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2022/06/10
Source: xint.dtx 1.4m 2022/06/10 (doc 2022/06/11)
Author: Jean-Francois Burnol
Info: Expandable operations on big integers, decimals, fractions
License: LPPL 1.3c1.4m (2022/06/10)The fix of a compatibility bug with miniltx and the
already in place documentation improvements (in particular, hyperlinked
macro names in code lines) motivated release 1.4m. With
some hesitation I decided to not revert the removals and breaking
changes listed here and which had been already acted in preparation of
an hypothetic future 1.5.
xintexpr: \xintdefefunc et al.,
deprecated at 1.4 have been removed.
xintexpr: \thexintexpr et al.,
deprecated at 1.4b have been removed. Use
\xinttheexpr et al.
xintlog: \poormanloghack which was
a no-op since 1.4e has been removed.
xintfrac: \xintFrac,
\xintFwOver, \xintSignedFrac,
\xintSignedFwOver now raise errors. They were deprecated at
1.4g, check the documentation for the new names
\xintTeXFrac et al.
xintexpr: \xinttheboolexpr now
outputs true or false (to match TeX
conventions) and not the True or False
employed since 1.4 (inside expressions true,
false, True and False are all
recognized keywords anyhow).
The \pdfstrcmp/\strcmp engine primitive is required.
With LuaTeX it is emulated via Lua code
basically copied over from LaTeX3. Not sure if this is
breaking as the package already requires the \expanded
primitive. Only used so far by (as expected) \xintiiCmp,
and macros which will end up calling it.
\input xintexpr.sty\relax in (pdf)eTeX plus
miniltx (naturally, if miniltx was already
loaded), and with versions up to 1.4k the
xinttrig and xintlog aborted their own
xintexpr-triggered input erroneously thinking the latter
had not yet been loaded, and emitted only a very discrete message to the
log file. With 1.4l it became worse as
\input xintexpr\relax auto-repeated itself about six times
until TeX called it quits.Documentation: most macros are hyperlinked in the source code to
the code line of their definitions. Furthermore, from the place of the
definition the main macros will link to either their descriptions in the
user manual (in xint-all.pdf) or in the implementation part
(sourcexint.pdf). Conversely inside
xint-all.pdf the macro descriptions are linked towards
their implementation. You may notice some time lag with some pdf viewers
on opening the heavily hyperlinked sourcexint.pdf compared
to previous releases.
Not sure if that counts as an improvement, but I have shortened
the wording of the expandable error messages, which had been last
modified at 1.4g.
1.4l (2022/05/29)xintkernel: ever since 1.4, loading
anyone of the xint*sty packages left the catcode of the
character of ascii code 1 to the internal custom value
3.
xintfrac: the \xintPFloat checks
for an output being an integer in decimal notation or a number with a
one-digit trimmed mantissa could fail if
\xintPFloatMinTrimmed (added at 1.4k) was
large enough, e.g. equal to the target precision. Then, the outputs
always kept trailing zeros, as expected in general but not for those
special cases.
xintlog, xinttrig: since
1.4e the message emitted if
\usepackage{xintlog} or \usepackage{xinttrig}
was encountered in place of the correct
\usepackage{xintexpr} was wrong. It advised to use
\input xintexpr.sty\relax, which would have failed with
LaTeX. The warning is corrected and now the macro file in place of
aborting will (be it with or without LaTeX) trigger the loading of
xintexpr (hence of itself after it).
The possibility to run latex directly on
xint.dtx had been broken since 1.4i.
xintfrac: \xintRawBraced as a
public alias to an xintfrac entry point to its core
input handler. Experimental additions \xintSignBit and
\xintFloatBraced. Deprecate \xintTeXfromSci in
favor of new name \xintTeXFromSci, and remove its
\expanded wrapper (so it is not f-expandable anymore). Add
\xintTeXFromScifracmacro.
xintfrac, xintexpr:
\xintFracToSci and \xintFracToDecimal now
behave like all other xintfrac macros in terms of
allowed arguments and f-expandability and have been moved back to
xintfrac.
Renewed random shuffling of large parts of the documentation has greatly improved it.
Simpler build flow to produce a pdf containing both
user manual and source code. Removal of dependency on grep
binary for such builds or the one of sourcexint.pdf. Fix of
various obsoleted comments in extracted files involved in the
documentation build process.
1.4k (2022/05/18)xintfrac: the longstanding (but documented as
undecided and unstable) way of \xintFloat to output the
zero value was 0.e0 and it has now been modified into
0.0e0. Now customizable via
\xintFloatZero.
xintfrac/xintexpr: the
behaviour of \xintPFloat (hence of
\xintfloateval) has again changed: when the output is an
integer (not using scientific notation) it does not get postfixed by
.0. This applies in particular for the zero value, now
printed 0. Similarly, in the case of scientific notation
with a single-digit (trimmed) mantissa, no .0 is used.
Customizable via \xintPFloatIntSuffix,
\xintPFloatLengthOneSuffix, and
\xintPFloatZero.
Also, \xintPFloat trims trailing zeros from the full
significand only if there are, by default, at least 4 of
them, see \xintPFloatMinTrimmed.
xintfrac/xintexpr: macro
definition of \xintFracToSci migrated from the former to
the latter (see 1.4l for update).
xintexpr:
\xintexpr{Safe,Restore}Catcodes pairs now behave like a
“last in first out” stack. Check the pdf documentation for
details.
xintexpr: the
\xintexpr{Safe,Restore}Catcodes were documented at user
level, but also used by the package \xintdefvar or
\xintdeffunc. This could result in some bad interaction due
to the somewhat strange (but documented) behaviour of nested
\xintexpr{Safe,Restore}Catcodes (which has now been
modified).
xintexpr: ever since 1.4,
\xintdefufunc (but not \xintdeffunc) forgot to
reset the catcodes to their status prior to the sanitization done by the
macro at the start of its execution.
xintfrac: \xintPFloatZero,
\xintPFloatIntSuffix,
\xintPFloatLengthOneSuffix,
\xintPFloatNoSciEmax, \xintPFloatNoSciEmin and
\xintPFloatMinTrimmed customize the output of
\xintPFloat, hence also of \xintfloateval (and
of \xinteval when scientific notation was used in the
expression). Also added \xintFloatZero.
xintfrac:
\xintFloatToDecimal.
xintexpr: \xintFracToDecimal, an
alternative to the default \xintFracToSci configuration of
\xintexprPrintOne.
xintexpr: long awaited syntax
\xintieval[D]{...} and \xintfloateval[Q]{...}
now implemented. The legacy syntax with \xintieval{[D]...}
and \xintfloateval{[Q]...} is kept for backwards
compatibility.
1.4j (2021/07/13)\xintSeq if producing a single number
(e.g. \xintSeq{10}{10} expanded to 10 not
{10}). Thanks to Christophe Poulain for report.1.4i (2021/06/11)xintexpr: the concept of simultaneous
assignments is extended: in case of more variables than values the
extraneous variables do not cause an error message but are simply set to
the nil value; in case of more values than variables, the
last variable is defined to be the ople concatenating all the extra
values.
xintexpr: built-in functions usable with
arbitrarily many arguments such as max(),
gcd(), or len() are now again usable with a
single numeric argument: since 1.4 a lone argument had to
be a nutple (which was automatically unpacked). It can now
again be a number.
xintexpr: simultaneous assignments via
\xintdefvar to 10 or more variables was broken if the right
hand side was an ople (of length at least 10, as it had prior to this
release to match the number of variables).
xintexpr: the mechanism which allows to define
variables with names already in use for pre-existing functions was
broken for some built-in functions: those handling syntax with dummy
variables (currently subs(), subsm(),
subsn(), seq(), add(),
mul(), ndseq(), ndmap(),
ndfillraw()) and the so-called “pseudo” functions
(currently bool(), togl(),
protect(), qint(), qfrac(),
qfloat(), qraw(), random(),
qrand(), rbit()). For example the function
seq() was broken if the user had defined a variable
seq.
1.4h (2021/05/27)xintexpr: the recent 1.4g
introduced a bug breaking input of the type
<operator><space token><macro>.
xintexpr: since 1.4
(2020/01/31) the omit and abort
keywords were broken if used inside a substitution, itself nested in a
seq() or similar construct.
xintexpr: since 1.4c the
\xintthespaceseparated (added at 1.4a)
inserted two, not one, spaces at one specific location near the end of
its output. A bit cosmetic problem, fixed nevertheless.
1.4g (2021/05/25)xintexpr: the parsing of power operators
** and ^ now proceeds in a right associative
way: 2^3^4==2^(3^4).
xintexpr: single-character operators
&, |, and = (deprecated since
1.1) have been removed. Use &&,
|| and == respectively.
1.03 and 1.04 releases \xintFrac,
\xintSignedFrac, \xintFwOver,
\xintSignedFwOver are deprecated. Please use the new names
\xintTeXFrac, \xintTeXsignedFrac,
\xintTeXOver, \xintTeXsignedOver. The old
names will emit warnings.Messages written to the terminal and log file during the handling
of recovery from exceptions use a new mechanism; when in interactive
mode, the user is prompted only once, not thrice, to enter
<return> for recovery and continued
processing.
xintfrac: \xintTeXfromSci (added
about 7 or 8 years too late) to help typesetting values output by
\xintfloateval in a more useful way than
\xintTeXFrac (formerly \xintFrac).
xintexpr: with xintbinhex
loaded, " is recognized as prefix for hexadecimal input;
but a bug (present ever since this support for hexadecimal input was
added) caused syntax such as "\macro to break the parser.
Also, leading zeros such as in "0000A where not properly
trimmed since 1.2m.
xintexpr: authorize x! == y without
parentheses. Formerly the parser mis-interpreted ! as first
character of the != not-equal-to comparison operator,
subsequently causing breakage when finding the second
=.
xintexpr: various error situations were badly handled.
