Data commit

Task/Humble-numbers/Nim/humble-numbers-1.nim

@@ -0,0 +1,58 @@
+import sets, strformat
+
+
+proc min[T](s: HashSet[T]): T =
+  ## Return the minimal value in a set.
+  if s.card == 0:
+    raise newException(ValueError, "set is empty.")
+  result = T.high
+  for n in s:
+    if n < result: result = n
+
+
+iterator humbleNumbers(): Positive =
+  ## Yield the successive humble numbers.
+  var s = [1].toHashSet()
+  while true:
+    let m = min(s)
+    yield m
+    s.excl(m)
+    for k in [2, 3, 5, 7]: s.incl(k * m)
+
+
+proc showHumbleNumbers(maxCount: Positive) =
+  ## Show the first "maxCount" humble numbers.
+  var currCount = 0
+  for n in humbleNumbers():
+    stdout.write n
+    inc currCount
+    if currCount == maxCount: break
+    stdout.write ' '
+  echo ""
+
+
+proc showHumbleCount(ndigits: Positive) =
+  ## Show the number of humble numbers with "n <= ndigits" digits.
+  echo "Digits   Count"
+  echo "------   -----"
+  var currdigits = 1
+  var count = 0
+  var next = 10   # First number with "currdigits + 1" digits.
+  for n in humbleNumbers():
+    if n >= next:
+      # Number of digits has changed.
+      echo &"  {currdigits:2d}     {count:5d}"
+      inc currdigits
+      if currdigits > ndigits: break
+      next *= 10
+      count = 1
+    else:
+      inc count
+
+
+when isMainModule:
+  echo "First 50 humble numbers:"
+  showHumbleNumbers(50)
+  echo ""
+  echo "Count of humble numbers with n digits:"
+  showHumbleCount(18)

Task/Humble-numbers/Nim/humble-numbers-2.nim

@@ -0,0 +1,89 @@
+import std/math, std/strutils
+from std/times import inMilliseconds
+from std/monotimes import getMonoTime, `-`
+
+let lgshft = 50; let lg10 =  1'u64 shl lgshft; let fac = 2'f64.pow lgshft.float64
+let lg7 = (7'f64.log10 * fac).round.uint64
+let lg5 = (5'f64.log10 * fac).round.uint64
+let lg3 = (3'f64.log10 * fac).round.uint64; let lg2 = lg10 - lg5
+
+proc lr2UInt64(lr: uint64): uint64 = pow(10, (lr.float64 / fac)).round.uint64
+
+iterator humblesLogQ(): uint64 = # {.closure.} =
+  var hd2 = lg2; var hd3 = lg3; var hd5 = lg5; var hd7 = lg7
+  var s2msk, s2hdi, s2tli, s3msk, s3hdi, s3tli, s5msk, s5hdi, s5tli = 0
+  var s2 = newSeq[uint64] 0
+  var s3 = newSeq[uint64] 0
+  var s5 = newSeq[uint64] 0
+  yield 0'u64
+  while true:
+    yield hd2
+    if s2tli == s2hdi:
+      let osz = if s2msk == 0: 512 else: s2msk + 1
+      s2.setLen (osz + osz); s2msk = s2.len - 1
+      if osz > 512:
+        if s2hdi == 0: s2tli = osz
+        else: # put extra space between tail and head...
+          copyMem(addr(s2[s2hdi + osz]), addr(s2[s2hdi]),
+                  sizeof(uint64) * (osz - s2hdi)); s2hdi += osz
+    s2[s2tli] = hd2 + lg2; s2tli = (s2tli + 1) and s2msk
+    hd2 = s2[s2hdi]
+    if hd2 < hd3: s2hdi = (s2hdi + 1) and s2msk
+    else:
+      hd2 = hd3
+      if s3tli == s3hdi:
+        let osz = if s3msk == 0: 512 else: s3msk + 1
+        s3.setLen (osz + osz); s3msk = s3.len - 1
+        if osz > 512:
+          if s3hdi == 0: s3tli = osz
+          else: # put extra space between tail and head...
+            copyMem(addr(s3[s3hdi + osz]), addr(s3[s3hdi]),
+                    sizeof(uint64) * (osz - s3hdi)); s3hdi += osz
+      s3[s3tli] = hd3 + lg3; s3tli = (s3tli + 1) and s3msk
+      hd3 = s3[s3hdi]
+      if hd3 < hd5: s3hdi = (s3hdi + 1) and s3msk
+      else:
+        hd3 = hd5
+        if s5tli == s5hdi:
+          let osz = if s5msk == 0: 512 else: s5msk + 1
+          s5.setLen (osz + osz); s5msk = s5.len - 1
+          if osz > 512:
+            if s5hdi == 0: s5tli = osz
+            else: # put extra space between tail and head...
+              copyMem(addr(s5[s5hdi + osz]), addr(s5[s5hdi]),
+                      sizeof(uint64) * (osz - s5hdi)); s5hdi += osz
+        s5[s5tli] = hd5 + lg5; s5tli = (s5tli + 1) and s5msk
+        hd5 = s5[s5hdi]
+        if hd5 < hd7: s5hdi = (s5hdi + 1) and s5msk
+        else: hd5 = hd7; hd7 += lg7
+
+proc commaString(s: string): string =
+  let sz = s.len; let sqlen = (sz + 2) div 3
+  var sq = newSeq[string](sqlen); var ndx = sqlen - 1
+  for i in countdown(sz - 1, 0, 3): sq[ndx] = s[(max(i-2, 0) .. i)]; ndx -= 1
+  sq.join ","
+
+# testing it...
+let numdigits = 255.uint64
+
+echo "First 50 Humble numbers:"
+var cnt = 0
+for h in humblesLogQ():
+  stdout.write $h.lr2UInt64, " "; cnt += 1
+  if cnt >= 50: break
+
+echo "\r\nCount of humble numbers for each digit length 1-", $numdigits, ":"
+echo "Digits       Count              Accum"
+let lmt = lg10 * numdigits
+let strt = getMonoTime()
+var cdigits = 0'u64; cnt = 0; var acnt = 0.int
+for h in humblesLogQ():
+  if (h shr lgshft) <= cdigits: cnt += 1
+  else:
+    cdigits += 1; acnt += cnt
+    echo ($cdigits).align(4) & ($cnt).commaString.align(14) &
+            ($acnt).commaString.align(19)
+    cnt = 1
+  if cdigits >= numdigits: break
+let elpsd = (getMonoTime() - strt).inMilliseconds
+echo "Counting took ", elpsd, " milliseconds."

