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math clean up

This commit is contained in:
~d6 2022-02-09 21:24:36 -05:00
parent 99e2ac5a1c
commit df971a1fc8
2 changed files with 99 additions and 103 deletions
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84
math32.tal
View File

@ -54,7 +54,6 @@
( - mul32 memory, 12 bytes ) ( - mul32 memory, 12 bytes )
( - _divmod32 memory, 16 bytes ) ( - _divmod32 memory, 16 bytes )
%RTN { JMP2r }
%TOR { ROT ROT } ( a b c -> c a b ) %TOR { ROT ROT } ( a b c -> c a b )
%COMPLEMENT32 { SWP2 #ffff EOR2 SWP2 #ffff EOR2 } %COMPLEMENT32 { SWP2 #ffff EOR2 SWP2 #ffff EOR2 }
%DUP4 { OVR2 OVR2 } %DUP4 { OVR2 OVR2 }
@ -73,7 +72,7 @@
,&loop JMP ,&loop JMP
&done &done
POP ( n ) POP ( n )
RTN JMP2r
@bitcount16 ( x* -> n^ ) @bitcount16 ( x* -> n^ )
SWP ( xlo xhi ) SWP ( xlo xhi )
@ -81,40 +80,40 @@
DUP #00 NEQ ( xlo nhi nhi!=0 ) DUP #00 NEQ ( xlo nhi nhi!=0 )
,&hi-set JCN ( xlo nhi ) ,&hi-set JCN ( xlo nhi )
SWP ;bitcount8 JSR2 ADD ( nhi+nlo ) SWP ;bitcount8 JSR2 ADD ( nhi+nlo )
RTN JMP2r
&hi-set &hi-set
SWP POP #08 ADD ( nhi+8 ) SWP POP #08 ADD ( nhi+8 )
RTN JMP2r
@bitcount32 ( x** -> n^ ) @bitcount32 ( x** -> n^ )
SWP2 ( xlo* xhi* ) SWP2 ( xlo* xhi* )
;bitcount16 JSR2 ( xlo* nhi ) ;bitcount16 JSR2 ( xlo* nhi )
DUP #00 NEQ ( xlo* nhi nhi!=0 ) DUP #00 NEQ ( xlo* nhi nhi!=0 )
,&hi-set JCN ( xlo* nhi ) ,&hi-set JCN ( xlo* nhi )
TOR ;bitcount16 JSR2 ADD RTN ( nhi+nlo ) TOR ;bitcount16 JSR2 ADD JMP2r ( nhi+nlo )
&hi-set &hi-set
TOR POP2 #10 ADD ( nhi+16 ) TOR POP2 #10 ADD ( nhi+16 )
RTN JMP2r
( equality ) ( equality )
( x == y ) ( x == y )
@eq32 ( xhi* xlo* yhi* ylo* -> bool^ ) @eq32 ( xhi* xlo* yhi* ylo* -> bool^ )
ROT2 EQU2 STH ROT2 EQU2 STH
EQU2 STHr AND RTN EQU2 STHr AND JMP2r
( x != y ) ( x != y )
@ne32 ( xhi* xlo* yhi* ylo* -> bool^ ) @ne32 ( xhi* xlo* yhi* ylo* -> bool^ )
ROT2 NEQ2 STH ROT2 NEQ2 STH
NEQ2 STHr ORA RTN NEQ2 STHr ORA JMP2r
( x == 0 ) ( x == 0 )
@is-zero32 ( x** -> bool^ ) @is-zero32 ( x** -> bool^ )
ORA2 #0000 EQU2 RTN ORA2 #0000 EQU2 JMP2r
( x != 0 ) ( x != 0 )
@non-zero32 ( x** -> bool^ ) @non-zero32 ( x** -> bool^ )
ORA2 #0000 NEQ2 RTN ORA2 #0000 NEQ2 JMP2r
( comparisons ) ( comparisons )
@ -122,51 +121,51 @@
@lt32 ( x** y** -> bool^ ) @lt32 ( x** y** -> bool^ )
ROT2 SWP2 ( xhi yhi xlo ylo ) ROT2 SWP2 ( xhi yhi xlo ylo )
LTH2 ,&lt-lo JCN ( xhi yhi ) LTH2 ,&lt-lo JCN ( xhi yhi )
LTH2 RTN LTH2 JMP2r
&lt-lo &lt-lo
GTH2 #00 EQU RTN GTH2 #00 EQU JMP2r
