
    assoc()

 TYPES
-    return	association
+    return      association

 DESCRIPTION
    This function returns an empty association array.
@@ -13,10 +13,10 @@ DESCRIPTION
    After A = assoc(), elements can be added to the association by
    assignments of the forms

-	A[a_1] = v_1
-	A[a_1, a_2] = v_2
-	A[a_1, a_2, a_3] = v_3
-	A[a_1, a_2, a_3, a_4] = v_4
+        A[a_1] = v_1
+        A[a_1, a_2] = v_2
+        A[a_1, a_2, a_3] = v_3
+        A[a_1, a_2, a_3, a_4] = v_4

    There are no restrictions on the values of the "indices" a_i or
    the "values" v_i.
@@ -52,7 +52,7 @@ DESCRIPTION
    a sequential scan through the elements difficult.

    The search and rsearch functions can search for an element in an
-    association which has the specified value.	They return the index
+    association which has the specified value.  They return the index
    of the found element, or a NULL value if the value was not found.

    Associations can be copied by an assignment, and can be compared
@@ -90,7 +90,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -98,8 +98,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/25 20:22:31
-## File existed as early as:	1994
+## Under source code control:   1994/09/25 20:22:31
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/atan
+++ b/help/atan
@@ -5,10 +5,10 @@ SYNOPSIS
    atan(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse trigonometric tangent of x to a multiple of eps with error less in
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:25
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:25
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/atan2
+++ b/help/atan2
@@ -5,11 +5,11 @@ SYNOPSIS
    atan2(y, x, [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    If x and y are not both zero, atan2(y, x, eps) returns, as a multiple of
@@ -44,7 +44,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -52,8 +52,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:26
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:26
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/atanh
+++ b/help/atanh
@@ -5,10 +5,10 @@ SYNOPSIS
    atanh(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the atanh of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    atanh(x) is the real number v for which tanh(v) = x.  It is given by

-		atanh(x) = ln((1 + x)/(1 - x))/2
+                atanh(x) = ln((1 + x)/(1 - x))/2

 EXAMPLE
    ; print atanh(.5,1e-5), atanh(.5,1e-10), atanh(.5,1e-15), atanh(.5,1e-20)
@@ -41,7 +41,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -49,8 +49,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:27
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:27
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/avercos
+++ b/help/avercos
@@ -5,10 +5,10 @@ SYNOPSIS
    avercos(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse versed trigonometric cosine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called averc, or arcvercos, is equivalent to:

-	avercos(x) = acos(x - 1)
+        avercos(x) = acos(x - 1)

 EXAMPLE
    ; print avercos(0), avercos(0.5), avercos(1)
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/05 23:40:24
-## File existed as early as:	2023
+## Under source code control:   2023/09/05 23:40:24
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/aversin
+++ b/help/aversin
@@ -5,10 +5,10 @@ SYNOPSIS
    aversin(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Returns the inverse versed trigonometric sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called avers, or arcversin, is equivalent to:

-	aversin(x) = acos(1 - x)
+        aversin(x) = acos(1 - x)

 EXAMPLE
    ; print aversin(0), aversin(0.5), aversin(1)
@@ -61,14 +61,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -78,7 +78,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -86,8 +86,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/03 00:26:24
-## File existed as early as:	2023
+## Under source code control:   2023/09/03 00:26:24
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/avg
+++ b/help/avg
@@ -5,16 +5,16 @@ SYNOPSIS
    avg(x_1, x_2, ...)

 TYPES
-    x_1, ...	arithmetic or list
+    x_1, ...    arithmetic or list

-    return	as determined by types of items averaged
+    return      as determined by types of items averaged

 DESCRIPTION
    If there are n non-list arguments x_1, x_2, ..., x_n,
    for which the required additions and division by n are defined,
    avg(x_1, x_2, ..., x_n) returns the value of:

-	(x_1 + x_2 + ... + x_n)/n.
+        (x_1 + x_2 + ... + x_n)/n.

    If the x_i are real, the result will be a real number; if the
    x_i are real or complex numbers, the result will be a real or complex
@@ -35,10 +35,10 @@ EXAMPLE
    ; avg(x,y)

    mat [2,2] (4 elements, 4 nonzero):
-	[0,0] = 1
-	[0,1] = 2
-	[1,0] = 3.5
-	[1,1] = 6
+        [0,0] = 1
+        [0,1] = 2
+        [1,0] = 3.5
+        [1,1] = 6

 LIMITS
   The number of arguments is not to exceed 1024.
@@ -57,7 +57,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -65,8 +65,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/25 20:22:31
-## File existed as early as:	1994
+## Under source code control:   1994/09/25 20:22:31
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/base
+++ b/help/base
@@ -5,9 +5,9 @@ SYNOPSIS
    base([mode])

 TYPES
-    mode	real
+    mode        real

-    return	real
+    return      real

 DESCRIPTION
    The base function allows one to specify how numbers should be
@@ -18,34 +18,34 @@ DESCRIPTION

    The following convention is used to declare modes:

-	     base	equivalent
-		      config("mode")'s
+             base       equivalent
+                      config("mode")'s

-	       2	"binary"	base 2 fractions
-			"bin"
+               2        "binary"        base 2 fractions
+                        "bin"

-	       8	"octal"		base 8 fractions
-			"oct"
+               8        "octal"         base 8 fractions
+                        "oct"

-	      10	"real"		base 10 floating point
-			"float"
-			"default"
+              10        "real"          base 10 floating point
+                        "float"
+                        "default"

-	     -10	"integer"	base 10 integers
-			"int"
+             -10        "integer"       base 10 integers
+                        "int"

-	      16	"hexadecimal"	base 16 fractions
-			"hex"
+              16        "hexadecimal"   base 16 fractions
+                        "hex"

-	     1/3	"fraction"	base 10 fractions
-			"frac"
+             1/3        "fraction"      base 10 fractions
+                        "frac"

-	    1e20	"scientific"	base 10 scientific notation
-			"sci"
-			"exp"
+            1e20        "scientific"    base 10 scientific notation
+                        "sci"
+                        "exp"

-	    1000	"engineering"	base 10 notation with exponent
-			"eng"		multiple of 3
+            1000        "engineering"   base 10 notation with exponent
+                        "eng"           multiple of 3

    For convenience, any non-integer value is assumed to mean base 10
    fractions and any integer >= 2^64 is assumed to mean base 10
@@ -53,21 +53,21 @@ DESCRIPTION

    These base() calls have the same meaning as config("mode", "fraction"):

-	base(1/3)	base(0.1415)	base(16/37)
+        base(1/3)       base(0.1415)    base(16/37)

    These base() calls have the same meaning as config("mode", "scientific"):

-	base(1e20)	base(2^64)	base(2^8191-1)
+        base(1e20)      base(2^64)      base(2^8191-1)

    However the base() function will only return one of the base values
    listed in the table above.

 EXAMPLE
    ; base()
-	    10
+            10

    ; base(8)
-	    012
+            012

    ; print 10
    012
@@ -79,7 +79,7 @@ LINK LIBRARY
    int math_setmode(int newmode)

    NOTE: newmode must be one of MODE_DEFAULT, MODE_FRAC, MODE_INT,
-	  MODE_REAL, MODE_EXP, MODE_ENG, MODE_HEX, MODE_OCTAL, MODE_BINARY
+          MODE_REAL, MODE_EXP, MODE_ENG, MODE_HEX, MODE_OCTAL, MODE_BINARY

 SEE ALSO
    base2, config, str
@@ -92,7 +92,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -100,8 +100,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 00:09:39
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 00:09:39
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/base2
+++ b/help/base2
@@ -5,9 +5,9 @@ SYNOPSIS
    base2([mode])

 TYPES
-    mode	real
+    mode        real

-    return	real
+    return      real

 DESCRIPTION
    By default, calc will output values according to the default base
@@ -19,41 +19,41 @@ DESCRIPTION
    to base2().  In double base output mode, the second time a value is
    displayed, it is displayed within comments:

-	21701 /* 0x54c5 */
+        21701 /* 0x54c5 */

    The arguments for base2() are identical to base() with the addition
    of the 0 value:

-	     base2	equivalent
-		      config("mode2")'s
+             base2      equivalent
+                      config("mode2")'s

-	       2	"binary"	base 2 fractions
-			"bin"
+               2        "binary"        base 2 fractions
+                        "bin"

-	       8	"octal"		base 8 fractions
-			"oct"
+               8        "octal"         base 8 fractions
+                        "oct"

-	      10	"real"		base 10 floating point
-			"float"
-			"default"
+              10        "real"          base 10 floating point
+                        "float"
+                        "default"

-	     -10	"integer"	base 10 integers
-			"int"
+             -10        "integer"       base 10 integers
+                        "int"

-	      16	"hexadecimal"	base 16 fractions
-			"hex"
+              16        "hexadecimal"   base 16 fractions
+                        "hex"

-	     1/3	"fraction"	base 10 fractions
-			"frac"
+             1/3        "fraction"      base 10 fractions
+                        "frac"

-	    1e20	"scientific"	base 10 scientific notation
-			"sci"
-			"exp"
+            1e20        "scientific"    base 10 scientific notation
+                        "sci"
+                        "exp"

-	    1000	"engineering"	base 10 notation with exponent
-			"eng"		multiple of 3
+            1000        "engineering"   base 10 notation with exponent
+                        "eng"           multiple of 3

-	       0	"off"		disable double base output
+               0        "off"           disable double base output

    For convenience, any non-integer non-zero value is assumed to mean
    base 10 fractions and any integer >= 2^64 is assumed to mean base 10
@@ -61,27 +61,27 @@ DESCRIPTION

    These base2() calls have the same meaning as config("mode2", "fraction"):

-	base2(1/3)	base2(0.1415)	base2(16/37)
+        base2(1/3)      base2(0.1415)   base2(16/37)

    These base2() calls have the same meaning as config("mode2", "scientific"):

-	base2(1e20)	base2(2^64)	base2(2^8191-1)
+        base2(1e20)     base2(2^64)     base2(2^8191-1)

    However the base2() function will only return one of the base values
    listed in the table above.

 EXAMPLE
    ; base2()
-	    0
+            0
    ; base2(8)
-	    0 /* 0 */
+            0 /* 0 */
    ; print 10
    10 /* 012 */
    ; base2(16),
    ; 131072
-	131072 /* 0x20000 */
+        131072 /* 0x20000 */
    ; 2345
-	2345 /* 0x929 */
+        2345 /* 0x929 */

 LIMITS
    none
@@ -90,8 +90,8 @@ LINK LIBRARY
    int math_setmode2(int newmode)

    NOTE: newmode must be one of MODE_DEFAULT, MODE_FRAC, MODE_INT,
-	  MODE_REAL, MODE_EXP, MODE_ENG, MODE_HEX, MODE_OCTAL, MODE_BINARY,
-	  MODE2_OFF
+          MODE_REAL, MODE_EXP, MODE_ENG, MODE_HEX, MODE_OCTAL, MODE_BINARY,
+          MODE2_OFF

 SEE ALSO
    base, config, str
@@ -104,7 +104,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -112,8 +112,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2002/12/29 00:21:07
-## File existed as early as:	2002
+## Under source code control:   2002/12/29 00:21:07
+## File existed as early as:    2002
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/bernoulli
+++ b/help/bernoulli
@@ -5,15 +5,15 @@ SYNOPSIS
    bernoulli(n)

 TYPES
-    n		integer, n < 2^31 if even
+    n           integer, n < 2^31 if even

-    return	rational
+    return      rational

 DESCRIPTION
    Returns the Bernoulli number with index n, i.e. the coefficient B_n in
    the expansion

-		t/(exp(t) - 1) = Sum B_n * t^n/n!
+                t/(exp(t) - 1) = Sum B_n * t^n/n!

    bernoulli(n) is zero both for n < 0 and for n odd and > 2.
    When bernoulli(n) is computed for positive even n, the values for
@@ -49,7 +49,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -57,7 +57,7 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2000/07/13 01:33:00
-## File existed as early as:	2000
+## Under source code control:   2000/07/13 01:33:00
+## File existed as early as:    2000
 ##
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/bit
+++ b/help/bit
@@ -5,17 +5,17 @@ SYNOPSIS
    bit(x, y)

 TYPES
-    x		real
-    y		int
+    x           real
+    y           int

-    return	int
+    return      int

 DESCRIPTION
-    Determine if the binary bit y is set in x.	If:
+    Determine if the binary bit y is set in x.  If:

-	     x
-	int(---) mod 2 == 1
-	    2^y
+             x
+        int(---) mod 2 == 1
+            2^y

    return 1, otherwise return 0.

@@ -50,7 +50,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -58,8 +58,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/10/21 02:21:30
-## File existed as early as:	1994
+## Under source code control:   1994/10/21 02:21:30
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/blk
+++ b/help/blk
@@ -6,11 +6,11 @@ SYNOPSIS
    blk(val [, len, chunk]);

 TYPES
-    len		null or integer
-    chunk	null or integer
-    val		non-null string, block, or named block
+    len         null or integer
+    chunk       null or integer
+    val         non-null string, block, or named block

-    return	block or named block
+    return      block or named block

 DESCRIPTION
    With only integer arguments, blk(len, chunk) attempts to
@@ -26,23 +26,23 @@ DESCRIPTION
    ... , B[len-1], these all initially having zero value.

    The octets B[i] for i >= len always have zero value.  If B[i] with
-    some i >= len is referenced, size(B) is increased to i + 1.	For example:
+    some i >= len is referenced, size(B) is increased to i + 1. For example:

-			B[i] = x
+                        B[i] = x

    has an effect like that of two operations on a file stream fs:

-			fseek(fs, pos);
-			fputc(fs, x).
+                        fseek(fs, pos);
+                        fputc(fs, x).

    Similarly:

-			x = B[i]
+                        x = B[i]

    is like:

-			fseek(fs, pos);
-			x = fgetc(fs).
+                        fseek(fs, pos);
+                        x = fgetc(fs).

    The value of chunk is stored as the "chunksize" for B.

@@ -51,7 +51,7 @@ DESCRIPTION
    value.  Also size(B) is analogous to the length of a file stream in that
    if size(B) < sizeof(B):

-			B[size(B)] = x
+                        B[size(B)] = x

    will append one octet to B and increment size(B).

@@ -70,14 +70,14 @@ DESCRIPTION
    If a block value B created by B = blk(len, chunk) is assigned to
    another variable by C = B, a new block of the same structure as B
    is created to become the value of C, and the octets in B are copied
-    to this new block.	A block with possibly different length or
+    to this new block.  A block with possibly different length or
    chunksize is created by C = blk(B, newlen, newchunk), only the first
    min(len, newlen) octets being copied from B; later octets are
    assigned zero value.  If omitted, newlen and newchunk default to
    the current datalen and chunk-size for B.  The current datalen,
    chunksize and number of allocated octets for B may be changed by:

-			B = blk(B, newlen, newchunk).
+                        B = blk(B, newlen, newchunk).

    No data is lost if newlen is greater than or equal to the old
    size(B).
@@ -99,38 +99,38 @@ DESCRIPTION
    is that in assignments, a named block is not copied.  Thus, if a
    block A has been created by:

-			A = blk("foo")
+                        A = blk("foo")
    any subsequent:
-			B = A
+                        B = A
    or:
-			B = blk("foo")
+                        B = blk("foo")

    will give a second variable B referring to the same block as A.
    Either  A[i] = x  or  B[i] = x  may then be used to assign a value
    to an octet in the block.  Its length or chunksize may be changed by
    instructions like:

-			blk(A, len, chunk);
+                        blk(A, len, chunk);

-			A = blk(A, len, chunk);
+                        A = blk(A, len, chunk);

-			null(blk(A, len, chunk)).
+                        null(blk(A, len, chunk)).

    These have the same effect on A; when working interactively, the
    last two avoid printing of the new value for A.

    Named blocks are assigned index numbers 0, 1, 2, ..., in the order
-    of their creation.	The block with index id is returned by blocks(id).
+    of their creation.  The block with index id is returned by blocks(id).
    With no argument, blocks() returns the number of current unfreed
    named blocks.

    The memory allocated to a named block is freed by the blkfree()
    function with argument the named block, its name, or its id number.
    The block remains in existence but with a null data pointer,
-    its length and size being reduced to zero.	A new block of memory
+    its length and size being reduced to zero.  A new block of memory
    may be allocated to it, with possibly new length and chunksize by:

-			blk(val [, len, chunk])
+                        blk(val [, len, chunk])

    where val is either the named block or its name.

@@ -141,7 +141,7 @@ DESCRIPTION

    The identifying numbers and names of the current named blocks are
    displayed by:
-			show blocks
+                        show blocks

    If A and B are named blocks, A == B will be true only if they refer
    to the same block of memory.  Thus, blocks with the same data and
@@ -158,13 +158,13 @@ EXAMPLE

    ; B[7] = 0xff
    ; B
-	chunksize = 10, maxsize = 20, datalen = 15
-	00000000000000ff00000000000000
+        chunksize = 10, maxsize = 20, datalen = 15
+        00000000000000ff00000000000000

    ; B[18] = 127
    ; B
-	chunksize = 10, maxsize = 20, datalen = 18
-	00000000000000ff0000000000000000007f
+        chunksize = 10, maxsize = 20, datalen = 18
+        00000000000000ff0000000000000000007f

    ; B[20] = 2
    Index out of bounds for block
@@ -174,38 +174,38 @@ EXAMPLE

    ; B = blk(B, 100, 20)
    ; B
-	chunksize = 20, maxsize = 120, datalen = 100
-	00000000000000ff0000000000000000007f000000000000000000000000...
+        chunksize = 20, maxsize = 120, datalen = 100
+        00000000000000ff0000000000000000007f000000000000000000000000...

    ; C = blk(B, 10} = {1,2,3}
    ; C
-	chunksize = 20, maxsize = 20, datalen = 10
-	01020300000000ff0000
+        chunksize = 20, maxsize = 20, datalen = 10
+        01020300000000ff0000

    ; A1 = blk("alpha")
    ; A1
-	block 0: alpha
-	chunksize = 256, maxsize = 256, datalen = 0
+        block 0: alpha
+        chunksize = 256, maxsize = 256, datalen = 0

    ; A1[7] = 0xff
    ; A2 = A1
    ; A2[17] = 127
    ; A1
-	block 0: alpha
-	chunksize = 256, maxsize = 256, datalen = 18
-	00000000000000ff0000000000000000007f
+        block 0: alpha
+        chunksize = 256, maxsize = 256, datalen = 18
+        00000000000000ff0000000000000000007f

    ; A1 = blk(A1, 1000)
    ; A1
-	block 0: alpha
-	chunksize = 256, maxsize = 1024, datalen = 1000
-	00000000000000ff0000000000000000007f000000000000000000000000...
+        block 0: alpha
+        chunksize = 256, maxsize = 1024, datalen = 1000
+        00000000000000ff0000000000000000007f000000000000000000000000...

