Data commit

Task/Pi/Jq/pi-1.jq

@@ -0,0 +1,59 @@
+# The Gibbons spigot, in the mold of the [[#Groovy]] and [[#Python]] programs shown on this page.
+# The "bigint" functions needed are:
+# long_minus long_add long_multiply long_div
+
+def pi_spigot:
+
+  # S is the sixtuple:
+  # q      r      t      k      n      l
+  # 0      1      2      3      4      5
+
+  def long_lt(x;y): if x == y then false else lessOrEqual(x;y) end;
+
+  def check:
+     long_lt(long_minus(long_add(long_multiply("4"; .[0]); .[1]) ; .[2]);
+             long_multiply(.[4]; .[2]));
+
+  # state: [d, S] where digit is null or a digit ready to be printed
+  def next:
+    .[1] as $S
+    | $S[0] as $q | $S[1] as $r | $S[2] as $t | $S[3] as $k | $S[4] as $n | $S[5] as $l
+    | if $S|check
+      then [$n,
+             [long_multiply("10"; $q),
+              long_multiply("10"; long_minus($r; long_multiply($n;$t))),
+              $t,
+              $k,
+              long_minus( long_div(long_multiply("10";long_add(long_multiply("3"; $q); $r)); $t );
+                          long_multiply("10";$n)),
+              $l ]]
+      else [null,
+             [long_multiply($q;$k),
+              long_multiply( long_add(long_multiply("2";$q); $r); $l),
+              long_multiply($t;$l),
+              long_add($k; "1"),
+              long_div( long_add(long_multiply($q; long_add(long_multiply("7";$k); "2")) ; long_multiply($r;$l));
+                        long_multiply($t;$l) ),
+              long_add($l; "2") ]]
+      end;
+
+  # Input: input to the filter "nextstate"
+  # Output:  [count, space, digit] for successive digits produced by "nextstate"
+  def decorate( nextstate ):
+
+     # For efficiency it is important that the recursive
+     # function have arity 0 and be tail-recursive:
+     def count:
+       .[0] as $count
+       | .[1] as $state
+       | $state[0] as $value
+       | ($state[1] | map(length) | add) as $space
+       | (if $value then [$count, $space, $value] else empty end),
+         ( [if $value then $count+1 else $count end, ($state | nextstate)] | count);
+  [0, .] | count;
+
+  #       q=1, r=0, t=1, k=1, n=3, l=3
+  [null, ["1", "0", "1", "1", "3", "3"]] | decorate(next)
+;
+
+pi_spigot

Task/Pi/Jq/pi-2.jq

@@ -0,0 +1,305 @@
+$ jq -M -n -c -f pi.bigint.jq
+[0,9,"3"]
+[1,14,"1"]
+[2,29,"4"]
+[3,36,"1"]
+[4,51,"5"]
+[5,69,"9"]
+[6,80,"2"]
+[7,95,"6"]
+[8,115,"5"]
+[9,125,"3"]
+[10,142,"5"]
+[11,167,"8"]
+[12,181,"9"]
+[13,197,"7"]
+[14,226,"9"]
+[15,245,"3"]
+[16,263,"2"]
+[17,276,"3"]
+[18,300,"8"]
+[19,320,"4"]
+[20,350,"6"]
+[21,363,"2"]
+[22,383,"6"]
+[23,408,"4"]
+[24,429,"3"]
+[25,442,"3"]
+[26,475,"8"]
+[27,502,"3"]
+[28,510,"2"]
+[29,531,"7"]
+[30,563,"9"]
+[31,611,"5"]
+[32,613,"0"]
+[33,628,"2"]
+[34,649,"8"]
+[35,676,"8"]
+[36,711,"4"]
+[37,720,"1"]
+[38,748,"9"]
+[39,783,"7"]
+[40,792,"1"]
+[41,814,"6"]
+[42,849,"9"]
+[43,870,"3"]
+[44,886,"9"]
+[45,923,"9"]
+[46,939,"3"]
+[47,967,"7"]
+[48,1004,"5"]
+[49,1041,"1"]
+[50,1043,"0"]
+[51,1059,"5"]
+[52,1103,"8"]
+[53,1133,"2"]
+[54,1135,"0"]
+[55,1165,"9"]
+[56,1195,"7"]
+[57,1212,"4"]
+[58,1242,"9"]
+[59,1273,"4"]
+[60,1297,"4"]
+[61,1313,"5"]
+[62,1358,"9"]
+[63,1375,"2"]
+[64,1421,"3"]
+[65,1423,"0"]
+[66,1447,"7"]
+[67,1493,"8"]
+[68,1501,"1"]
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+[70,1579,"4"]
+[71,1581,"0"]
+[72,1613,"6"]
+[73,1630,"2"]
+[74,1662,"8"]
+[75,1701,"6"]
+[76,1733,"2"]
+[77,1735,"0"]
+[78,1781,"8"]
+[79,1792,"9"]
+[80,1816,"9"]
+[81,1849,"8"]
+[82,1889,"6"]
+[83,1898,"2"]
+[84,1961,"8"]
+[85,1963,"0"]
+[86,1988,"3"]
+[87,2013,"4"]
+[88,2054,"8"]
+[89,2071,"2"]
+[90,2104,"5"]
+[91,2129,"3"]
+[92,2162,"4"]
+[93,2195,"2"]
+[94,2220,"1"]
+[95,2230,"1"]
+[96,2287,"7"]
+[97,2289,"0"]
+[98,2314,"6"]
+[99,2340,"7"]
+[100,2373,"9"]
+[101,2414,"8"]
+[102,2448,"2"]
+[103,2458,"1"]
+[104,2484,"4"]
+[105,2534,"8"]
+[106,2536,"0"]
+[107,2569,"8"]
+[108,2602,"6"]
+[109,2645,"5"]
+[110,2662,"1"]
+[111,2696,"3"]
+[112,2707,"2"]
+[113,2756,"8"]
+[114,2775,"2"]
+[115,2825,"3"]
+[116,2827,"0"]
+[117,2853,"6"]
+[118,2887,"6"]
+[119,2914,"4"]
+[120,2964,"7"]
+[121,2966,"0"]
+[122,3008,"9"]
+[123,3027,"3"]
+[124,3061,"8"]
+[125,3088,"4"]
+[126,3114,"4"]
+[127,3165,"6"]
+[128,3167,"0"]
+[129,3202,"9"]
+[130,3237,"5"]
+[131,3287,"5"]
+[132,3289,"0"]
+[133,3316,"5"]
+[134,3360,"8"]
+[135,3387,"2"]
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+[138,3466,"1"]
+[139,3510,"7"]
+[140,3529,"2"]
+[141,3564,"5"]
+[142,3583,"3"]
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+[147,3752,"8"]
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+[150,3825,"8"]
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+[152,3905,"8"]
+[153,3933,"1"]
+[154,3960,"1"]
+[155,3970,"1"]
+[156,4006,"7"]
+[157,4033,"4"]
+[158,4102,"5"]
+[159,4104,"0"]
+[160,4124,"2"]
+[161,4159,"8"]
+[162,4203,"4"]
+[163,4248,"1"]
+[164,4250,"0"]
+[165,4269,"2"]
+[166,4348,"7"]
+[167,4350,"0"]
+[168,4361,"1"]
+[169,4405,"9"]
+[170,4424,"3"]
+[171,4460,"8"]
+[172,4497,"5"]
+[173,4542,"2"]
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+[175,4605,"1"]
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+[183,4820,"4"]
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+[302,8623,"2"]
+...