\xinteval{1/0} did not recover gracefully due to
longstanding bug in xintfrac.\xintfloateval{1/0} did not recover gracefully either…
due to some other reason.1.4; also, with an unknown function name if in
\xintfloatexpr.\xinteval{_4} caused an infinite loop (with underscore
_ having its normal catcode). This was unexpected, as the
_ is documented to be ignored if in-between digits (and is
ignored if last after some digits). It will be now ignored also if
encountered upfront. A similar problem existed with variable names
starting with a _ (of normal catcode), which however are
clearly not legal. The (normal catcode) _ will then be
ignored as well if encountered in front of a variable or function name
(but not inside of course).\xinteval{\catcode`@} crashed (one had to use an added
\the or \number).\xinteval{/3} was not intercepted and
ultimately caused low-level errors (same with ^).Surely, further situations remain where bad input will crash parser.
1.4f (2021/05/10)xintexpr: \xintieval{[-D]...},
which rounds to a multiple of 1eD for D
positive now does not insert the trailing zeros (as done at
1.4e) nor a scientific part eD (as
prior to 1.4e). The use case envisioned is for the
quantized value to be used with an appropriate unit, for example
k for D=3 or M for
D=6 etc… Sorry for the very long process which was needed
to reach this final decision.
xintexpr: for Digits beyond the officially
supported range for accurate math functions, i.e. for
D>62, computations were still done and printed with full
number of digits, but the extra digits were meaningless; they now
operate on and output mantissas limited to min(D,64)
digits.
xintexpr: for powers a^b with
Digits at most 8, the number a is now
float-rounded to Digits before computation, as is done for
Digits>8; previously 9 significant digits
were kept.
xintexpr: further changes in the computation of powers, see the bug fixes below.
xintexpr: the float_() function got
renamed into float_dgt().
xintexpr: the documentation said
float_() function had been renamed float_dgt()
but actually that was not yet the case.
xintexpr: powers a^b (with exponent
b neither integer nor half-integer) stopped being accurate
regarding the last digits for |b| about 1000
and beyond. Except for 0.8<a<1.25 for which accuracy
was maintained up to about |b|=10^7. Fixed via keeping the
same suitable number of extra digits for internal computations of
logarithms, independently of whether a is close to
1 or not.
xintexpr: powers a^b in
\xinteval with |b| an integer at least
10000 were paradoxically computed with less accuracy than
in \xintfloateval… although they were documented to be
handled exactly the same in the two parsers.
xintexpr: powers a^b for Digits at
most 8 unconditionally used log10()/pow10()
approach but due to the limited accuracy of the poorman logarithm
(9 fractional digits) this was inaccurate already for
b about 100. So, the handling is now as for
Digits at least 9, i.e. integer and half-integer exponents
are handled via the legacy \xintFloatPower/\xintFloatSqrt
allowing arbitrarily big exponents. It is advised to split big powers
with non integer non half integer exponents into a product; this is not
done internally to avoid costly overhead for possibly rare use
cases.
xintexpr: the invalid input
(-1)^2.5 triggered an undefined control sequence error if
Digits was at most 8.
1.4e (2021/05/05)xintlog: \poormanloghack now a
no-op.
xinttrig: loading the package does not define left-over variables holding the values of the inverse factorials used in the sine and cosine series.
xintexpr: the output format of
\xinteval, which uses \xintFracToSci, has
changed. In particular, if the number has a power of ten part, it is not
output with an integer mantissa, but with a scientific mantissa
d.d... with always at least one digit after the decimal
mark (possibly 0) and trailing zeros are trimmed out. This
is the same output format as used for \xintfloateval, apart
of course from the fact that the mantissa lengths are not
limited.
xintexpr: the output format of
\xintfloateval, which uses \xintPFloat,
changed. The \xintfloatexprPrintOne macro has changed its
signature to [#1]{#2} i.e. its first argument will be
within brackets not braces.
xintexpr: when using
\xintieval{[D]...} optional [D] with a
negative D, which triggers quantization to a positive power
of ten, the output (if not the zero value) will be an integer with
N=abs(D) explicit trailing zeros, not an integer mantissa
followed by eN.
xintexpr: \xinteval will not
compute powers a^N exactly if N in absolute
value is at least the (rounded) quotient of 10000 by the
number of digits of a; it will then use the
logarithm/exponential (in base 10) approach, according to the prevailing
Digits setting (at 1.4f this got modified again and integer
exponents large enough to trigger floating point evaluation are handled
exactly as in \xintfloateval, i.e. using the legacy
xintfrac \xintFloatPower, not the
logarithm/exponential approach which loses accuracy for exponents of the
order of 100000000 and beyond).
xintexpr: \xintdeffloatvar now
always rounds the assigned value to the target precision. Formerly,
inputs actually involving no float operations, such as for example a
sub-expression \xintexpr1/20!\relax (in contrast to
1/20!), or an explicit single number having more digits
than the precision, got stored “as is” in the defined variable, without
pre-rounding to the Digits precision.
xintfrac:\xintPFloat and
\xintFracToSci have both been modified. The macro
\xintFracToSciE does not exist anymore, as
\xintFracToSci in the case of scientific exponents hands
over the process to \xintPFloat (without the rounding to
Digits, of course).
xintlog: now working up to 62
digits. The legacy faster poormanlog-based macros are kept
for computations with Digits up to 8. Fractional powers are
now available both in xinteval and
xintfloateval, per default.
xinttrig: now working up to 62
digits and with increased accuracy. Special faster (or not as slow if
you prefer) mode at 8 digits or less.
xintexpr: the constraints on the
\xintexprPrintOne replacement macro, which defaults to
\xintFracToSci, have been much simplified.
xintexpr: \xintiexprPrintOne
(defaults to \xintDecToString)
xintfrac: \xintPFloatE may be
redefined as a macro which fetches the scientific exponent as a
mandatory argument delimited with a dot, and outputs a suitable
formatted result (f-expandably), also delimited with a dot which will be
removed by internal processing. The default however simply expands to
the letter e.
xintfrac: \xintDecToStringREZ is
like \xintDecToString but starts by removing trailing
zeroes.
\xinttheDigits in the right hand side of an
\xintDigits assignment. For example:
\xintDigits*:=\numexpr\xinttheDigits+4;. This is now
allowed, and the same applies to the macro interface, for example
\xintSetDigits*{\xinttheDigits+4}.1.4d (2021/03/29)quo() and rem() in
\xintiiexpr/\xintiieval renamed to iquo() and
irem().
The output of gcd() and lcm() as
applied to fractions is now always in lowest terms.
The log message to report a variable creation (if
\xintverbosetrue) does not use (double) quotes anymore
around the name. By the way, quotes were never used for function
names.
Ever since 1.3 the quo() and
rem() functions in \xintexpr (not the ones in
\xintiiexpr) were broken as their (officially deprecated)
support macros had been removed! They had somewhat useless definitions
anyway. They have now been officially removed from the syntax. Their
siblings in \xintiieval were renamed to iquo()
and irem().
Sadly, gcd() was broken in \xintexpr
since 1.4, if the first argument vanished. And
gcd() was broken in \xintiiexpr since
1.3d if any argument vanished. I did have a unit
test! (which obviously was too limited …)
Further, the \xintGCDof and \xintLCMof
xintfrac macros were added at 1.4 but did
not behave like other xintfrac macros with respect to
parsing their arguments: e.g. \xintGCDof{2}{03} gave an
unexpected non-numeric result.
The first() and last() functions, if
used as arguments to numerical functions such as sqr()
inside an \xintdeffunc caused the defined function to be
broken.
1.4c (2021/02/20)1.4 regression which broke syntax
varname(...) which supposedly is allowed and inserts a
tacit multiplication.1.4b (2020/02/25)All changes regard the xintexpr module.
&, |, (as Boolean operators) and
= (as equality test) have long been deprecated in favour of
&&, || and ==. They will
be removed at next major release.
At next major release the power operators ** and
^ will turn from left to right associative. I.e.
2**2**3 will give 256, not 64.
This is to match with Python and l3fp.
\thexintexpr et al. (introduced at 1.2h
but not documented anymore for some time) will be removed at next major
release. The original \xinttheexpr et al. have always been
so much better names. Besides, since 1.4,
\xintexpr can be used directly in typesetting
flow.
Function zip() is modeled on Python’s function of
the same name.
Function flat() removes all nesting to produce a
“one-dimensional” list having the exact same leaves (some possibly
empty) as the original (in the same order).
Chaining of comparison operators (e.g. x<y<z)
as in Python (but all comparisons are done even if one is found false)
and l3fp.
It was possible since 1.4’s
\xintFracToSciE to configure the separator between
mantissas and exponents in the output of \xinteval but
strangely there was no way to customize the output of
\xintfloateval. The added \xintPFloatE fixes
this.
\xintieval{[D]...} with a negative D (a
feature added at 1.4a) used erroneously a catcode 12
e in output, which moreover remained immuned to the
\xintFracToSciE setting.1.4a (2020/02/19)All changes regard the xintexpr module.
\xintthealign
have modified meanings and names.\xintthespaceseparated (serves to provide suitable
input to PS-Tricks \listplot).
The optional argument [D] to
\xintieval/\xintiexpr can be negative, with the same
meaning as the non-negative case, i.e. rounding to an integer multiple
of 10^(-D).
The same applies to the functions trunc() and
round(). And to the \xintTrunc,
\xintRound, \xintiTrunc, and
\xintiRound macros of xintfrac.
Usage of round() and trunc() within
\xintdeffunc got broken at 1.4.
add() and mul() were supposedly
accepting the omit, abort and
break() keywords since 1.4 but this was
broken.
1.4 (2020/01/31)Please note that this list may still be incomplete. If not otherly specified all items regard the xintexpr module.
The \expanded primitive (TeXLive 2019) is
required. This does not affect the macro layer
xintcore, xint,
xintfrac, xinttools (yet).
Formerly square brackets [...] were, on their own,
not different from parentheses (and thus disappeared from the output),
but they are now a genuine constructor of nested lists. For example
\xinteval{1, [2, [3, 4]], 5} produces
1, [2, [3, 4]], 5 (recall this is free bloatware).
The output of \xinteval has changed (besides
containing brackets). It does not use anymore the so-called raw
xintfrac format, i.e. things such as
A/B[N] (which can still be used in input but are
discouraged in xintexpr context), but scientific
notation AeN/B. As formerly, the denominator is printed
only if B>1 and the scientific part is dropped if the
exponent vanishes. In this way the output of \xinteval can
be pasted to alternative software.