    ; A1 = blk(A1, , 16)
    ; A1
-	block 0: alpha
-	chunksize = 16, maxsize = 1008, datalen = 1000
-	00000000000000ff0000000000000000007f000000000000000000000000...
+        block 0: alpha
+        chunksize = 16, maxsize = 1008, datalen = 1000
+        00000000000000ff0000000000000000007f000000000000000000000000...

 LIMITS
    0 <= len < 2^31
@@ -241,7 +241,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -249,8 +249,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/04/05 13:07:13
-## File existed as early as:	1997
+## Under source code control:   1997/04/05 13:07:13
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/blkcpy
+++ b/help/blkcpy
@@ -6,20 +6,20 @@ SYNOPSIS
    copy(src, dest [, [ssi [, num [, dsi]]])

 TYPES
-    src		block, file, string, matrix, or list
-    dest	block, file, matrix or list - compatible with src
+    src         block, file, string, matrix, or list
+    dest        block, file, matrix or list - compatible with src

-    ssi		nonnegative integer, defaults to zero
-    num		nonnegative integer, defaults to maximum possible
-    dsi		nonnegative integer, defaults to datalen for a block, filepos
-			for a file, zero for other structures
+    ssi         nonnegative integer, defaults to zero
+    num         nonnegative integer, defaults to maximum possible
+    dsi         nonnegative integer, defaults to datalen for a block, filepos
+                        for a file, zero for other structures

-    return	null if successful, error value otherwise
+    return      null if successful, error value otherwise

 DESCRIPTION
    A call to:

-	blkcpy(dst, src, num, dsi, ssi)
+        blkcpy(dst, src, num, dsi, ssi)

    attempts to copy 'num' consecutive items (octets or values) starting
    from the source item 'src' with index 'ssi'.  By default, 'num'
@@ -27,7 +27,7 @@ DESCRIPTION

    A call to:

-	copy(src, dst, ssi, num, dsi)
+        copy(src, dst, ssi, num, dsi)

    does the same thing, but with a different arg order.

@@ -40,30 +40,30 @@ DESCRIPTION

    The following pairs of source-type, destination-type are permitted:

-	block to
-		 int
-		 block
-		 matrix
-		 file
+        block to
+                 int
+                 block
+                 matrix
+                 file

-	matrix to
-		 block
-		 matrix
-		 list
+        matrix to
+                 block
+                 matrix
+                 list

-	string to
-		 block
-		 file
+        string to
+                 block
+                 file

-	list to
-		 list
-		 matrix
+        list to
+                 list
+                 matrix

-	file to
-		 block
+        file to
+                 block

-	int to
-		 block
+        int to
+                 block

    In the above table, int refers to integer values.  However if a
    rational value is supplied, only the numerator is copied.
@@ -79,18 +79,18 @@ DESCRIPTION
    sufficient memory allocated for the copying.  For example, to copy
    a matrix M of size 100 to a newly created list, one may use:

-	; L = makelist(100);
-	; copy(M, L);
+        ; L = makelist(100);
+        ; copy(M, L);
   or:
-	; L = makelist(100);
-	; blkcpy(L, M);
+        ; L = makelist(100);
+        ; blkcpy(L, M);

    For copying from a block B (named or unnamed), the total number of octets
    available for copying is taken to the datalen for that block,
    so that num can be at most size(B) - ssi.

    For copying to a block B (named or unnamed), reallocation will be
-    required if dsi + num > sizeof(B).	(This will not be permitted if
+    required if dsi + num > sizeof(B).  (This will not be permitted if
    protect(B) has bit 4 set.)

    For copying from a file stream fs, num can be at most size(fs) - ssi.
@@ -111,74 +111,74 @@ EXAMPLE
    ; B = blk()
    ; blkcpy(B,A)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 4
-	01020304
+        chunksize = 256, maxsize = 256, datalen = 4
+        01020304
    ; blkcpy(B,A)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 8
-	0102030401020304
+        chunksize = 256, maxsize = 256, datalen = 8
+        0102030401020304
    ; blkcpy(B, A, 2, 10)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 12
-	010203040102030400000102
+        chunksize = 256, maxsize = 256, datalen = 12
+        010203040102030400000102
    ; blkcpy(B,32767)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 16
-	010203040102030400000102ff7f0000
+        chunksize = 256, maxsize = 256, datalen = 16
+        010203040102030400000102ff7f0000
    ; mat M[2,2]
    ; blkcpy(M, A)
    ; M
-	mat [2,2] (4 elements, 4 nonzero):
-	  [0,0] = 1
-	  [0,1] = 2
-	  [1,0] = 3
-	  [1,1] = 4
+        mat [2,2] (4 elements, 4 nonzero):
+          [0,0] = 1
+          [0,1] = 2
+          [1,0] = 3
+          [1,1] = 4
    ; blkcpy(M, A, 2, 2)
    ; M
-	mat [2,2] (4 elements, 4 nonzero):
-	  [0,0] = 1
-	  [0,1] = 2
-	  [1,0] = 1
-	  [1,1] = 2
+        mat [2,2] (4 elements, 4 nonzero):
+          [0,0] = 1
+          [0,1] = 2
+          [1,0] = 1
+          [1,1] = 2

    ; A = blk() = {1,2,3,4}
    ; B = blk()
    ; copy(A,B)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 4
-	01020304
+        chunksize = 256, maxsize = 256, datalen = 4
+        01020304
    ; copy(A,B)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 8
-	0102030401020304
+        chunksize = 256, maxsize = 256, datalen = 8
+        0102030401020304
    ; copy(A,B,1,2)
    ; B
-	chunksize = 256, maxsize = 256, datalen = 10
-	01020304010203040203
+        chunksize = 256, maxsize = 256, datalen = 10
+        01020304010203040203
    ; mat M[2,2]
    ; copy(A,M)
    ; M
-	mat [2,2] (4 elements, 4 nonzero):
-	  [0,0] = 1
-	  [0,1] = 2
-	  [1,0] = 3
-	  [1,1] = 4
+        mat [2,2] (4 elements, 4 nonzero):
+          [0,0] = 1
+          [0,1] = 2
+          [1,0] = 3
+          [1,1] = 4

    ; copy(A,M,2)
    ; M
-	mat [2,2] (4 elements, 4 nonzero):
-	  [0,0] = 3
-	  [0,1] = 4
-	  [1,0] = 3
-	  [1,1] = 4
+        mat [2,2] (4 elements, 4 nonzero):
+          [0,0] = 3
+          [0,1] = 4
+          [1,0] = 3
+          [1,1] = 4

    ; copy(A,M,0,2,2)
    ; M
-	mat [2,2] (4 elements, 4 nonzero):
-	  [0,0] = 3
-	  [0,1] = 4
-	  [1,0] = 1
-	  [1,1] = 2
+        mat [2,2] (4 elements, 4 nonzero):
+          [0,0] = 3
+          [0,1] = 4
+          [1,0] = 1
+          [1,1] = 2

 LIMITS
    none
@@ -197,7 +197,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -205,8 +205,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/04/05 14:08:50
-## File existed as early as:	1997
+## Under source code control:   1997/04/05 14:08:50
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/blkfree
+++ b/help/blkfree
@@ -5,14 +5,14 @@ SYNOPSIS
    blkfree(val)

 TYPES
-    val		named block, string, or integer
+    val         named block, string, or integer

-    return	null value
+    return      null value

 DESCRIPTION
    If val is a named block, or the name of a named block, or the
    identifying index for a named block, blkfree(val) frees the
-    memory block allocated to this named block.	 The block remains
+    memory block allocated to this named block.  The block remains
    in existence with the same name, identifying index, and chunksize,
    but its size and maxsize becomes zero and the pointer for the start
    of its data block null.
@@ -26,27 +26,27 @@ EXAMPLE
    ; B1 = blk("foo")
    ; B2 = blk("Second block")
    show blocks
-     id	  name
+     id   name
    ----  -----
-     0	 foo
-     1	 Second block
+     0   foo
+     1   Second block

    ; blkfree(B1)
    ; show blocks
-     id	  name
+     id   name
    ----  -----
-     1	 Second block
+     1   Second block

    ; B1
-	block 0: foo
-	chunksize = 256, maxsize = 0, datalen = 0
-	NULL
+        block 0: foo
+        chunksize = 256, maxsize = 0, datalen = 0
+        NULL

    ; blk(B1); B[7] = 5
    ; B1
-	block 0: foo
-	chunksize = 256, maxsize = 256, datalen = 8
-	0000000000000005
+        block 0: foo
+        chunksize = 256, maxsize = 256, datalen = 8
+        0000000000000005

 LIMITS
    none
@@ -65,7 +65,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -73,8 +73,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/04/05 13:07:13
-## File existed as early as:	1997
+## Under source code control:   1997/04/05 13:07:13
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/blocks
+++ b/help/blocks
@@ -5,9 +5,9 @@ SYNOPSIS
    blocks([id])

 TYPES
-    id		non-negative integer
+    id          non-negative integer

-    return	named block or null value
+    return      named block or null value

 DESCRIPTION
    With no argument blocks() returns the number of blocks that have
@@ -22,15 +22,15 @@ EXAMPLE
    ; A = blk("alpha")
    ; B = blk("beta") = {1,2,3}
    ; blocks()
-	2
+        2
    ; blocks(1)
-	block 1: beta
-	chunksize = 256, maxsize = 256, datalen = 3
-	010203
+        block 1: beta
+        chunksize = 256, maxsize = 256, datalen = 3
+        010203
    ; blocks(2)
-	Error E_BLOCKS_2
+        Error E_BLOCKS_2
    ; strerror()
-	"Non-allocated index number for blocks"
+        "Non-allocated index number for blocks"

 LIMITS
    none
@@ -49,7 +49,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -57,8 +57,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/04/05 13:07:13
-## File existed as early as:	1997
+## Under source code control:   1997/04/05 13:07:13
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/bround
+++ b/help/bround
@@ -12,16 +12,16 @@ TYPES
    Otherwise, if x is an object of type tt, or if x is not an object or
    number but y is an object of type tt, and the function tt_bround has
    to be defined; the types for x, plcs, rnd, and the returned value,
-    if any, are as required for specified in tt_bround.	 For the object
+    if any, are as required for specified in tt_bround.  For the object
    case, plcs and rnd default to the null value.

    For other cases:

-    x		number (real or complex)
-    plcs	integer, defaults to zero
-    rnd		integer, defaults to config("round")
+    x           number (real or complex)
+    plcs        integer, defaults to zero
+    rnd         integer, defaults to config("round")

-    return	number
+    return      number

 DESCRIPTION
    For real x, bround(x, plcs, rnd) returns x rounded to either
@@ -31,39 +31,39 @@ DESCRIPTION
    If the number of binary places is n and eps = 10^-n, the
    result is the same as for appr(x, eps, rnd).  This will be
    exactly x if x is a multiple of eps; otherwise rounding occurs
-    to one of the nearest multiples of eps on either side of x.	 Which
+    to one of the nearest multiples of eps on either side of x.  Which
    of these multiples is returned is determined by z = rnd & 31, i.e.
    the five low order bits of rnd, as follows:

-	    z = 0 or 4:		round down, i.e. towards minus infinity
-	    z = 1 or 5:		round up, i.e. towards plus infinity
-	    z = 2 or 6:		round towards zero
-	    z = 3 or 7:		round away from zero
-	    z = 8 or 12:	round to the nearest even multiple of eps
-	    z = 9 or 13:	round to the nearest odd multiple of eps
-	    z = 10 or 14:	round to nearest even or odd multiple of eps
-				    according as x > or < 0
-	    z = 11 or 15:	round to nearest odd or even multiple of eps
-				    according as x > or < 0
-	    z = 16 to 31:	round to the nearest multiple of eps when
-				    this is uniquely determined.  Otherwise
-				    rounding is as if z is replaced by z - 16
+            z = 0 or 4:         round down, i.e. towards minus infinity
+            z = 1 or 5:         round up, i.e. towards plus infinity
+            z = 2 or 6:         round towards zero
+            z = 3 or 7:         round away from zero
+            z = 8 or 12:        round to the nearest even multiple of eps
+            z = 9 or 13:        round to the nearest odd multiple of eps
+            z = 10 or 14:       round to nearest even or odd multiple of eps
+                                    according as x > or < 0
+            z = 11 or 15:       round to nearest odd or even multiple of eps
+                                    according as x > or < 0
+            z = 16 to 31:       round to the nearest multiple of eps when
+                                    this is uniquely determined.  Otherwise
+                                    rounding is as if z is replaced by z - 16

    For complex x:

-	The real and imaginary parts are rounded as for real x; if the
-	imaginary part rounds to zero, the result is real.
+        The real and imaginary parts are rounded as for real x; if the
+        imaginary part rounds to zero, the result is real.

    For matrix or list x:

-	The returned values has element bround(x[[i]], plcs, rnd) in
-	the same position as x[[i]] in x.
+        The returned values has element bround(x[[i]], plcs, rnd) in
+        the same position as x[[i]] in x.

    For object x or plcs:

-	When bround(x, plcs, rnd) is called, x is passed by address so may be
-	changed by assignments; plcs and rnd are copied to temporary
-	variables, so their values are not changed by the call.
+        When bround(x, plcs, rnd) is called, x is passed by address so may be
+        changed by assignments; plcs and rnd are copied to temporary
+        variables, so their values are not changed by the call.

 EXAMPLE
    ; a = 7/32, b = -7/32
@@ -100,18 +100,18 @@ EXAMPLE
    ; print round(A,2,24)

    list(7 elements, 7 nonzero):
-	[[0]] = 0.12
-	[[1]] = 0.25
-	[[3]] = 0.38
-	[[4]] = 0.5
-	[[5]] = 0.62
-	[[6]] = 0.75
-	[[7]] = 0.88
+        [[0]] = 0.12
+        [[1]] = 0.25
+        [[3]] = 0.38
+        [[4]] = 0.5
+        [[5]] = 0.62
+        [[6]] = 0.75
+        [[7]] = 0.88

 LIMITS
    For non-object case:
-	0 <= abs(plcs) < 2^31
-	0 <= abs(rnd) < 2^31
+        0 <= abs(plcs) < 2^31
+        0 <= abs(rnd) < 2^31

 LINK LIBRARY
    void broundvalue(VALUE *x, VALUE *plcs, VALUE *rnd, VALUE *result)
@@ -130,7 +130,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -138,8 +138,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 00:22:35
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 00:22:35
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/btrunc
+++ b/help/btrunc
@@ -5,10 +5,10 @@ SYNOPSIS
    btrunc(x [,plcs])

 TYPES
-    x		real
-    plcs	integer, defaults to zero
+    x           real
+    plcs        integer, defaults to zero

-    return	real
+    return      real

 DESCRIPTION
    Truncate x to plcs binary places, rounding if necessary towards zero,
@@ -51,7 +51,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -59,8 +59,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 00:44:27
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 00:44:27
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/builtin.end
+++ b/help/builtin.end
@@ -1,203 +1,203 @@

-	The config function sets or reads the value of a configuration
-	parameter.  The first argument is a string which names the parameter
-	to be set or read.  If only one argument is given, then the current
-	value of the named parameter is returned.  If two arguments are given,
-	then the named parameter is set to the value of the second argument,
-	and the old value of the parameter is returned.	 Therefore you can
-	change a parameter and restore its old value later.  The possible
-	parameters are explained in the next section.
+        The config function sets or reads the value of a configuration
+        parameter.  The first argument is a string which names the parameter
+        to be set or read.  If only one argument is given, then the current
+        value of the named parameter is returned.  If two arguments are given,
+        then the named parameter is set to the value of the second argument,
+        and the old value of the parameter is returned.  Therefore you can
+        change a parameter and restore its old value later.  The possible
+        parameters are explained in the next section.

-	The scale function multiplies or divides a number by a power of 2.
-	This is used for fractional calculations, unlike the << and >>
-	operators, which are only defined for integers.	 For example,
-	scale(6, -3) is 3/4.
+        The scale function multiplies or divides a number by a power of 2.
+        This is used for fractional calculations, unlike the << and >>
+        operators, which are only defined for integers.  For example,
+        scale(6, -3) is 3/4.

-	The quomod function is used to obtain both the quotient and remainder
-	of a division in one operation.	 The first two arguments a and b are
-	the numbers to be divided.  The last two arguments c and d are two
-	variables which will be assigned the quotient and remainder.  For
-	nonnegative arguments, the results are equivalent to computing a//b
-	and a%b.  If a is negative and the remainder is nonzero, then the
-	quotient will be one less than a//b.  This makes the following three
-	properties always hold:	 The quotient c is always an integer.  The
-	remainder d is always 0 <= d < b.  The equation a = b * c + d always
-	holds.	This function returns 0 if there is no remainder, and 1 if
-	there is a remainder.  For examples, quomod(10, 3, x, y) sets x to 3,
-	y to 1, and returns the value 1, and quomod(-4, 3.14159, x, y) sets x
-	to -2, y to 2.28318, and returns the value 1.
+        The quomod function is used to obtain both the quotient and remainder
+        of a division in one operation.  The first two arguments a and b are
+        the numbers to be divided.  The last two arguments c and d are two
+        variables which will be assigned the quotient and remainder.  For
+        nonnegative arguments, the results are equivalent to computing a//b
+        and a%b.  If a is negative and the remainder is nonzero, then the
+        quotient will be one less than a//b.  This makes the following three
+        properties always hold:  The quotient c is always an integer.  The
+        remainder d is always 0 <= d < b.  The equation a = b * c + d always
+        holds.  This function returns 0 if there is no remainder, and 1 if
+        there is a remainder.  For examples, quomod(10, 3, x, y) sets x to 3,
+        y to 1, and returns the value 1, and quomod(-4, 3.14159, x, y) sets x
+        to -2, y to 2.28318, and returns the value 1.

-	The eval function accepts a string argument and evaluates the
-	expression represented by the string and returns its value.
-	The expression can include function calls and variable references.
-	For example, eval("fact(3) + 7") returns 13.  When combined with
-	the prompt function, this allows the calculator to read values from
-	the user.  For example, x=eval(prompt("Number: ")) sets x to the
-	value input by the user.
+        The eval function accepts a string argument and evaluates the
+        expression represented by the string and returns its value.
+        The expression can include function calls and variable references.
+        For example, eval("fact(3) + 7") returns 13.  When combined with
+        the prompt function, this allows the calculator to read values from
+        the user.  For example, x=eval(prompt("Number: ")) sets x to the
+        value input by the user.