Task/Humble-numbers/Nim/humble-numbers-3.nim

@@ -0,0 +1,91 @@
+import std/math, std/strutils
+from std/times import inMilliseconds
+from std/monotimes import getMonoTime, `-`
+
+let lgshft = 50; let lg10 =  1'u64 shl lgshft; let fac = 2'f64.pow lgshft.float64
+let lg7 = (7'f64.log10 * fac).round.uint64
+let lg5 = (5'f64.log10 * fac).round.uint64
+let lg3 = (3'f64.log10 * fac).round.uint64; let lg2 = lg10 - lg5
+
+proc lr2UInt64(lr: uint64): uint64 = pow(10, (lr.float64 / fac)).round.uint64
+
+iterator humblesLogQ(): uint64 = # {.closure.} =
+  var hd2 = lg2; var hd3 = lg3; var hd5 = lg5; var hd7 = lg7
+  var s2msk, s2hdi, s2tli, s3msk, s3hdi, s3tli, s5msk, s5hdi, s5tli = 0
+  var s2 = newSeq[uint64] 0
+  var s3 = newSeq[uint64] 0
+  var s5 = newSeq[uint64] 0
+  yield 0'u64
+  while true:
+    yield hd2
+    if s2tli == s2hdi:
+      let osz = if s2msk == 0: 512 else: s2msk + 1
+      s2.setLen (osz + osz); s2msk = s2.len - 1
+      if osz > 512:
+        if s2hdi == 0: s2tli = osz
+        else: # put extra space between tail and head...
+          copyMem(addr(s2[s2hdi + osz]), addr(s2[s2hdi]),
+                  sizeof(uint64) * (osz - s2hdi)); s2hdi += osz
+    s2[s2tli] = hd2 + lg2; s2tli = (s2tli + 1) and s2msk
+    hd2 = s2[s2hdi]
+    if hd2 < hd3: s2hdi = (s2hdi + 1) and s2msk
+    else:
+      hd2 = hd3
+      if s3tli == s3hdi:
+        let osz = if s3msk == 0: 512 else: s3msk + 1
+        s3.setLen (osz + osz); s3msk = s3.len - 1
+        if osz > 512:
+          if s3hdi == 0: s3tli = osz
+          else: # put extra space between tail and head...
+            copyMem(addr(s3[s3hdi + osz]), addr(s3[s3hdi]),
+                    sizeof(uint64) * (osz - s3hdi)); s3hdi += osz
+      s3[s3tli] = hd3 + lg3; s3tli = (s3tli + 1) and s3msk
+      hd3 = s3[s3hdi]
+      if hd3 < hd5: s3hdi = (s3hdi + 1) and s3msk
+      else:
+        hd3 = hd5
+        if s5tli == s5hdi:
+          let osz = if s5msk == 0: 512 else: s5msk + 1
+          s5.setLen (osz + osz); s5msk = s5.len - 1
+          if osz > 512:
+            if s5hdi == 0: s5tli = osz
+            else: # put extra space between tail and head...
+              copyMem(addr(s5[s5hdi + osz]), addr(s5[s5hdi]),
+                      sizeof(uint64) * (osz - s5hdi)); s5hdi += osz
+        s5[s5tli] = hd5 + lg5; s5tli = (s5tli + 1) and s5msk
+        hd5 = s5[s5hdi]
+        if hd5 < hd7: s5hdi = (s5hdi + 1) and s5msk
+        else: hd5 = hd7; hd7 += lg7
+
+proc commaString(s: string): string =
+  let sz = s.len; let sqlen = (sz + 2) div 3
+  var sq = newSeq[string](sqlen); var ndx = sqlen - 1
+  for i in countdown(sz - 1, 0, 3): sq[ndx] = s[(max(i-2, 0) .. i)]; ndx -= 1
+  sq.join ","
+
+# testing it...
+let numdigits = 877.uint64
+
+echo "First 50 Humble numbers:"
+var cnt = 0
+for h in humblesLogQ():
+  stdout.write $h.lr2UInt64, " "; cnt += 1
+  if cnt >= 50: break
+
+echo "\r\nCount of humble numbers for each digit length 1-", $numdigits, ":"
+echo "Digits       Count              Accum"
+let lmt = lg10 * numdigits
+let strt = getMonoTime()
+var bins = newSeq[int](numdigits)
+for w in countup(0'u64, lmt, lg7):
+  for x in countup(w, lmt, lg5):
+    for y in countup(x, lmt, lg3):
+      for z in countup(y, lmt, lg2):
+        bins[z shr lgshft] += 1
+var a = 0
+for i, c in bins:
+  a += c
+  echo ($(i + 1)).align(4) & ($c).commaString.align(14) &
+            ($a).commaString.align(19)
+let elpsd = (getMonoTime() - strt).inMilliseconds
+echo "Counting took ", elpsd, " milliseconds."