The output format of \xinthe\xintboolexpr also has
changed. It uses True and False (which are
accepted on input), and this can easily be configured otherwise (also
true and false are accepted on
input).
The “broadcasting” (as it turned out, à la NumPy) of
scalar operations on one-dimensional “lists”, e.g
3*[1,3,5,7]+10 acting itemwise is dropped.
It is hoped to implement such operations again in stronger form in
future releases. Pre-existing alternative syntax is available, also to
produce the bracketed (cf. next item) [13,19,25,31] which
will be the output in future.
The divmod() function now produces on output such a
bracketed pair, but simultaneous assignment such as
\xintdefvar xq, xr = divmod(a,b); will work
transparently.
The syntax for using conditionals in function declarations has
changed. Now, one must use the ? and
?? short-circuit boolean branching operators whereas in the
past it was explained that the syntax had to use the if()
and ifsgn() functions.
Macros \xintGCD, \xintLCM,
\xintGCDof and \xintLCMof formerly provided by
xintgcd got moved to xintfrac (which
is not loaded by xintgcd). Moreover, they were extended
to handle general fractions on input but this also means that their
output is now obiding by the raw xintfrac format. The
integer only \xintiiGCD, \xintiiLCM also got
moved out of xintgcd, but to xint
which is now loaded automatically by xintgcd. The few
remaining macros of xintgcd at least do not need other
imports as xintgcd now loads also automatically
xinttools which is a dependency for two of
them.
Please note that this list is currently incomplete. For more
information look at the user manual and the documented source code
sourcexint.pdf.
Unless otherwise specified all changes commented upon here regard xintexpr. Important: all the new syntax is to be considered experimental. The author may change some names in future release, or even the interface (whether to use semi-colons or colons etc…).
The \csname encapsulation technique used since
xintexpr initial release (1.07 2013/05/25)
to move around possibly large data during expansion-only operations is
replaced with methods based on the \expanded engine
primitive. The latter is available in all major engines since TeXLive
2019.
Formerly, and with default memory settings, one would typically saturate the string pool memory after about of the order of 50,000 independent floating point evaluations of expressions of average complexity on 16-digits numbers.
There is thus no string pool memory impact at all but one can now hit TeX’s main memory limit (which typically stands at 5,000,000 words) from defining large variables or generating on the fly large data. TeX distributions have a configuration file allowing to enlarge TeX memory parameters and regenerate the (eTeX based) formats.
The package supports input and output of arbitrarily nested
lists, a.k.a. oples or nlists, with
[...] as the constructor of bracketed lists, a.k.a
nut-ples. Operations on these objects (as briefly surveyed in
later items) are inspired from syntax and functionalities of
NumPy’s ndarrays. Our oples (hence also
their packaged form nut-ples) may have leaves at
varying depths rather than obeying an N-dimensional hyperrectangular
shape. But the syntax does provide specific constructors for
ndlists (i.e. hyperrectangular oples or
nut-ples).
In a (distant?) future, perhaps xintexpr itself or a
third-party package will provide an interface, say
\xintstorearray, \xintgetarray, to store
(which can not be expandable) and retrieve (which can be expandable and
thus be embedded inside expressions parsed by \xintexpr,
\xintiiexpr or \xintfloatexpr) such
ndlists from TeX memory. This is why the package does not use
the word ndarray and reserves it for such memory stored
objects.
The * serves as unpacking operator on
nut-ples, i.e. reversing the [] bracketing of an
ople.
oples have no exact equivalent in Python.
For example xintexpr allows foo(Var1, x)
if foo is a function of 4 variables and Var1
is a variable producing a length 3 ople, or
foo(Var2) if Var2 is a variable producing a
length 4 ople. Python would require here to use explicitly the
*-unpacking notation on some “packed” objects.
Variable and function values may be oples (even nil), but in function declarations variables must stand for one-ples, i.e. either numbers or nut-ples (as there is no non-ambiguous way to split e.g. 5 arguments into two separate oples).
Simultaneous assignment to at least two variables via
\xintdefvar et al. automatically unpacks the assigned value
if it is a one-ple. If this value was in fact a
number, low-level errors will result shortly afterwards as no
check is done if the unpacking was illicit. (update: this last remark
does not apply since the 1.4i extension to the concept of
simultaneous assignments)
The NumPy concept and syntax for nested slicing and
item selection are implemented. Currently stepping and the
Ellipsis object are not yet available. Only so-called basic
slicing is currently supported. (The author has not yet read the section
of NumPy documentation on so-called advanced
indexing).
The broadcasting of scalar operations, such as itemwise addition or multiplication of nut-ples of the same shape is not yet implemented.
Slicing and indexing apply also at top level to the
oples with behaviour conforming to intuitive expectations (see
user manual); if it turns out the ople is in fact a
nut-ple, the top-level slicing/indexing switches to the
Python/NumPy conventions, i.e. it operates inside the
brackets for slicing and removes brackets if indexing.
The syntax
ndseq(expression in x, y, ..., x = values; y = values; ...)
constructs a (bracketed) ndlist by evaluation the expression on
all possible Cartesian n-uples, where the first variable indexes the
first axis, the second the next, etc…
The ndmap(foo, values1; values2; ...; valuesN)
syntax constructs a (bracketed) ndlist by evaluating the
function foo on all elements of the cartesian product of
the given (one-dimensional) value lists.
The two concepts of \xintdeffunc (for recursive
definitions) and \xintdefefunc (for functions which expand
immediately in other function declarations) have been merged. The
\xintdefefunc et al. are deprecated and kept as aliases for
\xintdeffunc et al.
\xintdefufunc allows to define so-called
universal functions, i.e. functions foo such that
foo(myople) will apply itemwise at arbitrary depth in the
nested structure. The function foo is allowed to produce
from a scalar an ople…
The variables in function declarations can now be multi-letter words.
The last positional variable in a function declaration can be
prefixed with a * meaning exactly as in Python
(variadic function argument) that it stands for a
one-dimensional nut-ple receiving all remaining arguments from
the function call beyond the first positional ones. It is thus an
optional argument, but syntax for named optional arguments with default
values is not yet implemented.
Dummy variables used in constructors can also be multi-letter words, if they have been declared as such.
In variable and function declarations, if the expression contains inner semi-colons, it is not needed anymore to brace them to avoid mis-interpretation as the final semi-colon which is mandated by the syntax to serve as expression terminator.
subsm(expression, var1 = value1; var2 = value2; ...)
provides a leaner syntax for multiple substitutions; they must be
independent, though.
subsn(expression, var1 = value1; var2 = value2; ...)
provides a leaner syntax for nested substitutions, i.e., each
valueJ may be an expression using the dummy variables
varK with K>J. And finally of course the
evaluated expression can refer to all variables.
\xintthealign\xintexpr...\relax (or with
\xintfloatexpr or \xintiiexpr or
\xintboolexpr…) will use a TeX alignment to display
oples. The output (for regular N-dimensional lists) looks very
similar to what Python/NumPy produces in interactive
session. This is entirely configurable and can also be set-up to be used
for writing into external files.
Attention that \xintthealign only works if followed by
\xintexpr et al., not by \xinteval{}.
It is now possible to use \xintexpr...\relax
directly for typesetting. The syntax \xinteval{...} or
\xintthe\xintexpr...\relax is needed only if one wants the
expansion to give the explicit digits, but
\xintexpr...\relax by itself will typeset as would have the
other ones. Further it can be used in so-called moving arguments,
because when output to an external file it uses only characters with
standard catcodes (and produces the same protected and re-tokenizable
result it would in an \edef.)
As formerly, \xintexpr...\relax is the preferred way to
include an expression into another one. Using \xinteval is
a waste because it forces the outer parser to re-digest all the digits
(or now also the square brackets).
The output format of \xintfloateval with scientific
notation has not changed (apart from possible presence of bracketed
lists), but the author hesitates because the prettifying it
does by default is not really adapted to display of arrays (see
\xintthealign). Anyway, this is configurable by the user.
It is possible to specify whether to use e or
E.
Function declarations are able to parse a much wider part of the syntax, but some severe limitations remain. Refer to the user manual for related information.
We have made an effort on some error messages, and when working interactively in a shell it may even be sometimes possible to insert for example a correct variable or function name in place of the not recognized one. But don’t expect miracles when trying to intervene in the midst of a purely expandable expansion…
Bugs? Those identified in 1.3f were almost features. As
per 1.4 the code base of xintexpr received
multiple successive core refactorings and added numerous new features,
and our test suite although significantly enlarged is not yet extensive
enough. Please report bugs by mail.
The long delayed overhaul of how floating point numbers are
handled is delayed again. It has remained basically identical to its
initial provisory version from 1.07 2013/05/25 (which was
based upon what was originally only a set of expandable macros for
computations with big integers), and suffers from the author lack of
knowledge of the notion of “data type” in modern programming. Indeed, he
never took a CS class, and disables JavaScript in his browser (or allows
only select non-tracking scripts, a rare beast in modern days).
Prior to integrating all of NumPy, it is envisioned
to start with matrix algebra first.
1.3f (2019/09/10)xintfrac: \xintDigits = P; syntax
(i.e. without a colon) is now accepted in addition to
\xintDigits := P;.
Document that the ending semi-colon can not be an active character
and that it has always been allowed to use in its place a non-expanding
token e.g. \xintDigits := 32\relax.
Add \xintSetDigits.
xintexpr: add starred variants
\xintDigits* and \xintSetDigits* which execute
\xintreloadxinttrig.
Revert 1.3e ban on usage of \xinteval et al. inside
expressions by \xintdeffunc. And make them usable also
inside macro definitions via \xintNewExpr.
xintexpr: fix bug preventing usage of
\xintdefefunc to define a function without variables.
Fix some issue with \xintfloatexpr[D]..\relax if used
inside an expression parsed by \xintdeffunc et al.
1.3e (2019/04/05)\xint(float)expr...\relax syntax. One can
not use there the \xint(float)eval wrappers.The xinttrig library is automatically loaded by xintexpr. It provides direct and inverse trigonometrical functions using either degrees or radians with a precision of up to (a bit less than) 60 digits. It is for the most part implemented using high level user interface, but will probably get some optimizations in future (and perhaps extension to more digits).
