1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
|
fp-package
(c) Michael Mehlich 1994, 1995, 1996
contributions by: Denis Girou
acknowledgment to: Denis Girou, Miroslav Balda, Ricardo Sanchez Carmenes
(current) e-mail: mmehlich@semdesigns.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
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.
|