( x <= y ) ( x <= y )
@lteq32 ( x** y** -> bool^ ) @lteq32 ( x** y** -> bool^ )
ROT2 SWP2 ( xhi yhi xlo ylo ) ROT2 SWP2 ( xhi yhi xlo ylo )
GTH2 ,&gt-lo JCN ( xhi yhi ) GTH2 ,&gt-lo JCN ( xhi yhi )
GTH2 #00 EQU RTN GTH2 #00 EQU JMP2r
&gt-lo &gt-lo
LTH2 RTN LTH2 JMP2r
( x > y ) ( x > y )
@gt32 ( x** y** -> bool^ ) @gt32 ( x** y** -> bool^ )
ROT2 SWP2 ( xhi yhi xlo ylo ) ROT2 SWP2 ( xhi yhi xlo ylo )
GTH2 ,&gt-lo JCN ( xhi yhi ) GTH2 ,&gt-lo JCN ( xhi yhi )
GTH2 RTN GTH2 JMP2r
&gt-lo &gt-lo
LTH2 #00 EQU RTN LTH2 #00 EQU JMP2r
( x > y ) ( x > y )
@gteq32 ( x** y** -> bool^ ) @gteq32 ( x** y** -> bool^ )
ROT2 SWP2 ( xhi yhi xlo ylo ) ROT2 SWP2 ( xhi yhi xlo ylo )
LTH2 ,&lt-lo JCN ( xhi yhi ) LTH2 ,&lt-lo JCN ( xhi yhi )
LTH2 #00 EQU RTN LTH2 #00 EQU JMP2r
&lt-lo &lt-lo
GTH2 RTN GTH2 JMP2r
( bitwise operations ) ( bitwise operations )
( x & y ) ( x & y )
@and32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* ) @and32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
ROT2 AND2 STH2 AND2 STH2r RTN ROT2 AND2 STH2 AND2 STH2r JMP2r
( x | y ) ( x | y )
@or32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* ) @or32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
ROT2 ORA2 STH2 ORA2 STH2r RTN ROT2 ORA2 STH2 ORA2 STH2r JMP2r
( x ^ y ) ( x ^ y )
@xor32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* ) @xor32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
ROT2 EOR2 STH2 EOR2 STH2r RTN ROT2 EOR2 STH2 EOR2 STH2r JMP2r
( ~x ) ( ~x )
@complement32 ( x** -> ~x** ) @complement32 ( x** -> ~x** )
COMPLEMENT32 RTN COMPLEMENT32 JMP2r
( temporary registers ) ( temporary registers )
( shared by most operations, except mul32 and div32 ) ( shared by most operations, except mul32 and div32 )
@ -183,7 +182,6 @@
DUP #10 LTH ;rshift32-1 JCN2 ( x n ) DUP #10 LTH ;rshift32-1 JCN2 ( x n )
DUP #18 LTH ;rshift32-2 JCN2 ( x n ) DUP #18 LTH ;rshift32-2 JCN2 ( x n )
;rshift32-3 JMP2 ( x n ) ;rshift32-3 JMP2 ( x n )
RTN
( shift right by 0-7 bits ) ( shift right by 0-7 bits )
@rshift32-0 ( x** n^ -> x<<n ) @rshift32-0 ( x** n^ -> x<<n )
@ -192,7 +190,7 @@
#00 STHkr SFT2 #00 ;m32/z2 LDA ORA2 ;m32/z1 STA2 ( write z1,z2 ) #00 STHkr SFT2 #00 ;m32/z2 LDA ORA2 ;m32/z1 STA2 ( write z1,z2 )
#00 STHr SFT2 #00 ;m32/z1 LDA ORA2 ( compute z0,z1 ) #00 STHr SFT2 #00 ;m32/z1 LDA ORA2 ( compute z0,z1 )
;m32/z2 LDA2 ;m32/z2 LDA2
RTN JMP2r
( shift right by 8-15 bits ) ( shift right by 8-15 bits )
