primes32

primes32.tal

@@ -0,0 +1,76 @@
+( primes32.tal )
+( )
+( Uses a simple trial-divion method to find primes.    )
+( )
+( To determine if x is prime we:                       )
+( 1. Check if x is 2 (prime)                           )
+( 2. Check if x is even (not prime)                    )
+( 3. Starting with i=3, we see if x%i is 0             )
+(   a. We increment i by 2 to avoid even i             )
+(   b. We stop when x < i*i                            )
+( 4. If we didn't find an i, x is prime.               )
+( )
+( This method can be fast for some large composite     )
+( numbers but is quite slow for large primes.          )
+( )
+( On my machine, 0x7fffffff was determined to be prime )
+( in 0.5 seconds, but 0xfffffffb ran for 7 minutes     )
+( without finishing. Both are prime. By contrast       )
+( 0xffffffff was found be composite in 0.02 seconds.   )
+( )
+( Smaller primes also run fairly quickly: 0x17b5d was  )
+( determined to be prime in 0.02 seconds.              )
+
+%EMIT { #18 DEO }
+%DIGIT { #00 SWP ;digits ADD2 LDA EMIT }
+%SPACE { #20 EMIT }
+%NEWLINE { #0a EMIT }
+%EMIT-BYTE { DUP #04 SFT DIGIT #0f AND DIGIT }
+%DEBUG { #ff #0e DEO }
+
+|0100
+    ( number to check comes first )
+    #7fff #ffff
+    OVR2 OVR2 ;is-prime32 JSR2 ( test for primality )
+    STH ;emit-long JSR2 SPACE STHr EMIT-BYTE NEWLINE ( output )
+    #00 DIV #00 ( exit with /0 to make timing easier )
+    BRK
+
+( include 32-bit math library )
+~math32.tal
+
+( return 01 if x is a prime number, else 00 )
+( works for x >= 2 )
+@is-prime32 ( x** -> bool^ )
+    ,&x1 STR2 ,&x0 STR2 ,&x0 LDR2 ,&x1 LDR2 ( store and reload x )
+    DUP4 LIT2 &two0 0000 LIT2 &two1 0002 ;ne32 JSR2 ( x is 2? )
+    ,&not-two JCN POP4 #01 JMP2r ( 2 is prime )
+    &not-two DUP #01 AND ( x x&1 )
+    ,&not-even JCN POP4 #00 JMP2r ( x is even: not prime )
+    &not-even #0000 ,&i0 STR2 #0003 ,&i1 STR2 ( x i<-3 )
+    ,&i0 LDR2 ,&i1 LDR2 ( load our candidate, i )
+    ,&loop JMP ( jump over register data to loop label )
+    [ &i0 0000 &i1 0000 &x0 0000 &x1 0000 ] ( registers )
+    &loop ( x i )
+    ,&x0 LDR2 ,&x1 LDR2 ,&i0 LDR2 ,&i1 LDR2 ( x i x i )
+    DUP4 ;mul32 JSR2 ;lt32 JSR2 ( x i x<i*i )
+    ,&finished JCN ( x i )
+    ,&x0 LDR2 ,&x1 LDR2 ,&i0 LDR2 ,&i1 LDR2 ( x i x i )
+    ;mod32 JSR2 ;is-zero32 JSR2 ( x i x//i^ )
+    STH ,&two0 LDR2 ,&two1 LDR2 ;add32 JSR2 ( x i+2 )
+    ,&i1 STR2 ,&i0 STR2 ,&i0 LDR2 ,&i1 LDR2 ( write i+2 to register )
+    STHr ( x i+2 x//i^ )
+    ,&i-divides-x JCN ( x j )
+    ,&loop JMP ( if x<j*j, loop )
+    &i-divides-x POP4 POP4 #00 JMP2r ( since i divides x, not prime )
+    &finished POP4 POP4 #01 JMP2r ( didn't find divisors, prime )
+
+( print a long value as hex )
+@emit-long ( x** -> )
+    SWP2 SWP EMIT-BYTE EMIT-BYTE
+         SWP EMIT-BYTE EMIT-BYTE JMP2r
+
+( convenience for less branching when printing hex )
+@digits
+    30 31 32 33 34 35 36 37
+    38 39 61 62 63 64 65 66