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Klaus2m5

Post subject: Re: A coding challenge: prime numbers

Posted: Sat Oct 24, 2015 6:18 am

Joined: Sat Jul 28, 2012 11:41 am
Posts: 442
Location: Wiesbaden, Germany

As Ed already said it is taking the square root all the time instead of finding the next highest number by the square of the divisor once until a higher divisor must be used. Strange, that nobody spotted that at the time...

_________________
6502 sources on GitHub: https://github.com/Klaus2m5

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BigEd

Post subject: Re: A coding challenge: prime numbers

Posted: Sat Oct 24, 2015 11:57 am

Joined: Thu Dec 11, 2008 1:28 pm
Posts: 10800
Location: England

I had a look at Primes4. Oddly, fixing up the SQR calls didn't help all that much. Suppressing the printing of each prime with timings did help rather more. Replacing the decimal constant 6 with a variable didn't help much at all. End result, 132s to find all primes up to and including 7919.

Code:

   40MODE128:PRINT2;" is prime number 1":PRINT3;" is prime number 2"
   50H%=6:N%=5:S=SQR(N%):I%=2:O%=2:T%=TIME:REPEAT
   60D%=1:A%=4:F%=FALSE:IF(N%MOD3):REPEATD%=D%+A%:A%=H%-A%:F%=(N%MODD%)=0:UNTILF% OR D%>=S
   70IFN%=7919:PRINTN%;" is prime number ";O%;" after ";(TIME-T%)/100;" secs"
   80N%=N%+I%:S=SQR(N%):I%=6-I%:UNTILFALSE

(I'm using BASIC 4 on a Master - indeed, it's a 2MHz machine, mostly.)

As integer variables are used almost everywhere, this is a 32-bit program, compared to VTL's 16-bit nature. Another advantage VTL has is computing the quotient and remainder in one go.

I had a quick go at porting Klaus' program to BBC Basic, but it's not working yet...

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barrym95838

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Oct 27, 2015 6:57 am

Joined: Sun Jun 30, 2013 10:26 pm
Posts: 1929
Location: Sacramento, CA, USA

BigEd wrote:

... I had a quick go at porting Klaus' program to BBC Basic, but it's not working yet...

I believe that I captured the essence of what Klaus was doing, translated to Apple Integer BASIC:

Code:

   10 GOTO 1000
  100 N=N+2: GOSUB 200
  120 N=N+4: GOSUB 200: GOTO 100
  200 IF N<25 THEN 400
  210 IF N<U THEN 300
  230 V=V+2:U=V*V
  300 D=5
  310 IF N MOD D=0 THEN RETURN
  330 D=D+2: IF D>=V THEN 400
  350 IF N MOD D=0 THEN RETURN
  370 D=D+4: IF D<V THEN 310
  400 PRINT N:X=X-1
  430 IF X#0 THEN RETURN
  440 END
 1000 V=5:U=25
 1220 X=20: REM NUMBER OF PRIMES
 1230 N=2: GOSUB 200
 1240 N=3: GOSUB 200
 1250 N=5: GOSUB 200
 1260 GOTO 100

Mike B.

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Klaus2m5

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Oct 27, 2015 9:57 am

Joined: Sat Jul 28, 2012 11:41 am
Posts: 442
Location: Wiesbaden, Germany

I made some changes to Mike's Apple Integer Basic version to be able to run in EHBasic and ran it in my emulator.

Code:

   10 GOTO 1000
  100 N=N+2: GOSUB 200
  120 N=N+4: GOSUB 200: GOTO 100
  200 IF N<25 THEN 400
  210 IF N<U THEN 300
  230 V=V+2:U=V*V
  300 D=5
  310 Z=N/D: IF Z = INT(Z) THEN RETURN
  330 D=D+2: IF D>=V THEN 400
  350 Z=N/D: IF Z = INT(Z) THEN RETURN
  370 D=D+4: IF D<V THEN 310
  400 PRINT N:X=X-1
  430 IF X>0 THEN RETURN
  440 END
 1000 V=5:U=25
 1220 X=20: REM NUMBER OF PRIMES
 1230 N=2: GOSUB 200
 1240 N=3: GOSUB 200
 1250 N=5: GOSUB 200
 1260 GOTO 100

The search for 1000 primes took 165 seconds to complete.

Please be reminded, that EHBasic does not have integer variables (In BBC Basic I believe they even have a fixed location like VTL, no search needed) and EHBasic does not have a modulo function. In addition the BBC Basic versions utilizes loop structures VTL does not have.