The xintlog library is automatically loaded by xintexpr. It uses poormanlog to provide logarithms and exponentials with almost 9 digits of precision. Extended precision is for a future release.
xintexpr: \xintdefefunc,
\xintdeffloatefunc, \xintdefiiefunc define
functions which are not protected against expansion in the definition of
other functions; refer to xint.pdf for the related
explanations.
Notice that whole area of \xintdef(e)func,
\xintNewExpr, \xintNewFunction is complex and
to be considered still as work in progress as it has a number of
shortcomings.
xintexpr: inv(),
ilog10(), sfloat(), behaviour of
qfloat() slightly modified.
xintexpr: \xintensuredummy,
\xintrestorelettervar.
The optional argument of \xintfloatexpr or
\xintfloateval (it must be at start of braced argument) can
be negative; it then means to trim (and round) from the output at float
precision that many least significant digits.
1.3d (2019/01/06)xintexpr: the gcd() and
lcm() functions formerly converted their arguments to
integers via \xintNum. They now handle general input with
no such modification.
xintexpr: former \xinteval,
\xintieval, \xintiieval, and
\xintfloateval renamed to \xintexpro,
\xintiexpro, \xintiiexpro, and
\xintfloatexpro.
xintexpr: the gcd() and
lcm() multi-arguments functions have been refactored to
handle general fractions. The dependency on xintgcd is
removed.
xintexpr: three-way branching
\xintifsgnexpr, \xintifsgnfloatexpr,
\xintifsgniiexpr conditional macros.
xintexpr: \xintunassignexprfunc,
\xintunassigniiexprfunc,
\xintunassignfloatexprfunc to “undefine”
functions.
xintexpr: \xintunassignvar really
makes the (multi-letter) variable unknown (formerly, it only gave it
value zero),
xintexpr: functions isone() and
isint().
xintexpr: \xinteval,
\xintieval, \xintiieval, and
\xintfloateval as synonyms to
\xinttheexpr...\relax etc…, but with the (comma-separated)
expression as a usual braced macro argument.
\xintiiexpr was broken for a zero dividend and a one-digit
divisor (e.g. 0//7) since 1.2p due to a bug in
\xintiiDivMod for such arguments. The bug was signaled
(thanks to Kpym for report) and fixed shortly after 1.3c
release but I then completely forgot to upload a bugfix release to CTAN
at that time, apologies for that.1.3c (2018/06/17)xintexpr: with \xintglobaldefstrue,
\xintdefvar, \xintdeffunc,
\xintNewExpr et al. make definitions with global
scope.
xintexpr: qraw() for fast input of
(very many) comma separated numbers (in suitable raw format).
xintexpr: the colon in the := part
of the syntax for \xintdefvar and variants is now optional;
and if present it may be an active character or have any (reasonable)
catcode.
xintexpr: \xintdefvar,
\xintdeffunc and their variants try to set the catcode of
the semi-colon which delimits their arguments; of course this will not
work if that catcode is already frozen.
\xintUniformDeviate is better documented and
sourcexint.pdf is better hyperlinked and includes indices
for the macros defined by each package.
1.3 release, it loaded
xintgcd in contradiction to what the documentation says
(hence also xintexpr loaded xintgcd
automatically). There is no actual dependency so the loading is removed
for now.1.3b (2018/05/18)All additions related to randomness are marked as work-in-progress.
They require an engine providing the \(pdf)uniformdeviate
primitive.
xintkernel:
\xintUniformDeviate.
xint: \xintRandomDigits,
\xintXRandomDigits, \xintiiRandRange,
\xintiiRandRangeAtoB.
xintfrac: support macros (not public, mainly
because internal format for floats is surely not final) for
random() and qrand().
xintexpr: random(),
qrand(), and randrange(A[, B]).
xintexpr: when a function foo() is
declared via \xintdeffunc (et al.) to be parameter-less, it
can be used as foo(); formerly foo(nil) syntax
was required.
The usual provision of user manual “improvements”.
1.3a (2018/03/07)1.2o to add a deprecation mechanism; all deprecated
macros have been removed at 1.3 so there was no reason to
keep the code used for deprecating them.xintexpr: new conditionals ifone()
and ifint().
xintfrac: \xintREZ is faster on
inputs having one hundred digits or more.
Added to the user manual mention of macros such as
\xintDivFloor, \xintMod,
\xintModTrunc, which had been left out so far.
1.3: in particular recursive
definitions became possible. But an oversight made these recursive
functions quite inefficient (to remain polite.) This release fixes the
problem.1.3 (2018/03/01)xintcore, xint,
xintfrac: all macros deprecated at 1.2o
got removed.
xintfrac: addition and subtraction of
a/b and c/d now use the l.c.m. of the
denominators. Similarly the macro supporting the modulo operator
/: uses a l.c.m. for the denominator of the
result.
xintexpr: the addition, subtraction, modulo
/:, and the mod() and divmod()
functions produce generally smaller denominators (see previous
item).
xintexpr: formerly, the internal macros which
are internally associated to user-declared functions were using comma
separated parameter texts. They now do not use such commas (their
meanings, which may again change in future, are written for information
to the log under \xintverbosetrue).
xintexpr: user-defined functions may now be of a
recursive nature. This was made possible by a refactoring of the
\xintNewExpr mechanism. It became both leaner and more
extensive than formerly.
xintfrac: new macros \xintPIrr and
\xintDecToString. The latter is a backport of a
polexpr 0.4 utility, and it is to be considered
unstable.
xintexpr: new function preduce()
associated with \xintPIrr.
1.2q (2018/02/06)3!4!5! or (1+2)3.1.2l
of subtraction left an extra character in an inner macro causing
breakage in some rare circumstances. This should not have escaped our
test suite!1.2p (2017/12/05)xintgcd: \xintBezout{a}{b}’s output
consists of {u}{v}{d} with u*a+v*b==d, with
d the GCD. Formerly it was {a}{b}{u}{v}{d},
and with u*a-v*b==d.
xintgcd: \xintBezout{0}{0} expands
to {0}{0}{0}. Formerly (since 1.2l) it raised
InvalidOperation.
xintcore: \xintiiMod is now
associated with floored division. The former meaning (associated with
truncated division) is available as
\xintiiModTrunc.
xintfrac: \xintMod is now
associated with floored division. The former meaning is available as
\xintModTrunc.
xintexpr: the // operator and its
associated modulo 'mod' (or /:) now correspond
to floored division, like the Python language //,
%, and divmod(x, y). Formerly they had been
associated to truncated division. This is breaking change for operands
of opposite signs.
xinttools: \xintListWithSep, which
had remained unchanged since its introduction at
1.04 (2013/04/25), was rewritten for increased
speed.
xintexpr: \xintdefvar’s syntax is
extended to allow simultaneous assignments. Examples:
\xintdefvar x1, x2, x3 := 1, 3**10, 3**20; or
\xintdefiivar A, B := B, A 'mod' B; for already defined
variables A and B.
xintexpr: added divmod() to the
built-in functions. It is associated with floored division, like the
Python language divmod(). Related support macros added to
xintcore, and xintfrac.
xintgcd: \xintBezout{6}{3} (for
example) expanded to {6}{3}{-0}{-1}{3}, but the
-0 should have been 0.
xintgcd: it still used macro
\xintiAbs although the latter had been deprecated from
xintcore.
xintexpr: in float expressions the
// and /: (aka 'mod') operators
did not round their operands to the float precision prior to computing
with them, contrarily to other infix arithmetic operators and to the
mod(f,g) function; thus, mod(f,g) and
f 'mod' g were not completely equivalent.
various documentation fixes; in particular, the partial dependency of xintcfrac on xinttools had not been mentioned.
1.2o (2017/08/29)\xintAND, \xintOR,
… and similar Boolean logic macros do not apply anymore
\xintNum (or \xintRaw if
xintfrac is loaded), to their arguments (often, from
internal usage of \xintSgn), but only f-expand them (using
e.g. \xintiiSgn). This is kept un-modified even if loading
xintfrac.Deprecated macros raise an error but, generally, then expand as in former releases. They will all get removed at some future release.
xintcore: \xintiOpp,
\xintiAbs, \xintiAdd, \xintiSub,
\xintiMul, \xintiDivision,
\xintiQuo, \xintiRem,
\xintiDivRound, \xintiDivTrunc,
\xintiMod, \xintiSqr, \xintiPow,
and \xintiFac are deprecated. Only the
ii-named variants get defined.
xintcore: \xintCmp and
\xintSgn are deprecated from xintcore
(which only defines \xintiiCmp and \xintiiSgn)
as they actually belong to xintfrac.
xintcore: \xintiiFDg, resp.
\xintiiLDg, are renamed \xintFDg, resp.
\xintLDg. Former denominations are deprecated.
xint: \xintMON,
\xintMMON, \xintiMax, \xintiMin,
\xintiMaxof, \xintiMinof,
\xintiSquareRoot, \xintiSqrt,
\xintiSqrtR, \xintiBinomial, and
\xintiPFactorial are deprecated. Only ii-named
variants get defined.
xint: \xintEq,
\xintGeq, \xintGt, \xintLt,
\xintGtorEq, \xintLtorEq,
\xintIsZero, \xintIsNotZero,
\xintIsOne, \xintOdd, \xintEven,
\xintifSgn, \xintifCmp,
\xintifEq, \xintifGt, \xintifLt,
\xintifZero, \xintifNotZero,
\xintifOne, \xintifOdd, are deprecated. These
macros belong to xintfrac. Package
xint defines only the ii-named
variants.
xint: \xintNeq was renamed to
\xintNotEq which however is only provided by
xintfrac. Package xint defines
\xintiiNotEq, and \xintNeq is
deprecated.
xint: \xintNot was renamed to
\xintNOT, former denomination is deprecated. See also item
about Boolean logic macros in the Incompatible Changes
section.
1.2n (2017/08/06)xintbinhex has only xintkernel as dependency.
Macros of xintbinhex have been improved for speed and increased maximal sizes of allowable inputs.
1.2m (2017/07/31)xintbinhex: the length of the input is now
limited. The maximum size depends on the macro and ranges from about
4000 to about 19900 digits.
xintbinhex: \xintCHexToBin is now
the variant of \xintHexToBin which does not remove leading
binary zeroes: N hex-digits give on output exactly
4N binary digits.
