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1. a 1 2 b c 1 2 e same bug fix for xintApplyInline 1 09c 2013 10 09 e xintexpr added bool and togl to the xintexpr syntax also added xintboolexpr and xintifboolexpr added xintNewNumExpr now xintNewlIExpr and xintNewBoolExpr 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 new 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 xintNthE1t with a negative index returns from the tail of the list new macro xintPRaw to have something like what xintFrac does
2. a float expression the operations are executed according to the current value of xintDigits Within an xintexpr ession the binary operators are computed exactly To write the xintexpr parser I benefited from the commented source of the 13fp parser the xintexpr parser has its own features and peculiarities See its documentation 11 e 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 The macro incarnations of the binary operations admit an optional argument which will replace pointwise D this argument may exceed the 32767 bound e 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 e Minor code and documentation improvements Everywhere in the source code a more modern underscore has replaced the sign 1 06 2013 05 07 e Some code improvements particularly for macros of xint doing loops e New utilities in xint for expandable manipulations of lists xintNthElt xintCSVtoList xintRevWithBraces e The macros did only a double expansion of their arguments They now fully expand them using romannumeral 0 Furthermore in the case of a
3. 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 lt gt and logical amp 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 3457 relax def y xintexpr x 2 relax def z xintexpr y 34 114 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 10 e new commands xintFloor xintCeil xintMaxof xintMinof package xint frac xintGCDof xintLCM xintLCMof package xintged xintifLt xintifGt xintifSgn xintANDof e 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 previo
4. 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 1 091 did an unexplainable change to KINT_infloat_zero which broke the floating point routines for vanishing operands bug fix the 1 091 xint ins file produced a buggy xint tex file 1 091 2013 12 18 xintexpr xintiiexpr is a variant
5. 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 bug fixes e xintZapFirstSpaces hence also xintZapSpaces from package xinttools were buggy when used with an argument either empty or containing only space tokens e xintiiexpr did not strip leading zeroes hence xinttheiiexpr 001 1 relax did not obtain the expected result e xinttheexpr xintiexpr 1 23 relax relax should have produced 1 but it produced 1 23 e the catcode of was not set at package launching time e the XINTinFloatPrd csv macro name had a typo hence prd was non functional in xintfloatexpr breaking changes e in xintiiexpr does rounded division rather than the Euclidean division for positive arguments this is truncated division The new operator does truncated division e 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
6. 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 although amp and are still available as Boolean operators the use of amp amp and is strongly recommended The single letter operators might be assigned some other meaning in later releases bitwise operations perhaps Do not use them 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 novelties e new package xintcore has been split off xint It contains the core arithmetic macros It is loaded by package bnumexpr e 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 xint
7. of xintexpr which is optimized to deal only with long integers does a euclidean quotient xintnumexpr xintthenumexpr xintNewNumExpr are renamed respectively xintiexpr xinttheiexpr xintNewIExpr The earlier denominations are kept but 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 e xintfrac new conditional xintifOne xintifTrueFalse renamed to xintifTrueAelseB new 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 Le 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 d
8. used xintNum e bugfix in xintexpr release 1 2d had broken the recognition of sub expressions immediately after variable names with tacit multiplication new macro xintunassignvar slight modifications of the logged messages in case of xintverbosetrue a space in xintdeffunc f x lt space gt expression is now accepted contrarily to what 1 2d documentation said tacit multiplication was not yet always done with enhanced precedence Now yes e 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 1 2d 2015 11 18 bugfix in xintcore release 1 2c had inadvertently broken the xintiiDivRound macro 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 2015 11 16 e bugfix in xintcore recent release 1 2 introduced a bug in the subtraction happened when 00000001 was found under certain circumstances at certain mod 8 locations e new macros xintdeffunc xintdefiifunc xintdeffloatfunc and boolean ifxintverbose e on going
9. CHANGE LOG xint v1 2e 2015 11 22 tse 2005 11 22 cs wes hws p 1 1 09g 2013 11 22 p 8 1 24 2005 11 18 6 ec s h wes p2 4 096 2013 11 04 gt cada p 9 26 COIS IG cedok etei p2 109e 2013 10 29 os soeren p 9 1 2b 2015 10 29 p 2 1 09d 2013 10 22 p 9 1 20 2015 10 19 lt s s he wks p2 1 09c 2013 10 09 2 scranu p 9 12 2015 10 10 si s snac a p 2 1 00 2013 10 03 cu oS p 10 1 1c 2015 09 12 p 3 1 09a 2013 09 24 p 10 1 1b 2015 08 31 nw oaoa p 3 1 08b 2013 06 14 p 11 tla GOMsTOT sedo ie ee po 1 08a 2013 06 11 o p 11 1 1 2014 10 28 2c ce eae p 4 1 08 2013 06 07 p 11 1 09n 2014 04 01 p6 1 07 2013 05 25 6 kw eas p 11 1 09m 2014 02 26 p 6 1 06b 2013 05 14 p 12 1 09kb 2014 02 13 p 6 1 06 2013 05 07 p 12 1 09k 2014 01 21 p 7 1 05 2013 05 01 gn eh 8 p 12 1 09 2014 01 09 pT 1 04 2013 04 25 6 che ss p 12 1 091 2013 12 18 p 7 1 03 2013 04 14 p 12 1 09 2013 11 28 eu ks pS 4 0 2013 03 28 4 ch wee a p 13 Source xint dtx v1 2e 2015 11 22 doc 2015 11 22 Author Jean Francois Burnol Info Expandable operations on big integers decimals fractions License LPPL 1 3c 1 2e 2015 11 22 e bugfix in xintfrac the xintFloatFac from release 1 2 parsed its argument only through numexpr but it should have
10. 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 e xint new xintintegers xintdimensions xintrationals for infinite xintFor loops interrupted with xintBreakFor and xintBreakForAndDo new 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 new 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 e 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 lt space gt do stuff spaces at other locations were already harmless Fur thermore 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
