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Active Forums => Programs => Topic started by: bplus on September 04, 2021, 02:28:15 pm

Title: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 02:28:15 pm
ref http://rosettacode.org/wiki/Iterated_digits_squaring

Who tried this recursively?
Code: QB64: [Select]
  2. _Title "Iterated digits squaring - Rosetta Code" ' b+ try 2021-09-04
  3. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. start = Timer(.001)
  5. For i& = 1 To 100000000 ' 100 million
  6.     If i& Mod 1000000 = 0 Then Print i&, c& ' progress almost 8 minutes on my system
  7.     c& = c& + sumSQRdigitsIs89%(i&)
  9. Print c&, Timer(.001) - start
  10.  
  11. Function sumSQRdigitsIs89% (number&)
  12.     n$ = _Trim$(Str$(number&))
  13.     For i = 1 To Len(n$)
  14.         sum& = sum& + Val(Mid$(n$, i, 1)) ^ 2
  15.     Next
  16.     If sum& = 89 Then
  17.         sumSQRdigitsIs89% = 1
  18.     ElseIf sum& <> 1 Then
  19.         sumSQRdigitsIs89% = sumSQRdigitsIs89%(sum&)
  20.     End If
  22.  

Of course there must be faster ways even for QB64 ;-))

Hint get rid of the string stuff :)
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 05:20:36 pm
All afternoon to shave off 3.5 mins:
Code: QB64: [Select]
  1. _Title "Iterated digits squaring v2 - Rosetta Code" ' b+ try 2021-09-04
  2. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. DefLng A-Z
  5. Dim Shared did(649), t(10), sq(10) '9*81 + 1 max sum number
  6. start = Timer(.001)
  7. For i = 1 To 100000000 ' 100 million   now a tad over 4.5 mins shaved off over 3 min.
  8.     t(1) = t(1) + 1: sq(1) = t(1) * t(1)
  9.     For j = 1 To 8
  10.         If t(j) = 10 Then t(j) = 0: sq(j) = 0: t(j + 1) = t(j + 1) + 1: sq(j + 1) = t(j + 1) * t(j + 1)
  11.     Next
  12.     'check this 100 million times less
  13.     'If t(10) = 10 Then Beep: Print "You've just exceeded the limit of the tabulator, goodbye.": End
  14.     sum = sq(1) + sq(2) + sq(3) + sq(4) + sq(5) + sq(6) + sq(7) + sq(8) + sq(9)
  15.     'check this 100 million times less
  16.     'If i Mod 1000000 = 0 Then Print i, c   ' <<< progress
  17.     If sumSQRdigits(sum) = 89 Then c = c + 1
  19. Print c, Timer(.001) - start
  20.  
  21. Function sumSQRdigits (number)
  22.     If number = 89 Then sumSQRdigits = 89: Exit Function
  23.     If number = 1 Then sumSQRdigits = 1: Exit Function
  24.     Dim As Integer sum
  25.     If number < 649 Then
  26.         If did(number) Then
  27.             sumSQRdigits = did(number)
  28.         Else
  29.             n$ = _Trim$(Str$(number))
  30.             For i = 1 To Len(n$)
  31.                 sum = sum + Val(Mid$(n$, i, 1)) ^ 2
  32.             Next
  33.             If sum = 89 Or sum = 1 Then
  34.                 did(number) = sum
  35.                 sumSQRdigits = sum: Exit Function
  36.             Else
  37.                 sumSQRdigits = sumSQRdigits(sum)
  38.             End If
  39.         End If
  40.     Else
  41.         Print " Error: number into sumSQRdigits is > 730."; " end"
  42.     End If
  44.  

