fp-package
(c) Michael Mehlich 1994 -- 1999
contributions by: Denis Girou
acknowledgment to: Denis Girou, Miroslav Balda, Ricardo Sanchez Carmenes
% Copyright 1994 -- 1999 Michael Mehlich
% This package can be redistributed and/or modified under the terms
% of the LaTeX Project Public License Distributed from CTAN
% archives at http://www.latex-project.org/lppl.txt either
% version 1 of the License, or any later version.
(current) e-mail: mmehlich@semdesigns.com; michael@mehlich.com
Fixed point arithmetic for TeX with numbers ranging from
-999999999999999999.999999999999999999
to
+999999999999999999.999999999999999999
TODO:
- better documentation (it is really bad)
USAGE:
- LaTeX2e:
\usepackage[<options>]{fp}
where the following options are known:
nomessages: don't print messages about the functions that are
just computed
debug: print debug messages (mainly for \FPupn)
- LaTeX2.09:
include lfp.sty in the document preamble, i.e.
\documentstyle[...,lfp,...]{...}
- TeX:
\input fp.tex
MsDos/Windows Users:
It may be necessary to rename some files such that they just have a length of
eight characters (plus a three character suffix).
The following renaming e.g. works for emtex:
Original name Name for emtex
defpattern.sty defpaern.sty
fp-addons.sty fp-adons.sty
fp-random.sty fp-radom.sty
FILES AND THEIR CONTENTS:
- readme.fp:
this file
- fp.sty
includes all files
- defpattern.sty:
only for internal usage
- fp-basic.sty:
The following macros are public ones to be used in the document:
%controlling messages
\FPmessagestrue % print standard FP-messages (default)
\FPmessagesfalse % suppress standard FP-messages
\FPdebugtrue % print debug messages (mainly for upn)
\FPdebugfalse % suppress debug messages (default)
%introduction of new values
\FPset#1#2 % #1 := #2 (#1 may be macro or string)
%print values
\FPprint#1 % prints #1 (#1 may be macro or string)
%binary operations
\FPadd#1#2#3 % #1 := #2+#3
\FPdiv#1#2#3 % #1 := #2/#3
\FPmul#1#2#3 % #1 := #2*#3
\FPsub#1#2#3 % #1 := #2-#3
%unary operations
\FPabs#1#2 % #1 := abs(#2)
\FPneg#1#2 % #1 := -#2
%binary relations
\FPiflt#1#2...\else...\fi % #1 < #2 ?
\FPifeq#1#2...\else...\fi % #1 = #2 ?
\FPifgt#1#2...\else...\fi % #1 > #2 ?
%unary relations
\FPifneg#1 ...\else...\fi % #1 < 0 ?
\FPifpos#1 ...\else...\fi % #1 >= 0 ?
\FPifzero#1...\else...\fi % #1 = 0 ?
\FPifint#1 ...\else...\fi % #1 is integer ?
%repeat last test
\ifFPtest ...\else...\fi % repeat last test
- fp-addons.sty
The following macros are public ones to be used in the document:
%binary operations
\FPmin#1#2#3 % #1 = min(#2,#3)
\FPmax#1#2#3 % #1 = max(#2,#3)
- fp-eqn.sty (No warranty on correctness and especially on numerical problems!)
The following macros are public ones to be used in the document:
\FPlsolve#1#2#3
% #1 := x with #2*x+#3=0
\FPqsolve#1#2#3#4#5
% #1,#2 := x with #3*x^2+#4*x+#5 = 0
\FPcsolve#1#2#3#4#5#6#7
% #1,#2,#3 := x with #4*x^3+#5*x^2+#6*x+#7 = 0
\FPqqsolve#1#2#3#4#5#6#7#8#9
% #1,#2,#3,#4 := x with #5*x^4+#6*x^3+#7*x^2+#8*x+#9 = 0
The resulting solutions are all real values. If there do not
exist as much solutions you get a warning message and some
other solutions occur several times in the solution vector.
- fp-exp.sty
The following macros are public ones to be used in the document:
\FPe % 2.718281828459045235
\FPexp#1#2 % #1 := e^(#2)
\FPln#1#2 % #1 := ln(#2)
\FPpow#1#2#3 % #1 := (#2)^(#3)
\FProot#1#2#3 % #1 := (#2)^(1/#3)
- fp-random.sty
The following macros are public ones to be used in the document:
\FPseed=#1 % set seed counter for random number generation
\FPrandom#1 % #1 := a random number between 0 and 1
- fp-pas.sty
The following macros are public ones to be used in the document:
\FPpascal#1#2 % #1 := #2-th line of the pascal triangle
- fp-snap.sty:
The following macros are public ones to be used in the document:
\FPround#1#2#3 % #1 := #2 rounded to #3 digits after '.'
