rpn.1: made more precise

docs/rpn.1

@@ -1,4 +1,5 @@
 .\" Copyright (c) 2024 Emma Tebibyte <emma@tebibyte.media>
+.\" Copyright (c) 2024 DTB <trinity@trinity.moe>
 .\"
 .\" This work is licensed under CC BY-SA 4.0. To see a copy of this license,
 .\" visit <http://creativecommons.org/licenses/by-sa/4.0/>.
@@ -7,47 +8,48 @@
 
 .SH NAME
 
-npc \(en reverse polish notation evaluation
+rpn \(en reverse polish notation evaluation
 
 .SH SYNOPSIS
 
-rpn [integers...] [operations...]
+rpn
+.RB [numbers...]\ [operators...]
 
 .SH DESCRIPTION
 
-Rpn parses reverse polish notation and adds characters to the stack until there
-is an operation. See rpn(7) for more details on the syntax of reverse polish
-notation.
+Rpn parses and and evaluates reverse polish notation either from the standard
+input or by parsing its arguments. See the STANDARD INPUT section.
+
+For information on for reverse polish notation syntax, see rpn(7).
 
 .SH STANDARD INPUT
 
-If rpn is passed arguments, it interprets those arguments as an expression to
-be evaluated. Otherwise, it reads characters from standard input to add to the
-stack.
+If rpn is passed arguments, it interprets them as an expression to be evaluated.
+Otherwise, it reads whitespace-delimited numbers and operations from the
+standard input.
+
+.SH CAVEATS
+
+Due to precision constraints and the way floats are represented in accordance
+with the IEEE Standard for Floating Point Arithmetic (IEEE 754), floating-point
+arithmetic has rounding errors. This is somewhat curbed by using the
+second-highest float that can be represented in line with this standard to round
+numbers to before outputting.
 
 .SH DIAGNOSTICS
 
 If encountering a syntax error, rpn will exit with the appropriate error code
 as defined by sysexits.h(3) and print an error message.
 
-.SH CAVEATS
-
-Due to the complexity of integer storage in memory, rpn is only capable of
-parsing decimal integers.
-
-Additionally, due to the laws of physics, floating-point math can only be as
-precise as slightly less than the machine epsilon of the hardware on which rpn
-is running.
-
 .SH RATIONALE
 
-POSIX has its own calculator in the form of bc(1p), which uses standard input
-for its calculations. Pair the clunkiness of piping expressions into it and its
-use of standard notation, it was clear what rpn should be.
-
-There are no mathematics in the qi(1) shell because it was decided early on that
-math was the job of a specific tool and not the shell itself. Thus, rpn was
-born.
+An infix notation calculation utility, bc(1p), is included in the POSIX
+standard, but it doesn’t accept expressions as arguments; in scripts, any
+predefined, non-interactive input must be piped into the program. A dc(1)
+pre-dates the standardized bc(1p), the latter originally being a preprocessor
+for the former, and was included in UNIX v2 onward. While it implements reverse
+polish notation, it still suffers from being unable to accept an expression as
+an argument.
 
 .SH AUTHOR
 
@@ -60,4 +62,4 @@ Copyright (c) 2024 Emma Tebibyte. License AGPLv3+: GNU AGPL version 3 or later
 
 .SH SEE ALSO
 
-bc(1p), dc(1)
+rpn(7), bc(1p), dc(1), IEEE 754