Didn't make much difference to comment out progress.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: jack on September 04, 2021, 06:40:52 pm
hi bplus
instead of val use asc($)-48
your first example modified
Code: QB64: [Select]
  2. _Title "Iterated digits squaring - Rosetta Code" ' b+ try 2021-09-04
  3. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. start = Timer(.001)
  5. For i& = 1 To 100000000 ' 100 million
  6.     If i& Mod 1000000 = 0 Then Print i&, c& ' progress almost 8 minutes on my system
  7.     c& = c& + sumSQRdigitsIs89%(i&)
  9. Print c&, Timer(.001) - start
  10.  
  11. Function sumSQRdigitsIs89% (number&)
  12.     n$ = _Trim$(Str$(number&))
  13.     For i = 1 To Len(n$)
  14.         d& = Asc(Mid$(n$, i, 1)) - 48
  15.         sum& = sum& + d& * d&
  16.     Next
  17.     If sum& = 89 Then
  18.         sumSQRdigitsIs89% = 1
  19.     ElseIf sum& <> 1 Then
  20.         sumSQRdigitsIs89% = sumSQRdigitsIs89%(sum&)
  21.     End If
  23.  
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 07:42:34 pm
Yes! nice one @jack  :)

Try this:
Code: QB64: [Select]
  2. _Title "Iterated digits squaring - Rosetta Code" ' b+ try 2021-09-04
  3. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. start = Timer(.001)
  5. For i& = 1 To 100000000 ' 100 million
  6.     If i& Mod 1000000 = 0 Then Print i&, c& ' progress almost 8 minutes on my system
  7.     c& = c& + sumSQRdigitsIs89%(i&)
  9. Print c&, Timer(.001) - start
  10.  
  11. Function sumSQRdigitsIs89% (number&)
  12.     n$ = _Trim$(Str$(number&))
  13.     For i = 1 To Len(n$)
  14.         d& = Asc(n$, i) - 48
  15.         sum& = sum& + d& * d&
  16.     Next
  17.     If sum& = 89 Then
  18.         sumSQRdigitsIs89% = 1
  19.     ElseIf sum& <> 1 Then
  20.         sumSQRdigitsIs89% = sumSQRdigitsIs89%(sum&)
  21.     End If
  23.  

Man 3 mins!
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 09:25:10 pm
OK now we're cooking with butter!
Code: QB64: [Select]
  2. _Title "Iterated digits squaring v4 - Rosetta Code" ' b+ try 2021-09-04
  3. DefLng A-Z
  4. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  5. start! = Timer(.001)
  6. For i = 1 To 100000000 ' 100 million
  7.     'If i Mod 1000000 = 0 Then Print i, c ' progress  36 secs on my system
  8.     c = c + sumSQRdigitsIs89(i)
  10. Print c, Timer(.001) - start!
  11.  
  12. Function sumSQRdigitsIs89 (number)
  13.     n = number
  14.     While n > 0
  15.         d = n Mod 10
  16.         sum = sum + d * d
  17.         n = n \ 10
  18.     Wend
  19.     If sum = 89 Then
  20.         sumSQRdigitsIs89 = 1
  21.     ElseIf sum <> 1 Then
  22.         sumSQRdigitsIs89 = sumSQRdigitsIs89(sum)
  23.     End If
  25.  
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 09:33:12 pm
Man that's the way to isolate the digits for these challenges, don't mess with string conversions.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: jack on September 04, 2021, 09:47:58 pm
about 18% faster
Code: QB64: [Select]
  2. _Title "Iterated digits squaring - Rosetta Code" ' b+ try 2021-09-04
  3. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. start = Timer(.001)
  5. For i& = 1 To 100000000 ' 100 million
  6.     If i& Mod 1000000 = 0 Then Print i&, c& ' progress almost 8 minutes on my system
  7.     c& = c& + sumSQRdigitsIs89%(i&)
  9. Print c&, Timer(.001) - start
  10.  
  11. Function sumSQRdigitsIs89% (number&)
  12.     n$ = _Trim$(Str$(number&))
  13.     m% = Len(n$)
  14.     For i% = 1 To m%
  15.         d% = Asc(n$, i%) - 48
  16.         sum& = sum& + d% * d%
  17.     Next
  18.     If sum& = 89 Then
  19.         sumSQRdigitsIs89% = 1
  20.     ElseIf sum& <> 1 Then
  21.         sumSQRdigitsIs89% = sumSQRdigitsIs89%(sum&)
  22.     End If
  24.  
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 10:06:45 pm
I started looking at FreeBASIC's, 2 millisecs!!!