-	The digit and bit functions return individual digits of a number,
-	either in base 10 or in base 2, where the lowest digit of a number
-	is at digit position 0.	 For example, digit(5678, 3) is 5, and
-	bit(0b1000100, 2) is 1.	 Negative digit positions indicate places
-	to the right of the decimal or binary point, so that for example,
-	digit(3.456, -1) is 4.
+        The digit and bit functions return individual digits of a number,
+        either in base 10 or in base 2, where the lowest digit of a number
+        is at digit position 0.  For example, digit(5678, 3) is 5, and
+        bit(0b1000100, 2) is 1.  Negative digit positions indicate places
+        to the right of the decimal or binary point, so that for example,
+        digit(3.456, -1) is 4.

-	The ptest builtin is a primality testing function.  The
-	1st argument is the suspected prime to be tested.  The
-	absolute value of the 2nd argument is an iteration count.
+        The ptest builtin is a primality testing function.  The
+        1st argument is the suspected prime to be tested.  The
+        absolute value of the 2nd argument is an iteration count.

-	If ptest is called with only 2 args, the 3rd argument is
-	assumed to be 0.  If ptest is called with only 1 arg, the
-	2nd argument is assumed to be 1.  Thus, the following
-	calls are equivalent:
+        If ptest is called with only 2 args, the 3rd argument is
+        assumed to be 0.  If ptest is called with only 1 arg, the
+        2nd argument is assumed to be 1.  Thus, the following
+        calls are equivalent:

-		ptest(a)
-		ptest(a,1)
-		ptest(a,1,0)
+                ptest(a)
+                ptest(a,1)
+                ptest(a,1,0)

-	Normally ptest performs a some checks to determine if the
-	value is divisible by some trivial prime.  If the 2nd
-	argument is < 0, then the trivial check is omitted.
+        Normally ptest performs a some checks to determine if the
+        value is divisible by some trivial prime.  If the 2nd
+        argument is < 0, then the trivial check is omitted.

-	For example, ptest(a,10) performs the same work as:
+        For example, ptest(a,10) performs the same work as:

-		ptest(a,-3)	(7 tests without trivial check)
-		ptest(a,-7,3)	(3 more tests without the trivial check)
+                ptest(a,-3)     (7 tests without trivial check)
+                ptest(a,-7,3)   (3 more tests without the trivial check)

-	The ptest function returns 0 if the number is definitely not
-	prime, and 1 is the number is probably prime.  The chance
-	of a number which is probably prime being actually composite
-	is less than 1/4 raised to the power of the iteration count.
-	For example, for a random number p, ptest(p, 10) incorrectly
-	returns 1 less than once in every million numbers, and you
-	will probably never find a number where ptest(p, 20) gives
-	the wrong answer.
+        The ptest function returns 0 if the number is definitely not
+        prime, and 1 is the number is probably prime.  The chance
+        of a number which is probably prime being actually composite
+        is less than 1/4 raised to the power of the iteration count.
+        For example, for a random number p, ptest(p, 10) incorrectly
+        returns 1 less than once in every million numbers, and you
+        will probably never find a number where ptest(p, 20) gives
+        the wrong answer.

-	The first 3 args of nextcand and prevcand functions are the same
-	arguments as ptest.  But unlike ptest, nextcand and prevcand return
-	the next and previous values for which ptest is true.
+        The first 3 args of nextcand and prevcand functions are the same
+        arguments as ptest.  But unlike ptest, nextcand and prevcand return
+        the next and previous values for which ptest is true.

-	For example, nextcand(2^1000) returns 2^1000+297 because
-	2^1000+297 is the smallest value x > 2^1000 for which
-	ptest(x,1) is true.  And for example, prevcand(2^31-1,10,5)
-	returns 2147483629 (2^31-19) because 2^31-19 is the largest
-	value y < 2^31-1 for which ptest(y,10,5) is true.
+        For example, nextcand(2^1000) returns 2^1000+297 because
+        2^1000+297 is the smallest value x > 2^1000 for which
+        ptest(x,1) is true.  And for example, prevcand(2^31-1,10,5)
+        returns 2147483629 (2^31-19) because 2^31-19 is the largest
+        value y < 2^31-1 for which ptest(y,10,5) is true.

-	The nextcand and prevcand functions also have a 5 argument form:
+        The nextcand and prevcand functions also have a 5 argument form:

-		nextcand(num, count, skip, modval, modulus)
-		prevcand(num, count, skip, modval, modulus)
+                nextcand(num, count, skip, modval, modulus)
+                prevcand(num, count, skip, modval, modulus)

-	return the smallest (or largest) value ans > num (or < num) that
-	is also == modval % modulus for which ptest(ans,count,skip) is true.
+        return the smallest (or largest) value ans > num (or < num) that
+        is also == modval % modulus for which ptest(ans,count,skip) is true.

-	The builtins nextprime(x) and prevprime(x) return the
-	next and previous primes with respect to x respectively.
-	As of this release, x must be < 2^32.  With one argument, they
-	will return an error if x is out of range.  With two arguments,
-	they will not generate an error but instead will return y.
+        The builtins nextprime(x) and prevprime(x) return the
+        next and previous primes with respect to x respectively.
+        As of this release, x must be < 2^32.  With one argument, they
+        will return an error if x is out of range.  With two arguments,
+        they will not generate an error but instead will return y.

-	The builtin function pix(x) returns the number of primes <= x.
-	As of this release, x must be < 2^32.  With one argument, pix(x)
-	will return an error if x is out of range.  With two arguments,
-	pix(x,y) will not generate an error but instead will return y.
+        The builtin function pix(x) returns the number of primes <= x.
+        As of this release, x must be < 2^32.  With one argument, pix(x)
+        will return an error if x is out of range.  With two arguments,
+        pix(x,y) will not generate an error but instead will return y.

-	The builtin function factor may be used to search for the
-	smallest factor of a given number.  The call factor(x,y)
-	will attempt to find the smallest factor of x < min(x,y).
-	As of this release, y must be < 2^32.  If y is omitted, y
-	is assumed to be 2^32-1.
+        The builtin function factor may be used to search for the
+        smallest factor of a given number.  The call factor(x,y)
+        will attempt to find the smallest factor of x < min(x,y).
+        As of this release, y must be < 2^32.  If y is omitted, y
+        is assumed to be 2^32-1.

-	If x < 0, factor(x,y) will return -1.  If no factor <
-	min(x,y) is found, factor(x,y) will return 1.  In all other
-	cases, factor(x,y) will return the smallest prime factor
-	of x.  Note except for the case when abs(x) == 1, factor(x,y)
-	will not return x.
+        If x < 0, factor(x,y) will return -1.  If no factor <
+        min(x,y) is found, factor(x,y) will return 1.  In all other
+        cases, factor(x,y) will return the smallest prime factor
+        of x.  Note except for the case when abs(x) == 1, factor(x,y)
+        will not return x.

-	If factor is called with y that is too large, or if x or y
-	is not an integer, calc will report an error.  If a 3rd argument
-	is given, factor will return that value instead.  For example,
-	factor(1/2,b,c) will return c instead of issuing an error.
+        If factor is called with y that is too large, or if x or y
+        is not an integer, calc will report an error.  If a 3rd argument
+        is given, factor will return that value instead.  For example,
+        factor(1/2,b,c) will return c instead of issuing an error.

-	The builtin lfactor(x,y) searches a number of primes instead
-	of below a limit.  As of this release, y must be <= 203280221
-	(y <= pix(2^32-1)).  In all other cases, lfactor is operates
-	in the same way as factor.
+        The builtin lfactor(x,y) searches a number of primes instead
+        of below a limit.  As of this release, y must be <= 203280221
+        (y <= pix(2^32-1)).  In all other cases, lfactor is operates
+        in the same way as factor.

-	If lfactor is called with y that is too large, or if x or y
-	is not an integer, calc will report an error.  If a 3rd argument
-	is given, lfactor will return that value instead.  For example,
-	lfactor(1/2,b,c) will return c instead of issuing an error.
+        If lfactor is called with y that is too large, or if x or y
+        is not an integer, calc will report an error.  If a 3rd argument
+        is given, lfactor will return that value instead.  For example,
+        lfactor(1/2,b,c) will return c instead of issuing an error.

-	The lfactor function is slower than factor.  If possible factor
-	should be used instead of lfactor.
+        The lfactor function is slower than factor.  If possible factor
+        should be used instead of lfactor.

-	The builtin isprime(x) will attempt to determine if x is prime.
-	As of this release, x must be < 2^32.  With one argument, isprime(x)
-	will return an error if x is out of range.  With two arguments,
-	isprime(x,y) will not generate an error but instead will return y.
+        The builtin isprime(x) will attempt to determine if x is prime.
+        As of this release, x must be < 2^32.  With one argument, isprime(x)
+        will return an error if x is out of range.  With two arguments,
+        isprime(x,y) will not generate an error but instead will return y.

-	The functions rcin, rcmul, rcout, rcpow, and rcsq are used to
-	perform modular arithmetic calculations for large odd numbers
-	faster than the usual methods.	To do this, you first use the
-	rcin function to convert all input values into numbers which are
-	in a format called REDC format.	 Then you use rcmul, rcsq, and
-	rcpow to multiply such numbers together to produce results also
-	in REDC format.	 Finally, you use rcout to convert a number in
-	REDC format back to a normal number.  The addition, subtraction,
-	negation, and equality comparison between REDC numbers are done
-	using the normal modular methods.  For example, to calculate the
-	value 13 * 17 + 1 (mod 11), you could use:
+        The functions rcin, rcmul, rcout, rcpow, and rcsq are used to
+        perform modular arithmetic calculations for large odd numbers
+        faster than the usual methods.  To do this, you first use the
+        rcin function to convert all input values into numbers which are
+        in a format called REDC format.  Then you use rcmul, rcsq, and
+        rcpow to multiply such numbers together to produce results also
+        in REDC format.  Finally, you use rcout to convert a number in
+        REDC format back to a normal number.  The addition, subtraction,
+        negation, and equality comparison between REDC numbers are done
+        using the normal modular methods.  For example, to calculate the
+        value 13 * 17 + 1 (mod 11), you could use:

-		p = 11;
-		t1 = rcin(13, p);
-		t2 = rcin(17, p);
-		t3 = rcin(1, p);
-		t4 = rcmul(t1, t2, p);
-		t5 = (t4 + t3) % p;
-		answer = rcout(t5, p);
+                p = 11;
+                t1 = rcin(13, p);
+                t2 = rcin(17, p);
+                t3 = rcin(1, p);
+                t4 = rcmul(t1, t2, p);
+                t5 = (t4 + t3) % p;
+                answer = rcout(t5, p);

-	The swap function exchanges the values of two variables without
-	performing copies.  For example, after:
+        The swap function exchanges the values of two variables without
+        performing copies.  For example, after:

-		x = 17;
-		y = 19;
-		swap(x, y);
+                x = 17;
+                y = 19;
+                swap(x, y);

-	then x is 19 and y is 17.  This function should not be used to
-	swap a value which is contained within another one.  If this is
-	done, then some memory will be lost.  For example, the following
-	should not be done:
+        then x is 19 and y is 17.  This function should not be used to
+        swap a value which is contained within another one.  If this is
+        done, then some memory will be lost.  For example, the following
+        should not be done:

-		mat x[5];
-		swap(x, x[0]);
+                mat x[5];
+                swap(x, x[0]);

-	The hash function returns a relatively small non-negative integer
-	for one or more input values.  The hash values should not be used
-	across runs of the calculator, since the algorithms used to generate
-	the hash value may change with different versions of the calculator.
+        The hash function returns a relatively small non-negative integer
+        for one or more input values.  The hash values should not be used
+        across runs of the calculator, since the algorithms used to generate
+        the hash value may change with different versions of the calculator.

-	The base function allows one to specify how numbers should be
-	printed.  The base function provides a numeric shorthand to the
-	config("mode") interface.  With no args, base() will return the
-	current mode.  With 1 arg, base(val) will set the mode according to
-	the arg and return the previous mode.
+        The base function allows one to specify how numbers should be
+        printed.  The base function provides a numeric shorthand to the
+        config("mode") interface.  With no args, base() will return the
+        current mode.  With 1 arg, base(val) will set the mode according to
+        the arg and return the previous mode.

-	The following convention is used to declare modes:
+        The following convention is used to declare modes:

-		 base	 config
-		value	 string
+                 base    config
+                value    string

-		   2	"binary"	binary fractions
-		   8	"octal"		octal fractions
-		  10	"real"		decimal floating point
-		  16	"hex"		hexadecimal fractions
-		 -10	"int"		decimal integer
-		 1/3	"frac"		decimal fractions
-		1e20	"exp"		decimal exponential
+                   2    "binary"        binary fractions
+                   8    "octal"         octal fractions
+                  10    "real"          decimal floating point
+                  16    "hex"           hexadecimal fractions
+                 -10    "int"           decimal integer
+                 1/3    "frac"          decimal fractions
+                1e20    "exp"           decimal exponential

-	For convenience, any non-integer value is assumed to mean "frac",
-	and any integer >= 2^64 is assumed to mean "exp".
+        For convenience, any non-integer value is assumed to mean "frac",
+        and any integer >= 2^64 is assumed to mean "exp".

 ## Copyright (C) 1999-2017,2021  Landon Curt Noll
 ##
@@ -207,7 +207,7 @@
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -215,8 +215,8 @@
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/07/10 01:17:53
-## File existed as early as:	1995
+## Under source code control:   1995/07/10 01:17:53
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/builtin.top
+++ b/help/builtin.top
@@ -1,11 +1,11 @@
 Builtin functions

-	There is a large number of built-in functions.	Many of the
-	functions work on several types of arguments, whereas some only
-	work for the correct types (e.g., numbers or strings).	In the
-	following description, this is indicated by whether or not the
-	description refers to values or numbers.  This display is generated
-	by the 'show builtin' command.
+        There is a large number of built-in functions.  Many of the
+        functions work on several types of arguments, whereas some only
+        work for the correct types (e.g., numbers or strings).  In the
+        following description, this is indicated by whether or not the
+        description refers to values or numbers.  This display is generated
+        by the 'show builtin' command.

 ## Copyright (C) 1999  Landon Curt Noll
 ##
@@ -15,7 +15,7 @@ Builtin functions
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -23,8 +23,8 @@ Builtin functions
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/07/10 01:17:53
-## File existed as early as:	1995
+## Under source code control:   1995/07/10 01:17:53
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/calc_tty
+++ b/help/calc_tty
@@ -5,7 +5,7 @@ SYNOPSIS
    calc_tty()

 TYPES
-    return	none if appears to be successful, error-value otherwise
+    return      none if appears to be successful, error-value otherwise

 DESCRIPTION
    This may enable a return to normal operation if abnormal activity
@@ -13,9 +13,9 @@ DESCRIPTION
    may occur when activity is resumed by an fg command after a ctrl-Z
    interrupt, or by any of the three commands:

-	; !stty echo
-	; !stty -cbreak
-	; !stty echo -cbreak
+        ; !stty echo
+        ; !stty -cbreak
+        ; !stty echo -cbreak

 EXAMPLE
    ; calc_tty();
@@ -34,7 +34,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -42,7 +42,7 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2000/12/14 01:33:00
-## File existed as early as:	2000
+## Under source code control:   2000/12/14 01:33:00
+## File existed as early as:    2000
 ##
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/calclevel
+++ b/help/calclevel
@@ -5,12 +5,12 @@ SYNOPSIS
    calclevel()

 TYPES
-    return	nonnegative integer
+    return      nonnegative integer

 DESCRIPTION
    This function returns the calculation level at which it is called.
    When a command is being read from a terminal or from a file,
-    calc is at calculation level zero.	The level is increased
+    calc is at calculation level zero.  The level is increased
    by 1 each time calculation starts of a user-defined function
    or of eval(S) for some expression S which evaluates to a string.  It
    decreases to zero if an error occurs or a quit or abort statement
@@ -45,7 +45,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -53,8 +53,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1999/10/31 06:01:21
-## File existed as early as:	1999
+## Under source code control:   1999/10/31 06:01:21
+## File existed as early as:    1999
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/calcpath
+++ b/help/calcpath
@@ -5,7 +5,7 @@ SYNOPSIS
    calcpath()

 TYPES
-    return	string
+    return      string

 DESCRIPTION
    This function returns the current value of the CALCPATH search path.
@@ -40,7 +40,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -48,8 +48,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 ##
-## Under source code control:	2006/05/07 23:56:04
-## File existed as early as:	2006
+## Under source code control:   2006/05/07 23:56:04
+## File existed as early as:    2006
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cas
+++ b/help/cas
@@ -5,10 +5,10 @@ SYNOPSIS
    cas(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the trigonometric cosine plus sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called cosine and sine, is equivalent to:

-	cas(x) = cos(x) + sin(x)
+        cas(x) = cos(x) + sin(x)

 EXAMPLE
    ; print cas(1/2), cas(5/7), cas(42/7)
@@ -54,14 +54,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -71,7 +71,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -79,8 +79,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/10/02 23:11:18
-## File existed as early as:	2023
+## Under source code control:   2023/10/02 23:11:18
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/catalan
+++ b/help/catalan
@@ -5,14 +5,14 @@ SYNOPSIS
    catalan(n)

 TYPES
-    n		integer
+    n           integer

-    return	integer
+    return      integer

 DESCRIPTION
    If n >= 0, this returns the Catalan number for index n:

-	catalan(n) = comb(2*n,n)/(n + 1)
+        catalan(n) = comb(2*n,n)/(n + 1)

    Zero is returned for negative n.

@@ -45,7 +45,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -53,7 +53,7 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2000/12/14 01:33:00
-## File existed as early as:	2000
+## Under source code control:   2000/12/14 01:33:00
+## File existed as early as:    2000
 ##
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ceil
+++ b/help/ceil
@@ -5,9 +5,9 @@ SYNOPSIS
    ceil(x)

 TYPES
-    x		real, complex, list, matrix
+    x           real, complex, list, matrix

-    return	real or complex, list, matrix
+    return      real or complex, list, matrix

 DESCRIPTION
    For real x, ceil(x) is the least integer not less than x.
@@ -40,7 +40,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -48,8 +48,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 01:12:01
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 01:12:01
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cfappr
+++ b/help/cfappr
@@ -5,12 +5,12 @@ SYNOPSIS
    cfappr(x [,eps [,rnd]]) or cfappr(x, n [,rnd])

 TYPES
-    x		real
-    eps		real with abs(eps) < 1, defaults to epsilon()
-    n		real with n >= 1
-    rnd		integer, defaults to config("cfappr")
+    x           real
+    eps         real with abs(eps) < 1, defaults to epsilon()
+    n           real with n >= 1
+    rnd         integer, defaults to config("cfappr")

-    return	real
+    return      real

 DESCRIPTION
    If x is an integer or eps is zero, either form returns x.
@@ -21,23 +21,23 @@ DESCRIPTION

    If n >= 1 and den(x) > n, cfappr(x, n) returns the nearest above,
    nearest below, or nearest, approximation to x with denominator less
-    than or equal to n.	 If den(x) <= n, cfappr(x,n) returns x.
+    than or equal to n.  If den(x) <= n, cfappr(x,n) returns x.