1.08 of 2013/06/07.) The new macros are faster
but limited to a few thousand digits. The 1.08 routines
could handle tens of thousands of digits, but not in a reasonable
time.user manual: the Changes section wrongly stated at
1.2l that the macros of xintbinhex had
been made robust against non terminated input such as
\number\mathcode`\-. Unfortunately the author fell into the
trap of believing his own documentation and he forgot to actually
implement the change. Now done.
user manual: the PDF bookmarks were messed up.
xint, xintfrac:
\xintGeq, \xintMax, \xintMin,
suffered from some extra overhead. This was caused by use of some
auxiliaries from the very early days which got redefined at some stage.
This is fixed here with some additional efficiency improvements and
pruning of old code.
1.2l (2017/07/26)\xintiiSumExpr, \xintiiPrdExpr
(xint) and \xintSumExpr,
\xintPrdExpr (xintfrac). They had not been
formally deprecated, but had been left un-documented since
1.09d (2013/10/22).
internal macro \xint_gob_til_xint_relax
removed.
the underscore character _ is accepted by the
xintexpr parsers as a digit separator (the space
character already could be used for improved readability of big
numbers). It is not allowed as first character of a number, as
it would then be mis-interpreted as the start of a possible variable
name.
some refactoring in xintcore auxiliary routines
and in \xintiiSub and \xintiiCmp for some
small efficiency gains.
code comments in xintcore are better formatted, but remain sparse.
xintcore, xint,
xintfrac, … : some macros were not robust against
arguments whose expansion looks forward for some termination
(e.g. \number\mathcode`\-), and particularly, most were
fragile against inputs using non-terminated \numexpr (such
as \xintiiAdd{\the\numexpr1}{2} or
\xintRaw{\numexpr1}). This was not a bug per se, as the
user manual did not claim such inputs were legal, but it was slightly
inconvenient. Most macros (particularly those of
xintfrac) have now been made robust against such
inputs. Some macros from xintcore primarily destined to
internal usage still accept only properly terminated arguments such as
\the\mathcode`\-<space> or
\the\numexpr1\relax.
The situation with expressions is unchanged: syntax such as
\xintexpr \numexpr1+2\relax is illegal as the ending
\relax token will get swallowed by the
\numexpr; but it is needed by the
xintexpr-ession parser, hence the parser will expand
forward and presumably end with in an “illegal token” error, or provoke
some low-level TeX error (N.B.: a closing brace } for
example can not terminate an xintexpr-ession, the parser
must find a \relax token at some point). Thus there must be
in this example a second \relax.
experimental code for error conditions; there is no complete user interface yet, it is done in preparation for next major release and is completely unstable and undocumented.
xintbinhex: since 1.2 (2015/10/10),
\xintHexToDec was broken due to an undefined macro (it was
in xint.sty, but the module by itself is supposedly
dependent only upon xintcore.sty).
xintgcd: macro \xintBezout produced
partially wrong output if one of its two arguments was zero.
xintfrac: the manual said one could use directly
\numexpr compatible expressions in arithmetic macros
(without even a \numexpr encapsulation) if they were
expressed with up to 8 tokens. There was a bug if these 8 tokens
evaluated to zero. The bug has been fixed, and up to 9 tokens are now
accepted. But it is simpler to use \the\numexpr prefix and
not to worry about the token count… The ending \relax is
now un-needed.
1.2k (2017/01/06)macro \xintFloat which rounds its input to a
floating point number does not print anymore
10.0...0eN to signal an upwards rounding to the next power
of ten. The mantissa has in all cases except the zero input exactly one
digit before the decimal mark.
some floating point computations may differ in the least significant digits, due to a change in the rounding algorithm applied to macro arguments expressed as fractions and to an improvement in precision regarding half-integer powers in expressions. See next.
the initial rounding to the target precision P which
is applied by the floating point macros from xintfrac
to their arguments achieves the exact (aka correct) rounding
even for inputs which are fractions with more than P+2
digits in their numerators and denominators (>1.) Hence
the computed values depend only on the arguments as rational numbers and
not upon their representatives. This is not relevant to
expressions (xintexpr), because the
\xintfloatexpr parser sees there / as an
operator and does not (apart from special constructs) get to manipulate
fractions as such.
\xintnewdummy is public interface to a
1.2e macro which serves to declare any given catcode 11
character as a dummy variable for expressions
(xintexpr). This is useful for Unicode engines (the
Latin letters being already all pre-declared as dummy
variables.)
added \xintiSqrtR, there was only
\xintiiSqrtR alongside \xintiSqrt and
\xintiiSqrt (xint).
added non public \xintLastItem:f:csv to
xinttools for faster last() function, and
improved \xintNewExpr compatibility. Also
\xintFirstItem:f:csv.
the 1.2f half-integer powers computed within
\xintfloatexpr had a silly rounding to the target precision
just before the final square-root extraction, thus possibly
losing some precision. The 1.2k implementation keeps guard
digits for this final square root extraction. As for integer exponents,
it is guaranteed that the computed value differs from the exact one by
less than 0.52 ulp (for inputs having at most
\xinttheDigits digits.)
more regressions from 1.2i were fixed:
\xintLen (xint, xintfrac)
and \xintDouble (xintcore) had forgotten
that their argument was allowed to be negative. A regression test suite
is now in place and is being slowly expanded to cover more
macros.
\xintiiSquareRoot{0} now produces
{1}{1}, which fits better the general documented behaviour
of this macro than 11.
1.2j (2016/12/22)xinttools and xintexpr:
slightly improves the speed of \xintTrim.
speed gains for the handlers of comma separated lists
implementing Python-like slicing and item extraction. Relevant non
(user) documented macros better documented in
sourcexint.pdf.
significant documentations tweaks (inclusive of suppressing things!), and among them two beautiful hyperlinked tables with both horizontal and vertical rules which bring the documentation of the xintexpr syntax to a kind of awe-inspiring perfection… except that implementation of some math functions is still lacking.
1.2i regressions caused by undefined macros
(\xintNthElt in certain branches and [list][N]
item extraction in certain cases.) The test files existed but were not
executed prior to release. Automation in progress.1.2i (2016/12/13)\xintDecSplit second argument must have no sign (former
code replaced it with its absolute value, a sign now may cause an
error.)\xintifTrue,
\xintifTrueFalse, \xintQuo,
\xintRem, \xintquo,
\xintrem.xintkernel: \xintLength is faster.
New macros:
\xintLastItem to fetch the last item from its
argument,
\romannumeral\xintgobble for gobbling many (up to
531440) upstream braced items or tokens.
\romannumeral\xintreplicate which is copied over
from the expl3 \prg_replicate:nn with some minor
changes.
xinttools: general token list handling routines
\xintKeep, \xintTrim and
\xintNthElt are faster; but the novel
\xintTrim can only remove up to a maximum of 531440
items.
Also, \xintFor partially improves on some issues which
are reported upon in the documentation.
some old macros have been rewritten entirely or partially using
techniques which xint started using in release
1.2:
xintcore: \xintDouble,
\xintHalf, \xintInc, \xintDec,
\xintiiLDg, \xintDSR (originally from
xint), a novel \xintDSRr.
xint: \xintDSH,
\xintDSx, \xintDecSplit,
\xintiiE.
xintfrac: as a result of the above
\xintTrunc, \xintRound and
\xintXTrunc got faster. But the main improvement for them
is with decimal inputs which formerly had not been treated separately
from the general fraction case. Also, \xintXTrunc does not
anymore create a dependency of xintfrac on
xinttools.
the documentation has again been (slightly) re-organized; it has
a new sub-section on the Miller-Rabin primality test, to illustrate some
use of \xintNewFunction for recursive definitions.
the documentation has dropped the LaTeX “command” terminology
(which had been used initially in 2013 for some forgotten reasons and
should have been removed long ago) and uses only the more apt “macro”,
as after all, all of xint is about expansion of macros
(plus the use of \numexpr).
\xintDecSplitL and \xintDecSplitR from
xint produced their output in a spurious brace pair
(bug introduced in 1.2f).1.2h (2016/11/20)new macro \xintNewFunction in
xintexpr which allows to extend the parser syntax with
functions in situations where \xintdeffunc is not usable
(typically, because dummy variables are used over a not yet determined
range of values because it depends on the variables).
after three years of strict obedience to xint
prefix, now \thexintexpr, \thexintiexpr,
\thexintfloatexpr, and \thexintiiexpr are
provided as synonyms to \xinttheexpr, etc…
the (cond)?{foo}{bar} operator from
xintexpr mis-behaved in certain circumstances (such as
an empty foo).
the xintexpr 1.2f
binomial function (which uses \xintiiBinomial
from xint.sty or \xintFloatBinomial from
xintfrac.sty) deliberately raised an error for
binomial(x,y) with y<0 or
x<y. This was unfortunate, and it now simply evaluates
to zero in such cases.
similarly the pfactorial function was very strict
and pfactorial(x,y) deliberately raised an out-of-range
error if not used with non-negative integers with x less
than y. It now avoids doing that and allows negative
arguments.
the add and mul from
xintexpr, which work with dummy variables since
1.1, raised an error since 1.2c 2015/11/16
when the dummy variable was given an empty range (or list) of values,
rather than producing respectively 0 and 1 as
formerly.
1.2g (2016/03/19)inside expressions, list item selector [L][n] counts
starting at zero, not at one. This is more coherent with
[L][a:b] which was already exactly like in Python since its
introduction. A function len(L) replaces earlier
[L][0].
former iter keyword now called iterr.
Indeed it matched with rrseq, the new iter
(which was somehow missing from 1.1) is the one matching
rseq. Allows to iterate more easily with a “list”
variable.
in xintexpr.sty: list selectors
[L][n] and [L][a:b] are more efficient: the
earlier 1.1 routines did back and forth conversions from
comma separated values to braced tokens, the 1.2g routines
use macros from xinttools.sty handling directly the
encountered lists of comma separated values.
in xinttools.sty: slight improvements in the
efficiency of the \xintNthElt, \xintKeep,
\xintTrim routines and new routines handling directly comma
separated values. The latter are not included in the user manual (they
are not \long, they don’t make efforts to preserve some
braces, do not worry about spaces, all those worries being irrelevant to
the use in expressions for list selectors).
a slight speed improvement to \xintFloatSqrt in its
quest of correct rounding.
float multiplication and division handle more swiftly operands (non-fractional) with few digits, when the float precision is large.
the syntax of expressions is described in a devoted chapter of
the documentation; an example shows how to implement (expandably) the
Brent-Salamin algorithm for computation of Pi using iter in
a float expression.