For one thing they aren't using recursion but something like this for function:
Code: QB64: [Select]
  2. _Title "Iterated digits squaring v5 - Rosetta Code" ' b+ try 2021-09-04
  3. DefLng A-Z
  4. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  5. start! = Timer(.001)
  6. For i = 1 To 100000000 ' 100 million
  7.     If i Mod 1000000 = 0 Then Print i, c ' progress  18 secs on my system
  8.     c = c + sumSQRdigitsIs89(i)
  10. Print c, Timer(.001) - start!
  11.  
  12. Function sumSQRdigitsIs89 (number)
  13.     n = number
  14.     Do
  15.         While n > 0
  16.             d = n Mod 10
  17.             sum = sum + d * d
  18.             n = n \ 10
  19.         Wend
  20.         If sum = 89 Then
  21.             sumSQRdigitsIs89 = 1: Exit Function
  22.         ElseIf sum = 1 Then
  23.             sumSQRdigitsIs89 = 0: Exit Function
  24.         Else
  25.             n = sum
  26.             sum = 0
  27.         End If
  28.     Loop

I am down from 36 secs v4 to 18 secs now v5 but no where near 2 millisecs. They do a bunch more though in main that I have to figure out.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 10:28:10 pm
OMG, Don't know what they did but it works in thousandths of a sec!
Code: QB64: [Select]
  2. _Title "Iterated digits squaring v6 - Rosetta Code" ' b+ try 2021-09-04
  3. DefLng A-Z
  4. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  5. start! = Timer(.001)
  6.  
  7. Dim sums(0 To 8 * 81) ' copied and translated to QB64 from FreeBASIC entry at Rosetta Code
  8. sums(0) = 1
  9. sums(1) = 0
  10. For n = 1 To 8
  11.     For i = n * 81 To 1 Step -1
  12.         For j = 1 To 9
  13.             s = j * j
  14.             If s > i Then Exit For
  15.             sums(i) = sums(i) + sums(i - s)
  16.         Next j
  17.     Next i
  18.     If n = 8 Then
  19.         count89 = 0
  20.         For i = 1 To n * 81
  21.             If sumSQRdigitsIs89(i) Then count89 = count89 + sums(i)
  22.         Next i
  23.         Print "There are"; count89; " numbers from 1 to 100 million ending with 89"
  24.     End If
  26. Print Timer(.001) - start!
  27.  
  28. Function sumSQRdigitsIs89 (number)
  29.     n = number
  30.     Do
  31.         While n > 0
  32.             d = n Mod 10
  33.             sum = sum + d * d
  34.             n = n \ 10
  35.         Wend
  36.         If sum = 89 Then
  37.             sumSQRdigitsIs89 = 1: Exit Function
  38.         ElseIf sum = 1 Then
  39.             sumSQRdigitsIs89 = 0: Exit Function
  40.         Else
  41.             n = sum
  42.             sum = 0
  43.         End If
  44.     Loop
  46.  