On the other hand #= (GOTO, GOSUB) in VTL accepts variables which allowed

Code:

  210 #=N<U*Q
  220 Q=300
while U starts at 25 and Q at 400

to replace
  200 IF N<25 THEN 400
  210 IF N<U THEN 300

_________________
6502 sources on GitHub: https://github.com/Klaus2m5

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BigEd

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Oct 27, 2015 5:10 pm

Joined: Thu Dec 11, 2008 1:28 pm
Posts: 10800
Location: England

Thanks for those conversions! BBC Basic does allow GOTO <Variable> so I'd hoped to be able to emulate the behaviour of !. It should be possible, but I didn't get it working.

I made some small changes to both your conversions, to convert to BBC Basic, and then in one case to convert to integer variables - as Klaus says, they have the advantage of being integers, and in the case of single-letter variables the advantage of being placed in fixed locations known to the interpreter.

Klaus' EhBASIC version needs a tweak or two:

Code:

  400 PRINT;N;" ";:X=X-1
 1220 X=1000:REM NUMBER OF PRIMES

and then takes 153s on a BBC Master (2 MHz)

Mike's Integer Basic version needs a tweak or two:

Code:

  400 PRINT;" ";N;:X=X-1
  430 IF X<>0 THEN RETURN
 1220 X=1000: REM NUMBER OF PRIMES

and then takes 125s on a BBC Master (2 MHz)

After further conversion of this version to integer variables, it takes 93s on a BBC Master (2 MHz)
That version reads as:

Code:

   10 GOTO 1000
  100 N%=N%+2: GOSUB 200
  120 N%=N%+4: GOSUB 200: GOTO 100
  200 IF N%<25 THEN 400
  210 IF N%<U% THEN 300
  230 V%=V%+2:U%=V%*V%
  300 D%=5
  310 IF N% MOD D%=0 THEN RETURN
  330 D%=D%+2: IF D%>=V% THEN 400
  350 IF N% MOD D%=0 THEN RETURN
  370 D%=D%+4: IF D%<V% THEN 310
  400 PRINT ;" ";N%;:X%=X%-1
  430 IF X%<>0 THEN RETURN
  440 END
 1000 V%=5:U%=25
 1220 X%=1000: REM NUMBER OF PRIMES
 1230 N%=2: GOSUB 200
 1240 N%=3: GOSUB 200
 1250 N%=5: GOSUB 200
 1260 GOTO 100

I further converted the constant integers and constant line numbers to variables, but it slowed down slightly to 96s. So instead I stripped spaces and removed some comparisons to zero, and got it down to a tad under 89s. It's less readable:

Code:

   10GOTO1000
  100N%=N%+2:GOSUB200:N%=N%+4:GOSUB200:GOTO100
  200IFN%<25THEN400
  210IFN%<U%THEN300
  230V%=V%+2:U%=V%*V%
  300D%=5
  310IFN%MODD%:ELSERETURN
  330D%=D%+2:IFD%>=V%THEN400
  350IFN%MODD%:ELSERETURN
  370D%=D%+4:IFD%<V%THEN310
  400PRINT;" ";N%;:X%=X%-1
  430IFX%RETURN
  440END
 1000V%=5:U%=25
 1220X%=1000: REM NUMBER OF PRIMES
 1230N%=2: GOSUB 200
 1240N%=3: GOSUB 200
 1250N%=5: GOSUB 200
 1260GOTO 100

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Klaus2m5

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Oct 27, 2015 7:06 pm

Joined: Sat Jul 28, 2012 11:41 am
Posts: 442
Location: Wiesbaden, Germany

Quote:

Klaus' EhBASIC version needs a tweak or two and then takes 153s on a BBC Master (2 MHz)
Mike's Integer Basic version needs a tweak or two and then takes 125s on a BBC Master (2 MHz)

I had to work around EHBasic not having a modulo function. So the difference in runtime should be from converting the trial divisions:

Code:

  310 IF N MOD D=0 THEN RETURN
  350 IF N MOD D=0 THEN RETURN

to:

Code:

  310 Z=N/D: IF Z = INT(Z) THEN RETURN
  350 Z=N/D: IF Z = INT(Z) THEN RETURN

_________________
6502 sources on GitHub: https://github.com/Klaus2m5

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BigEd

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Oct 27, 2015 7:14 pm

Joined: Thu Dec 11, 2008 1:28 pm
Posts: 10800
Location: England

I ran a quick test: MOD is very slightly faster than / (on reals, on the Beeb) but the call to INT costs some more too.