@rshift32-1 ( x** n^ -> x<<n ) @rshift32-1 ( x** n^ -> x<<n )
@ -201,7 +199,7 @@
#00 STHkr SFT2 #00 ;m32/z3 LDA ORA2 ;m32/z2 STA2 ( write z2,z3 ) #00 STHkr SFT2 #00 ;m32/z3 LDA ORA2 ;m32/z2 STA2 ( write z2,z3 )
#00 STHr SFT2 #00 ;m32/z2 LDA ORA2 ( compute z1,z2 ) #00 STHr SFT2 #00 ;m32/z2 LDA ORA2 ( compute z1,z2 )
#00 TOR ;m32/z3 LDA #00 TOR ;m32/z3 LDA
RTN JMP2r
( shift right by 16-23 bits ) ( shift right by 16-23 bits )
@rshift32-2 ( x** n^ -> x<<n ) @rshift32-2 ( x** n^ -> x<<n )
@ -209,14 +207,14 @@
STHkr SFT ;m32/z3 STA ( write z3 ) STHkr SFT ;m32/z3 STA ( write z3 )
#00 STHr SFT2 #00 ;m32/z3 LDA ORA2 ( compute z2,z3 ) #00 STHr SFT2 #00 ;m32/z3 LDA ORA2 ( compute z2,z3 )
#0000 SWP2 #0000 SWP2
RTN JMP2r
( shift right by 16-23 bits ) ( shift right by 16-23 bits )
@rshift32-3 ( x** n^ -> x<<n ) @rshift32-3 ( x** n^ -> x<<n )
#18 SUB STH POP2 POP ( x0 ) #18 SUB STH POP2 POP ( x0 )
#00 SWP #0000 SWP2 ( 00 00 00 x0 ) #00 SWP #0000 SWP2 ( 00 00 00 x0 )
STHr SFT STHr SFT
RTN JMP2r
( x << n ) ( x << n )
@lshift32 ( x** n^ -> x<<n ) @lshift32 ( x** n^ -> x<<n )
@ -224,7 +222,6 @@
DUP #10 LTH ;lshift32-1 JCN2 ( x n ) DUP #10 LTH ;lshift32-1 JCN2 ( x n )
DUP #18 LTH ;lshift32-2 JCN2 ( x n ) DUP #18 LTH ;lshift32-2 JCN2 ( x n )
;lshift32-3 JMP2 ( x n ) ;lshift32-3 JMP2 ( x n )
RTN
( shift left by 0-7 bits ) ( shift left by 0-7 bits )
@lshift32-0 ( x** n^ -> x<<n ) @lshift32-0 ( x** n^ -> x<<n )
@ -234,7 +231,7 @@
#00 SWP STHkr SFT2 #00 ;m32/z1 LDA ORA2 ;m32/z0 STA2 ( store z0,z1 ) #00 SWP STHkr SFT2 #00 ;m32/z1 LDA ORA2 ;m32/z0 STA2 ( store z0,z1 )
STHr SFT ;m32/z0 LDA ORA ( calculate z0 ) STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
;m32/z1 LDA ;m32/z2 LDA2 ;m32/z1 LDA ;m32/z2 LDA2
RTN JMP2r
( shift left by 8-15 bits ) ( shift left by 8-15 bits )
@lshift32-1 ( x** n^ -> x<<n ) @lshift32-1 ( x** n^ -> x<<n )
@ -244,7 +241,7 @@
STHr SFT ;m32/z0 LDA ORA ( calculate z0 ) STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
SWP POP ( x0 unused ) SWP POP ( x0 unused )
;m32/z1 LDA2 #00 ;m32/z1 LDA2 #00
RTN JMP2r
( shift left by 16-23 bits ) ( shift left by 16-23 bits )
@lshift32-2 ( x** n^ -> x<<n ) @lshift32-2 ( x** n^ -> x<<n )
@ -253,14 +250,14 @@
STHr SFT ;m32/z0 LDA ORA ( calculate z0 ) STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
STH POP2 STHr STH POP2 STHr
;m32/z1 LDA #0000 ;m32/z1 LDA #0000
RTN JMP2r
( shift left by 24-31 bits ) ( shift left by 24-31 bits )
@lshift32-3 ( x** n^ -> x<<n ) @lshift32-3 ( x** n^ -> x<<n )