\FPtrunc#1#2#3 % #1 := #2 truncated to #3 digits after '.'
\FPclip#1#2 % #1 := #2 with all unnecessary 0's removed
- fp-trigo.sty:
The following macros are public ones to be used in the document:
\FPpi % 3.141592653589793238
\FPsin#1#2 % #1 := sin(#2)
\FPcos#1#2 % #1 := cos(#2)
\FPsincos#1#2#3 % #1 := sin(#3), #2 := cos(#3)
\FPtan#1#2 % #1 := tan(#2)
\FPcot#1#2 % #1 := cot(#2)
\FPtancot#1#2#3 % #1 := tan(#3), #2 := cot(#3)
\FParcsin#1#2 % #1 := arcsin(#2)
\FParccos#1#2 % #1 := arccos(#2)
\FParcsincos#1#2#3 % #1 := arcsin(#3), #2 := arccos(#3)
\FParctan#1#2 % #1 := arctan(#2)
\FParccot#1#2 % #1 := arccot(#2)
\FParctancot#1#2#3 % #1 := arctan(#3), #2 := arccot(#3)
- fp-upn.sty:
The following macros are public ones to be used in the document:
\FPupn#1#2 % #1 := eval(#2) where eval evaluates the
upn-expression #2
Known operations are:
+,add,-,sub,*,mul,/,div,abs,neg,min,max,
round,trunc,clip,e,exp,ln,pow,root,pi,sin,cos,
sincos,tan,cot,tancot,arcsin,arccos,arcsincos,
arctan,arccot,arctancot,pop,swap,copy
where
pop removes the top element
swap exchanges the first two elements
copy copies the top element
Example 1:
The macro call
\FPupn\result{17 2.5 + 17.5 - 2 1 + * 2 swap /}
is equivalent to
\result := ((17.5 - (17 + 2.5)) * (2 + 1)) / 2
and evaluates to
\def\result{-3.000000000000000000}
Afterwards the macro call
\FPupn\result{\result{} -1 * 0.2 + sin 2 round}
^^ the "{}" is necessary!
is equivalent to
\result := round_2(sin((\result * -1) + 0.2))
and evaluates to
\def\result{-0.06}
Example 2:
As "result" is an abbreviation of "\result{}" you may
write
\FPupn{result}{17 2.5 + 17.5 - 2 1 + * 2 swap /}
and
\FPupn{result}{result -1 * 0.2 + sin 2 round}
instead leading to the same results.
This is even true for other macro names using e.g. "x" for "\x{}"
and so on. But be careful with it. We may introduce new constants
in further versions overwriting these abbreviations.
- fp-eval.sty:
The following macros are public ones to be used in the document:
\FPeval#1#2 % #1 := eval(#2) where eval evaluates the
expression #2
ATTENTION: Do not use macro names with \. for its own
Use only the name or the macro surrounded by (, and ) instead,
i.e. do not write "\value{}" but "value" or "(\value)".
This is needed to avoid problems with a prefix "-" of numbers.
(I do not intend to write a more complex parsing routine in future.
But if you do so, just send it to me.
)
Known infix operations are
+, -, *, /, ^ for add, sub, mul, div, pow
Each other operation is a prefix one that needs
a (comma or colon seperated) list of subexpressions.
Exception: The unary prefix operation - is not known!
(Use the function neg instead.)
Example 1:
With
\edef\result{11}
and
\FPeval\result{round(root(2,sin(result + 2.5)):2)}
or
\FPeval{result}{round(root(2,sin(result + 2.5)):2)}
\result becomes the value 0.90
Example 2:
\FPeval\result{clip(2*3+5*6)} results to 36
\FPeval\result{clip(2*(3+5)*6)} results to 96
KNOWN BUGS:
- does not work with multido.sty/multido.tex
Reason:
multido uses the same macro names \FPadd and \FPsub
Recommended Solution:
Patch multido.tex, i.e. apply the following substitutions:
FPadd -> mdo@FPadd
FPsub -> mdo@FPsub
- incompatibility with french style of babel
this only affects macros using the colon (:)
Recommended Solution:
Load the fp-package before babel with french style
Other Possible Solution:
Use \catcode`\:=12 after loading babel with french style
- others:
Currently not known, but, though we do not, we could give
a warranty of their existence ...
HISTORY:
Date By File New Version
Jan. 14, 2019 Peter Wang documentation V2.1d
improved documentation based on the original README.txt, with examples to show the syntax.
