> For the complete documentation index, see [llms.txt](https://trizen.gitbook.io/perl6-rosettacode/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://trizen.gitbook.io/perl6-rosettacode/programming_tasks/n/negative_base_numbers.md). # Negative base numbers ### Explicit Raku provides built-in methods / routines base and parse-base to convert to and from bases 2 through 36. We'll just shadow the core routines with versions that accept negative bases. As a stretch goal, rather than implement something that can "Spell the name of the language with correct capitalization" (which is silly, trivial, and has absolutely ***nothing*** to do with negative base numbers,) we'll implement routines that correctly work with any Real number, not just integers. The Real candidate has a 'precision' parameter, default -15, (15 places after the decimal point,) to limit the length of the fractional portion of the converted value. Change it if you need or want different precision. The Integer only routine is kept here as a multi-dispatch candidate since it is potentially much faster than the Real capable routine. The dispatcher will automatically use the most appropriate (fastest) routine. Note that the parse-base routine will handle 'illegal' negative negative-base values without blowing up. ```perl multi sub base ( Int $value is copy, Int $radix where -37 < * < -1) { my $result; while $value { my $r = $value mod $radix; $value div= $radix; if $r < 0 { $value++; $r -= $radix } $result ~= $r.base(-$radix); } flip $result || ~0; } multi sub base ( Real $num, Int $radix where -37 < * < -1, :$precision = -15 ) { return '0' unless $num; my $value = $num; my $result = ''; my $place = 0; my $upper-bound = 1 / (-$radix + 1); my $lower-bound = $radix * $upper-bound; $value = $num / $radix ** ++$place until $lower-bound <= $value < $upper-bound; while ($value or $place > 0) and $place > $precision { my $digit = ($radix * $value - $lower-bound).Int; $value = $radix * $value - $digit; $result ~= '.' unless $place or $result.contains: '.'; $result ~= $digit == -$radix ?? ($digit-1).base(-$radix)~'0' !! $digit.base(-$radix); $place-- } $result } multi sub parse-base (Str $str, Int $radix where -37 < * < -1) { return -1 * $str.substr(1).&parse-base($radix) if $str.substr(0,1) eq '-'; my ($whole, $frac) = $str.split: '.'; my $fraction = 0; $fraction = [+] $frac.comb.kv.map: { $^v.parse-base(-$radix) * $radix ** -($^k+1) } if $frac; $fraction + [+] $whole.flip.comb.kv.map: { $^v.parse-base(-$radix) * $radix ** $^k } } # TESTING for <4 -4 0 -7 10 -2 146 -3 15 -10 -19 -10 107 -16 227.65625 -16 2.375 -4 -1.3e2 -8 41371457.268272761 -36> -> $v, $r { my $nbase = $v.&base($r, :precision(-5)); printf "%20s.&base\(%3d\) = %-11s : %13s.&parse-base\(%3d\) = %s\n", $v, $r, $nbase, "'$nbase'", $r, $nbase.&parse-base($r); } # 'Illegal' negative-base value say q| '-21'.&parse-base(-10) = |, '-21'.&parse-base(-10); ``` #### Output: ``` 4.&base( -4) = 130  : '130'.&parse-base( -4) = 4 0.&base( -7) = 0  : '0'.&parse-base( -7) = 0 10.&base( -2) = 11110  : '11110'.&parse-base( -2) = 10 146.&base( -3) = 21102  : '21102'.&parse-base( -3) = 146 15.&base(-10) = 195  : '195'.&parse-base(-10) = 15 -19.&base(-10) = 21  : '21'.&parse-base(-10) = -19 107.&base(-16) = 1AB  : '1AB'.&parse-base(-16) = 107 227.65625.&base(-16) = 124.68  : '124.68'.&parse-base(-16) = 227.65625 2.375.&base( -4) = 3.32  : '3.32'.&parse-base( -4) = 2.375 -1.3e2.&base( -8) = 1616  : '1616'.&parse-base( -8) = -130 41371457.268272761.&base(-36) = PERL6.ROCKS : 'PERL6.ROCKS'.&parse-base(-36) = 41371457.268272761 '-21'.&parse-base(-10) = 19 ``` ### Module Using the module [Base::Any](https://modules.raku.org/search/?q=Base%3A%3AAny) from the Raku ecosystem. Does everything the explicit version does but also handles a **much** larger range of negative bases. Doing pretty much the same tests as the explicit version. ```perl use Base::Any; for < 4 -4 0 -7 10 -2 146 -3 15 -10 -19 -10 107 -16 227.65625 -16 2.375 -4 -1.3e2 -8 41371457.268272761 -36 -145115966751439403/3241792 -1184 > -> $v, $r { my $nbase = $v.&to-base($r, :precision(-5)); printf "%21s.&to-base\(%5d\) = %-11s : %13s.&from-base\(%5d\) = %s\n", +$v, $r, $nbase, "'$nbase'", $r, $nbase.&from-base($r); } ``` #### Output: ``` 4.&to-base( -4) = 130  : '130'.&from-base( -4) = 4 0.&to-base( -7) = 0  : '0'.&from-base( -7) = 0 10.&to-base( -2) = 11110  : '11110'.&from-base( -2) = 10 146.&to-base( -3) = 21102  : '21102'.&from-base( -3) = 146 15.&to-base( -10) = 195  : '195'.&from-base( -10) = 15 -19.&to-base( -10) = 21  : '21'.&from-base( -10) = -19 107.&to-base( -16) = 1AB  : '1AB'.&from-base( -16) = 107 227.65625.&to-base( -16) = 124.68  : '124.68'.&from-base( -16) = 227.65625 2.375.&to-base( -4) = 3.32  : '3.32'.&from-base( -4) = 2.375 -130.&to-base( -8) = 1616  : '1616'.&from-base( -8) = -130 41371457.268272761.&to-base( -36) = PERL6.ROCKS : 'PERL6.ROCKS'.&from-base( -36) = 41371457.268272761 -44764120200.01264825.&to-base(-1184) = Raku.FTW  : 'Raku.FTW'.&from-base(-1184) = -44764120200.01264825 ``` --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://trizen.gitbook.io/perl6-rosettacode/programming_tasks/n/negative_base_numbers.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.