 
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 04, 2021, 10:49:35 pm
I remove the 2nd block For loop in main and move it outside to save a couple lines of code:
Code: QB64: [Select]
  2. _Title "Iterated digits squaring v7 - Rosetta Code" ' b+ try 2021-09-04
  3. DefLng A-Z
  4. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  5. start! = Timer(.001)
  6. Dim sums(0 To 8 * 81) ' copied and translated to QB64 from FreeBASIC entry at Rosetta Code
  7. sums(0) = 1
  8. sums(1) = 0
  9. For n = 1 To 8
  10.     For i = n * 81 To 1 Step -1
  11.         For j = 1 To 9
  12.             s = j * j
  13.             If s > i Then Exit For
  14.             sums(i) = sums(i) + sums(i - s)
  15.         Next j
  16.     Next i
  18. For i = 1 To 8 * 81
  19.     If sumSQRdigitsIs89(i) Then count89 = count89 + sums(i)
  21. Print "There are"; count89; " numbers from 1 to 100 million ending with 89"
  22. Print Timer(.001) - start!
  23.  
  24. Function sumSQRdigitsIs89 (number)
  25.     n = number
  26.     Do
  27.         While n > 0
  28.             d = n Mod 10
  29.             sum = sum + d * d
  30.             n = n \ 10
  31.         Wend
  32.         If sum = 89 Then
  33.             sumSQRdigitsIs89 = 1: Exit Function
  34.         ElseIf sum = 1 Then
  35.             sumSQRdigitsIs89 = 0: Exit Function
  36.         Else
  37.             n = sum
  38.             sum = 0
  39.         End If
  40.     Loop
  42.  
  43.  
  44.  
Title: Re: Iterated digits squaring - Rosetta Code
Post by: SMcNeill on September 04, 2021, 11:25:22 pm
You could probably do some precalculation and save time too.  For example:

s = j * j


Instead:

FOR j = 1 TO 9
   s(j) = j * j
NEXT

Then use s(j) directly, rather than calculating the value each loop.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 05, 2021, 02:08:57 am
Thanks @SMcNeill that s=j*j looks like it is needed in line 14, but I don't know.

I definitely don't know what is going in the first For loops in the main block.

Can anyone explain it?

The 81's are the maximum square for a digit if you have n digits then the maximum sum of them is n * 81 which is  allot less than the numbers we run through for the 89 sums. I did start a table that recorded where the sums would go, the did() array (in V2) so we could avoid doing those calculation sequences over and over. But I don't think the FreeBASIC code is doing quite the same thing.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: david_uwi on September 06, 2021, 03:57:14 am
We can't let freebasic beat QB64 so here's my code. The timing is not accurate because of the small execution time.
Code: QB64: [Select]
  1. nn = 8 'this is the number of digits 8 --> 100,000,000
  2. pp = 81 * nn
  3. DIM xa(pp) AS LONG
  4. DIM xb(pp, nn) AS LONG
  5. DIM qsq(12) AS INTEGER
  6. DIM sum AS LONG
  8. start! = TIMER(.001) 'this is not reliable for these short execution times
  9. FOR i = 1 TO 9
  10.     sq1 = i * i
  11.     qsq(i + 1) = sq1
  12.     xb(sq1, 1) = xb(sq1, 1) + 1
  14. qsq(1) = 0
  15. FOR jkl = 2 TO nn
  16.     FOR j = 1 TO pp
  17.         IF xb(j, jkl - 1) <> 0 THEN
  18.             FOR k = 1 TO 10
  19.                 ind = j + qsq(k)
  20.                 xb(ind, jkl) = xb(ind, jkl) + xb(j, jkl - 1)
  21.             NEXT k
  22.         END IF
  23.     NEXT j
  24. NEXT jkl
  25. FOR i = 1 TO pp
  26.     FOR jkl = 1 TO nn
  27.         xa(i) = xb(i, jkl) + xa(i)
  28.     NEXT jkl
  30. FOR i = 1 TO pp
  31.     IF xa(i) <> 0 THEN
  32.         sum = sum + xa(i)
  33.     END IF
  35. FOR i = 1 TO pp
  36.     IF xa(i) <> 0 THEN
  37.         z1 = i
  38.         k = 0
  39.         DO
  40.             k = k + 1
  41.             a = 0
  42.             a = z1 \ 100
  43.             z1 = z1 MOD 100
  44.             b = z1 \ 10
  45.             c = z1 MOD 10
  46.             z1 = a * a + b * b + c * c
  47.             IF z1 = 89 THEN m89 = m89 + xa(i): EXIT DO
  48.             IF z1 = 1 THEN m1 = m1 + xa(i): EXIT DO
  49.         LOOP
  50.     END IF
  52. PRINT "time taken= "; TIMER(.001) - start!
  53. PRINT "number ending in 89 = "; m89; ""
  54. PRINT "number ending in 1 = "; m1 + 1
  55. PRINT "total numbers = "; m1 + m89 + 1
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 06, 2021, 06:55:50 am
@david_uwi

