nxu/primes32.tal

77 lines
2.8 KiB
Tal

( 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