1.2f (2016/03/12)\xintFac macro but
\xintiFac/\xintiiFac/\xintFloatFac.functions binomial, pfactorial and
factorial in both integer and float versions.
macros \xintiiBinomial,
\xintiiPFactorial (xint.sty) and
\xintFloatBinomial, \xintFloatPFactorial
(xintfrac.sty). Improvements to
\xintFloatFac.
faster implementation and increased accuracy of float power macros. Half-integer exponents are now accepted inside float expressions.
faster implementation of both integral and float square root macros.
the float square root achieves correct (aka exact) rounding in arbitrary precision.
modified behaviour for the \xintPFloat macro, used
by \xintthefloatexpr to prettify its output. It now opts
for decimal notation if and only if scientific notation would use an
exponent between -5 and 5 inclusive. The zero
value is printed 0. with a dot.
the float macros for addition, subtraction, multiplication, division now first round their two operands to P, not P+2, significant places before doing the actual computation (P being the target precision). The same applies to the power macros and to the square root macro.
the documentation offers a more precise (and accurate) discussion of floating point issues.
various under-the-hood code improvements; the floatexpr operations are chained in a faster way, from skipping some unneeded parsing on results of earlier computations. The absence of a real inner data structure for floats (incorporating their precisions, for one) is however still a bit hair raising: currently the lengths of the mantissas of the operands are computed again by each float macro or expression operation.
(TeXperts only) the macros defined (internally) from
\xintdeffunc et al. constructs do not incorporate an
initial \romannumeral anymore.
renewed desperate efforts at improving the documentation by random shuffling of sections and well thought additions; cuts were considered and even performed.
squaring macro \xintSqr from
xintfrac.sty was broken due to a misspelled sub-macro
name. Dates back to 1.1 release of 2014/10/28
:-((.
1.2c’s fix to the subtraction bug from
1.2 introduced another bug, which in some cases could
create leading zeroes in the output, or even worse. This could
invalidate other routines using subtractions, like
\xintiiSquareRoot.
the comparison operators were not recognized by
\xintNewIIExpr and \xintdefiifunc
constructs.
1.2e (2015/11/22)macro \xintunassignvar.
slight modifications of the logged messages in case of
\xintverbosetrue.
a space in
\xintdeffunc f(x)<space>:= expression ; is now
accepted.
documentation enhancements: the Quick Sort section with its included code samples has been entirely re-written; the Commands of the xintexpr package section has been extended and reviewed entirely.
in xintfrac: the \xintFloatFac from
release 1.2 parsed its argument only through
\numexpr but it should have used
\xintNum.
in xintexpr: release 1.2d had
broken the recognition of sub-expressions immediately after variable
names (with tacit multiplication).
in xintexpr: contrarily to what
1.2d documentation said, tacit multiplication was not yet
always done with enhanced precedence. Now yes.
1.2d (2015/11/18)the function definitions done by \xintdeffunc et
al., as well as the macro declarations by \xintNewExpr et
al. now have only local scope.
tacit multiplication applies to more cases, for example (x+y)z, and always ties more than standard * infix operator, e.g. x/2y is like x/(2*y).
some documentation enhancements, particularly in the chapter on xintexpr.sty, and also in the code source comments.
1.2c had
inadvertently broken the \xintiiDivRound macro.1.2c (2015/11/16)macros \xintdeffunc, \xintdefiifunc,
\xintdeffloatfunc and boolean
\ifxintverbose.
on-going code improvements and documentation enhancements, but stopped in order to issue this bugfix release.
1.2
introduced a bug in the subtraction (happened when 00000001 was found
under certain circumstances at certain mod 8 locations).1.2b (2015/10/29)1.2
introduced a bug in the division macros, causing a crash when the
divisor started with 99999999 (it was attempted to use with 1+99999999 a
subroutine expecting only 8-digits numbers).1.2a (2015/10/19)added \xintKeepUnbraced,
\xintTrimUnbraced (xinttools) and fixed
documentation of \xintKeep and \xintTrim
regarding brace stripping.
added \xintiiMaxof/\xintiiMinof
(xint).
TeX hackers only: replaced all code uses of
\romannumeral-`0 by the quicker
\romannumeral`&&@ (^ being used as
letter, had to find another character usable with catcode 7).
1.2
introduced a bad bug in the parsing of decimal numbers and as a result
\xinttheexpr 0.01\relax expanded to 0 !
(sigh…)1.2 (2015/10/10)\xintAdd, \xintSub,
\xintMul, \xintMax, \xintMin,
\xintMaxof, \xintMinof are removed from
package xint, and only exist in the versions from
xintfrac. With only xintcore or
xint loaded, one must use
\xintiiAdd, \xintiiSub, …, or
\xintiAdd, \xintiSub, etc…the basic arithmetic implemented in xintcore has
been entirely rewritten. The mathematics remains the elementary school
one, but the TeX implementation achieves higher speed
(except, regarding addition/subtraction, for numbers up to about thirty
digits), the gains becoming quite significant for numbers with hundreds
of digits.
the inputs must have less than 19959 digits. But computations with thousands of digits take time.
a previously standing limitation of \xintexpr,
\xintiiexpr, and of \xintfloatexpr to numbers
of less than 5000 digits has been lifted.
a qint function is provided to help the parser gather huge integers in one-go, as an exception to its normal mode of operation which expands token by token.
\xintFloatFac macro for computing the factorials of
integers as floating point numbers to a given precision. The
! postfix operator inside \xintfloatexpr maps
to this new macro rather than to the exact factorial as used by
\xintexpr and \xintiiexpr.
there is more flexibility in the parsing done by the macros from
xintfrac on fractional input: the decimal parts of both
the numerator and the denominator may arise from a separate expansion
via \romannumeral-`0. Also the strict A/B[N]
format is a bit relaxed: N may be anything understood by
\numexpr (it could even be empty but that possibility has
been removed by later 1.2f release.)
on the other hand an isolated dot . is not legal
syntax anymore inside the expression parsers: there must be digits
either before or after. It remains legal input for the macros of
xintfrac.
added \ht, \dp, \wd,
\fontcharht, etc… to the tokens recognized by the parsers
and expanded by \number.
an obscure bug in package xintkernel has been
fixed, regarding the sanitization of catcodes: under certain
circumstances (which could not occur in a normal LaTeX
context), unusual catcodes could end up being propagated to the external
world.
an effort at randomly shuffling around various pieces of the documentation has been done.
1.1c (2015/09/12)bugfix regarding macro \xintAssign from
xinttools which did not behave correctly in some
circumstances (if there was a space before \to, in
particular).
very minor code improvements, and correction of some issues
regarding the source code formatting in sourcexint.pdf, and
minor issues in Makefile.mk.
1.1b (2015/08/31)bugfix: some macros needed by the integer division routine from
xintcore had been left in xint.sty
since release 1.1. This for example broke the
\xintGCD from xintgcd if package
xint was not loaded.
Slight enhancements to the documentation, particularly in the
Read this first section.
1.1a (2014/11/07)fixed a bug which prevented \xintNewExpr from
producing correctly working macros from a comma separated replacement
text.
\xintiiSqrtR for rounded integer square root; former
\xintiiSqrt already produced truncated integer square root;
corresponding function sqrtr added to
\xintiiexpr..\relax syntax.
use of straight quotes in the documentation for better legibility.
added \xintiiIsOne, \xintiiifOne,
\xintiiifCmp, \xintiiifEq,
\xintiiifGt, \xintiiifLt,
\xintiiifOdd, \xintiiCmp,
\xintiiEq, \xintiiGt, \xintiiLt,
\xintiiLtorEq, \xintiiGtorEq,
\xintiiNeq, mainly for efficiency of
\xintiiexpr.
for the same reason, added \xintiiGCD and
\xintiiLCM.
added the previously mentioned ii macros, and some
others from 1.1, to the user manual. But their main usage
is internal to \xintiiexpr, to skip unnecessary
overheads.
various typographical fixes throughout the documentation, and a
bit of clean up of the code comments. Improved \Factors
example of nested subs, rseq,
iter in \xintiiexpr.
1.1 (2014/10/28)in \xintiiexpr, / does rounded
division, rather than the Euclidean division (for positive arguments,
this is truncated division). The // operator does truncated
division,
the : operator for three-way branching is gone,
replaced with ??,
1e(3+5) is now illegal. The number parser identifies
e and E in the same way it does for the
decimal mark, earlier versions treated e as E
rather as infix operators of highest precedence,
the add and mul have a new syntax, old
syntax is with `+` and `*` (left quotes
mandatory), sum and prd are gone,
no more special treatment for encountered brace pairs
{..} by the number scanner, a/b[N] notation
can be used without use of braces (the N will end up as is
in a \numexpr, it is not parsed by the
\xintexpr-ession scanner),
in earlier releases, place holders for \xintNewExpr
could either be denoted #1, #2, … or also
$1, $2, … Only the usual # form
is now accepted and the special cases previously treated via the second
form are now managed via a protect(...) function.
xintfrac: \xintFloor and
\xintCeil add a trailing /1[0] to their
(integer) output. New \xintiFloor and
\xintiCeil do not.
\xintnumexpr, \xintthenumexpr,
\xintNewNumExpr: use \xintiexpr,
\xinttheiexpr, \xintNewIExpr.\xintDivision, \xintQuo,
\xintRem: use \xintiDivision,
\xintiQuo, \xintiRem.