Jan. 14, 2019 Enrico Gregorio `fp-exp.sty' and `lfp.sty` V2.1d
Fixed two unprotected end-of-lines in the above files that can, under certain circumstances, add spaces in the output, causing unwanted drifting.
Oct. 21, 1996 Michael Mehlich fp-upn.sty V2.1c
better debug messages (especially giving results of one step computations)
May. 13, 1996 Michael Mehlich fp-basic.sty V1.2d
\newcount and \countdef have interfered each other
when the first newcount uses a counter number less
than 60, the result has been wrong results when using
the package with plain tex (a problem that has been
reported by Ricardo Sanchez Carmenes)
May. 13, 1996 Michael Mehlich all files -
problems with unwanted spaces removed
(bug reported by Ricardo Sanchez Carmenes)
May. 28, 1995 Michael Mehlich fp-basic.sty V1.2c
modified \FPset and added \FPprint
Apr. 27, 1995 Michael Mehliche fp-trigo.sty V0.9e
incorrect result of sine for 3/2pi fixed
(bug reported by Miroslav Balda)
Apr. 14, 1995 Michael Mehlich fp-trigo.sty V0.9d
infinite loop in computing sine and cosine fixed
(bug reported by Miroslav Balda)
Apr. 05, 1995 Michael Mehlich fp-snap.sty V1.0a
rounding bug in FPround fixed
(bug reported by Miroslav Balda)
Apr. 04, 1995 Michael Mehlich fp.tex -
lfp.sty -
a redefinition of \loop..\repeat added not to get into
trouble with its behaviour within my macros
(bug reported by Miroslav Balda)
Apr. 04, 1995 Michael Mehlich fp-basic.sty V1.2b
added a value introduction command FPset
Apr. 03, 1995 Michael Mehlich fp-eqn.sty V0.4
added solution algorithms for cubic and 4-th degree equations
Apr. 03, 1995 Michael Mehlich fp-trigo.sty V0.9c
added some % at end of lines not to introduce unwanted spaces
removed some debug informations that have accidently been left in
Apr. 03, 1995 Michael Mehlich fp-exp.sty V0.7e
added some % at end of lines not to introduce unwanted spaces
Apr. 03, 1995 Michael Mehlich fp-upn.sty V2.1b
fp-eval.sty V0.9a
added support of sgn
Apr. 03, 1995 Michael Mehlich fp-basic.sty V1.2a
added new command \FPsgn
Apr. 02, 1995 Michael Mehlich fp-exp.sty V0.7d
bug corrected, power of 0 by f # 0 now is 0 and no longer
leads to an error message
Apr. 02, 1995 Michael Mehlich fp.sty V0.8
added fp-eval.sty to list of required packages
Apr. 02, 1995 Michael Mehlich fp-upn.sty V2.1a
some modifications to work with fp-eval.sty
Apr. 02, 1995 Michael Mehlich fp-eval.sty V0.9
inital version
Mar. 15, 1995 Michael Mehlich fp.sty V0.7a
added fp-addons.sty, fp-eqn.sty to list of required packages
Mar. 15, 1995 Michael Mehlich fp-eqn.sty V0.2
initial version
Mar. 15, 1995 Michael Mehlich fp-exp.sty V0.7c
bug corrected, root of 0 now is 0 and no longer leads to
an error message
Mar. 15, 1995 Michael Mehlich fp-upn.sty V2.1
allow macros to be given without \ and {} surrounding
support of min, max added
Mar. 15, 1995 Michael Mehlich fp-addons.sty V0.1
initial version
Feb. 23, 1995 Denis Girou fp-random.sty V1.0a
more elaborated comments
Feb. 21, 1995 Michael Mehlich fp-trigo.sty V0.9b
corrected overflow test for arcsin and arccos
Feb. 18, 1995 Michael Mehlich fp-upn.sty V2.0
added debug messages for fp-upn.sty
(recommended by Denis Girou)
Feb. 18, 1995 Michael Mehlich fp.sty V0.7
added fp-random.sty to list of required packages
Feb. 18, 1995 Michael Mehlich fp-basic.sty V1.2
printing fp-messages is conditional only (default: true)
introduced macro for printing debug messages (default: do not print)
(recommmended by Denis Girou)
Feb. 18, 1995 Michael Mehlich fp-exp.sty V0.7c
corrected bugs in \FP@pow and \FP@root writing messages to
ordinary text
(reported by Denis Girou)
Feb. 17, 1995 Denis Girou fp-random.sty V1.0
introduced
Feb. 17, 1995 Michael Mehlich fp-basic.sty V1.1f
corrected \FP@strip introduced in version V1.1e
as it has to but did not hande + and -
Feb. 17, 1995 Michael Mehlich fp-basic.sty V1.1e