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pebmeister

Post subject: Re: A coding challenge: prime numbers

Posted: Mon Dec 07, 2015 1:31 am

Joined: Tue Feb 19, 2013 12:29 am
Posts: 32
Location: Marlborough, Ma

I used my assembler scripting feature I can generate the primes in preprocessing :lol:

It theoretically uses 0 cycles

Code:

;***************************************
;  C:\Users\Paul\Perforce\paul_Paul-PC_2148\pasm64\windows\pasms64\..\..\test\prime.a
;***************************************
                                                  
                                                      .org $1000
                                                  
                                                      .var LoopCounter
                                                      .var LoopCounter2
                                                      .var prime
                                                      .var remainder
                                                  
                                                      .for LoopCounter = 2 .To 100
                                                          prime = 1
                                                          .For LoopCounter2 = 2 .To LoopCounter - 1
                                                              Remainder = LoopCounter % LoopCounter2
                                                              .If (Remainder == 0)
                                                                  Prime = 0
                                                                  LoopCounter2 = LoopCounter + 1
                                                              .endif
                                                          .Next LoopCounter2
                                                  
                                                          .If (Prime > 0)
                                                              .byte LoopCounter
                                                          .endif
                                                  
$1000: $02               .db $02                      .Next LoopCounter
$1001: $03               .db $03
$1002: $05               .db $05
$1003: $07               .db $07
$1004: $0B               .db $0B
$1005: $0D               .db $0D
$1006: $11               .db $11
$1007: $13               .db $13
$1008: $17               .db $17
$1009: $1D               .db $1D
$100A: $1F               .db $1F
$100B: $25               .db $25
$100C: $29               .db $29
$100D: $2B               .db $2B
$100E: $2F               .db $2F
$100F: $35               .db $35
$1010: $3B               .db $3B
$1011: $3D               .db $3D
$1012: $43               .db $43
$1013: $47               .db $47
$1014: $49               .db $49
$1015: $4F               .db $4F
$1016: $53               .db $53
$1017: $59               .db $59
$1018: $61               .db $61

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Martin_H

Post subject: Re: A coding challenge: prime numbers

Posted: Tue Dec 08, 2015 1:01 am

Joined: Wed Jan 08, 2014 3:31 pm
Posts: 575

OK, that's a riot.

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pebmeister

Post subject: Re: A coding challenge: prime numbers

Posted: Wed Dec 09, 2015 9:43 pm

Joined: Tue Feb 19, 2013 12:29 am
Posts: 32
Location: Marlborough, Ma

Here another method. When I first created the loops the second loop max was of course the square root to the first loop index.
I noticed a pattern with the square roots
2 2 3 3 3 4 4 4 4 etc.

Using this pattern I came up with this for C.
Notice how the max of the second loop is calculated.

Code:

void Prime(int max)
{
   int loopCounter = 0;
   int loopCounter2 = 0;
   int prime = 0;
   int remainder = 0;
   int maxCheckCount = 0;  
   int maxCheck = 1;
   int numPrimes = 0;
   
   if (max >= 2)
      printf(" %d\n", 2);
      
   for (loopCounter = 3; loopCounter <= max; loopCounter += 2)
   {
      prime = 1;
      maxCheckCount++;
      if (maxCheckCount == maxCheck)
      {
         maxCheck++;
         maxCheckCount = 0;
      }

      for (loopCounter2 = 3; loopCounter2 <= maxCheck; loopCounter2 += 2)
      {
         remainder = loopCounter % loopCounter2;
         if (remainder == 0)
         {
            prime = 0;
            break;
         }
      }

      if (prime > 0)
      {
         printf(" %d\n", loopCounter);
      }   
   }   
}

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tmr4

Post subject: Re: A coding challenge: prime numbers

Posted: Thu Jul 14, 2022 8:02 am

Joined: Sat Feb 19, 2022 10:14 pm
Posts: 147

I came across the Sieve of Eratosthenes routine in the E&L '816 programming manual (Listing 14.11, E&L pages 228-229 in my version) and decided to add some benchmarking to my system. Interesting contrasting with the routines here.

As a clarification for future readers:

BigEd wrote:

Thanks for your two offerings Michael - I notice one prints out 1900 which is I think the correct number of primes less than 16384, but the other prints out 1899. One thing I like about the 20 primes challenge is that it could easily show up an off-by-one error in the counting. Points deducted for off-by-one errors!

The two offerings mentioned (Forth routines listed here) are actually consistent. The first calculates the primes between 2 and 16384. The second, a slightly modified version from the Jan 1983 Byte benchmarking article (links here) calculates the primes between 3 and 16384.