#18 SUB #40 SFT ( x0 x1 x2 x3 r=[n-24]<<4 ) #18 SUB #40 SFT ( x0 x1 x2 x3 r=[n-24]<<4 )
SFT ( x0 x1 x2 x3<<r ) SFT ( x0 x1 x2 x3<<r )
SWP2 POP2 SWP POP #0000 #00 SWP2 POP2 SWP POP #0000 #00
RTN JMP2r
( arithmetic ) ( arithmetic )
@ -287,7 +284,7 @@
( load zhi,zlo ) ( load zhi,zlo )
;m32/z0 LDA2 ;m32/z2 LDA2 ;m32/z0 LDA2 ;m32/z2 LDA2
RTN JMP2r
( -x ) ( -x )
@negate32 ( x** -> -x** ) @negate32 ( x** -> -x** )
@ -297,11 +294,11 @@
,&done JCN ( xlo non-zero => don't inc hi ) ,&done JCN ( xlo non-zero => don't inc hi )
SWP2 INC2 SWP2 ( -xhi -xlo ) SWP2 INC2 SWP2 ( -xhi -xlo )
&done &done
RTN JMP2r
( x - y ) ( x - y )
@sub32 ( x** y** -> z** ) @sub32 ( x** y** -> z** )
;negate32 JSR2 ;add32 JSR2 RTN ;negate32 JSR2 ;add32 JMP2
( 16-bit multiplication ) ( 16-bit multiplication )
@mul16 ( x* y* -> z** ) @mul16 ( x* y* -> z** )
@ -325,8 +322,7 @@
( add z and a<<8 ) ( add z and a<<8 )
#00 ;m32/z1 LDA2 ;m32/z3 LDA #00 ;m32/z1 LDA2 ;m32/z3 LDA
;m32/w0 LDA2 ;m32/w2 LDA #00 ;m32/w0 LDA2 ;m32/w2 LDA #00
;add32 JSR2 ;add32 JMP2
RTN
( x * y ) ( x * y )
@mul32 ( x** y** -> z** ) @mul32 ( x** y** -> z** )
@ -339,7 +335,7 @@
( [x0*y0]<<32 will completely overflow ) ( [x0*y0]<<32 will completely overflow )
ADD2 ,&z0 LDR2 ADD2 ( sum += x0*y1<<16 + x1*y0<<16 ) ADD2 ,&z0 LDR2 ADD2 ( sum += x0*y1<<16 + x1*y0<<16 )
,&z1 LDR2 ,&z1 LDR2
RTN JMP2r
[ &x0 $2 &x1 $2 [ &x0 $2 &x1 $2
&y0 $2 &y1 $2 &y0 $2 &y1 $2
&z0 $2 &z1 $2 ] &z0 $2 &z1 $2 ]
@ -347,18 +343,18 @@
@div32 ( x** y** -> q** ) @div32 ( x** y** -> q** )
;_divmod32 JSR2 ;_divmod32 JSR2
;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2 ;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2
RTN JMP2r
@mod32 ( x** y** -> r** ) @mod32 ( x** y** -> r** )
;_divmod32 JSR2 ;_divmod32 JSR2
;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2 ;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2
RTN JMP2r
@divmod32 ( x** y** -> q** r** ) @divmod32 ( x** y** -> q** r** )
;_divmod32 JSR2 ;_divmod32 JSR2
;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2 ;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2
;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2 ;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2
RTN JMP2r
( calculate and store x / y and x % y ) ( calculate and store x / y and x % y )
@_divmod32 ( x** y** -> ) @_divmod32 ( x** y** -> )
@ -371,7 +367,7 @@
,&div0 LDR2 ,&div1 LDR2 ,&div0 LDR2 ,&div1 LDR2