corrected \FP@strip introduced in version V1.1d
as it has to but did not hande empty parameters
Feb. 17, 1995 Michael Mehlich fp-basic.sty V1.1d
bug in scanning numbers by \FP@readvalue in connection
with number-macros of \FPupn corrected
(thanks for Denis Girou reporting this bug)
Nov. 19, 1994 Michael Mehlich fp.sty V0.6
package date changed
Nov. 19, 1994 Michael Mehlich fp-basic.sty V1.1c
bug in \FP@correctintcounter corrected
Nov. 19, 1994 Michael Mehlich fp-upn.sty V1.1
handling of arctan, arccot, arctancot added
Nov. 19, 1994 Michael Mehlich fp-trigo.sty V0.9a
\FParctan, \FParccot, \FParctancot added
Oct. 27, 1994 Michael Mehlich lfp.sty -
introduced
Oct. 27, 1994 Michael Mehlich fp.tex -
introduced
Oct. 15, 1994 Michael Mehlich readme.fp -
this history changed for better readability
Oct. 15, 1994 Michael Mehlich fp-exp.sty V0.7b
subtraction bug in \FP@@exp corrected
Oct. 15, 1994 Michael Mehlich fp-basic.sty V1.1b
subtraction in \FP@counttimes changed
Oct. 15, 1994 Michael Mehlich fp-trigo.sty V0.7b
error message, if \FP@modtwopi does not lead to correct result
(this shouldn't be possible)
subtraction in \FP@@cos corrected
Oct. 12, 1994 Michael Mehlich fp.sty V0.5b
prevent files included from sending messages
Oct. 12, 1994 Michael Mehlich readme.fp -
changed entry for defpattern.sty in this history to reflect
original source for defpattern.sty
Oct. 12, 1994 Michael Mehlich defpattern.sty -
source notice in message corrected
Oct. 12, 1994 Michael Mehlich fp-exp.sty -
start message for \FPpow changed
Oct. 12, 1994 Michael Mehlich fp-trigo.sty -
unnecessary \typeout removed
Oct. 3, 1994 Michael Mehlich, fp.sty V0.5
additional styles included by fp.sty
Oct. 3, 1994 Michael Mehlich fp-upn.sty V1.0
first version
Oct. 3, 1994 Michael Mehlich defpattern.sty -
modification of the \howto-macro in TeX and TUG NEWS
from an article by Alan Jeffrey
no version number, no copyright (public domain)
TeX and TUG News 2(2) writes in the section "Mission Statement":
"The entire contents of this newsletter are being placed in
the public domain."
Oct. 3, 1994 Michael Mehlich fp-basic.sty V1.1
bug in \FPadd corrected
Aug. 29, 1994 Michael Mehlich fp.sty V0.3
additional styles included by fp.sty
Aug. 29, 1994 Michael Mehlich fp-trigo.sty V0.7
first version
Aug. 29, 1994 Michael Mehlich fp-pas.sty V1.0
first version
Aug. 29, 1994 Michael Mehlich fp-exp.sty V0.7
first version
Aug. 12, 1994 Michael Mehlich fp.sty V0.2
first version
Aug. 10, 1994 Michael Mehlich fp-snap.sty V1.0
first version
Apr. 20, 1994 Michael Mehlich fp-basic.sty V1.0
\FPabs added
Apr. 12, 1994 Michael Mehlich fp-basic.sty V0.99
division algorithm added
Feb. 03, 1994 Michael Mehlich fp-basic.sty V0.8
all macros are completely rewritten to be able to use an increased
range of numbers
Jan. 18, 1994 Michael Mehlich fp-basic.sty V0.2
bug in \FP@store corrected
Jan. 17, 1994 Michael Mehlich fp-basic.sty V0.1
the file realcalc.tex V1.0, (C) Frank Buchholz has been renamed to
fp-basic.sty V0.1 with all macros renamed, \@trunc removed
COPYING:
- Permission to use, copy, modify, and distribute this software and its
documentation for any purpose and without fee is hereby granted,
provided that the above copyright notice, the above history with your
modifications added, and this permission notice appear in all copies
and modified versions.
- The copyright holder disclaim all warranties with regard to this
software, including all implied warranties of merchantability and
fitness, in no event shall the copyright holder be liable for any
special, indirect or consequential damages or any damages whatsoever
resulting from loss of use, data or profits, whether in an action of
contract, negligence or other tortious action, arising out of or in
connection with the use or performance of this software.
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