new, improved, optimized
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math32.tal
296
math32.tal
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@ -52,55 +52,29 @@
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( )
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( - shared memory, 16 bytes )
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( - mul32 memory, 12 bytes )
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( - _divmod32 memory, 16 bytes )
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( - z_divmod32 memory, 16 bytes )
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( bitcount: number of bits needed to represent number )
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( equivalent to floor[log2[x]] + 1 )
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@bitcount8 ( x^ -> n^ )
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#00 SWP ( n x )
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&loop
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DUP #00 EQU ( n x x=0 )
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,&done JCN ( n x )
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#01 SFT ( n x>>1 )
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SWP INC SWP ( n+1 x>>1 )
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,&loop JMP
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&done
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POP ( n )
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JMP2r
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LITr 00 &loop DUP ?{ POP STHr JMP2r } #01 SFT INCr !&loop
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@bitcount16 ( x* -> n^ )
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SWP ( xlo xhi )
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;bitcount8 JSR2 ( xlo nhi )
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DUP #00 NEQ ( xlo nhi nhi!=0 )
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,&hi-set JCN ( xlo nhi )
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SWP ;bitcount8 JSR2 ADD ( nhi+nlo )
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JMP2r
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&hi-set
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NIP #08 ADD ( nhi+8 )
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JMP2r
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LITr 00 &loop ORAk ?{ POP2 STHr JMP2r } #01 SFT2 INCr !&loop
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@bitcount32 ( x** -> n^ )
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SWP2 ( xlo* xhi* )
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;bitcount16 JSR2 ( xlo* nhi )
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DUP #00 NEQ ( xlo* nhi nhi!=0 )
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,&hi-set JCN ( xlo* nhi )
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ROT ROT ;bitcount16 JSR2 ADD JMP2r ( nhi+nlo )
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&hi-set
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ROT ROT POP2 #10 ADD ( nhi+16 )
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JMP2r
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SWP2 bitcount16 DUP ?{ POP !bitcount16 } #10 NIP2 ADD JMP2r
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( equality )
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( x == y )
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@eq32 ( xhi* xlo* yhi* ylo* -> bool^ )
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ROT2 EQU2 STH
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EQU2 STHr AND JMP2r
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ROT2 EQU2 STH EQU2 STHr AND JMP2r
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( x != y )
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@ne32 ( xhi* xlo* yhi* ylo* -> bool^ )
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ROT2 NEQ2 STH
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NEQ2 STHr ORA JMP2r
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ROT2 NEQ2 STH NEQ2 STHr ORA JMP2r
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( x == 0 )
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@is-zero32 ( x** -> bool^ )
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@ -114,35 +88,19 @@
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( x < y )
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@lt32 ( x** y** -> bool^ )
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ROT2 SWP2 ( xhi yhi xlo ylo )
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LTH2 ,<-lo JCN ( xhi yhi )
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LTH2 JMP2r
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<-lo
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GTH2 #00 EQU JMP2r
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ROT2 SWP2 LTH2 ?{ LTH2 JMP2r } GTH2 #00 EQU JMP2r
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( x <= y )
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@lteq32 ( x** y** -> bool^ )
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ROT2 SWP2 ( xhi yhi xlo ylo )
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GTH2 ,>-lo JCN ( xhi yhi )
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GTH2 #00 EQU JMP2r
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>-lo
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LTH2 JMP2r
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ROT2 SWP2 GTH2 ?{ GTH2 #00 EQU JMP2r } LTH2 JMP2r
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( x > y )
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@gt32 ( x** y** -> bool^ )
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ROT2 SWP2 ( xhi yhi xlo ylo )
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GTH2 ,>-lo JCN ( xhi yhi )
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GTH2 JMP2r
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>-lo