    In either case when the result v is not x, how v relates to x is
    determined by bits 0, 1, 2 and 4 of the argument rnd in the same way as
    these bits are used in the functions round() and appr().  In the
    following y is either eps or n.

-		rnd	sign of remainder x - v
+                rnd     sign of remainder x - v

-		0		sgn(y)
-		1		-sgn(y
-		2		sgn(x), "rounding to zero"
-		3		-sgn(x), "rounding from zero"
-		4		+, "rounding down"
-		5		-, "rounding up"
-		6		sgn(x/y)
-		7		-sgn(x/y)
+                0               sgn(y)
+                1               -sgn(y
+                2               sgn(x), "rounding to zero"
+                3               -sgn(x), "rounding from zero"
+                4               +, "rounding down"
+                5               -, "rounding up"
+                6               sgn(x/y)
+                7               -sgn(x/y)

    If bit 4 of rnd is set, the other bits are irrelevant for the eps case;
    thus for 16 <= rnd < 24, cfappr(x, eps, rnd) is the smallest-denominator
@@ -96,7 +96,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -104,8 +104,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 01:23:59
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 01:23:59
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cfsim
+++ b/help/cfsim
@@ -5,10 +5,10 @@ SYNOPSIS
    cfsim(x [,rnd])

 TYPES
-    x		real
-    rnd		integer, defaults to config("cfsim")
+    x           real
+    rnd         integer, defaults to config("cfsim")

-    return	real
+    return      real

 DESCRIPTION
    If x is not an integer, cfsim(x, rnd) returns either the nearest
@@ -20,23 +20,23 @@ DESCRIPTION
    For 0 <= rnd < 4, the sign of the remainder x - cfsim(x, rnd) is
    as follows:

-		rnd		sign of x - cfsim(x, rnd)
+                rnd             sign of x - cfsim(x, rnd)

-		0		+, as if rounding down
-		1		-. as if rounding up
-		2		sgn(x), as if rounding to zero
-		3		-sgn(x), as if rounding from zero
+                0               +, as if rounding down
+                1               -. as if rounding up
+                2               sgn(x), as if rounding to zero
+                3               -sgn(x), as if rounding from zero

    This corresponds to the use of rnd for functions like round(x, n, rnd).

    If bit 3 or 4 of rnd is set, the lower order bits are ignored; bit 3
-    is ignored if bit 4 is set.	 Thus, for rnd > 3, it sufficient to
+    is ignored if bit 4 is set.  Thus, for rnd > 3, it sufficient to
    consider the two cases rnd = 8 and rnd = 16.

    If den(x) > 2, cfsim(x, 8) returns the value of the penultimate simple
    continued-fraction approximate to x, i.e. if:

-	x = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/a_n) ...)),
+        x = a_0 + 1/(a_1 + 1/(a_2 + ... + 1/a_n) ...)),

    where a_0 is an integer, a_1, ..., a_n are positive integers,
    and a_n >= 2, the value returned is that of the continued fraction
@@ -53,10 +53,10 @@ DESCRIPTION

    In summary, for cfsim(x, rnd) when rnd = 8 or 16, the results are:

-	rnd		integer x	half-integer x		den(x) > 2
+        rnd             integer x       half-integer x          den(x) > 2

-	 8		0		x - sgn(x)/2		approximate
-	16		x - sgn(x)	x + sgn(x)/2		nearest
+         8              0               x - sgn(x)/2            approximate
+        16              x - sgn(x)      x + sgn(x)/2            nearest

     From either cfsim(x, 0) and cfsim(x, 1), the other is easily
     determined: if one of them has value w, the other has value
@@ -72,7 +72,7 @@ DESCRIPTION
     Iteration of cfsim(x,8) until an integer is obtained gives a sequence of
     "good" approximations to x with decreasing denominators and
     correspondingly decreasing accuracy; each denominator is less than half
-     the preceding denominator.	 (Unlike the "forward" sequence of
+     the preceding denominator.  (Unlike the "forward" sequence of
     continued-fraction approximates these are not necessarily alternately
     greater than and less than x.)

@@ -80,19 +80,19 @@ DESCRIPTION

     For rnd = 0 or 1 and any x, or rnd = 8 or 16 and x with den(x) > 2:

-		cfsim(n + x, rnd) = n + cfsim(x, rnd).
+                cfsim(n + x, rnd) = n + cfsim(x, rnd).

     This equation also holds for the other values of rnd if n + x and x
     have the same sign.

     For rnd = 2, 3, 8 or 16, and any x:

-		cfsim(-x, rnd) = -cfsim(x, rnd).
+                cfsim(-x, rnd) = -cfsim(x, rnd).

     If rnd = 8 or 16, except for integer x or 1/x for rnd = 8, and
     zero x for rnd = 16:

-		cfsim(1/x, rnd) = 1/cfsim(x, rnd).
+                cfsim(1/x, rnd) = 1/cfsim(x, rnd).

 EXAMPLE
    ; c = config("mode", "frac");
@@ -121,7 +121,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -129,8 +129,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 01:29:45
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 01:29:45
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/char
+++ b/help/char
@@ -5,9 +5,9 @@ SYNOPSIS
    char(j)

 TYPES
-    j		integer, 0 <= j < 256
+    j           integer, 0 <= j < 256

-    return	string
+    return      string

 DESCRIPTION
    For j > 0, returns a string of length 1 with a character that has
@@ -34,7 +34,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -42,8 +42,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/09/30 01:45:45
-## File existed as early as:	1994
+## Under source code control:   1994/09/30 01:45:45
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cis
+++ b/help/cis
@@ -5,10 +5,10 @@ SYNOPSIS
    cis(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the Euler's formula value of x to a multiple of eps with error less in
@@ -16,8 +16,8 @@ DESCRIPTION

    This function is sometimes called cosine and sine, is equivalent to:

-	cis(x) = cos(x) + 1i*sin(x)
-	cis(x) = exp(1i * x)
+        cis(x) = cos(x) + 1i*sin(x)
+        cis(x) = exp(1i * x)

 EXAMPLE
    ; print cis(1/2), cis(5/7)
@@ -60,14 +60,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -77,7 +77,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -85,8 +85,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/10/02 23:11:18
-## File existed as early as:	2023
+## Under source code control:   2023/10/02 23:11:18
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cmdbuf
+++ b/help/cmdbuf
@@ -5,7 +5,7 @@ SYNOPSIS
    cmdbuf()

 TYPES
-    return	str
+    return      str

 DESCRIPTION
    This function returns the command string that was formed by calc based
@@ -37,7 +37,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -45,8 +45,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/07/09 04:05:58
-## File existed as early as:	1995
+## Under source code control:   1995/07/09 04:05:58
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cmp
+++ b/help/cmp
@@ -12,79 +12,79 @@ TYPES

    For non-object x and y:

-    x		any
-    y		any
+    x           any
+    y           any

-    return	if x and y are both real: -1, 0, or 1
-		if x and y are both numbers but not both real:
-			-1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
-		if x and y are both strings: -1, 0, or 1
-		all other cases: the null value
+    return      if x and y are both real: -1, 0, or 1
+                if x and y are both numbers but not both real:
+                        -1, 0, 1, -1+1i, 1i, 1+1i, -1-1i, -1i, or 1-1i
+                if x and y are both strings: -1, 0, or 1
+                all other cases: the null value

 DESCRIPTION

    x and y both real: cmp(x, y) = sgn(x - y), i.e. -1, 0, or 1
-	according as x < y, x == y, or x > y
+        according as x < y, x == y, or x > y

    x and y both numbers, at least one being complex:
-	cmp(x,y) = sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i
+        cmp(x,y) = sgn(re(x) - re(y)) + sgn(im(x) - im(y)) * 1i

    x and y both strings: successive characters are compared until either
-	different characters are encountered or at least one string is
-	completed.  If the comparison ends because of different characters,
-	cmp(x,y) = 1 or -1 according as the greater character is in x or y.
-	If all characters compared in both strings are equal, then
-	cmp(x,y) = -1, 0 or 1 according as the length of x is less than,
-	equal to, or greater than the length of y.  (This comparison
-	is performed via the strcmp() libc function.)
+        different characters are encountered or at least one string is
+        completed.  If the comparison ends because of different characters,
+        cmp(x,y) = 1 or -1 according as the greater character is in x or y.
+        If all characters compared in both strings are equal, then
+        cmp(x,y) = -1, 0 or 1 according as the length of x is less than,
+        equal to, or greater than the length of y.  (This comparison
+        is performed via the strcmp() libc function.)

    objects: comparisons of objects are usually intended for some total or
-	partial ordering and appropriate definitions of cmp(a,b) may
-	make use of comparison of numerical or string components.
-	definitions using comparison of numbers or strings are usually
-	appropriate.  For example, after
+        partial ordering and appropriate definitions of cmp(a,b) may
+        make use of comparison of numerical or string components.
+        definitions using comparison of numbers or strings are usually
+        appropriate.  For example, after

-		obj point {x,y};
+                obj point {x,y};

-	if points with real components are to be partially ordered by their
-	Euclidean distance from the origin, an appropriate point_rel
-	function may be that given by
+        if points with real components are to be partially ordered by their
+        Euclidean distance from the origin, an appropriate point_rel
+        function may be that given by

-		define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);
+                define point_rel(a,b) = sgn(a.x^2 + a.y^2 - b.x^2 - b.y^2);

-	A total "lexicographic" ordering is that given by:
+        A total "lexicographic" ordering is that given by:

-		define point_rel(a,b) {
-			if (a.y != b.y)
-				return sgn(a.y - b.y);
-			return (a.x - b.x);
-		}
+                define point_rel(a,b) {
+                        if (a.y != b.y)
+                                return sgn(a.y - b.y);
+                        return (a.x - b.x);
+                }

-	A comparison function that compares points analogously to
-	cmp(a,b) for real and complex numbers is that given by
+        A comparison function that compares points analogously to
+        cmp(a,b) for real and complex numbers is that given by

-		define point_rel(P1, P2) {
-			return obj point = {sgn(P1.x-P2.x), sgn(P1.y-P2.y)};
-		}
+                define point_rel(P1, P2) {
+                        return obj point = {sgn(P1.x-P2.x), sgn(P1.y-P2.y)};
+                }

-	The range of this function is the set of nine points with zero
-	or unit components.
+        The range of this function is the set of nine points with zero
+        or unit components.


    Some properties of cmp(a,b) for real or complex a and b are:

-	cmp(a + c, b + c) = cmp(a, b)
+        cmp(a + c, b + c) = cmp(a, b)

-	cmp(a, b) == 0 if and only if a == b
+        cmp(a, b) == 0 if and only if a == b

-	cmp(b, a) = -cmp(a, b)
+        cmp(b, a) = -cmp(a, b)

-	if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)
+        if c is real or pure imaginary, cmp(c * a, c * b) = c * cmp(a,b)

    Then a function that defines "b is between a and c" in an often useful
    sense is

-	define between(a,b,c) = (cmp(a,b) == cmp(b,c)).
+        define between(a,b,c) = (cmp(a,b) == cmp(b,c)).

    For example, in this sense, 3 + 4i is between 1 + 5i and 4 + 2i.

@@ -122,7 +122,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -130,8 +130,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/10/20 02:52:30
-## File existed as early as:	1994
+## Under source code control:   1994/10/20 02:52:30
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/comb
+++ b/help/comb
@@ -5,17 +5,17 @@ SYNOPSIS
    comb(x, y)

 TYPES
-    x		integer
-    y		integer
+    x           integer
+    y           integer

-    return	integer
+    return      integer

 DESCRIPTION
    Return the combinatorial number C(x,y) which is defined as:

-	       x!
-	    ---------
-	    y!*(x-y)!
+               x!
+            ---------
+            y!*(x-y)!

    This function computes the number of combinations in which y things
    may be chosen from x items ignoring the order in which they are chosen.
@@ -46,7 +46,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -54,8 +54,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/10/20 04:03:02
-## File existed as early as:	1994
+## Under source code control:   1994/10/20 04:03:02
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/command
+++ b/help/command
@@ -3,7 +3,7 @@ Command sequence
    This is a sequence of any the following command formats, where
    each command is terminated by a semicolon or newline.  Long command
    lines can be extended by using a back-slash followed by a newline
-    character.	When this is done, the prompt shows a double angle
+    character.  When this is done, the prompt shows a double angle
    bracket to indicate that the line is still in progress.  Certain
    cases will automatically prompt for more input in a similar manner,
    even without the back-slash.  The most common case for this is when
@@ -19,26 +19,26 @@ Command sequence
    define function(params) { body }
    define function(params) = expression

-	This first form defines a full function which can consist
-	of declarations followed by many statements which implement
-	the function.
+        This first form defines a full function which can consist
+        of declarations followed by many statements which implement
+        the function.

-	The second form defines a simple function which calculates
-	the specified expression value from the specified parameters.
-	The expression cannot be a statement.  However, the comma
-	and question mark operators can be useful.	Examples of
-	simple functions are:
+        The second form defines a simple function which calculates
+        the specified expression value from the specified parameters.
+        The expression cannot be a statement.  However, the comma
+        and question mark operators can be useful.      Examples of
+        simple functions are:

-		define sumcubes(a, b) = a^3 + b^3
-		define pimod(a) = a % pi()
-		define printnum(a, n, p)
-		{
-		    if (p == 0) {
-			print a: "^": n, "=", a^n;
-		    } else {
-			print a: "^": n, "mod", p, "=", pmod(a,n,p);
-		    }
-		}
+                define sumcubes(a, b) = a^3 + b^3
+                define pimod(a) = a % pi()
+                define printnum(a, n, p)
+                {
+                    if (p == 0) {
+                        print a: "^": n, "=", a^n;
+                    } else {
+                        print a: "^": n, "mod", p, "=", pmod(a,n,p);
+                    }
+                }


    read calc commands
@@ -48,70 +48,70 @@ Command sequence
    read filename
    read -once filename

-	This reads definitions from the specified calc resource filename.
+        This reads definitions from the specified calc resource filename.

-	In the 1st and 2nd forms, if var is a global variable string
-	value, then the value of that variable is used as a filename.
+        In the 1st and 2nd forms, if var is a global variable string
+        value, then the value of that variable is used as a filename.

-	The following is equivalent to read lucas.cal or read "lucas.cal":
+        The following is equivalent to read lucas.cal or read "lucas.cal":

-	    global var = "lucas.cal";
-	    read $var;
+            global var = "lucas.cal";
+            read $var;

-	In the 3rd or 4th forms, the filename argument is treated
-	as a literal string, not a variable.  In these forms, the
-	name can be quoted if desired.
+        In the 3rd or 4th forms, the filename argument is treated
+        as a literal string, not a variable.  In these forms, the
+        name can be quoted if desired.

-	The calculator uses the CALCPATH environment variable to
-	search through the specified directories for the filename,
-	similarly to the use of the PATH environment variable.
-	If CALCPATH is not defined, then a default path which is
-	usually ":/usr/local/lib/calc" is used.
+        The calculator uses the CALCPATH environment variable to
+        search through the specified directories for the filename,
+        similarly to the use of the PATH environment variable.
+        If CALCPATH is not defined, then a default path which is
+        usually ":/usr/local/lib/calc" is used.

-	The ".cal" extension is defaulted for input files, so that
-	if "filename" is not found, then "filename.cal" is then
-	searched for.  The contents of the filename are command
-	sequences which can consist of expressions to evaluate or
-	functions to define, just like at the top level command level.
+        The ".cal" extension is defaulted for input files, so that
+        if "filename" is not found, then "filename.cal" is then
+        searched for.  The contents of the filename are command
+        sequences which can consist of expressions to evaluate or
+        functions to define, just like at the top level command level.

-	When -once is given, the read command acts like the regular
-	read expect that it will ignore filename if is has been
-	previously read.
+        When -once is given, the read command acts like the regular
+        read expect that it will ignore filename if is has been
+        previously read.

-	The read -once form is particularly useful in a resource
-	file that needs to read a 2nd resource file.  By using the
-	READ -once command, one will not reread that 2nd resource
-	file, nor will once risk entering into a infinite READ loop
-	(where that 2nd resource file directly or indirectly does
-	a READ of the first resource file).
+        The read -once form is particularly useful in a resource
+        file that needs to read a 2nd resource file.  By using the
+        READ -once command, one will not reread that 2nd resource
+        file, nor will once risk entering into a infinite READ loop
+        (where that 2nd resource file directly or indirectly does
+        a READ of the first resource file).

-	If the -m mode disallows opening of files for reading,
-	this command will be disabled.
+        If the -m mode disallows opening of files for reading,
+        this command will be disabled.

-	To read a calc resource file without printing various
-	messages about defined functions, the "resource_debug"
-	config should be set to zero.  For example:
+        To read a calc resource file without printing various
+        messages about defined functions, the "resource_debug"
+        config should be set to zero.  For example:

-	    read lucas;
+            read lucas;

-	will, by default, print messages such as:
+        will, by default, print messages such as:

-	    lucas(h,n) defined
-	    gen_u2(h,n,v1) defined
-	    gen_u0(h,n,v1) defined
-	    rodseth_xhn(x,h,n) defined
-	    gen_v1(h,n) defined
-	    ldebug(funct,str) defined
-	    legacy_gen_v1(h,n) defined
+            lucas(h,n) defined
+            gen_u2(h,n,v1) defined
+            gen_u0(h,n,v1) defined
+            rodseth_xhn(x,h,n) defined
+            gen_v1(h,n) defined
+            ldebug(funct,str) defined
+            legacy_gen_v1(h,n) defined

        When "resource_debug" is zero, such messages are silenced.