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drogon

Post subject: Re: A coding challenge: prime numbers

Posted: Thu Jul 14, 2022 7:13 pm

Joined: Wed Feb 14, 2018 2:33 pm
Posts: 1412
Location: Scotland

Old thread resurrected, so since I have a 65816 BCPL system, then the naive "trial division" test version is:

Code:

GET "libhdr.h"
GET "stringLib.h"
GET "sys.h"
GET "math.h"

LET start (argc, argv) = VALOF
{
  LET numPrimes = 20
  LET numFound  =  1
  LET prime     =  2
  LET isPrime   =  ?
  LET limit     =  ?

  IF argc = 2 THEN
    numPrimes := str2numb (argv!1)

  writef ("Calculating the first %n prime numbers*n", numPrimes)

// We know 2 is prime, so..

  writef ("%4d", prime)

  WHILE numFound < numPrimes DO
  {
    isPrime := TRUE     // Until we find otherwise...
    prime := prime + 1
    limit := FIX sys (Sys_flt, fl_sqrt, FLOAT prime)
    FOR i = 2 TO limit DO
      IF (prime MOD i) = 0 THEN
      {
        isPrime := FALSE
        BREAK
      }

    IF isPrime THEN
    {
      numFound := numFound + 1
      writef ("%4d", prime)
      IF (numFound MOD 16) = 0 THEN
        writef ("*n")
    }
  }

  newline ()

  RESULTIS 0
}

And running it:

Code:

% time primes
Calculating the first 20 prime numbers
   2   3   5   7  11  13  17  19  23  29  31  37  41  43  47  53
  59  61  67  71
Time: 171mS

It is, of-course non-linear in time:

Code:

% time primes 100
Calculating the first 100 prime numbers
   2   3   5   7  11  13  17  19  23  29  31  37  41  43  47  53
  59  61  67  71  73  79  83  89  97 101 103 107 109 113 127 131
 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223
 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311
 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409
 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503
 509 521 523 541
Time: 907mS

And for more fun, the first 1000 primes:

Code:

Calculating the first 1000 prime numbers
    2    3    5    7   11   13   17   19   23   29   31   37   41   43
   47   53   59   61   67   71   73   79   83   89   97  101  103  107
  109  113  127  131  137  139  149  151  157  163  167  173  179  181
  191  193  197  199  211  223  227  229  233  239  241  251  257  263
  269  271  277  281  283  293  307  311  313  317  331  337  347  349
  353  359  367  373  379  383  389  397  401  409  419  421  431  433
  439  443  449  457  461  463  467  479  487  491  499  503  509  521
  523  541  547  557  563  569  571  577  587  593  599  601  607  613
  617  619  631  641  643  647  653  659  661  673  677  683  691  701
  709  719  727  733  739  743  751  757  761  769  773  787  797  809
  811  821  823  827  829  839  853  857  859  863  877  881  883  887
  907  911  919  929  937  941  947  953  967  971  977  983  991  997
 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 1087 1091
 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 1193
 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291
 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423
 1427 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493
 1499 1511 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601
 1607 1609 1613 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699
 1709 1721 1723 1733 1741 1747 1753 1759 1777 1783 1787 1789 1801 1811
 1823 1831 1847 1861 1867 1871 1873 1877 1879 1889 1901 1907 1913 1931
 1933 1949 1951 1973 1979 1987 1993 1997 1999 2003 2011 2017 2027 2029
 2039 2053 2063 2069 2081 2083 2087 2089 2099 2111 2113 2129 2131 2137
 2141 2143 2153 2161 2179 2203 2207 2213 2221 2237 2239 2243 2251 2267
 2269 2273 2281 2287 2293 2297 2309 2311 2333 2339 2341 2347 2351 2357
 2371 2377 2381 2383 2389 2393 2399 2411 2417 2423 2437 2441 2447 2459
 2467 2473 2477 2503 2521 2531 2539 2543 2549 2551 2557 2579 2591 2593
 2609 2617 2621 2633 2647 2657 2659 2663 2671 2677 2683 2687 2689 2693
 2699 2707 2711 2713 2719 2729 2731 2741 2749 2753 2767 2777 2789 2791
 2797 2801 2803 2819 2833 2837 2843 2851 2857 2861 2879 2887 2897 2903
 2909 2917 2927 2939 2953 2957 2963 2969 2971 2999 3001 3011 3019 3023
 3037 3041 3049 3061 3067 3079 3083 3089 3109 3119 3121 3137 3163 3167
 3169 3181 3187 3191 3203 3209 3217 3221 3229 3251 3253 3257 3259 3271
 3299 3301 3307 3313 3319 3323 3329 3331 3343 3347 3359 3361 3371 3373
 3389 3391 3407 3413 3433 3449 3457 3461 3463 3467 3469 3491 3499 3511
 3517 3527 3529 3533 3539 3541 3547 3557 3559 3571 3581 3583 3593 3607
 3613 3617 3623 3631 3637 3643 3659 3671 3673 3677 3691 3697 3701 3709
 3719 3727 3733 3739 3761 3767 3769 3779 3793 3797 3803 3821 3823 3833
 3847 3851 3853 3863 3877 3881 3889 3907 3911 3917 3919 3923 3929 3931
 3943 3947 3967 3989 4001 4003 4007 4013 4019 4021 4027 4049 4051 4057
 4073 4079 4091 4093 4099 4111 4127 4129 4133 4139 4153 4157 4159 4177
 4201 4211 4217 4219 4229 4231 4241 4243 4253 4259 4261 4271 4273 4283
 4289 4297 4327 4337 4339 4349 4357 4363 4373 4391 4397 4409 4421 4423
 4441 4447 4451 4457 4463 4481 4483 4493 4507 4513 4517 4519 4523 4547
 4549 4561 4567 4583 4591 4597 4603 4621 4637 4639 4643 4649 4651 4657
 4663 4673 4679 4691 4703 4721 4723 4729 4733 4751 4759 4783 4787 4789
 4793 4799 4801 4813 4817 4831 4861 4871 4877 4889 4903 4909 4919 4931
 4933 4937 4943 4951 4957 4967 4969 4973 4987 4993 4999 5003 5009 5011
 5021 5023 5039 5051 5059 5077 5081 5087 5099 5101 5107 5113 5119 5147
 5153 5167 5171 5179 5189 5197 5209 5227 5231 5233 5237 5261 5273 5279
 5281 5297 5303 5309 5323 5333 5347 5351 5381 5387 5393 5399 5407 5413
 5417 5419 5431 5437 5441 5443 5449 5471 5477 5479 5483 5501 5503 5507
 5519 5521 5527 5531 5557 5563 5569 5573 5581 5591 5623 5639 5641 5647
 5651 5653 5657 5659 5669 5683 5689 5693 5701 5711 5717 5737 5741 5743
 5749 5779 5783 5791 5801 5807 5813 5821 5827 5839 5843 5849 5851 5857
 5861 5867 5869 5879 5881 5897 5903 5923 5927 5939 5953 5981 5987 6007
 6011 6029 6037 6043 6047 6053 6067 6073 6079 6089 6091 6101 6113 6121
 6131 6133 6143 6151 6163 6173 6197 6199 6203 6211 6217 6221 6229 6247
 6257 6263 6269 6271 6277 6287 6299 6301 6311 6317 6323 6329 6337 6343
 6353 6359 6361 6367 6373 6379 6389 6397 6421 6427 6449 6451 6469 6473
 6481 6491 6521 6529 6547 6551 6553 6563 6569 6571 6577 6581 6599 6607
 6619 6637 6653 6659 6661 6673 6679 6689 6691 6701 6703 6709 6719 6733
 6737 6761 6763 6779 6781 6791 6793 6803 6823 6827 6829 6833 6841 6857
 6863 6869 6871 6883 6899 6907 6911 6917 6947 6949 6959 6961 6967 6971
 6977 6983 6991 6997 7001 7013 7019 7027 7039 7043 7057 7069 7079 7103
 7109 7121 7127 7129 7151 7159 7177 7187 7193 7207 7211 7213 7219 7229
 7237 7243 7247 7253 7283 7297 7307 7309 7321 7331 7333 7349 7351 7369
 7393 7411 7417 7433 7451 7457 7459 7477 7481 7487 7489 7499 7507 7517
 7523 7529 7537 7541 7547 7549 7559 7561 7573 7577 7583 7589 7591 7603
 7607 7621 7639 7643 7649 7669 7673 7681 7687 7691 7699 7703 7717 7723
 7727 7741 7753 7757 7759 7789 7793 7817 7823 7829 7841 7853 7867 7873
 7877 7879 7883 7901 7907 7919
Time: 18796mS

As for the sieve method... I might do that later, but years back when I first started programming (like 1978 or so!) I'd write Basic programs to calculate grids and grids of varying width and height, convinced that one day I'd find a magic pattern and "solve" the prime number algorithm once and for all... I found many patterns but none worked for very long... (and I probably wasted far too much printer paper to boot!)

Cheers,

-Gordon

_________________
--
Gordon Henderson.
See my Ruby 6502 and 65816 SBC projects here: https://projects.drogon.net/ruby/

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