81 lines
3.0 KiB
Tal
81 lines
3.0 KiB
Tal
( primes32.tal )
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( )
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( Uses a simple trial-divion method to find primes. )
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( )
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( To determine if x is prime we: )
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( 1. Check if x is 2 (prime) )
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( 2. Check if x is even (not prime) )
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( 3. Starting with i=3, we see if x%i is 0 )
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( a. We increment i by 2 to avoid even i )
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( b. We stop when x < i*i or i=0xffff )
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( 4. If we didn't find an i, x is prime. )
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( )
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( This method can be fast for some large composite )
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( numbers but is slower for large primes. )
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( )
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( On my machine, checking 0x7fffffff took 0.5 seconds )
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( and checking 0xfffffffb took 0.9 seconds. Both are )
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( prime numbers. )
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( )
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( Smaller primes also run fairly quickly: 0x17b5d was )
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( determined to be prime in 0.02 seconds. )
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%EMIT { #18 DEO }
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%DIGIT { #00 SWP ;digits ADD2 LDA EMIT }
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%SPACE { #20 EMIT }
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%NEWLINE { #0a EMIT }
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%EMIT-BYTE { DUP #04 SFT DIGIT #0f AND DIGIT }
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%DEBUG { #ff #0e DEO }
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|0100
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( number to check comes first )
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#fffe #0001
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OVR2 OVR2 ;is-prime32 JSR2 ( test for primality )
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STH ;emit-long JSR2 SPACE STHr EMIT-BYTE NEWLINE ( output )
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#00 DIV #00 ( exit with /0 to make timing easier )
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BRK
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( include 32-bit math library )
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~math32.tal
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( return 01 if x is a prime number, else 00 )
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( works for x >= 2 )
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@is-prime32 ( x** -> bool^ )
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,&x1 STR2 ,&x0 STR2 ,&x0 LDR2 ,&x1 LDR2 ( store and reload x )
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DUP4 #0000 LIT2 &two 0002 ;ne32 JSR2 ( x is 2? )
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,¬-two JCN POP4 #01 JMP2r ( 2 is prime )
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¬-two DUP #01 AND ( x x&1 )
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,¬-even JCN POP4 #00 JMP2r ( x is even: not prime )
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¬-even DUP4 #0000 #0003 ;ne32 JSR2 ( x is 3? )
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,¬-three JCN POP4 #01 JMP2r ( 3 is prime )
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¬-three #0000 ,&i0 STR2 #0005 ,&i1 STR2 ( x i<-5 )
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,&two LDR2 ,&inc STR2
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,&i0 LDR2 ,&i1 LDR2 ( load our candidate, i )
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,&loop JMP ( jump over register data to loop label )
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[ &i0 0000 &i1 0000 &x0 0000 &x1 0000 &inc 0000 &mask 0006 ] ( registers )
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&loop ( x i )
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,&x0 LDR2 ,&x1 LDR2 ,&i0 LDR2 ,&i1 LDR2 ( x i x i )
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DUP4 ;mul32 JSR2 ;lt32 JSR2 ( x i x<i*i )
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STH DUP2 #ffff EQU2 STHr ORA ( x i x<i*i||i=0xffff )
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,&finished JCN ( x i )
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,&x0 LDR2 ,&x1 LDR2 ,&i0 LDR2 ,&i1 LDR2 ( x i x i )
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;mod32 JSR2 ;is-zero32 JSR2 ( x i x//i^ )
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STH #0000 ,&inc LDR2 ;add32 JSR2 ( x i+2 )
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,&inc LDR2 ,&mask LDR2 EOR2 ,&inc STR2 ( inc<-inc^6 )
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,&i1 STR2 ,&i0 STR2 ,&i0 LDR2 ,&i1 LDR2 ( write i+2 to register )
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STHr ( x i+2 x//i^ )
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,&i-divides-x JCN ( x j )
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,&loop JMP ( if x<j*j, loop )
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&i-divides-x POP4 POP4 #00 JMP2r ( since i divides x, not prime )
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&finished POP4 POP4 #01 JMP2r ( didn't find divisors, prime )
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( print a long value as hex )
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@emit-long ( x** -> )
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SWP2 SWP EMIT-BYTE EMIT-BYTE
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SWP EMIT-BYTE EMIT-BYTE JMP2r
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( convenience for less branching when printing hex )
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@digits
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30 31 32 33 34 35 36 37
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38 39 61 62 63 64 65 66
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