-	    config("resource_debug", 0),;
-	    read lucas;
+            config("resource_debug", 0),;
+            read lucas;

-	To silence such messages on the calc command line, try:
+        To silence such messages on the calc command line, try:

-	    calc -p -D :0 'read -once lucas; lucas(1, 23209);'
+            calc -p -D :0 'read -once lucas; lucas(1, 23209);'


    write calc commands
@@ -119,29 +119,29 @@ Command sequence
    write $var
    write filename

-	This writes the values of all global variables to the
-	specified filename, in such a way that the file can be
-	later read in order to recreate the variable values.
-	For speed reasons, values are written as hex fractions.
-	This command currently only saves simple types, so that
-	matrices, lists, and objects are not saved.	 Function
-	definitions are also not saved.
+        This writes the values of all global variables to the
+        specified filename, in such a way that the file can be
+        later read in order to recreate the variable values.
+        For speed reasons, values are written as hex fractions.
+        This command currently only saves simple types, so that
+        matrices, lists, and objects are not saved.      Function
+        definitions are also not saved.

-	In the 1st form, if var is a global variable string
-	value, then the value of that variable is used as a filename.
+        In the 1st form, if var is a global variable string
+        value, then the value of that variable is used as a filename.

-	The following is equivalent to write dump.out or
-	write "dump.out":
+        The following is equivalent to write dump.out or
+        write "dump.out":

-	    global var = "dump.out";
-	    write $var;
+            global var = "dump.out";
+            write $var;

-	In the 2nd form, the filename argument is treated as a literal
-	string, not a variable.  In this form, the name can be quoted
-	if desired.
+        In the 2nd form, the filename argument is treated as a literal
+        string, not a variable.  In this form, the name can be quoted
+        if desired.

-	If the -m mode disallows opening of files for writing,
-	this command will be disabled.
+        If the -m mode disallows opening of files for writing,
+        this command will be disabled.


    quit or exit
@@ -151,35 +151,35 @@ Command sequence
    exit
    exit string

-	The action of these commands depends on where they are used.
-	At the interactive level, they will cause calc to exit.
-	This is the normal way to leave the calculator.  In any
-	other use, they will stop the current calculation as if
-	an error had occurred.
+        The action of these commands depends on where they are used.
+        At the interactive level, they will cause calc to exit.
+        This is the normal way to leave the calculator.  In any
+        other use, they will stop the current calculation as if
+        an error had occurred.

-	If a string is given, then the string is printed as the reason
-	for quitting, otherwise a general quit message is printed.
-	The routine name and line number which executed the quit is
-	also printed in either case.
+        If a string is given, then the string is printed as the reason
+        for quitting, otherwise a general quit message is printed.
+        The routine name and line number which executed the quit is
+        also printed in either case.

-	Exit is an alias for quit.
+        Exit is an alias for quit.

-	Quit is useful when a routine detects invalid arguments,
-	in order to stop a calculation cleanly.  For example,
-	for a square root routine, an error can be given if the
-	supplied parameter was a negative number, as in:
+        Quit is useful when a routine detects invalid arguments,
+        in order to stop a calculation cleanly.  For example,
+        for a square root routine, an error can be given if the
+        supplied parameter was a negative number, as in:

-		define mysqrt(n)
-		{
-		    if (! isnum(n))
-			quit "non-numeric argument";
-		    if (n < 0)
-			quit "Negative argument";
-		    return sqrt(n);
-		}
+                define mysqrt(n)
+                {
+                    if (! isnum(n))
+                        quit "non-numeric argument";
+                    if (n < 0)
+                        quit "Negative argument";
+                    return sqrt(n);
+                }

-	See 'more information about abort and quit' below for
-	more information.
+        See 'more information about abort and quit' below for
+        more information.


    abort
@@ -187,12 +187,12 @@ Command sequence
    abort
    abort string

-	This command behaves like QUIT except that it will attempt
-	to return to the interactive level if permitted, otherwise
-	calc exit.
+        This command behaves like QUIT except that it will attempt
+        to return to the interactive level if permitted, otherwise
+        calc exit.

-	See 'more information about abort and quit' below for
-	more information.
+        See 'more information about abort and quit' below for
+        more information.


    change current directory
@@ -200,45 +200,45 @@ Command sequence
    cd
    cd dir

-	Change the current directory to 'dir'.  If 'dir' is omitted,
-	change the current directory to the home directory, if $HOME
-	is set in the environment.
+        Change the current directory to 'dir'.  If 'dir' is omitted,
+        change the current directory to the home directory, if $HOME
+        is set in the environment.


    show information
    ----------------
    show item

-	This command displays some information where 'item' is
-	one of the following:
+        This command displays some information where 'item' is
+        one of the following:

-		blocks		unfreed named blocks
-		builtin		built in functions
-		config		config parameters and values
-		constants	cache of numeric constants
-		custom		custom functions if calc -C was used
-		errors		new error-values created
-		files		open files, file position and sizes
-		function	user-defined functions
-		globaltypes	global variables
-		objfunctions	possible object functions
-		objtypes	defined objects
-		opcodes 	internal opcodes for function `func'
-		sizes		size in octets of calc value types
-		realglobals	numeric global variables
-		statics		un-scoped static variables
-		numbers		calc number cache
-		redcdata	REDC data defined
-		strings		calc string cache
-		literals	calc literal cache
+                blocks          unfreed named blocks
+                builtin         built in functions
+                config          config parameters and values
+                constants       cache of numeric constants
+                custom          custom functions if calc -C was used
+                errors          new error-values created
+                files           open files, file position and sizes
+                function        user-defined functions
+                globaltypes     global variables
+                objfunctions    possible object functions
+                objtypes        defined objects
+                opcodes         internal opcodes for function `func'
+                sizes           size in octets of calc value types
+                realglobals     numeric global variables
+                statics         un-scoped static variables
+                numbers         calc number cache
+                redcdata        REDC data defined
+                strings         calc string cache
+                literals        calc literal cache

-	Only the first 4 characters of item are examined, so:
+        Only the first 4 characters of item are examined, so:

-		show globals
-		show global
-		show glob
+                show globals
+                show global
+                show glob

-	do the same thing.
+        do the same thing.


    calc help
@@ -246,20 +246,20 @@ Command sequence
    help $var
    help name

-	This displays a help related to 'name' or general
-	help of none is given.
+        This displays a help related to 'name' or general
+        help of none is given.

-	In the 1st form, if var is a global variable string
-	value, then the value of that variable is used as a name.
+        In the 1st form, if var is a global variable string
+        value, then the value of that variable is used as a name.

-	The following is equivalent to help command or help "command":
+        The following is equivalent to help command or help "command":

-	    global var = "command";
-	    help $var;
+            global var = "command";
+            help $var;

-	In the 2nd form, the filename argument is treated as a literal
-	string, not a variable.  In this form, the name can be quoted
-	if desired.
+        In the 2nd form, the filename argument is treated as a literal
+        string, not a variable.  In this form, the name can be quoted
+        if desired.


    =-=
@@ -269,28 +269,28 @@ Command sequence

    Consider the following calc file called myfile.cal:

-	print "start of myfile.cal";
-	define q() {quit "quit from q()"; print "end of q()"}
-	define a() {abort "abort from a()"}
-	x = 3;
-	{print "start #1"; if (x > 1) q()} print "after #1";
-	{print "start #2"; if (x > 1) a()} print "after #2";
-	{print "start #3"; if (x > 1) quit "quit from 3rd statement"}
-	print "end of myfile.cal";
+        print "start of myfile.cal";
+        define q() {quit "quit from q()"; print "end of q()"}
+        define a() {abort "abort from a()"}
+        x = 3;
+        {print "start #1"; if (x > 1) q()} print "after #1";
+        {print "start #2"; if (x > 1) a()} print "after #2";
+        {print "start #3"; if (x > 1) quit "quit from 3rd statement"}
+        print "end of myfile.cal";

    The command:

-	calc read myfile
+        calc read myfile

    will produce:

-	q() defined
-	a() defined
-	start statement #1
-	quit from q()
-	after statement #1
-	start statement #2
-	abort from a()
+        q() defined
+        a() defined
+        start statement #1
+        quit from q()
+        after statement #1
+        start statement #2
+        abort from a()

    The QUIT within the q() function prevented the ``end of q()''
    statement from being evaluated.  This QUIT command caused
@@ -303,38 +303,38 @@ Command sequence

    The command:

-	calc -i read myfile
+        calc -i read myfile

    will produce:

-	q() defined
-	a() defined
-	start statement #1
-	quit from q()
-	after statement #1
-	start statement #2
-	abort from a()
-	;		<==== calc interactive prompt
+        q() defined
+        a() defined
+        start statement #1
+        quit from q()
+        after statement #1
+        start statement #2
+        abort from a()
+        ;               <==== calc interactive prompt

    because the '-i' calc causes ABORT to drop into an
-    interactive prompt.	 However typing a QUIT or ABORT
+    interactive prompt.  However typing a QUIT or ABORT
    at the interactive prompt level will always calc to exit,
    even when calc is invoked with '-i'.

    Also observe that both of these commands:

-	cat myfile.cal | calc
-	cat myfile.cal | calc -i
+        cat myfile.cal | calc
+        cat myfile.cal | calc -i

    will produce:

-	q() defined
-	a() defined
-	start statement #1
-	quit from q()
-	after statement #1
-	start statement #2
-	abort from a()
+        q() defined
+        a() defined
+        start statement #1
+        quit from q()
+        after statement #1
+        start statement #2
+        abort from a()

    The ABORT inside function a() halts the processing of statements
    from the input source (standard input).  Because standard input
@@ -344,23 +344,23 @@ Command sequence
    If one were to type in the contents of myfile.cal interactively,
    calc will produce:

-	; print "start of myfile.cal";
-	start of myfile.cal
-	; define q() {quit "quit from q()"; print "end of q()"}
-	q() defined
-	; define a() {abort "abort from a()"}
-	a() defined
-	; x = 3;
-	; {print "start #1"; if (x > 1) q()} print "after #1";
-	start statement #1
-	quit from q()
-	after statement #1
-	; {print "start #2"; if (x > 1) a()} print "after #2";
-	start statement #2
-	abort from a()
-	; {print "start #3"; if (x > 1) quit "quit from 3rd statement"}
-	start #3
-	quit from 3rd statement
+        ; print "start of myfile.cal";
+        start of myfile.cal
+        ; define q() {quit "quit from q()"; print "end of q()"}
+        q() defined
+        ; define a() {abort "abort from a()"}
+        a() defined
+        ; x = 3;
+        ; {print "start #1"; if (x > 1) q()} print "after #1";
+        start statement #1
+        quit from q()
+        after statement #1
+        ; {print "start #2"; if (x > 1) a()} print "after #2";
+        start statement #2
+        abort from a()
+        ; {print "start #3"; if (x > 1) quit "quit from 3rd statement"}
+        start #3
+        quit from 3rd statement

    The ABORT from within the a() function returned control to
    the interactive level.
@@ -372,8 +372,8 @@ Command sequence

    Also see the help topic:

-	statement   flow control and declaration statements
-	usage	    how to invoke the calc command and calc -options
+        statement   flow control and declaration statements
+        usage       how to invoke the calc command and calc -options

 ## Copyright (C) 1999-2006,2018,2021  Landon Curt Noll
 ##
@@ -383,7 +383,7 @@ Command sequence
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -391,8 +391,8 @@ Command sequence
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1991/07/21 04:37:17
-## File existed as early as:	1991
+## Under source code control:   1991/07/21 04:37:17
+## File existed as early as:    1991
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/config
+++ b/help/config
--- a/help/conj
+++ b/help/conj
@@ -9,9 +9,9 @@ TYPES

    For non-object x:

-    x		real, complex, or matrix
+    x           real, complex, or matrix

-    return	real, complex, or matrix
+    return      real, complex, or matrix

 DESCRIPTION

@@ -48,7 +48,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -56,8 +56,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/03 10:40:01
-## File existed as early as:	1995
+## Under source code control:   1995/10/03 10:40:01
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cos
+++ b/help/cos
@@ -5,10 +5,10 @@ SYNOPSIS
    cos(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the trigonometric cosine of x to a multiple of eps with error less in
@@ -50,14 +50,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -67,7 +67,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -75,8 +75,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:27
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:27
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cosh
+++ b/help/cosh
@@ -5,10 +5,10 @@ SYNOPSIS
    cosh(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Calculate the cosh of x to the nearest or next to nearest multiple of
@@ -39,7 +39,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -47,8 +47,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 01:40:28
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 01:40:28
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cot
+++ b/help/cot
@@ -5,10 +5,10 @@ SYNOPSIS
    cot(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Calculate the trigonometric cotangent of x to a multiple of eps, with error less
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is equivalent to:

-	cot(x) = cos(x) / sin(x)
+        cot(x) = cos(x) / sin(x)

 EXAMPLE
    ; print cot(1/2), cot(5/7), cot(42/7)
@@ -56,14 +56,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2021,2023  Landon Curt Noll
 ##
@@ -73,7 +73,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -81,8 +81,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/coth
+++ b/help/coth
@@ -5,10 +5,10 @@ SYNOPSIS
    coth(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Calculate the coth of x to a multiple of eps with error less in
@@ -39,7 +39,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -47,8 +47,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/count
+++ b/help/count
@@ -5,10 +5,10 @@ SYNOPSIS
    count(x, y)

 TYPES
-    x		list or matrix
-    y		string
+    x           list or matrix
+    y           string

-    return	integer
+    return      integer

 DESCRIPTION
    For count(x, y), y is to be the name of a user-defined function;
@@ -19,7 +19,7 @@ EXAMPLE
    ; define f(a) = (a < 5)
    ; A = list(1,2,7,6,4,8)
    ; count(A, "f")
-	3
+        3

 LIMITS
    none
@@ -38,7 +38,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -46,8 +46,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/07/10 02:09:31
-## File existed as early as:	1995
+## Under source code control:   1995/07/10 02:09:31
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/covercos
+++ b/help/covercos
@@ -5,10 +5,10 @@ SYNOPSIS
    covercos(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the coversed trigonometric cosine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called cvc, or covercosine, is equivalent to:

-	covercos(x) = 1 + sin(x)
+        covercos(x) = 1 + sin(x)

 EXAMPLE
    ; print covercos(1/2), covercos(5/7), covercos(42/7)
@@ -54,14 +54,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -71,7 +71,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -79,8 +79,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/09/05 23:31:08
-## File existed as early as:	2023
+## Under source code control:   2023/09/05 23:31:08
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/coversin
+++ b/help/coversin
@@ -5,10 +5,10 @@ SYNOPSIS
    coversin(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate the coversed trigonometric sine of x to a multiple of eps with error less in
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is sometimes called covers, or cvs, is equivalent to:

-	coversin(x) = 1 - sin(x)
+        coversin(x) = 1 - sin(x)

 EXAMPLE
    ; print coversin(1/2), coversin(5/7), coversin(42/7)
@@ -54,14 +54,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -71,7 +71,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -79,8 +79,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/08/31 23:07:08
-## File existed as early as:	2023
+## Under source code control:   2023/08/31 23:07:08
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/cp
+++ b/help/cp
@@ -5,16 +5,16 @@ SYNOPSIS
    cp(x, y)

 TYPES
-    x, y	1-dimensional matrices with 3 elements
+    x, y        1-dimensional matrices with 3 elements

-    return	1-dimensional matrix with 3 elements
+    return      1-dimensional matrix with 3 elements

 DESCRIPTION
    Calculate the product of two 3 1-dimensional matrices.
    If x has elements (x0, x1, x2), and y has elements (y0, y1, y2),
    cp(x,y) returns the matrix of type [0:2] with elements:

-	{x1 * y2 - x2 * y1, x3 * y1 - x1 * y3, x1 * y2 - x2 * y1}
+        {x1 * y2 - x2 * y1, x3 * y1 - x1 * y3, x1 * y2 - x2 * y1}

 EXAMPLE
    ; mat x[3] = {2,3,4}
@@ -44,7 +44,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -52,8 +52,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 59 Temple Place, Suite 330, Boston, MA  02111-1307, USA.
 ##
-## Under source code control:	1995/10/05 04:52:26
-## File existed as early as:	1995
+## Under source code control:   1995/10/05 04:52:26
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/crd
+++ b/help/crd
@@ -5,10 +5,10 @@ SYNOPSIS
    crd(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Calculate length of unit circle chord with angle x to a multiple of eps with error less in
@@ -19,7 +19,7 @@ DESCRIPTION

    This function is sometimes called chord, is equivalent to:

-	crd(x) = 2 * sin(x / 2)
+        crd(x) = 2 * sin(x / 2)

 EXAMPLE
    ; print crd(1/2), crd(5/7), crd(42/7)
@@ -57,14 +57,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 2023  Landon Curt Noll
 ##
@@ -74,7 +74,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -82,8 +82,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2023/10/02 16:49:42
-## File existed as early as:	2023
+## Under source code control:   2023/10/02 16:49:42
+## File existed as early as:    2023
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/credit
+++ b/help/credit
@@ -15,7 +15,7 @@ Credits
    hist.c which is used to do the command line editing.

    Thanks to Ernest W. Bowen for supplying many improvements in
-    accuracy and generality for some numeric functions.	 Much of
+    accuracy and generality for some numeric functions.  Much of
    this was in terms of actual code which I gratefully accepted.
    Ernest also supplied the original text for many of the help files.