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LTH2 #00 EQU JMP2r
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ROT2 SWP2 GTH2 ?{ GTH2 JMP2r } LTH2 #00 EQU JMP2r
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( x > y )
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@gteq32 ( x** y** -> bool^ )
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ROT2 SWP2 ( xhi yhi xlo ylo )
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LTH2 ,<-lo JCN ( xhi yhi )
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LTH2 #00 EQU JMP2r
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<-lo
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GTH2 JMP2r
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ROT2 SWP2 LTH2 ?{ LTH2 #00 EQU JMP2r } GTH2 JMP2r
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( bitwise operations )
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@ -162,197 +120,128 @@
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@complement32 ( x** -> ~x** )
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SWP2 #ffff EOR2 SWP2 #ffff EOR2 JMP2r
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( temporary registers )
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( shared by most operations, except mul32 and div32 )
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@m32 [ &x0 $1 &x1 $1 &x2 $1 &x3 $1
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&y0 $1 &y1 $1 &y2 $1 &y3 $1
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&z0 $1 &z1 $1 &z2 $1 &z3 $1
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&w0 $1 &w1 $1 &w2 $2 ]
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( bit shifting )
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( x >> n )
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@rshift32 ( x** n^ -> x<<n )
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DUP #08 LTH ;rshift32-0 JCN2 ( x n )
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DUP #10 LTH ;rshift32-1 JCN2 ( x n )
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DUP #18 LTH ;rshift32-2 JCN2 ( x n )
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;rshift32-3 JMP2 ( x n )
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@rshift32 ( x** n^ -> x>>n )
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DUP #08 LTH ?shift32-0 ( x n )
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DUP #10 LTH ?rshift32-1 ( x n )
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DUP #18 LTH ?rshift32-2 ( x n )
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!rshift32-3 ( x n )
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( shift right by 0-7 bits )
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@rshift32-0 ( x** n^ -> x<<n )
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STHk SFT ;m32/z3 STA ( write z3 )
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#00 STHkr SFT2 #00 ;m32/z3 LDA ORA2 ;m32/z2 STA2 ( write z2,z3 )
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#00 STHkr SFT2 #00 ;m32/z2 LDA ORA2 ;m32/z1 STA2 ( write z1,z2 )
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#00 STHr SFT2 #00 ;m32/z1 LDA ORA2 ( compute z0,z1 )
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;m32/z2 LDA2
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JMP2r
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( shift by 0-7 bits; used by both lshift and rshift )
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@shift32-0 ( x** n^ -> x>>n )
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STH DUP2 STHkr SFT2 ,&z2 STR2
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POP DUP2 STHkr SFT2 ,&z2 LDR ORA ,&z2 STR ,&z1 STR
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POP STHr SFT2 ,&z1 LDR ORA ,&z1 STR
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LIT [ &z1 $1 ] LIT2 [ &z2 $2 ] JMP2r
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( shift right by 8-15 bits )
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@rshift32-1 ( x** n^ -> x<<n )
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#08 SUB STH POP
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STHkr SFT ;m32/z3 STA ( write z3 )
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#00 STHkr SFT2 #00 ;m32/z3 LDA ORA2 ;m32/z2 STA2 ( write z2,z3 )
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#00 STHr SFT2 #00 ;m32/z2 LDA ORA2 ( compute z1,z2 )
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#00 ROT ROT ;m32/z3 LDA
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JMP2r
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@rshift32-1 ( x** n^ -> x>>n )
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#08 SUB STH ( stash [n>>8] )
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POP DUP2 STHkr SFT2 ,&z2 STR2
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POP STHr SFT2 ,&z2 LDR ORA ,&z2 STR
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#00 SWP LIT2 [ &z2 $2 ] JMP2r
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( shift right by 16-23 bits )
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@rshift32-2 ( x** n^ -> x<<n )
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#10 SUB STH POP2
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STHkr SFT ;m32/z3 STA ( write z3 )
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#00 STHr SFT2 #00 ;m32/z3 LDA ORA2 ( compute z2,z3 )
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#0000 SWP2
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JMP2r
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@rshift32-2 ( x** n^ -> x>>n )
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#10 SUB STH ( stash [n>>16] )
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POP2 STHr SFT2 #0000 SWP2 JMP2r
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( shift right by 16-23 bits )
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@rshift32-3 ( x** n^ -> x<<n )
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#18 SUB STH POP2 POP ( x0 )