I tried to give our codes more work to do so the times would be extended for comparing. I got the FB version timing number of digits 1 through 19 (after that even _Unsigned _Integer64 has overflow errors)
Code: QB64: [Select]
  2. _Title "Iterated digits squaring v8 - Rosetta Code" ' b+ try 2021-09-04  v8 2021-09-06
  3. ' ref http://rosettacode.org/wiki/Iterated_digits_squaring
  4. ' add more chores to v7 so takes enough time to differentiate with david_uwi's version
  5.  
  7. start! = Timer(.001)
  8. For nDigits = 1 To 19 ' it's wrong after 19
  9.     ReDim sums(0 To nDigits * 81) ' copied and translated to QB64 from FreeBASIC entry at Rosetta Code
  10.     sums(0) = 1
  11.     sums(1) = 0
  12.     For n = 1 To nDigits
  13.         For i = n * 81 To 1 Step -1
  14.             For j = 1 To 9
  15.                 s = j * j
  16.                 If s > i Then Exit For
  17.                 sums(i) = sums(i) + sums(i - s)
  18.             Next j
  19.         Next i
  20.     Next
  21.     count89 = 0
  22.     For i = 1 To nDigits * 81
  23.         If sumSQRdigitsIs89(i) Then count89 = count89 + sums(i)
  24.     Next i
  25.     Print "For 10 ^"; nDigits; "there are"; count89; "numbers ending with 89."
  27. Print Timer(.001) - start!
  28.  
  29. Function sumSQRdigitsIs89 (number)
  30.     n = number
  31.     Do
  32.         While n > 0
  33.             d = n Mod 10
  34.             sum = sum + d * d
  35.             n = n \ 10
  36.         Wend
  37.         If sum = 89 Then
  38.             sumSQRdigitsIs89 = 1: Exit Function
  39.         ElseIf sum = 1 Then
  40.             sumSQRdigitsIs89 = 0: Exit Function
  41.         Else
  42.             n = sum
  43.             sum = 0
  44.         End If
  45.     Loop
  47.  

Ha! still not enough work for one click of the clock!

I tried modifying your code but my attempts ran into wrong numbers after the number of digits hit 14?
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 06, 2021, 07:27:31 am
@david_uwi maybe you can see what's happening:

My attempt to mod your code (I tried to do one time stuff outside main loop but kept getting errors so tried just redoing everything at start of new nn (number of Digits) set in main For loop, better but errors after 13 digits).
Code: QB64: [Select]
  1. _Title "Iterated digits squaring - Rosetta Code david_uwi version mod b+"
  2. ' from   https://www.qb64.org/forum/index.php?topic=4160.msg135168#msg135168
  3. ' copied and modified by b+ for a timed test with FB version 2021-09-06
  4. ' mod notes: change all to _Integer64 and Loop nDigits 1 to 19
  5.  
  7. nn = 8 'this is the number of digits 8 --> 100,000,000
  8. start! = Timer(.001) 'this is not reliable for these short execution times
  9. For nn = 1 To 19
  10.     pp = 81 * nn
  11.     ReDim xa(pp)
  12.     ReDim xb(pp, nn)
  13.     ReDim qsq(12)
  14.     sum = 0
  15.     For i = 1 To 9
  16.         sq1 = i * i
  17.         qsq(i + 1) = sq1
  18.         xb(sq1, 1) = xb(sq1, 1) + 1
  19.     Next i
  20.     qsq(1) = 0
  21.     m89 = 0
  22.     For jkl = 2 To nn
  23.         For j = 1 To pp
  24.             If xb(j, jkl - 1) <> 0 Then
  25.                 For k = 1 To 10
  26.                     ind = j + qsq(k)
  27.                     xb(ind, jkl) = xb(ind, jkl) + xb(j, jkl - 1)
  28.                 Next k
  29.             End If
  30.         Next j
  31.     Next jkl
  32.     For i = 1 To pp
  33.         For jkl = 1 To nn
  34.             xa(i) = xb(i, jkl) + xa(i)
  35.         Next jkl
  36.     Next i
  37.     For i = 1 To pp
  38.         If xa(i) <> 0 Then
  39.             sum = sum + xa(i)
  40.         End If
  41.     Next i
  42.     For i = 1 To pp
  43.         If xa(i) <> 0 Then
  44.             z1 = i
  45.             k = 0
  46.             Do
  47.                 k = k + 1
  48.                 a = 0
  49.                 a = z1 \ 100
  50.                 z1 = z1 Mod 100
  51.                 b = z1 \ 10
  52.                 c = z1 Mod 10
  53.                 z1 = a * a + b * b + c * c
  54.                 If z1 = 89 Then m89 = m89 + xa(i): Exit Do
  55.                 If z1 = 1 Then m1 = m1 + xa(i): Exit Do
  56.             Loop
  57.         End If
  58.     Next i
  59.  
  60.     Print "For 10 ^"; nn; " the number ending in 89 ="; m89
  61.     'Print "number ending in 1 = "; m1 + 1
  62.     'Print "total numbers = "; m1 + m89 + 1
  64. Print "time taken= "; Timer(.001) - start!
  65.  
Title: Re: Iterated digits squaring - Rosetta Code
Post by: david_uwi on September 06, 2021, 07:58:32 am
It will not work after 13 digits because 81*13 >1000.
I was assuming that after the first iteration the numbers were <1000.

Code: QB64: [Select]
  1.     FOR i = 1 TO pp
  2.         IF xa(i) <> 0 THEN
  3.             z1 = i
  4.             DO
  5.                 d=0
  6.                 if z1>1000 then z1=z1-1000:d=1
  7.                 a = z1 \ 100
  8.                 z1 = z1 MOD 100
  9.                 b = z1 \ 10
  10.                 c = z1 MOD 10
  11.                 z1 = a * a + b * b + c * c + d
  12.                 IF z1 = 89 THEN m89 = m89 + xa(i): EXIT DO
  13.                 IF z1 = 1 THEN m1 = m1 + xa(i): EXIT DO
  14.             LOOP
  15.         END IF
  16.     NEXT i
Change the loop near the end that checks the numbers after the first iteration

I like these problems that cannot easily be "brute forced".
The trick with this one is that after the first iteration the all the numbers are reduced to 3 digits (or less).
So the program calculates these. Many of the original n-digit numbers will give the same value after the first iteration.
So instead of using the digits 1-9 you start with the square of these 1,4,9,16...
Then build up the (squares of) two digit numbers by combining all permutation of the one digit numbers.
Then build up the 3 digit numbers by combining the 2-digit with the one digit and so on.
Then add them all up. then check the <=3 digit number for 89 convergence (without using strings -because these are slow).
Title: Re: Iterated digits squaring - Rosetta Code
Post by: david_uwi on September 06, 2021, 10:31:41 am
Ah rookie mistake there on line 6. It should (of course) be >999 (not >1000)
Title: Re: Iterated digits squaring - Rosetta Code
Post by: bplus on September 07, 2021, 06:01:46 pm
@david_uwi  thanks for more clues in reply #15 and your fix for for going beyond 13 digits worked fine.
Title: Re: Iterated digits squaring - Rosetta Code
Post by: david_uwi on September 08, 2021, 03:29:50 am
There is actually no need for the outer loop (for ndigits =1 to 19).
The matrix ib contains all the information. ib(x,1) contains all the 1 digit numbers, ib(x,2) all the two digit numbers..
ib(x,9) all the nine digit numbers. So to get up to 5 digits add ib(x,1)+ib(x,2)+ib(x,3),ib(x,4)+ib(x,5).
When I say 5 digit I mean 10000-99999.
So it might be even quicker! May even beat the C++, but as qb64 is converted to C before compiling this is not surprising.
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