@@ -26,17 +26,17 @@ Credits

    Most of this source and binary has one of the following copyrights:

-	Copyright (C) year  David I. Bell
-	Copyright (C) year  David I. Bell and Landon Curt Noll
-	Copyright (C) year  David I. Bell and Ernest Bowen
-	Copyright (C) year  David I. Bell, Landon Curt Noll and Ernest Bowen
-	Copyright (C) year  Landon Curt Noll
-	Copyright (C) year  Ernest Bowen and Landon Curt Noll
-	Copyright (C) year  Ernest Bowen
-	Copyright (C) year  Petteri Kettunen and Landon Curt Noll
-	Copyright (C) year  Christoph Zurnieden
-	Copyright (C) year  Landon Curt Noll and Thomas Jones-Low
-	Copyright (C) year  Klaus Alexander Seistrup and Landon Curt Noll
+        Copyright (C) year  David I. Bell
+        Copyright (C) year  David I. Bell and Landon Curt Noll
+        Copyright (C) year  David I. Bell and Ernest Bowen
+        Copyright (C) year  David I. Bell, Landon Curt Noll and Ernest Bowen
+        Copyright (C) year  Landon Curt Noll
+        Copyright (C) year  Ernest Bowen and Landon Curt Noll
+        Copyright (C) year  Ernest Bowen
+        Copyright (C) year  Petteri Kettunen and Landon Curt Noll
+        Copyright (C) year  Christoph Zurnieden
+        Copyright (C) year  Landon Curt Noll and Thomas Jones-Low
+        Copyright (C) year  Klaus Alexander Seistrup and Landon Curt Noll

    A few files in calc are covered under "The Unlicense".  For more
    information on this license, see:
@@ -50,8 +50,8 @@ Copying / Calc GNU Lesser General Public License
    Lesser General Public License.  You are welcome to change it and/or
    distribute copies of it under certain conditions.  The calc commands:

-	help copying
-	help copying-lgpl
+        help copying
+        help copying-lgpl

    should display the contents of the COPYING and COPYING-LGPL files.
    Those files contain information about the calc's GNU Lesser General
@@ -62,17 +62,17 @@ Copying / Calc GNU Lesser General Public License
    Lesser General Public License.  If you do not have these
    files, write to:

-	Free Software Foundation, Inc.
-	51 Franklin Street
-	Fifth Floor
-	Boston, MA  02110-1301
-	USA
+        Free Software Foundation, Inc.
+        51 Franklin Street
+        Fifth Floor
+        Boston, MA  02110-1301
+        USA

 See also:

-	help copyright
-	help copying
-	help copying-lgpl
+        help copyright
+        help copying
+        help copying-lgpl

 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##
@@ -82,7 +82,7 @@ See also:
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -90,8 +90,8 @@ See also:
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1991/07/23 05:47:24
-## File existed as early as:	1991
+## Under source code control:   1991/07/23 05:47:24
+## File existed as early as:    1991
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/csc
+++ b/help/csc
@@ -5,10 +5,10 @@ SYNOPSIS
    csc(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Calculate the trigonometric cosecant of x to a multiple of eps, with error less
@@ -16,7 +16,7 @@ DESCRIPTION

    This function is equivalent to:

-	csc(x) = 1 / sin(x)
+        csc(x) = 1 / sin(x)

 EXAMPLE
    ; print csc(1/2), csc(5/7), csc(42/7)
@@ -56,14 +56,14 @@ SEE ALSO
 EXTERNAL RESOURCES
    For general information on trigonometric functions, see:

-	https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
-	https://en.wikipedia.org/wiki/Versine
-	https://en.wikipedia.org/wiki/Exsecant
-	https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
-	https://en.wikipedia.org/wiki/Chord_(geometry)
-	https://en.wikipedia.org/wiki/Secant_line
-	https://en.wikipedia.org/wiki/Hartley_transform#cas
-	https://en.wikipedia.org/wiki/Cis_(mathematics)
+        https://en.wikipedia.org/wiki/Trigonometric_functions#Unit-circle_definitions
+        https://en.wikipedia.org/wiki/Versine
+        https://en.wikipedia.org/wiki/Exsecant
+        https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
+        https://en.wikipedia.org/wiki/Chord_(geometry)
+        https://en.wikipedia.org/wiki/Secant_line
+        https://en.wikipedia.org/wiki/Hartley_transform#cas
+        https://en.wikipedia.org/wiki/Cis_(mathematics)

 ## Copyright (C) 1999,2023  Landon Curt Noll
 ##
@@ -73,7 +73,7 @@ EXTERNAL RESOURCES
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -81,8 +81,8 @@ EXTERNAL RESOURCES
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/csch
+++ b/help/csch
@@ -5,10 +5,10 @@ SYNOPSIS
    csch(x [,eps])

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

-    return	real
+    return      real

 DESCRIPTION
    Calculate the csch of x to a multiple of epsilon, with error less in
@@ -39,7 +39,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -47,8 +47,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/13 03:49:00
-## File existed as early as:	1995
+## Under source code control:   1995/11/13 03:49:00
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/ctime
+++ b/help/ctime
@@ -5,13 +5,13 @@ SYNOPSIS
    ctime()

 TYPES
-    return	string
+    return      string

 DESCRIPTION
   The ctime() builtin returns the string formed by the
   characters returned by the C library function, ctime(): E.g.

-	"Mon Oct 28 00:47:00 1996\n"
+        "Mon Oct 28 00:47:00 1996\n"

 EXAMPLE
    ; ## NOTE: Your output will likely vary:
@@ -37,7 +37,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -45,8 +45,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1996/04/30 03:05:18
-## File existed as early as:	1996
+## Under source code control:   1996/04/30 03:05:18
+## File existed as early as:    1996
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/custom
+++ b/help/custom
@@ -5,10 +5,10 @@ SYNOPSIS
    custom([custname [, arg ...]])

 TYPES
-    custname	string
-    arg		any
+    custname    string
+    arg         any

-    return	any
+    return      any

 DESCRIPTION
    This function will invoke the custom function interface.  Custom
@@ -19,16 +19,16 @@ DESCRIPTION

    In order to use the custom interface, two things must happen:

-	1) Calc must be built to allow custom functions.  By default,
-	   the master Makefile is shipped with ALLOW_CUSTOM= -DCUSTOM
-	   which causes custom functions to be compiled in.
+        1) Calc must be built to allow custom functions.  By default,
+           the master Makefile is shipped with ALLOW_CUSTOM= -DCUSTOM
+           which causes custom functions to be compiled in.

-	2) Calc must be invoked with an argument of -C as in:
+        2) Calc must be invoked with an argument of -C as in:

-		calc -C
+                calc -C

    In other words, explicit action must be taken in order to
-    enable the use of custom functions.	 By default (no -C arg)
+    enable the use of custom functions.  By default (no -C arg)
    custom functions are compiled in but disabled so that only
    portable calc scripts may be used.

@@ -36,7 +36,7 @@ DESCRIPTION
    multi-precision calculations in a C-like environment.  You should
    consider implementing algorithms in the calc language as a first
    choice.  Sometimes an algorithm requires use of special hardware, a
-    non-portable OS or pre-compiled C library.	In these cases a custom
+    non-portable OS or pre-compiled C library.  In these cases a custom
    interface may be needed.

    The custom function interface is intended to make is easy for
@@ -48,16 +48,16 @@ DESCRIPTION
    To add a new custom function requires access to calc source.
    For information on how to add a new custom function, try:

-	    help new_custom
+            help new_custom

    To serve as examples, calc is shipped with a few custom functions.
    If calc if invoked with -C, then either of the following will
    display information about the custom functions that are available:

-	    show custom
+            show custom
    or:

-	    custom()
+            custom()

    A few resource files that uses these function are also provided
    to serve as usage examples.
@@ -65,20 +65,20 @@ DESCRIPTION
    We welcome submissions for new custom functions.  For information
    on how to submit new custom functions for general distribution, see:

-	    help contrib
+            help contrib

 EXAMPLE
    If calc compiled with ALLOW_CUSTOM="-UCUSTOM", the custom system
    is disabled, even when -C is used on the command line:

    ; print custom("sysinfo", "baseb")
-	    Calc was built with custom functions disabled
+            Calc was built with custom functions disabled
    Error E_NO_C_ARG

    If calc compiled with ALLOW_CUSTOM= -DCUSTOM and is invoked without -C:

    ; print custom("sysinfo", "baseb")
-	    Calc must be run with a -C argument to use custom function
+            Calc must be run with a -C argument to use custom function
    Error E_NO_C_ARG

    If calc compiled with ALLOW_CUSTOM= -DCUSTOM and is invoked with -C:
@@ -103,7 +103,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -111,8 +111,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/03/09 16:33:22
-## File existed as early as:	1997
+## Under source code control:   1997/03/09 16:33:22
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/d2dm
+++ b/help/d2dm
@@ -5,12 +5,12 @@ SYNOPSIS
    d2dm(degs, d, m [,rnd])

 TYPES
-    degs	real
-    d		null-or-real-valued lvalue with assign-to permission
-    m		null-or-real-valued lvalue with assign-to permission
-    rnd		nonnegative integer, defaults to config("mod")
+    degs        real
+    d           null-or-real-valued lvalue with assign-to permission
+    m           null-or-real-valued lvalue with assign-to permission
+    rnd         nonnegative integer, defaults to config("mod")

-    return	mod(degs, 360, rnd)
+    return      mod(degs, 360, rnd)

 DESCRIPTION
    Convert degs degrees into d degrees, and m minutes.
@@ -18,7 +18,7 @@ DESCRIPTION
    The return value is a normalized number of degrees, and is equivalent
    to the following:

-	return_value = mod(degs, 360, rnd);
+        return_value = mod(degs, 360, rnd);

    The argument rnd, if not given, defaults to config("mod").
    For more information on the effects of rnd, see "help mod".
@@ -31,7 +31,7 @@ DESCRIPTION

    The value d will be set as if the following were used:

-	d = int(return_value);
+        d = int(return_value);

    For some rounding modes, d will be an integer in the interval [0, 360).
    For other rounding modes, d will be an integer in the interval (-360, 0].
@@ -41,9 +41,9 @@ DESCRIPTION

    The value m will be set as if the following were used:

-	tmp = return_value - d;
-	m = tmp * 60;
-	free(tmp);
+        tmp = return_value - d;
+        m = tmp * 60;
+        free(tmp);

    For some rounding modes, m will be a real value in the interval [0, 60).
    For other rounding modes, m will be a real value in the interval (-60, 0].
@@ -52,7 +52,7 @@ DESCRIPTION
    The following shows relationship between the return value and the resulting
    d, and m values:

-	return_value == d + m/60;
+        return_value == d + m/60;

 EXAMPLE
    ; ## if args are undefined, pre-declare them or assign them as args
@@ -100,7 +100,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -108,8 +108,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2021/09/25 17:24:51
-## File existed as early as:	2021
+## Under source code control:   2021/09/25 17:24:51
+## File existed as early as:    2021
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/d2dms
+++ b/help/d2dms
@@ -5,13 +5,13 @@ SYNOPSIS
    d2dms(degs, d, m, s [,rnd])

 TYPES
-    degs	real
-    d		null-or-real-valued lvalue with assign-to permission
-    m		null-or-real-valued lvalue with assign-to permission
-    s		null-or-real-valued lvalue with assign-to permission
-    rnd		nonnegative integer, defaults to config("mod")
+    degs        real
+    d           null-or-real-valued lvalue with assign-to permission
+    m           null-or-real-valued lvalue with assign-to permission
+    s           null-or-real-valued lvalue with assign-to permission
+    rnd         nonnegative integer, defaults to config("mod")

-    return	mod(degs, 360, rnd)
+    return      mod(degs, 360, rnd)

 DESCRIPTION
    Convert degs degrees into d degrees, m minutes, and s seconds.
@@ -19,7 +19,7 @@ DESCRIPTION
    The return value is a normalized number of degrees, and is equivalent
    to the following:

-	return_value = mod(degs, 360, rnd);
+        return_value = mod(degs, 360, rnd);

    The argument rnd, if not given, defaults to config("mod").
    For more information on the effects of rnd, see "help mod".
@@ -32,7 +32,7 @@ DESCRIPTION

    The value d will be set as if the following were used:

-	d = int(return_value);
+        d = int(return_value);

    For some rounding modes, d will be an integer in the interval [0, 360).
    For other rounding modes, d will be an integer in the interval (-360, 0].
@@ -42,10 +42,10 @@ DESCRIPTION

    The value m will be set as if the following were used:

-	tmp = return_value - d;
-	tmp_m = tmp * 60;
-	free(tmp);
-	m = int(tmp_m);
+        tmp = return_value - d;
+        tmp_m = tmp * 60;
+        free(tmp);
+        m = int(tmp_m);

    For some rounding modes, m will be an integer in the interval [0, 60).
    For other rounding modes, m will be an integer in the interval (-60, 0].
@@ -55,10 +55,10 @@ DESCRIPTION

    The value s will be set as if the following were used:

-	tmp = tmp_m - m;
-	free(tmp_m);
-	s = tmp * 60;
-	free(tmp);
+        tmp = tmp_m - m;
+        free(tmp_m);
+        s = tmp * 60;
+        free(tmp);

    For some rounding modes, s will be a real value in the interval [0, 60).
    For other rounding modes, s will be a real value in the interval (-60, 0].
@@ -67,7 +67,7 @@ DESCRIPTION
    The following shows relationship between the return value and the resulting
    d, m, and s values:

-	return_value == d + m/60 + s/3600;
+        return_value == d + m/60 + s/3600;

 EXAMPLE
    ; ## if args are undefined, pre-declare them or assign them as args
@@ -115,7 +115,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -123,8 +123,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2021/09/25 17:24:51
-## File existed as early as:	2021
+## Under source code control:   2021/09/25 17:24:51
+## File existed as early as:    2021
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/d2g
+++ b/help/d2g
@@ -5,10 +5,10 @@ SYNOPSIS
    d2g(x [,eps])

 TYPES
-    x		number (real or complex)
-    eps		eps value is ignored
+    x           number (real or complex)
+    eps         eps value is ignored

-    return	number
+    return      number

 DESCRIPTION
    Given x degrees, return the equivalent number of gradians.
@@ -40,7 +40,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -48,8 +48,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2021/09/07 12:04:28
-## File existed as early as:	2021
+## Under source code control:   2021/09/07 12:04:28
+## File existed as early as:    2021
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/d2r
+++ b/help/d2r
@@ -5,10 +5,10 @@ SYNOPSIS
    d2r(x [,eps])

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

-    return	number
+    return      number

 DESCRIPTION
    Given x degrees, return the equivalent number of radians.
@@ -44,7 +44,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -52,8 +52,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2021/09/07 12:04:28
-## File existed as early as:	2021
+## Under source code control:   2021/09/07 12:04:28
+## File existed as early as:    2021
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/define
+++ b/help/define
@@ -6,11 +6,11 @@ SYNTAX
    define fname([param_1 [= default_1], ...]) { [statement_1 ... ] }

 TYPES
-    fname		identifier, not a builtin function name
-    param_1, ...	identifiers, no two the same
-    default_1, ...	expressions
-    expr		expression
-    statement_1, ...	statements
+    fname               identifier, not a builtin function name
+    param_1, ...        identifiers, no two the same
+    default_1, ...      expressions
+    expr                expression
+    statement_1, ...    statements

 DESCRIPTION
    The intention of a function definition is that the identifier fname
@@ -30,17 +30,17 @@ DESCRIPTION
    For example, suppose a function f and a global variable A have been
    defined by:

-	; define f(x) = (x = 3);
-	; global mat A[3];
+        ; define f(x) = (x = 3);
+        ; global mat A[3];

    If g() is  a function that evaluates to 2:

-	; f(A[g()]);
+        ; f(A[g()]);

    assigns the value of A[2] to the parameter x and then assigns the
    value 3 to x:

-	; f(`A[g()]);
+        ; f(`A[g()]);

    has essentially the effect of assigning A[2] as an lvalue to x and
    then assigning the value 3 to A[2].  (Very old versions of calc
@@ -79,7 +79,7 @@ DESCRIPTION

    If the expr is omitted from an expression definition, as in:

-	; define h() = ;
+        ; define h() = ;

    any call to the function will evaluate the arguments and return the
    null value.
@@ -105,11 +105,11 @@ DESCRIPTION

    After fname has been defined, the definition may be removed by the command:

-	; undefine fname
+        ; undefine fname

    The definitions of all user-defined functions may be removed by:

-	; undefine *
+        ; undefine *

    If bit 0 of config("resource_debug") is set and the define command is
    at interactive level, a message saying that fname has been defined
@@ -120,8 +120,8 @@ DESCRIPTION
    The identifiers used for the parameters in a function definition do
    not form part of the completed definition.  For example,

-	; define f(a,b) = a + b;
-	; define g(alpha, beta) = alpha + beta;
+        ; define f(a,b) = a + b;
+        ; define g(alpha, beta) = alpha + beta;

    result in identical code for the functions f, g.

@@ -129,22 +129,22 @@ DESCRIPTION
    function are displayed on completion of its definition, parameters
    being specified by names used in the definition.  For example:

-	; config("trace", 8),
-	; define f(a,b) = a + b
-	0: PARAMADDR a
-	2: PARAMADDR b
-	4: ADD
-	5: RETURN
-	f(a,b) defined
+        ; config("trace", 8),
+        ; define f(a,b) = a + b
+        0: PARAMADDR a
+        2: PARAMADDR b
+        4: ADD
+        5: RETURN
+        f(a,b) defined

    The opcodes may also be displayed later using the show opcodes command;
    parameters will be specified by indices instead of by names.  For example:

-	; show opco f
-	0: PARAMADDR 0
-	2: PARAMADDR 1
-	4: ADD
-	5: RETURN
+        ; show opco f
+        0: PARAMADDR 0
+        2: PARAMADDR 1
+        4: ADD
+        5: RETURN

    When a function is defined by the statement mode, the opcodes normally
    include DEBUG opcodes which specify statement boundaries at which
@@ -169,17 +169,17 @@ EXAMPLE
    ; define f(a,b) = 2*a + b;
    ; define g(alpha, beta)
    ;; {
-    ;;	   local a, pi2;
+    ;;     local a, pi2;
    ;;
-    ;;	   pi2 = 2 * pi();
-    ;;	   a = sin(alpha % pi2);
-    ;;	   if (a > 0.0) {
-    ;;	       return a*beta;
-    ;;	   }
-    ;;	   if (beta > 0.0) {
-    ;;	       a *= cos(-beta % pi2);
-    ;;	   }
-    ;;	   return a;
+    ;;     pi2 = 2 * pi();
+    ;;     a = sin(alpha % pi2);
+    ;;     if (a > 0.0) {
+    ;;         return a*beta;
+    ;;     }
+    ;;     if (beta > 0.0) {
+    ;;         a *= cos(-beta % pi2);
+    ;;     }
+    ;;     return a;
    ;; }

 LIMITS
@@ -192,7 +192,7 @@ SEE ALSO
    param, variable, undefine, show

 ## Copyright (C) 2000-2006,2021  David I. Bell, Landon Curt Noll
-##				 and Ernest Bowen
+##                               and Ernest Bowen
 ##
 ## 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
@@ -200,7 +200,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -209,8 +209,8 @@ SEE ALSO
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
 ##
-## Under source code control:	1991/07/21 04:37:18
-## File existed as early as:	1991
+## Under source code control:   1991/07/21 04:37:18
+## File existed as early as:    1991
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/delete
+++ b/help/delete
@@ -5,10 +5,10 @@ SYNOPSIS
    delete(lst, index)

 TYPES
-    lst		list
-    index	nonnegative integer less than the size of the list
+    lst         list
+    index       nonnegative integer less than the size of the list

-    return	type of the deleted element
+    return      type of the deleted element

 DESCRIPTION
     Deletes element at the specified index from list lst, and returns
@@ -24,7 +24,7 @@ EXAMPLE
      [[3]] = 5

    ; delete(lst, 2)
-	    4
+            4
    ; print lst

    list (3 elements, 3 nonzero):
@@ -50,7 +50,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -58,8 +58,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/03/19 03:13:18
-## File existed as early as:	1994
+## Under source code control:   1994/03/19 03:13:18
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/den
+++ b/help/den
@@ -5,23 +5,23 @@ SYNOPSIS
    den(x)

 TYPES
-    x		real
+    x           real

-    return	integer
+    return      integer

 DESCRIPTION
    For real x, den(x) returns the denominator of x when x is expressed
-    in lowest terms with positive denominator.	In calc,
+    in lowest terms with positive denominator.  In calc,
    real values are actually rational values.  Each calc real
    value can be uniquely expressed as:

-	n / d
+        n / d

    where:

-	n and d are integers
-	gcd(n,d) == 1
-	d > 0
+        n and d are integers
+        gcd(n,d) == 1
+        d > 0

    The denominator for this n/d is d.