\xintMax, \xintMin,
\xintAdd, \xintSub, \xintMul
(xint): their usage without xintfrac
is deprecated; use \xintiMax, \xintiMin,
\xintiAdd, \xintiSub,
\xintiMul.
the & and | as Boolean operators in
xintexpr-essions are deprecated in favour of
&& and ||. The single letter operators
might be assigned some other meaning in some later release (bitwise
operations, perhaps). Do not use them.
new package xintcore has been split off xint. It contains the core arithmetic macros (it is loaded by LaTeX package bnumexpr),
neither xint nor xintfrac load xinttools. Only xintexpr does,
whenever some portion of code has been revised, often use has
been made of the \xint_dothis and \xint_orthat
pair of macros for expandably branching,
these tiny helpful macros, and a few others are in package xintkernel which contains also the catcode and loading order management code, initially inspired by code found in Heiko Oberdiek’s packages,
the source code, which was suppressed from xint.pdf
in release 1.09n, is now compiled into a separate file
sourcexint.pdf,
faster handling by \xintAdd, \xintSub,
\xintMul, … of the case where one of the arguments is
zero,
the \xintAdd and \xintSub macros from
package xintfrac check if one of the denominators is a
multiple of the other, and only if this is not the case do they multiply
the denominators. But systematic reduction would be too costly,
this naturally will be also the case for the + and
- operations in \xintexpr,
xint added \xintiiDivRound,
\xintiiDivTrunc, \xintiiMod for rounded and
truncated division of big integers (next to \xintiiQuo and
\xintiiRem),
with xintfrac loaded, the \xintNum
macro does \xintTTrunc (which is truncation to an integer,
same as \xintiTrunc {0}),
added \xintMod to xintfrac for
modulo operation with fractional numbers,
added \xintiFloor and \xintiCeil to
xintfrac,
\xintiexpr, \xinttheiexpr admit an
optional argument within brackets [d], they round the
computation result (or results, if comma separated) to d
digits after decimal mark, (the whole computation is done exactly, as in
xintexpr),
\xintfloatexpr, \xintthefloatexpr
similarly admit an optional argument which serves to keep only
d digits of precision, getting rid of cumulated
uncertainties in the last digits (the whole computation is done
according to the precision set via \xintDigits),
\xinttheexpr and \xintthefloatexpr
pretty-print if possible, the former removing unit denominator
or [0] brackets, the latter avoiding scientific notation if
decimal notation is practical,
the // does truncated division and /:
is the associated modulo,
multi-character operators &&,
||, ==, <=,
>=, !=, **,
multi-letter infix binary words 'and',
'or', 'xor', 'mod' (straight
quotes mandatory),
functions even, odd,
\xintdefvar A3:=3.1415; for variable definitions
(non expandable, naturally), usable in subsequent expressions; variable
names may contain letters, digits, underscores. They should not start
with a digit, the @ is reserved, and single lowercase and
uppercase Latin letters are predefined to work as dummy variables (see
next),
generation of comma separated lists a..b,
a..[d]..b,
Python syntax-like list extractors [list][n:],
[list][:n], [list][a:b] allowing negative
indices, but no optional step argument, and [list][n]
(n=0 for the number of items in the list),
functions first, last,
reversed,
itemwise operations on comma separated lists
a*[list], etc.., possible on both sides
a*[list]^b, and obeying the same precedence rules as with
numbers,
add and mul must use a dummy variable:
add(x(x+1)(x-1), x=-10..10),
variable substitutions with subs:
subs(subs(add(x^2+y^2,x=1..y),y=t),t=20),
sequence generation using seq with a dummy variable:
seq(x^3, x=-10..10),
simple recursive lists with rseq, with
@ given the last value,
rseq(1;2@+1,i=1..10),
higher recursion with rrseq, @1,
@2, @3, @4, and
@@(n) for earlier values, up to n=K where
K is the number of terms of the initial stretch
rrseq(0,1;@1+@2,i=2..100),
iteration with iter which is like rrseq
but outputs only the last K terms, where K was
the number of initial terms,
inside seq, rseq, rrseq,
iter, possibility to use omit,
abort and break to control
termination,
n++ potentially infinite index generation for
seq, rseq, rrseq, and
iter, it is advised to use abort or
break(..) at some point,
the add, mul, seq, … are
nestable,
\xintthecoords converts a comma separated list of an
even number of items to the format expected by the TikZ
coordinates syntax,
completely new version \xintNewExpr,
protect function to handle external macros. The dollar sign
$ for place holders is not accepted anymore, only the
standard macro parameter #. Not all constructs are
compatible with \xintNewExpr.
\xintZapFirstSpaces hence also
\xintZapSpaces from package xinttools were
buggy when used with an argument either empty or containing only space
tokens.
\xintiiexpr did not strip leading zeroes, hence
\xinttheiiexpr 001+1\relax did not obtain the expected
result …
\xinttheexpr \xintiexpr 1.23\relax\relax should have
produced 1, but it produced 1.23
the catcode of ; was not set at package launching
time.
the \XINTinFloatPrd:csv macro name had a typo, hence
prd was non-functional in
\xintfloatexpr.
1.09n (2014/04/01)the user manual does not include by default the source code
anymore: the \NoSourceCode toggle in file
xint.tex has to be set to 0 before compilation to get
source code inclusion (later release 1.1 made source code
available as sourcexint.pdf).
bug fix (xinttools) in
\XINT_nthelt_finish (this bug was introduced in
1.09i of 2013/12/18 and showed up when the
index N was larger than the number of elements of the
list).
1.09m (2014/02/26)new in xinttools: \xintKeep keeps
the first N or last N elements of a list
(sequence of braced items); \xintTrim cuts out either the
first N or the last N elements from a
list.
new in xintcfrac: \xintFGtoC finds
the initial partial quotients common to two numbers or fractions
f and g; \xintGGCFrac is a clone
of \xintGCFrac which however does not assume that the
coefficients of the generalized continued fraction are numeric
quantities. Some other minor changes.
1.09kb (2014/02/13)bug fix (xintexpr): an aloof modification done
by 1.09i to \xintNewExpr had resulted in a
spurious trailing space present in the outputs of all macros created by
\xintNewExpr, making nesting of such macros
impossible.
bug fix (xinttools): \xintBreakFor
and \xintBreakForAndDo were buggy when used in the last
iteration of an \xintFor loop.
bug fix (xinttools): \xintSeq from
1.09k needed a \chardef which was missing from
xinttools.sty, it was in xint.sty.
1.09k (2014/01/21)inside \xintexpr..\relax (and its variants) tacit
multiplication is implied when a number or operand is followed directly
with an opening parenthesis,
the " for denoting (arbitrarily big) hexadecimal
numbers is recognized by \xintexpr and its variants
(package xintbinhex is required); a fractional
hexadecimal part introduced by a dot . is allowed.
re-organization of the first sections of the user manual.
bug fix (xinttools, xint, …):
forgotten catcode check of " at loading time has been
added.
1.09j (2014/01/09)(xint) the core division routines have been re-written for some (limited) efficiency gain, more pronounced for small divisors. As a result the computation of one thousand digits of π is close to three times faster than with earlier releases.
some various other small improvements, particularly in the power routines.
(xintfrac) a macro \xintXTrunc is
designed to produce thousands or even tens of thousands of digits of the
decimal expansion of a fraction. Although completely expandable it has
its use limited to inside an \edef, \write,
\message, . It can thus not be nested as argument to
another package macro.
(xintexpr) the tacit multiplication done in
\xintexpr..\relax on encountering a count register or
variable, or a \numexpr, while scanning a (decimal) number,
is extended to the case of a sub \xintexpr-ession.
\xintexpr can now be used in an \edef
with no \xintthe prefix; it will execute completely the
computation, and the error message about a missing \xintthe
will be inhibited. Previously, in the absence of \xintthe,
expansion could only be a full one (with \romannumeral-`0),
not a complete one (with \edef). Note that this differs
from the behavior of the non-expandable \numexpr:
\the or \number (or
\romannumeral) are needed not only to print but also to
trigger the computation, whereas \xintthe is mandatory only
for the printing step.
the default behavior of \xintAssign is changed, it
now does not do any further expansion beyond the initial full-expansion
which provided the list of items to be assigned to macros.
bug fix (xintfrac): 1.09i did an
unexplainable change to \XINT_infloat_zero which broke the
floating point routines for vanishing operands =:(((
bug fix: the 1.09i xint.ins file
produced a buggy xint.tex file.
1.09i (2013/12/18)(xintexpr) \xintiiexpr is a variant
of \xintexpr which is optimized to deal only with (long)
integers, / does a euclidean quotient.
deprecated: \xintnumexpr,
\xintthenumexpr, \xintNewNumExpr are renamed,
respectively, \xintiexpr, \xinttheiexpr,
\xintNewIExpr. The earlier denominations are kept but are
to be removed at some point.
it is now possible within \xintexpr...\relax and its
variants to use count, dimen, and skip registers or variables without
explicit \the/\number: the parser inserts automatically
\number and a tacit multiplication is implied when a
register or variable immediately follows a number or fraction. Regarding
dimensions and \number, see the further discussion in
Dimensions.
(xintfrac) conditional \xintifOne;
\xintifTrueFalse renamed to \xintifTrueAelseB;
macros \xintTFrac (fractional part, mapped to
function frac in \xintexpr-essions),
\xintFloatE.
(xinttools) \xintAssign admits an
optional argument to specify the expansion type to be used:
[] (none, default), [o] (once),
[oo] (twice), [f] (full), [e]
(\edef),… to define the macros
xinttools defines \odef,
\oodef, \fdef (if the names have already been
assigned, it uses \xintoodef etc…). These tools are
provided for the case one uses the package macros in a non-expandable
context. \oodef expands twice the macro replacement text,
and \fdef applies full expansion. They are useful in
situations where one does not want a full \edef.
\fdef appears to be faster than \oodef in
almost all cases (with less than thousand digits in the result), and
even faster than \edef for expanding the package macros
when the result has a few dozens of digits. \oodef needs
that expansion ends up in thousands of digits to become competitive with
the other two.
some across the board slight efficiency improvement as a result of modifications of various types to fork macros and branching conditionals which are used internally.
bug fix (xint): \xintAND and
\xintOR inserted a space token in some cases and did not
expand as promised in two steps :-(( (bug dating back to
1.09a I think; this bug was without consequences when using
& and | in \xintexpr-essions,
it affected only the macro form).
bug fix (xintcfrac): \xintFtoCCv
still ended fractions with the [0]’s which were supposed to
have been removed since release 1.09b.
deprecated: \xintifTrueFalse,
\xintifTrue; use \xintifTrueAelseB.