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#00 SWP #0000 SWP2 ( 00 00 00 x0 )
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STHr SFT
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JMP2r
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@rshift32-3 ( x** n^ -> x>>n )
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#18 SUB STH ( stash [n>>24] )
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POP2 POP STH SWPr SFTr #00 #0000 STHr JMP2r
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( x << n )
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@lshift32 ( x** n^ -> x<<n )
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DUP #08 LTH ;lshift32-0 JCN2 ( x n )
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DUP #10 LTH ;lshift32-1 JCN2 ( x n )
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DUP #18 LTH ;lshift32-2 JCN2 ( x n )
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;lshift32-3 JMP2 ( x n )
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DUP #08 LTH ?lshift32-0 ( x n )
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DUP #10 LTH ?lshift32-1 ( x n )
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DUP #18 LTH ?lshift32-2 ( x n )
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!lshift32-3 ( x n )
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( shift left by 0-7 bits )
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@lshift32-0 ( x** n^ -> x<<n )
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#40 SFT STH ( stash n<<4 )
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#00 SWP STHkr SFT2 ;m32/z2 STA2 ( store z2,z3 )
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#00 SWP STHkr SFT2 #00 ;m32/z2 LDA ORA2 ;m32/z1 STA2 ( store z1,z2 )
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#00 SWP STHkr SFT2 #00 ;m32/z1 LDA ORA2 ;m32/z0 STA2 ( store z0,z1 )
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STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
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;m32/z1 LDA ;m32/z2 LDA2
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JMP2r
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#40 SFT !shift32-0
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( shift left by 8-15 bits )
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@lshift32-1 ( x** n^ -> x<<n )
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#08 SUB #40 SFT STH ( stash [n-8]<<4 )
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#00 SWP STHkr SFT2 ;m32/z1 STA2 ( store z1,z2 )
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#00 SWP STHkr SFT2 #00 ;m32/z1 LDA ORA2 ;m32/z0 STA2 ( store z0,z1 )
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STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
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NIP ( x0 unused )
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;m32/z1 LDA2 #00
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JMP2r
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DUP2 STHkr SFT2 ,&z1 STR2
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POP STHr SFT2 ,&z1 LDR ORA ,&z1 STR
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NIP LIT2 [ &z1 $1 &z2 $1 ] #00 JMP2r
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( shift left by 16-23 bits )
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@lshift32-2 ( x** n^ -> x<<n )
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#10 SUB #40 SFT STH ( stash [n-16]<<4 )
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#00 SWP STHkr SFT2 ;m32/z0 STA2 ( store z0,z1 )
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STHr SFT ;m32/z0 LDA ORA ( calculate z0 )
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STH POP2 STHr
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;m32/z1 LDA #0000
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JMP2r
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NIP2 STHr SFT2 #0000 JMP2r
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( shift left by 24-31 bits )
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@lshift32-3 ( x** n^ -> x<<n )
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#18 SUB #40 SFT ( x0 x1 x2 x3 r=[n-24]<<4 )
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SFT ( x0 x1 x2 x3<<r )
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NIP2 NIP #0000 #00
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JMP2r
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#18 SUB #40 SFT ( stash [n-24]<<4 )
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SFT NIP2 NIP #0000 #00 JMP2r
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( arithmetic )
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( x + y )
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@add32 ( xhi* xlo* yhi* ylo* -> zhi* zlo* )
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;m32/y2 STA2 ;m32/y0 STA2 ( save ylo, yhi )
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;m32/x2 STA2 ;m32/x0 STA2 ( save xlo, xhi )
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#0000 DUP2 ;m32/z0 STA2 ;m32/z2 STA2 ( reset zhi, zlo )
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( x3 + y3 => z2z3 )
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#00 ;m32/x3 LDA #00 ;m32/y3 LDA ADD2 ;m32/z2 STA2
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( x2 + y2 + z2 => z1z2 )
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#00 ;m32/x2 LDA ;m32/z1 LDA2 ADD2 ;m32/z1 STA2
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#00 ;m32/y2 LDA ;m32/z1 LDA2 ADD2 ;m32/z1 STA2
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( x1 + y1 + z1 => z0z1 )
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#00 ;m32/x1 LDA ;m32/z0 LDA2 ADD2 ;m32/z0 STA2
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#00 ;m32/y1 LDA ;m32/z0 LDA2 ADD2 ;m32/z0 STA2
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( x0 + y0 + z0 => z0 )
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;m32/x0 LDA ;m32/z0 LDA ADD ;m32/z0 STA