@@ -46,7 +46,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -54,8 +54,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/05 04:52:26
-## File existed as early as:	1995
+## Under source code control:   1995/10/05 04:52:26
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/dereference
+++ b/help/dereference
@@ -5,9 +5,9 @@ SYNOPSIS
    * X

 TYPES
-    X		address or lvalue
+    X           address or lvalue

-    return	any
+    return      any

 DESCRIPTION
    When used as a binary operator, '*' performs multiplication.  When
@@ -33,17 +33,17 @@ DESCRIPTION
    structure rather than the structure identified by X.  For example,
    suppose B has been created by

-	; mat B[3] = {1,2,3}
+        ; mat B[3] = {1,2,3}

    then

-	; A = *B = {4,5,6}
+        ; A = *B = {4,5,6}

    will assign the values 4,5,6 to the elements of a copy of B, which
    will then become the value of A, so that the values of A and B will
    be different.  On the other hand,

-	; A = B = {4,5,6}
+        ; A = B = {4,5,6}

    will result in A and B having the same value.

@@ -52,9 +52,9 @@ DESCRIPTION
    The * operator may be iterated with suitable sequences of pointer-valued
    lvalues.  For example, after

-	; global a, b, c;
-	; b = &a;
-	; c = &b;
+        ; global a, b, c;
+        ; b = &a;
+        ; c = &b;

    **c returns the lvalue a;  ***c returns the value of a.

@@ -90,7 +90,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -98,8 +98,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/09/06 20:03:34
-## File existed as early as:	1997
+## Under source code control:   1997/09/06 20:03:34
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/det
+++ b/help/det
@@ -5,14 +5,14 @@ SYNOPSIS
    det(m)

 TYPES
-    m		square matrix with elements of suitable type
+    m           square matrix with elements of suitable type

-    return	zero or value of type determined by types of elements
+    return      zero or value of type determined by types of elements

 DESCRIPTION
    The matrix m has to be square, i.e. of dimension 2 with:

-	matmax(m,1) - matmin(m,1) == matmax(m,2) - matmin(m,2).
+        matmax(m,1) - matmin(m,1) == matmax(m,2) - matmin(m,2).

    If the elements of m are numbers (real or complex), det(m)
    returns the value of the determinant of m.
@@ -26,15 +26,15 @@ DESCRIPTION
    If m is a 2 x 2 matrix with elements a, b, c, d, where a tests as
    nonzero, det(m) is evaluated by

-	det(m) = (a * d) - (c * b).
+        det(m) = (a * d) - (c * b).

    If a tests as zero, det(m) = - ((c * b) - (a * d)) is used.

    If m is 3 * 3 with elements a, b, c, d, e, f, g, h, i, where a and
    a * e - d * b test as nonzero, det(m) is evaluated by

-	det(m) = ((a * e - d * b) * (a * i - g * c)
-			- (a * h - g * b) * (a * f - d * c))/a.
+        det(m) = ((a * e - d * b) * (a * i - g * c)
+                        - (a * h - g * b) * (a * f - d * c))/a.

 EXAMPLE
    ; mat A[3,3] = {2, 3, 5, 7, 11, 13, 17, 19, 23}
@@ -83,7 +83,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -91,8 +91,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/11/28 11:17:47
-## File existed as early as:	1995
+## Under source code control:   1995/11/28 11:17:47
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/digit
+++ b/help/digit
@@ -5,11 +5,11 @@ SYNOPSIS
    digit(x, n [, b])

 TYPES
-    x		real
-    n		integer
-    b		integer >= 2, default = 10
+    x           real
+    n           integer
+    b           integer >= 2, default = 10

-    return	integer
+    return      integer

 DESCRIPTION

@@ -28,11 +28,11 @@ DESCRIPTION
    left of the "decimal" point; the digit  d_n  at position n contributes
    additively  d_n * b^n  to the value of x.  For example,

-	; d_2 d_1 d_0 . d_-1 d_-2
+        ; d_2 d_1 d_0 . d_-1 d_-2

    represents the number

-	; d_2 * b^2 + d_1 * b + d0 + d_-1 * b^-1 + d_-2 * b^-2
+        ; d_2 * b^2 + d_1 * b + d0 + d_-1 * b^-1 + d_-2 * b^-2

    The sequence of digits has to be infinite if den(x) has a prime factor
    which is not a factor of the base b.  In cases where the representation
@@ -53,30 +53,30 @@ DESCRIPTION
    With base-b digits for x as explained above, the integer whose base-b
    representation is

-	; b_n+k-1 b_n_k-2 ... b_n,
+        ; b_n+k-1 b_n_k-2 ... b_n,

    i.e. the k digits with last digit b_n, is given by

-	; digit(b^-r * x, q, b^k)
+        ; digit(b^-r * x, q, b^k)

    if r and q satisfy  n = q * b + r.

 EXAMPLE
-	; a = 123456.789
-	; for (n = 6; n >= -6; n++) print digit(a, n),; print
-	0 1 2 3 4 5 6 7 8 9 0 0 0
+        ; a = 123456.789
+        ; for (n = 6; n >= -6; n++) print digit(a, n),; print
+        0 1 2 3 4 5 6 7 8 9 0 0 0

-	; for (n = 6; n >= -6; n--) print digit(a, n, 100),; print
-	0 0 0 0 12 34 56 78 90 0 0 0 0
+        ; for (n = 6; n >= -6; n--) print digit(a, n, 100),; print
+        0 0 0 0 12 34 56 78 90 0 0 0 0

-	; for (n = 6; n >= -6; n--) print digit(a, n, 256),; print
-	0 0 0 0 1 226 64 201 251 231 108 139 67
+        ; for (n = 6; n >= -6; n--) print digit(a, n, 256),; print
+        0 0 0 0 1 226 64 201 251 231 108 139 67

-	; for (n = 1; n >= -12; n++) print digit(10/7, n),; print
-	; 0 1 4 2 8 5 7 1 4 2 8 5 7 1
+        ; for (n = 1; n >= -12; n++) print digit(10/7, n),; print
+        ; 0 1 4 2 8 5 7 1 4 2 8 5 7 1

-	; print digit(10/7, -7e1000, 1e6)
-	428571
+        ; print digit(10/7, -7e1000, 1e6)
+        428571

 LIMITS

@@ -99,7 +99,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -107,8 +107,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/03 10:40:01
-## File existed as early as:	1995
+## Under source code control:   1995/10/03 10:40:01
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/digits
+++ b/help/digits
@@ -5,10 +5,10 @@ SYNOPSIS
    digits(x [,b])

 TYPES
-    x		real
-    b		integer >= 2, defaults to 10
+    x           real
+    b           integer >= 2, defaults to 10

-    return	integer
+    return      integer

 DESCRIPTION
    Returns number of digits in the standard base-b representation
@@ -23,10 +23,10 @@ DESCRIPTION

    One should remember these special cases:

-	digits(12.3456) == 2    computes with the integer part only
-	digits(-1234) == 4      computes with the absolute value only
-	digits(0) == 1          special case
-	digits(-0.123) == 1     combination of all of the above
+        digits(12.3456) == 2    computes with the integer part only
+        digits(-1234) == 4      computes with the absolute value only
+        digits(0) == 1          special case
+        digits(-0.123) == 1     combination of all of the above

 EXAMPLE
    ; print digits(100), digits(23209), digits(2^72)
@@ -58,7 +58,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -66,8 +66,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/03 10:40:01
-## File existed as early as:	1995
+## Under source code control:   1995/10/03 10:40:01
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/display
+++ b/help/display
@@ -5,9 +5,9 @@ SYNOPSIS
    display([d])

 TYPES
-    d		integer >= 0
+    d           integer >= 0

-    return	integer
+    return      integer

 DESCRIPTION
    When given an argument, this function sets the maximum number of
@@ -21,13 +21,13 @@ DESCRIPTION

    The builtin function:

-	display(d)
-	display()
+        display(d)
+        display()

    is an alias for:

-	config("display", d)
-	config("display")
+        config("display", d)
+        config("display")

    The display digit value does not change the stored value of a number.
    It only changes how a stored value is displayed.
@@ -108,7 +108,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -116,8 +116,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2004/07/25 23:50:40
-## File existed as early as:	2004
+## Under source code control:   2004/07/25 23:50:40
+## File existed as early as:    2004
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/dms2d
+++ b/help/dms2d
@@ -6,19 +6,19 @@ SYNOPSIS
    dms2d(d, m, s [,rnd])

 TYPES
-    d		real
-    m		real
-    s		real (defaults to 0)
-    rnd		nonnegative integer, defaults to config("mod")
+    d           real
+    m           real
+    s           real (defaults to 0)
+    rnd         nonnegative integer, defaults to config("mod")

-    return	degrees
+    return      degrees

 DESCRIPTION
    Convert degrees, m minutes, and s seconds returning degrees.

    The return value in degrees, is equivalent to the following:

-	mod(d + m/60 + s/3600, 360, rnd);
+        mod(d + m/60 + s/3600, 360, rnd);

    Depending on the rounding mode, the return could be a real value
    in the interval [0, 360) or a real value in the interval (-360, 0].
@@ -67,7 +67,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -75,8 +75,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	2021/09/25 17:24:51
-## File existed as early as:	2021
+## Under source code control:   2021/09/25 17:24:51
+## File existed as early as:    2021
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/dp
+++ b/help/dp
@@ -5,21 +5,21 @@ SYNOPSIS
    dp(x, y)

 TYPES
-    x, y	1-dimensional matrices of the same size
+    x, y        1-dimensional matrices of the same size

-    return	depends on the nature of the elements of x and y
+    return      depends on the nature of the elements of x and y

 DESCRIPTION
    Compute the dot product of two 1-dimensional matrices.

    Let:

-	x = {x0, x1, ... xn}
-	y = {y0, y1, ... yn}
+        x = {x0, x1, ... xn}
+        y = {y0, y1, ... yn}

    Then dp(x,y) returns the result of the calculation:

-	x0*y0 + x1*y1 + ... + xn*yn
+        x0*y0 + x1*y1 + ... + xn*yn

 EXAMPLE
    ; mat x[3] = {2,3,4}
@@ -44,7 +44,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -52,8 +52,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/05 04:52:26
-## File existed as early as:	1995
+## Under source code control:   1995/10/05 04:52:26
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/environment
+++ b/help/environment
@@ -2,119 +2,119 @@ Environment variables

    CALCPATH

-	A :-separated list of directories used to search for
-	resource filenames (*.cal files) that do not begin with:
+        A :-separated list of directories used to search for
+        resource filenames (*.cal files) that do not begin with:

-		/	./	../	~
+                /       ./      ../     ~

-	If this variable does not exist, or if this
-	variable is an empty string, a compiled value
-	is used.  Typically compiled in value is:
+        If this variable does not exist, or if this
+        variable is an empty string, a compiled value
+        is used.  Typically compiled in value is:

-		    .:./cal:~/cal:${CALC_SHAREDIR}:${CUSTOMCALDIR}
+                    .:./cal:~/cal:${CALC_SHAREDIR}:${CUSTOMCALDIR}

-	which is usually:
+        which is usually:

-		    .:./cal:~/cal:/usr/share/calc:/usr/share/calc/custom
+                    .:./cal:~/cal:/usr/share/calc:/usr/share/calc/custom

-	This value is used by the READ command.	 It is an error
-	if no such readable file is found.
+        This value is used by the READ command.  It is an error
+        if no such readable file is found.

-	The CALCBINDINGS file searches the CALCPATH as well.
+        The CALCBINDINGS file searches the CALCPATH as well.

    CALCRC

-	On startup (unless -h or -q was given on the command
-	line), calc searches for files along the :-separated
-	$CALCRC environment variable.
+        On startup (unless -h or -q was given on the command
+        line), calc searches for files along the :-separated
+        $CALCRC environment variable.

-	If this variable does not exist, or if this
+        If this variable does not exist, or if this
        variable is an empty string, a compiled value
-	is used.  Typically compiled in value is:
+        is used.  Typically compiled in value is:

-		    ${CALC_SHAREDIR}/startup:~/.calcrc:./.calcinit
+                    ${CALC_SHAREDIR}/startup:~/.calcrc:./.calcinit

-	which is usually:
+        which is usually:

-		    /usr/share/calc/startup:~/.calcrc:./.calcinit
+                    /usr/share/calc/startup:~/.calcrc:./.calcinit

-	Missing files along the $CALCRC path are silently ignored.
+        Missing files along the $CALCRC path are silently ignored.

    CALCBINDINGS

-	On startup (unless -h or -q was given on the command
-	line), calc reads key bindings from the filename specified
-	in the $CALCRC environment variable.  These key bindings
-	are used for command line editing and the command history.
+        On startup (unless -h or -q was given on the command
+        line), calc reads key bindings from the filename specified
+        in the $CALCRC environment variable.  These key bindings
+        are used for command line editing and the command history.

-	If this variable does not exist, a compiled value is used.
-	Typically compiled in value is:
+        If this variable does not exist, a compiled value is used.
+        Typically compiled in value is:

-		    bindings
+                    bindings

-	The bindings file is searched along the CALCPATH.  Unlike
-	the READ command, a .cal extension is not added.
+        The bindings file is searched along the CALCPATH.  Unlike
+        the READ command, a .cal extension is not added.

-	If the file could not be opened, or if standard input is not
-	a terminal, then calc will still run, but fancy command line
-	editing is disabled.
+        If the file could not be opened, or if standard input is not
+        a terminal, then calc will still run, but fancy command line
+        editing is disabled.

-	NOTE: If calc was compiled with GNU-readline support, the
-	      CALCBINDINGS facility is ignored and the standard
-	      readline mechanisms (see readline(3)) are used.
+        NOTE: If calc was compiled with GNU-readline support, the
+              CALCBINDINGS facility is ignored and the standard
+              readline mechanisms (see readline(3)) are used.

    HOME

-	This value is taken to be the home directory of the
-	current user.  It is used when files begin with '~/'.
+        This value is taken to be the home directory of the
+        current user.  It is used when files begin with '~/'.

-	If this variable does not exist, or if this
-	variable is an empty string, the home directory password
-	entry of the current user is used.  If that information
-	is not available, '.' is used.
+        If this variable does not exist, or if this
+        variable is an empty string, the home directory password
+        entry of the current user is used.  If that information
+        is not available, '.' is used.

    PAGER

-	When invoking help, this environment variable is used
-	to display a help file.
+        When invoking help, this environment variable is used
+        to display a help file.

-	If this variable does not exist, or if this
-	variable is an empty string, a compiled value
-	is used.  Typically compiled in value is something
-	such as 'more', 'less', 'pg' or 'cat'.
+        If this variable does not exist, or if this
+        variable is an empty string, a compiled value
+        is used.  Typically compiled in value is something
+        such as 'more', 'less', 'pg' or 'cat'.

    SHELL

-	When a !-command is used, the program indicated by
-	this environment variable is used.
+        When a !-command is used, the program indicated by
+        this environment variable is used.

-	If this variable does not exist, or if this
-	variable is an empty string, a compiled value
-	is used.  Typically compiled in value is something
-	such as 'sh' is used.
+        If this variable does not exist, or if this
+        variable is an empty string, a compiled value
+        is used.  Typically compiled in value is something
+        such as 'sh' is used.

    CALCHISTFILE

-	This value is taken to be the calc history file.
+        This value is taken to be the calc history file.

-	If this variable does not exist, or if this
-	variable is an empty string, then ~/.calc_history
-	is used.
+        If this variable does not exist, or if this
+        variable is an empty string, then ~/.calc_history
+        is used.

     CALCHELP

-	Location of the calc help directory.
+        Location of the calc help directory.

-	If this variable does not exist, or if this
-	variable is an empty string, then ${HELPDIR}
+        If this variable does not exist, or if this
+        variable is an empty string, then ${HELPDIR}

     CALCCUSTOMHELP

-	Location of the calc custom help directory.
+        Location of the calc custom help directory.

-	If this variable does not exist, or if this
-	variable is an empty string, then ${CUSTOMHELPDIR}
-	is used.
+        If this variable does not exist, or if this
+        variable is an empty string, then ${CUSTOMHELPDIR}
+        is used.

 ## Copyright (C) 1999,2021  Landon Curt Noll
 ##
@@ -124,7 +124,7 @@ Environment variables
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -132,8 +132,8 @@ Environment variables
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1991/07/23 05:47:25
-## File existed as early as:	1991
+## Under source code control:   1991/07/23 05:47:25
+## File existed as early as:    1991
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/epsilon
+++ b/help/epsilon
@@ -5,9 +5,9 @@ SYNOPSIS
    epsilon([eps])

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

-    return	real number greater than 0 and less than 1
+    return      real number greater than 0 and less than 1

 DESCRIPTION
    Without args, epsilon() returns the current epsilon value.
@@ -89,7 +89,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -97,8 +97,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/10/05 04:52:26
-## File existed as early as:	1995
+## Under source code control:   1995/10/05 04:52:26
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/errcount
+++ b/help/errcount
@@ -5,9 +5,9 @@ SYNOPSIS
    errcount([num])

 TYPES
-    num		integer
+    num         integer

-    return	integer
+    return      integer

 DESCRIPTION
    An internal variable keeps count of the number of functions
@@ -22,7 +22,7 @@ DESCRIPTION

    If an error value is assigned to a variable as in:

-			infty = 1/0;
+                        infty = 1/0;

    then a function returning that variable does not contribute to
    errcount.
@@ -31,9 +31,9 @@ EXAMPLE
    ; ## NOTE: Your output may vary:

    ; errmax(10)
-	    0
+            0
    ; errcount()
-	    0
+            0
    ; a = 1/0; b = 2 + ""; c = error(27); d = newerror("a");
    ; print errcount(), a, errcount(), errmax();
    4 Error E_DIVBYZERO 4 10
@@ -55,7 +55,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -63,8 +63,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/03/08 08:51:14
-## File existed as early as:	1997
+## Under source code control:   1997/03/08 08:51:14
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/errmax
+++ b/help/errmax
@@ -5,9 +5,9 @@ SYNOPSIS
    errmax([num])

 TYPES
-    num		integer
+    num         integer

-    return	integer
+    return      integer

 DESCRIPTION
    Without an argument, errmax() returns the current value of an
@@ -20,9 +20,9 @@ DESCRIPTION

 EXAMPLE
    ; errmax(2)
-	20
+        20
    ; errcount()
-	0
+        0
    ; a = 1/0; b = 2 + ""; c = error(27); d = newerror("alpha");
    Error 27 caused errcount to exceed errmax

@@ -33,7 +33,7 @@ EXAMPLE
    0 0

    ; errmax(-1)
-	2
+        2

 LIMITS
    -1 <= num <= 2147483647
@@ -52,7 +52,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -60,8 +60,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1997/03/08 08:51:14
-## File existed as early as:	1997
+## Under source code control:   1997/03/08 08:51:14
+## File existed as early as:    1997
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/errno
+++ b/help/errno
@@ -5,55 +5,55 @@ SYNOPSIS
    errno([errnum | "E_STRING"])

 TYPES
-    errnum	integer
-    E_STRING	string
+    errnum      integer
+    E_STRING    string

-    return	integer
+    return      integer

 DESCRIPTION
    With errno(errnum) numeric argument:

-	For 0 < errnum <= 32767:
+        For 0 < errnum <= 32767:

-	    errno(errnum) sets "global calc_errno value" to the value
-	    errnum and returns its previous value.  Unlike error(errnum)
-	    calling errno(errnum) does NOT increment the global calc
-	    error count (see help errcount).
+            errno(errnum) sets "global calc_errno value" to the value
+            errnum and returns its previous value.  Unlike error(errnum)
+            calling errno(errnum) does NOT increment the global calc
+            error count (see help errcount).