1.09h (2013/11/28)parts of the documentation have been re-written or re-organized, particularly the discussion of expansion issues and of input and output formats.
the expansion types of macro arguments are documented in the
margin of the macro descriptions, with conventions mainly taken over
from those in the LaTeX3 documentation.
a dependency of xinttools on
xint (inside \xintSeq) has been
removed.
(xintgcd)
\xintTypesetEuclideAlgorithm and
\xintTypesetBezoutAlgorithm have been slightly modified
(regarding indentation).
(xint) macros xintiSum and
xintiPrd are renamed to \xintiiSum and
\xintiiPrd.
(xinttools) a count register used in
1.09g in the \xintFor loops for parsing
purposes has been removed and replaced by use of a
\numexpr.
the few uses of \loop have been replaced by
\xintloop/\xintiloop.
all macros of xinttools for which it makes sense
are now declared \long.
1.09g (2013/11/22)a package xinttools is detached from
xint, to make tools such as \xintFor,
\xintApplyUnbraced, and \xintiloop available
without the xint overhead.
expandable nestable loops \xintloop and
\xintiloop.
bugfix: \xintFor and \xintFor* do not
modify anymore the value of \count 255.
1.09f (2013/11/04)(xint) \xintZapFirstSpaces,
\xintZapLastSpaces, \xintZapSpaces,
\xintZapSpacesB, for expandably stripping away leading
and/or ending spaces.
\xintCSVtoList by default uses
\xintZapSpacesB to strip away spaces around commas (or at
the start and end of the comma separated list).
also the \xintFor loop will strip out all spaces
around commas and at the start and the end of its list argument; and
similarly for \xintForpair, \xintForthree,
\xintForfour.
\xintFor et al. accept all macro parameters
from #1 to #9.
for reasons of inner coherence some macros previously with one
extra i in their names (e.g. \xintiMON) now
have a doubled ii (\xintiiMON) to indicate
that they skip the overhead of parsing their inputs via
\xintNum. Macros with a single i such
as \xintiAdd are those which maintain the
non-xintfrac output format for big integers, but do
parse their inputs via \xintNum (since release
1.09a). They too may have doubled-i variants
for matters of programming optimization when working only with (big)
integers and not fractions or decimal numbers.
1.09e (2013/10/29)(xint) \xintintegers,
\xintdimensions, \xintrationals for infinite
\xintFor loops, interrupted with \xintBreakFor
and \xintBreakForAndDo.
\xintifForFirst, \xintifForLast for the
\xintFor and \xintFor* loops,
the \xintFor and xintFor* loops are now
\long, the replacement text and the items may contain
explicit \par’s.
conditionals \xintifCmp, \xintifInt,
\xintifOdd.
bug fix (xint): the \xintFor loop
(not \xintFor*) did not correctly detect an empty
list.
bug fix (xint): \xintiSqrt {0}
crashed. :-((
the documentation has been enriched with various additional examples, such as the the quick sort algorithm illustrated or the various ways of computing prime numbers.
the documentation explains with more details various expansion related issues, particularly in relation to conditionals.
1.09d (2013/10/22)bug fix (xint): \xintFor* is
modified to gracefully handle a space token (or more than one) located
at the very end of its list argument (as the space before
\do in
\xintFor* #1 in {{a}{b}{c}<space>} \do {stuff};
spaces at other locations were already harmless). Furthermore this new
version f-expands the un-braced list items. After
\def\x{{1}{2}} and
\def\y{{a}\x {b}{c}\x }, \y will appear to
\xintFor* exactly as if it had been defined as
\def\y{{a}{1}{2}{b}{c}{1}{2}}.
same bug fix for \xintApplyInline.
1.09c (2013/10/09)(xintexpr) added bool and
togl to the \xintexpr syntax; also added
\xintboolexpr and \xintifboolexpr.
added \xintNewNumExpr.
the factorial ! and branching ?,
:, operators (in \xintexpr...\relax) have now
less precedence than a function name located just before,
(xint) \xintFor is a new type of
loop, whose replacement text inserts the comma separated values or list
items via macro parameters, rather than encapsulated in macros; the
loops are nestable up to four levels (nine levels since
1.09f) and their replacement texts are allowed to close
groups as happens with the tabulation in alignments,
\xintForpair, \xintForthree,
\xintForfour are experimental variants of
\xintFor,
\xintApplyInline has been enhanced in order to be
usable for generating rows (partially or completely) in an
alignment,
command \xintSeq to generate (expandably) arithmetic
sequences of (short) integers,
again various improvements and changes in the documentation.
1.09b (2013/10/03)various improvements in the documentation,
more economical catcode management and re-loading handling,
removal of all those [0]’s previously forcefully
added at the end of fractions by various macros of
xintcfrac,
\xintNthElt with a negative index returns from the
tail of the list,
macro \xintPRaw to have something like what
\xintFrac does in math mode; i.e. a \xintRaw
which does not print the denominator if it is one.
1.09a (2013/09/24)(xintexpr) \xintexpr..\relax and
\xintfloatexpr..\relax admit functions in their syntax,
with comma separated values as arguments, among them
reduce, sqr, sqrt, abs, sgn, floor, ceil, quo, rem, round, trunc, float, gcd, lcm, max, min, sum, prd, add, mul, not, all, any, xor.
comparison (<, >, =)
and logical (|, &) operators.
the command \xintthe which converts
\xintexpressions into printable format (like
\the with \numexpr) is more efficient, for
example one can do \xintthe\x if \x was
defined to be an \xintexpr..\relax:
\def\x{\xintexpr 3^57\relax}
\def\y{\xintexpr \x^(-2)\relax}
\def\z{\xintexpr \y-3^-114\relax}
\xintthe\z\xintnumexpr .. \relax (now renamed
\xintiexpr) is
\xintexpr round( .. ) \relax.
\xintNewExpr now works with the standard macro
parameter character #.
both regular \xintexpr-essions and commands defined
by \xintNewExpr will work with comma separated lists of
expressions,
commands \xintFloor, \xintCeil,
\xintMaxof, \xintMinof (package
xintfrac), \xintGCDof,
\xintLCM, \xintLCMof (package
xintgcd), \xintifLt,
\xintifGt, \xintifSgn,
\xintANDof, …
The arithmetic macros from package xint now
filter their operands via \xintNum which means that they
may use directly count registers and \numexpr-essions
without having to prefix them by \the. This is thus similar
to the situation holding previously already when
xintfrac was loaded.
a bug (xintfrac) introduced in
1.08b made \xintCmp crash when one of its
arguments was zero. :-((
1.08b (2013/06/14)(xintexpr) Correction of a problem with spaces
inside \xintexpr-essions.
(xintfrac) Additional improvements to the handling of floating point numbers.
section Use of count registers documenting how count registers may be directly used in arguments to the macros of xintfrac.
1.08a (2013/06/11)(xintfrac) Improved efficiency of the basic
conversion from exact fractions to floating point numbers, with ensuing
speed gains especially for the power function macros
\xintFloatPow and \xintFloatPower,
Better management by \xintCmp,
\xintMax, \xintMin and \xintGeq
of inputs having big powers of ten in them.
Macros for floating point numbers added to the xintseries package.
1.08 (2013/06/07)(xint and xintfrac) Macros for
extraction of square roots, for floating point numbers
(\xintFloatSqrt), and integers
(\xintiSqrt).
new package xintbinhex providing conversion routines to and from binary and hexadecimal bases.
1.07 (2013/05/25)The xintexpr package is a new core constituent (which loads automatically xintfrac and xint) and implements the expandable expanding parser
\xintexpr . . . \relax,and its variant
\xintfloatexpr . . . \relaxallowing on input formulas using the infix operators +,
-, *, /, and ^, and
arbitrary levels of parenthesizing. Within a float expression the
operations are executed according to the current value set by
\xintDigits. Within an \xintexpr-ession the
binary operators are computed exactly.
To write the \xintexpr parser I benefited from the
commented source of the l3fp parser; the
\xintexpr parser has its own features and peculiarities.
See its documentation.
The floating point precision D is set (this is a
local assignment to a \mathchar variable) with
\xintDigits := D; and queried with
\xinttheDigits. It may be set to anything up to
32767.1 The macro incarnations of the binary
operations admit an optional argument which will replace pointwise
D; this argument may exceed the 32767
bound.
The xintfrac macros now accept numbers written
in scientific notation, the \xintFloat command serves to
output its argument with a given number D of significant
figures. The value of D is either given as optional
argument to \xintFloat or set with
\xintDigits := D;. The default value is
16.
1.06b (2013/05/14)1.06 (2013/05/07)Some code improvements, particularly for macros of xint doing loops.
New utilities in xint for expandable manipulations of lists:
\xintNthElt, \xintCSVtoList, \xintRevWithBracesThe macros did only a double expansion of their arguments. They
now fully expand them (using \romannumeral-`0).
Furthermore, in the case of arguments constrained to obey the TeX bounds
they will be inserted inside a \numexpr..\relax, hence
completely expanded, one may use count registers, even infix arithmetic
operations, etc…
1.05 (2013/05/01)Minor changes and additions to xintfrac and xintcfrac.
1.04 (2013/04/25)New component xintcfrac devoted to continued fractions.
xint: faster division.
xint: added expandable macros
\xintListWithSep and \xintApply to handle
token lists.
xintfrac: added
\xintRound.
xintseries has a new implementation of
\xintPowerSeries based on a Horner scheme, and new macro
\xintRationalSeries. Both to help deal with the
denominator buildup plague.
tex xint.dtx extracts style files (no need for a
xint.ins).
Bug fix (xintfrac): \xintIrr {0}
crashed.
1.03 (2013/04/14)New modules xintfrac (expandable operations on fractions) and xintseries (expandable partial sums with xint package).
Slightly improved division and faster multiplication (the best ordering of the arguments is chosen automatically).
Added illustration of Machin algorithm to the documentation.
1.0 (2013/03/28)Initial announcement:
The xint package implements with expandable TeX macros the basic arithmetic operations of addition, subtraction, multiplication and division, as applied to arbitrarily long numbers represented as chains of digits with an optional minus sign.
The xintgcd package provides implementations of the Euclidean algorithm and of its typesetting.
The packages may be used with Plain and with LaTeX.
but values higher than 100 or 200 will presumably give too slow evaluations.↩︎
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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