Data update

Task/Balanced-ternary/11l/balanced-ternary.11l

@@ -9,7 +9,7 @@ T BalancedTernary
       I all(inp.map(d -> d C (0, 1, -1)))
          .digits = copy(inp)
       E
-         X ValueError(‘BalancedTernary: Wrong input digits.’)
+         X.throw ValueError(‘BalancedTernary: Wrong input digits.’)
 
    F :from_str(inp)
       R BalancedTernary(reversed(inp).map(c -> .:str2dig[c]))
@@ -21,7 +21,7 @@ T BalancedTernary
       I n3 == 0 {R  [0] [+] .:int2ternary(n -I/ 3)}
       I n3 == 1 {R  [1] [+] .:int2ternary(n -I/ 3)}
       I n3 == 2 {R [-1] [+] .:int2ternary((n + 1) -I/ 3)}
-      X RuntimeError(‘’)
+      X.throw RuntimeError(‘’)
 
    F :from_int(inp)
       R BalancedTernary(.:int2ternary(inp))

Task/Balanced-ternary/Jq/balanced-ternary.jq

@@ -0,0 +1,137 @@
+### Generic utilities
+
+# Emit a stream of the constituent characters of the input string
+def chars: explode[] | [.] | implode;
+
+# Flip "+" and "-" in the input string, and change other characters to 0
+def flip:
+  {"+": "-", "-": "+"} as $t
+  | reduce chars as $c (""; . + ($t[$c] // "0") );
+
+### Balanced ternaries (BT)
+
+# Input is assumed to be an integer (use `new` if checking is required)
+def toBT:
+  # Helper - input should be an integer
+  def mod3:
+    if . > 0 then . % 3
+    else ((. % 3) + 3) % 3
+    end;
+
+  if . < 0 then - . | toBT | flip
+  else if . == 0 then ""
+       else mod3 as $rem
+       | if   $rem == 0 then (. / 3 | toBT) + "0"
+         elif $rem == 1 then (. / 3 | toBT) + "+"
+         else                ((. + 1) / 3 | toBT) + "-"
+         end
+       end
+       | sub("^00*";"")
+       | if . == "" then "0" end
+  end ;
+
+# Input: BT
+def integer:
+  . as $in
+  | length as $len
+  | { sum: 0,
+      pow: 1 }
+  | reduce range (0;$len) as $i (.;
+       $in[$len-$i-1: $len-$i] as $c
+       | (if $c == "+" then 1 elif $c == "-" then -1 else 0 end) as $digit
+       | if $digit != 0 then .sum += $digit * .pow else . end
+       | .pow *= 3 )
+  | .sum ;
+
+# If the input is a string, check it is a valid BT, and trim leading 0s;
+# if the input is an integer, convert it to a BT;
+# otherwise raise an error.
+def new:
+  if type == "string" and all(chars; IN("0", "+", "-"))
+  then sub("^00*"; "") | if . == "" then "0" end
+  elif type == "number" and trunc == .
+  then toBT
+  else "'new' given invalid input: \(.)" | error
+  end;
+
+# . + $b
+def plus($b):
+  # Helper functions:
+  def at($i): .[$i:$i+1];
+
+  # $a and $b should each be "0", "+" or "-"
+  def addDigits2($a; $b):
+    if $a == "0" then $b
+    elif $b == "0" then $a
+    elif $a == "+"
+    then if $b == "+" then "+-" else "0" end
+    elif $b == "+" then "0" else "-+"
+    end;
+
+  def addDigits3($a; $b; $carry):
+    addDigits2($a; $b) as $sum1
+    | addDigits2($sum1[-1:]; $carry) as $sum2
+    | if ($sum1|length) == 1
+      then $sum2
+      elif ($sum2|length) == 1
+      then $sum1[0:1] + $sum2
+      else $sum1[0:1]
+      end;
+
+  { longer:  (if length > ($b|length) then . else $b end),
+    shorter: (if length > ($b|length) then $b else . end) }
+  | until ( (.shorter|length) >= (.longer|length); .shorter = "0" + .shorter )
+  | .a = .longer
+  | .b = .shorter
+  | .carry = "0"
+  | .sum = ""
+  | reduce range(0; .a|length) as $i (.;
+      ( (.a|length) - $i - 1) as $place
+      | addDigits3(.a | at($place); .b | at($place); .carry) as $digisum
+      | .carry = (if ($digisum|length) != 1 then $digisum[0:1] else "0" end)
+      | .sum = $digisum[-1:] + .sum )
+  | .carry + .sum
+  | new;
+
+def minus: flip;
+
+# . - $b
+def minus($b): plus($b | flip);
+
+def mult($b):
+  (1 | new) as $one
+  | (0 | new) as $zero
+  | { a: .,
+      $b,
+      mul: $zero,
+      flipFlag: false }
+  | if .b[0:1] == "-"  # i.e. .b < 0
+    then .b |= minus
+    | .flipFlag = true
+    end
+  | .i = $one
+  | .in = 1
+  | (.b | integer) as $bn
+  | until ( .in > $bn;
+      .a as $a
+      | .mul |= plus($a)
+      | .i |= plus($one)
+      | .in += 1 )
+  | if .flipFlag then .mul | minus else .mul end ;
+
+
+### Illustration
+
+def a: "+-0++0+";
+def b: -436 | new;
+def c:  "+-++-";
+
+  (a | integer) as $an
+| (b | integer) as $bn
+| (c | integer) as $cn
+| ($an * ($bn - $cn)) as $in
+| (a | mult( (b | minus(c)))) as $i
+| "a = \($an)",
+  "b = \($bn)",
+  "c = \($cn)",
+  "a * (b - c) = \($i) ~ \($in) => \($in|new)"