;lt32 JSR2 ,&is-zero JCN ,&not-zero JMP ;lt32 JSR2 ,&is-zero JCN ,&not-zero JMP
&is-zero &is-zero
#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 RTN #0000 ,&quo0 STR2 #0000 ,&quo1 STR2 JMP2r
( x >= y so the answer is >= 1 ) ( x >= y so the answer is >= 1 )
&not-zero &not-zero
@ -411,7 +407,7 @@
,&div0 LDR2 ,&div1 LDR2 #01 ;rshift32 JSR2 ,&div1 STR2 ,&div0 STR2 ( div >>= 1 ) ,&div0 LDR2 ,&div1 LDR2 #01 ;rshift32 JSR2 ,&div1 STR2 ,&div0 STR2 ( div >>= 1 )
,&cur0 LDR2 ,&cur1 LDR2 #01 ;rshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2 ( cur >>= 1 ) ,&cur0 LDR2 ,&cur1 LDR2 #01 ;rshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2 ( cur >>= 1 )
,&cur0 LDR2 ,&cur1 LDR2 ;non-zero32 JSR2 ,&loop JCN ( if cur>0, loop. else we're done ) ,&cur0 LDR2 ,&cur1 LDR2 ;non-zero32 JSR2 ,&loop JCN ( if cur>0, loop. else we're done )
RTN JMP2r
( greatest common divisor - euclidean algorithm ) ( greatest common divisor - euclidean algorithm )
@gcd32 ( x** y** -> z** ) @gcd32 ( x** y** -> z** )
@ -431,4 +427,4 @@
,&loop JMP ,&loop JMP
&done &done
POP4 ( x ) POP4 ( x )
RTN JMP2r

10
test-math32.tal
View File

@ -32,7 +32,7 @@
DUP #3a LTH ,&hi-digit JCN DUP #3a LTH ,&hi-digit JCN
#57 ,&hi JMP &hi-digit #30 #57 ,&hi JMP &hi-digit #30
&hi SUB #40 SFT ORA &hi SUB #40 SFT ORA
RTN JMP2r
@buf $24 ( buffer used by test-interact ) @buf $24 ( buffer used by test-interact )
@pos $2 ( position in buffer used by test-interact ) @pos $2 ( position in buffer used by test-interact )
@ -74,14 +74,14 @@ RTN
@read-byte ( addr* -> x^ ) @read-byte ( addr* -> x^ )
LDA2 ;parse-byte JSR2 LDA2 ;parse-byte JSR2
RTN JMP2r
@read-long ( addr* -> x** ) @read-long ( addr* -> x** )
DUP2 ,&loc STR2 LDA2 ;parse-byte JSR2 DUP2 ,&loc STR2 LDA2 ;parse-byte JSR2
,&loc LDR2 #0002 ADD2 LDA2 ;parse-byte JSR2 ,&loc LDR2 #0002 ADD2 LDA2 ;parse-byte JSR2
,&loc LDR2 #0004 ADD2 LDA2 ;parse-byte JSR2 ,&loc LDR2 #0004 ADD2 LDA2 ;parse-byte JSR2
,&loc LDR2 #0006 ADD2 LDA2 ;parse-byte JSR2 ,&loc LDR2 #0006 ADD2 LDA2 ;parse-byte JSR2
RTN JMP2r
[ &loc $2 ] [ &loc $2 ]
( format: ". xxxxxxxx" -> "zzzzzzzz" ) ( format: ". xxxxxxxx" -> "zzzzzzzz" )
@ -148,11 +148,11 @@ RTN
SWP2 SWP2
SWP EMIT-BYTE EMIT-BYTE SWP EMIT-BYTE EMIT-BYTE
SWP EMIT-BYTE EMIT-BYTE SWP EMIT-BYTE EMIT-BYTE
RTN JMP2r
@emit-byte ( x^ -> ) @emit-byte ( x^ -> )
EMIT-BYTE EMIT-BYTE
RTN JMP2r
( convenience for less branching when printing hex ) ( convenience for less branching when printing hex )
@digits @digits