From d5951e0a53e1299d66cea78ef43312c8591e50fd Mon Sep 17 00:00:00 2001
From: d6 <d_m@plastic-idolatry.com>
Date: Mon, 3 Jan 2022 00:31:29 -0500
Subject: [PATCH] primes bug fixes

---
 primes32.tal | 26 +++++++++++++++-----------
 1 file changed, 15 insertions(+), 11 deletions(-)

diff --git a/primes32.tal b/primes32.tal
index c53dc49..ad03ef0 100644
--- a/primes32.tal
+++ b/primes32.tal
@@ -7,16 +7,15 @@
 ( 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                            )
+(   b. We stop when x < i*i or i=0xffff                )
 ( 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.          )
+( numbers but is slower 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.   )
+( On my machine, checking 0x7fffffff took 0.5 seconds  )
+( and checking 0xfffffffb took 0.9 seconds. Both are   )
+( prime numbers.                                       )
 ( )
 ( Smaller primes also run fairly quickly: 0x17b5d was  )
 ( determined to be prime in 0.02 seconds.              )
@@ -30,7 +29,7 @@
 
 |0100
     ( number to check comes first )
-    #7fff #ffff
+    #fffe #0001
     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 )
@@ -43,21 +42,26 @@
 ( 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? )
+    DUP4 #0000 LIT2 &two 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 )
+    &not-even DUP4 #0000 #0003 ;ne32 JSR2 ( x is 3? )
+    ,&not-three JCN POP4 #01 JMP2r ( 3 is prime )
+    &not-three #0000 ,&i0 STR2 #0005 ,&i1 STR2 ( x i<-5 )
+    ,&two LDR2 ,&inc STR2
     ,&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 )
+    [ &i0 0000 &i1 0000 &x0 0000 &x1 0000 &inc 0000 &mask 0006 ] ( 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 )
+    STH DUP2 #ffff EQU2 STHr ORA ( x i x<i*i||i=0xffff )
     ,&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 )
+    STH #0000 ,&inc LDR2 ;add32 JSR2 ( x i+2 )
+    ,&inc LDR2 ,&mask LDR2 EOR2 ,&inc STR2 ( inc<-inc^6 )
     ,&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 )