11. binary words and or xor mod straight quotes mandatory functions even odd xintdefvar A3 3 1415 for variable definitions non expandable naturally usable in sub sequent 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 1 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 r
12. code improvements and documentation enhancements but stopped in order to issue this bugfix release 1 2b 2015 10 29 e bugfix in xintcore recent release 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 bugfix in xintexpr recent release 1 2 introduced a bad bug in the parsing of decimal numbers and as a result xinttheexpr 0 01 relax expanded to 0 sigh 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 amp amp being used as letter had to find another character usable with catcode 7 1 2 2015 10 10 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 num bers of less than 5000 digits has been lift
13. ed 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 new 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 the macros xintAdd xintSub now require package xintfrac With only xintcore or xint loaded one must use xintiiAdd xintiiSub or xintiAdd xintiSub etc 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 empty or anything understood by numexpr 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 shu
14. ffling around various pieces of the documentation has been done 1 1c 2015 09 12 e bugfix regarding macro xintAssign from xinttools which did not behave correctly in some circumstances if there was a space before to in particular e 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 e 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 xintged if package xint was not loaded e Slight enhancements to the documentation particularly in the Read this first section 1 1la 2014 11 07 e fixed a bug which prevented xintNewExpr from producing correctly working macros from a comma separated replacement text e new 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 v1 1 to the user
15. frac 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 new macros xintiiDivRound xintiiDivTrunc and xintiiMod for rounded and truncated division of big integers now in xintcore alongside the earlier xintiiQuo and xintiiRem with xintfrac loaded the xintNum macro does xintTTrunc which is truncation to an integer same as xintiTrunc 0 new macro xintMod in xintfrac for modulo operation with fractional numbers 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 de nominator 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 amp amp lt gt multi letter infix
16. igits 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 amp 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 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 xintged 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 xin
17. implementations of the Euclidean algorithm and of its type setting The packages may be used with Plain and with LaTeX 13
18. lized continued fraction are numeric quantities Some other minor changes 1 09kb 2014 02 13 e bug fix xintexpr an aloof modification done by 1 091 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 e bug fix xinttools xintBreakFor and xintBreakForAndDo were buggy when used in the last iteration of an xintFor loop e 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 x is close to three times faster than with earlier releases some various other small improvements particularly in the power routines xintfrac a new macro xintXTrunc
19. rguments 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 e New component xintcfrac devoted to continued fractions e bug fix xintfrac xintIrr 0 crashed e faster division routine in xint new macros to deal expandably with token lists e xintRound added e 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 e tex xint dtx extracts style files no need for a xint ins 1 03 2013 04 14 e new modules xintfrac expandable operations on fractions and xintseries expandable partial sums with xint package e slightly improved division and faster multiplication the best ordering of the arguments is chosen automatically e added illustration of Machin algorithm to the documentation but values higher than 100 or 200 will presumably give too slow evaluations 12 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 xintgced package provides
20. rseq 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 1 09n 2014 04 01 e 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 e 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 e 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 e 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 genera
21. tFor 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 e apackage xinttools is detached from xint to make tools such as xintFor xintApplyUnbraced and xintiloop available without the xint overhead e new expandable nestable loops xintloop and xintiloop e bugfix xintFor and xintFor do not modify anymore the value of count 255 1 09 2013 11 04 e xint new 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
22. usly already when xintfrac was loaded e a bug xintfrac introduced in 1 08b made xintCmp crash when one of its arguments was zero 7 CC 1 08b 2013 06 14 e xintexpr Correction of a problem with spaces inside xintexpr essions e xintfrac Additional improvements to the handling of floating point numbers e new 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 e xintfrac Improved efficiency of the basic conversion from exact fractions to floating point num bers with ensuing speed gains especially for the power function macros xintFloatPow and xintFloatPower e Better management by xintCmp xintMax xintMin and xintGeq of inputs having big powers of ten in them e Macros for floating point numbers added to the xintseries package 1 08 2013 06 07 e xint and xintfrac Macros for extraction of square roots for floating point numbers xintFloatSqrt and integers xintiSqrt e New package xintbinhex providing conversion routines to and from binary and hexadecimal bases 1 07 2013 05 25 e 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 relax allowing on input formulas using the infix operators and and arbitrary levels of parenthesizing Within

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