-	For all other errnum values:
+        For all other errnum values:

-	    An error error condition is raised about the valid errnum.
+            An error error condition is raised about the valid errnum.

    With errno("E_STRING") string argument:

-	If E_STRING is a valid errsym code, then the E_STRING errsym
-	is converted into an equivalent errnum and errno is set to errnum.
+        If E_STRING is a valid errsym code, then the E_STRING errsym
+        is converted into an equivalent errnum and errno is set to errnum.

-	If E_STRING is not a valid errsym code, an error error condition
-	is raised about the invalid E_STRING.
+        If E_STRING is not a valid errsym code, an error error condition
+        is raised about the invalid E_STRING.

-	For example, these two calls are equivalent:
+        For example, these two calls are equivalent:

-	    errno(10003);	/* error 10003 has a E_STRING of "E_ADD" */
-	    errno("E_ADD");	/* error 10003 has a E_STRING of "E_ADD" */
+            errno(10003);       /* error 10003 has a E_STRING of "E_ADD" */
+            errno("E_ADD");     /* error 10003 has a E_STRING of "E_ADD" */

-	See help errsym for information on E_STRING errsym codes.
+        See help errsym for information on E_STRING errsym codes.

-	For a list of the E_STRING associated with calc computation error
-	codes, see help errorcodes.
+        For a list of the E_STRING associated with calc computation error
+        codes, see help errorcodes.

    With errno() no argument:

-	errno() returns the current value of "global calc_errno
-	value".  Unlike error() calling errno() does NOT increment
-	the global calc error count (see help errcount).
+        errno() returns the current value of "global calc_errno
+        value".  Unlike error() calling errno() does NOT increment
+        the global calc error count (see help errcount).

    NOTE:

-	The errno() builtin should not be confused with the errno
-	used by libc in C.  The range of errnum extend beyond the
-	C's libc errno.  See help error for information on the mean
-	of various errnum ranges.
+        The errno() builtin should not be confused with the errno
+        used by libc in C.  The range of errnum extend beyond the
+        C's libc errno.  See help error for information on the mean
+        of various errnum ranges.

    Unlike error() calling errno() does NOT increment the global
    calc error count (see help errcount).
@@ -97,10 +97,10 @@ LIMITS
    E_STRING is string that must match the regular expression: ^E_[A-Z0-9_]+$

 LINK LIBRARY
-    int calc_errno;				/* global calc_errno value */
+    int calc_errno;                             /* global calc_errno value */
    int set_errno(int e);

-    CONST struct errtbl error_table[ECOUNT+2];	/* calc error codes, error symbols and error messages */
+    CONST struct errtbl error_table[ECOUNT+2];  /* calc error codes, error symbols and error messages */

    bool is_e_digits(CONST char *errsym);
    bool is_valid_errnum(int errnum);
@@ -126,7 +126,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -134,8 +134,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1994/10/27 03:05:08
-## File existed as early as:	1994
+## Under source code control:   1994/10/27 03:05:08
+## File existed as early as:    1994
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/error
+++ b/help/error
@@ -5,63 +5,63 @@ SYNOPSIS
    error([errnum | "E_STRING"])

 TYPES
-    errnum	integer, defaults to errno()
-    E_STRING	string
+    errnum      integer, defaults to errno()
+    E_STRING    string

-    return	null value or error value
+    return      null value or error value

 DESCRIPTION
    If errnum == 0:

-	error(errnum) returns the null value.
+        error(errnum) returns the null value.

-	The "global calc_errno value" is set to 0.
+        The "global calc_errno value" is set to 0.

-	The global calc error count is not changed.
+        The global calc error count is not changed.

    With error(errnum) numeric argument:

-	For 0 < errnum <= 32767:
+        For 0 < errnum <= 32767:

-	    error(errnum) returns a value that is of a special type called
-	    "error".  The "error" return value, when given to iserror()
-	    will cause that function to return a true value that happens
-	    to match the "global calc_errno value".
+            error(errnum) returns a value that is of a special type called
+            "error".  The "error" return value, when given to iserror()
+            will cause that function to return a true value that happens
+            to match the "global calc_errno value".

-	    The "global calc_errno value" is then set to errnum.
+            The "global calc_errno value" is then set to errnum.

-	For all other errnum values:
+        For all other errnum values:

-	    An error error condition is raised about the valid errnum.
+            An error error condition is raised about the valid errnum.

-	The global calc error count (see help errcount) is incremented.
-	If the global calc error count exceeds the maximum count
-	(see help errmax), any ongoing calc execution is aborted.
+        The global calc error count (see help errcount) is incremented.
+        If the global calc error count exceeds the maximum count
+        (see help errmax), any ongoing calc execution is aborted.

    With error("E_STRING") string argument:

-	If E_STRING is a valid errsym code, then the E_STRING errsym
-	is converted into an equivalent errnum and respective calc
-	error condition is raised.
+        If E_STRING is a valid errsym code, then the E_STRING errsym
+        is converted into an equivalent errnum and respective calc
+        error condition is raised.

-	If E_STRING is not a valid errsym code, an error error condition
-	is raised about the invalid E_STRING.
+        If E_STRING is not a valid errsym code, an error error condition
+        is raised about the invalid E_STRING.

-	For example, these two calls are equivalent:
+        For example, these two calls are equivalent:

-	    error(10003);	/* error 10003 has a E_STRING of "E_ADD" */
-	    error("E_ADD");	/* error 10003 has a E_STRING of "E_ADD" */
+            error(10003);       /* error 10003 has a E_STRING of "E_ADD" */
+            error("E_ADD");     /* error 10003 has a E_STRING of "E_ADD" */

-	See help errsym for information on E_STRING errsym codes.
+        See help errsym for information on E_STRING errsym codes.

-	For a list of the E_STRING associated with calc computation error
-	codes, see help errorcodes.
+        For a list of the E_STRING associated with calc computation error
+        codes, see help errorcodes.

    For no errnum arg:

-	Calling error() without an argument will return the current
-	"global calc_errno value" AND will also increment the
-	global calc error count.
+        Calling error() without an argument will return the current
+        "global calc_errno value" AND will also increment the
+        global calc error count.

    All other values of errnum are reserved for future use and currently
    will generate an error.
@@ -81,23 +81,23 @@ DESCRIPTION

    By convention, the "global calc_errno value" has the following ranges:

-	errnum < 0			Reserved for future use
-	errnum == 0			calc_errno cleared: libc errno codes above here
-	1 <= errnum <= 9999		system error and libc errno codes
-	errnum == 10000			Reserved for "No error" calc internal state
-	10001 <= errnum <= E__HIGHEST	calc computation error codes
-	E__HIGHEST < errnum < 20000	Reserved for future calc error codes
-	20000 < errnum <= 32767		User defined error codes start here
-	errnum >= 32768			Reserved for future use
+        errnum < 0                      Reserved for future use
+        errnum == 0                     calc_errno cleared: libc errno codes above here
+        1 <= errnum <= 9999             system error and libc errno codes
+        errnum == 10000                 Reserved for "No error" calc internal state
+        10001 <= errnum <= E__HIGHEST   calc computation error codes
+        E__HIGHEST < errnum < 20000     Reserved for future calc error codes
+        20000 < errnum <= 32767         User defined error codes start here
+        errnum >= 32768                 Reserved for future use

    The following constants are part of the calc error code mechanism:

-	E__BASE == 10000		1 less than the 1st calc computation error code
-	E__HIGHEST			highest assigned calc computation error code
-	E__USERDEF == 20000		user defined error codes start here
-	E__USERMAX == 32767		maximum user defined error code
+        E__BASE == 10000                1 less than the 1st calc computation error code
+        E__HIGHEST                      highest assigned calc computation error code
+        E__USERDEF == 20000             user defined error codes start here
+        E__USERMAX == 32767             maximum user defined error code

-	ECOUNT				number of calc computation error codes (not including E__BASE)
+        ECOUNT                          number of calc computation error codes (not including E__BASE)

    See help errorcodes for the actual values of the above constants.

@@ -134,9 +134,9 @@ LIMITS
    E_STRING is string that must match the regular expression: ^E_[A-Z0-9_]+$

 LINK LIBRARY
-    int calc_errno;				/* global calc_errno value */
+    int calc_errno;                             /* global calc_errno value */

-    CONST struct errtbl error_table[ECOUNT+2];	/* calc error codes, error symbols and error messages */
+    CONST struct errtbl error_table[ECOUNT+2];  /* calc error codes, error symbols and error messages */

    bool is_e_digits(CONST char *errsym);
    bool is_valid_errnum(int errnum);
@@ -163,7 +163,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -171,8 +171,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/12/18 03:30:59
-## File existed as early as:	1995
+## Under source code control:   1995/12/18 03:30:59
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/help/errsym
+++ b/help/errsym
@@ -5,96 +5,96 @@ SYNOPSIS
    errsym(errnum | "E_STRING")

 TYPES
-    errnum	integer
-    E_STRING	string
+    errnum      integer
+    E_STRING    string

-    return	integer or string or error value
+    return      integer or string or error value

 DESCRIPTION
    When called with in integer errnum argument:

-	When E__BASE < errnum <= E__HIGHEST, the corresponding errsym E_STRING
-	from the error_table[] array is returned.
+        When E__BASE < errnum <= E__HIGHEST, the corresponding errsym E_STRING
+        from the error_table[] array is returned.

-	For example:
+        For example:

-	    ; print errsym(10003)
-	    E_ADD
+            ; print errsym(10003)
+            E_ADD

-	When an errnum that matches one of the following errtbl.h #define,
-	then the #define string is returned:
+        When an errnum that matches one of the following errtbl.h #define,
+        then the #define string is returned:

-	    E__NONE
-	    E__BASE
-	    E__USERDEF
-	    E__USERMAX
+            E__NONE
+            E__BASE
+            E__USERDEF
+            E__USERMAX

-	    NOTE: For errnum == E__HIGHEST, the corresponding E_STRING that
-	    is returned is NOT "E__HIGHEST".  Instead the E_STRING corresponding
-	    to the highest errnum number from the error_table[] array is returned.
+            NOTE: For errnum == E__HIGHEST, the corresponding E_STRING that
+            is returned is NOT "E__HIGHEST".  Instead the E_STRING corresponding
+            to the highest errnum number from the error_table[] array is returned.

-	For example:
+        For example:

-	    ; print errsym(0)
-	    E_NONE
+            ; print errsym(0)
+            E_NONE

-	When E__NONE <= errnum < E__BASE, or when E__USERDEF <= errnum <= E__USERMAX,
-	an "E_STRING" errsym of the form "E_digits" is returned where "digits"
-	are the ASCII digits of the decimal value of errnum.
+        When E__NONE <= errnum < E__BASE, or when E__USERDEF <= errnum <= E__USERMAX,
+        an "E_STRING" errsym of the form "E_digits" is returned where "digits"
+        are the ASCII digits of the decimal value of errnum.

-	For example:
+        For example:

-	    ; print errsym(123)
-	    E_123
+            ; print errsym(123)
+            E_123

-	For all other errnum values, an error is returned.
+        For all other errnum values, an error is returned.

    When called with E_STRING string argument:

       When the E_STRING starts with "E_" followed by only decimal digits:

-	    If E_STRING is "E_0", 0 is returned.
+            If E_STRING is "E_0", 0 is returned.

-	    If E_STRING matches the regular expression:
+            If E_STRING matches the regular expression:

-		^E_[1-9][0-9]+$
+                ^E_[1-9][0-9]+$

-	    where digits 0 < errnum <= 32767, the errnum value is returned.
+            where digits 0 < errnum <= 32767, the errnum value is returned.

-	    For all other cases of "E_" by only decimal digits, an error is returned.
+            For all other cases of "E_" by only decimal digits, an error is returned.

-	When the E_STRING matches one of the following special
-	symbols, the symbol's numeric value as #define-d in errsym.h
-	or errtbl.h is returned:
+        When the E_STRING matches one of the following special
+        symbols, the symbol's numeric value as #define-d in errsym.h
+        or errtbl.h is returned:

-	    E__NONE
-	    E__BASE
-	    E__HIGHEST
-	    E__USERDEF
-	    E__USERMAX
+            E__NONE
+            E__BASE
+            E__HIGHEST
+            E__USERDEF
+            E__USERMAX

-	For example:
+        For example:

-	    ; print errsym("E_NONE")
-	    0
+            ; print errsym("E_NONE")
+            0

-	For all other E_STRING strings that start with "E__", an error is returned.
+        For all other E_STRING strings that start with "E__", an error is returned.

-	When the E_STRING starts with "E_" followed by an UPPER CASE LETTER that
-	also matches the regular expression:
+        When the E_STRING starts with "E_" followed by an UPPER CASE LETTER that
+        also matches the regular expression:

-	    ^E_[A-Z][A-Z0-9_]+$
+            ^E_[A-Z][A-Z0-9_]+$

-	The error_table[] is searched for an errsym that exactly matches
-	the E_STRING.  If a match is found, the corresponding errnum number
-	is returned.  If no match is found, an error is returned.
+        The error_table[] is searched for an errsym that exactly matches
+        the E_STRING.  If a match is found, the corresponding errnum number
+        is returned.  If no match is found, an error is returned.

-	For example:
+        For example:

-	    ; print errsym("E_ADD")
-	    10003
+            ; print errsym("E_ADD")
+            10003

-	For all other string arguments, an error is returned.
+        For all other string arguments, an error is returned.

    When errsym returns an integer, the global calc error count (see help errcount)
    is NOT changed.  And of course, when errsym("E_STRING") returns an error, the
@@ -102,30 +102,30 @@ DESCRIPTION

    Consider the E_MUL calc error condition:

-	Given a E_STRING errsym, errsym("E_STRING") will return the errnum integer
-	error code that is associated with the E_STRING errsym.
+        Given a E_STRING errsym, errsym("E_STRING") will return the errnum integer
+        error code that is associated with the E_STRING errsym.

-	The 4th entry of struct errtbl error_table is:
+        The 4th entry of struct errtbl error_table is:

-	    { 10005,        "E_MUL",                "Bad arguments for +" },
+            { 10005,        "E_MUL",                "Bad arguments for +" },

-	And errcode -d produces a errsym.h with the following #define:
+        And errcode -d produces a errsym.h with the following #define:

-	    #define E_MUL           10005   /* Bad arguments for * */
+            #define E_MUL           10005   /* Bad arguments for * */

-	Thus 10005 is the errnum, "E_MUL" is the E_STRING errsym that is
-	associated with the errmsg error message: "Bad arguments for +".
+        Thus 10005 is the errnum, "E_MUL" is the E_STRING errsym that is
+        associated with the errmsg error message: "Bad arguments for +".

-	In the above example, errsym("E_MUL") will return 10005.
-	Also errsym("E_10005") will also return 10005.
+        In the above example, errsym("E_MUL") will return 10005.
+        Also errsym("E_10005") will also return 10005.

-	To complete the E_STRING use in the above example:
+        To complete the E_STRING use in the above example:

-	    Both error(10005) and error("E_MUL") both raise the E_MUL calc error condition
+            Both error(10005) and error("E_MUL") both raise the E_MUL calc error condition

-	    Both errno(10005) and errno("E_MUL") both return 10005
+            Both errno(10005) and errno("E_MUL") both return 10005

-	    Both strerror(10005) and strerror("E_MUL") both return "Bad arguments for *"
+            Both strerror(10005) and strerror("E_MUL") both return "Bad arguments for *"

 EXAMPLE
    ; print errsym("E_ADD"), errsym("E_SUB"), errsym("E_MUL"), errsym("E_DIV")
@@ -146,9 +146,9 @@ LIMITS
    E_STRING is string that must match the regular expression: ^E_[A-Z0-9_]+$

 LINK LIBRARY
-    int calc_errno;				/* global calc_errno value */
+    int calc_errno;                             /* global calc_errno value */

-    CONST struct errtbl error_table[ECOUNT+2];	/* calc error codes, error symbols and error messages */
+    CONST struct errtbl error_table[ECOUNT+2];  /* calc error codes, error symbols and error messages */

    bool is_e_digits(CONST char *errsym);
    bool is_valid_errnum(int errnum);
@@ -174,7 +174,7 @@ SEE ALSO
 ##
 ## Calc is distributed in the hope that it will be useful, but WITHOUT
 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
-## or FITNESS FOR A PARTICULAR PURPOSE.	 See the GNU Lesser General
+## or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
 ## Public License for more details.
 ##
 ## A copy of version 2.1 of the GNU Lesser General Public License is
@@ -182,8 +182,8 @@ SEE ALSO
 ## received a copy with calc; if not, write to Free Software Foundation, Inc.
 ## 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
 ##
-## Under source code control:	1995/12/18 03:30:59
-## File existed as early as:	1995
+## Under source code control:   1995/12/18 03:30:59
+## File existed as early as:    1995
 ##
-## chongo <was here> /\oo/\	http://www.isthe.com/chongo/
-## Share and enjoy!  :-)	http://www.isthe.com/chongo/tech/comp/calc/
+## chongo <was here> /\oo/\     http://www.isthe.com/chongo/
+## Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
--- a/Show More
+++ b/Show More