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;m32/y0 LDA ;m32/z0 LDA ADD ;m32/z0 STA
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( load zhi,zlo )
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;m32/z0 LDA2 ;m32/z2 LDA2
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JMP2r
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ROT2 STH2k ADD2 STH2k ROT2 ROT2 GTH2r #00 STHr ADD2 ADD2 SWP2 JMP2r
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( -x )
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@negate32 ( x** -> -x** )
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;complement32 JSR2 ( ~x** )
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INC2 ( ~xhi -xlo )
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ORAk ( ~xhi -xlo non-zero? )
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,&done JCN ( xlo non-zero => don't inc hi )
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SWP2 INC2 SWP2 ( -xhi -xlo )
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&done
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JMP2r
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complement32 INC2 ORAk ?{ SWP2 INC2 SWP2 } JMP2r
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( x - y )
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@sub32 ( x** y** -> z** )
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;negate32 JSR2 ;add32 JMP2
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ROT2 STH2k SWP2 SUB2 STH2k ROT2 ROT2 LTH2r #00 STHr ADD2 SUB2 SWP2 JMP2r
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( 16-bit multiplication )
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@mul16 ( x* y* -> z** )
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;m32/y1 STA ;m32/y0 STA ( save ylo, yhi )
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;m32/x1 STA ;m32/x0 STA ( save xlo, xhi )
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#0000 #00 ;m32/z1 STA2 ;m32/z3 STA ( reset z1,z2,z3 )
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#0000 #00 ;m32/w0 STA2 ;m32/w2 STA ( reset w0,w1,w2 )
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,&y1 STR ,&y0 STR ( save ylo, yhi )
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,&x1 STR ,&x0 STR ( save xlo, xhi )
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#0000 ,&z1 STR ,&w0 STR ( reset z1 and w0 )
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( x1 * y1 => z1z2 )
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#00 ;m32/x1 LDA #00 ;m32/y1 LDA MUL2 ;m32/z2 STA2
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LIT2 00 [ &x1 $1 ] LIT2 00 [ &y1 $1 ] MUL2 ,&z3 STR ,&z2 STR
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( x0 * y1 => z0z1 )
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#00 ;m32/x0 LDA #00 ;m32/y1 LDA MUL2 ;m32/z1 LDA2 ADD2 ;m32/z1 STA2
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#00 ,&x0 LDR #00 ,&y1 LDR MUL2 ,&z1 LDR2 ADD2 ,&z1 STR2
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( x1 * y0 => w1w2 )
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#00 ;m32/x1 LDA #00 ;m32/y0 LDA MUL2 ;m32/w1 STA2
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#00 ,&x1 LDR #00 ,&y0 LDR MUL2 ,&w2 STR ,&w1 STR
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( x0 * y0 => w0w1 )
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#00 ;m32/x0 LDA #00 ;m32/y0 LDA MUL2 ;m32/w0 LDA2 ADD2 ;m32/w0 STA2
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LIT2 00 [ &x0 $1 ] LIT2 00 [ &y0 $1 ] MUL2 ,&w0 LDR2 ADD2 ,&w0 STR2
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( add z and a<<8 )
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#00 ;m32/z1 LDA2 ;m32/z3 LDA
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;m32/w0 LDA2 ;m32/w2 LDA #00
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;add32 JMP2
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#00 LIT2 [ &z1 $1 &z2 $1 ] LIT [ &z3 $1 ]
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LIT2 [ &w0 $1 &w1 $1 ] LIT [ &w2 $1 ] #00
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!add32
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( x * y )
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@mul32 ( x** y** -> z** )
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,&y1 STR2 ,&y0 STR2 ( save ylo, yhi )
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,&x1 STR2 ,&x0 STR2 ( save xlo, xhi )
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,&y1 LDR2 ,&x1 LDR2 ;mul16 JSR2 ( [x1*y1] )
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,&z1 STR2 ,&z0 STR2 ( sum = x1*y1, save zlo, zhi )
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,&y1 LDR2 ,&x0 LDR2 MUL2 ( [x0*y1]<<16 )
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,&y0 LDR2 ,&x1 LDR2 MUL2 ( [x1*y0]<<16 )
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ROT2k ( x0* x1* y0* y1* y0* y1* x1* )
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mul16 ,&z1 STR2 ,&z0 STR2 POP2 ( x0* x1* y0* y1* ; sum = [x1*y1] )
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STH2 ROT2 STH2 ( x1* y0* [y1* x0*] )
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MUL2r MUL2 STH2r ADD2 ( x1*y0+y1*x0* )
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( [x0*y0]<<32 will completely overflow )
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ADD2 ,&z0 LDR2 ADD2 ( sum += x0*y1<<16 + x1*y0<<16 )
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,&z1 LDR2
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JMP2r
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[ &x0 $2 &x1 $2
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&y0 $2 &y1 $2
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&z0 $2 &z1 $2 ]
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LIT2 [ &z0 $2 ] ADD2 ( sum += [x0*y1+x1*y0]<<16 )
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LIT2 [ &z1 $2 ] JMP2r
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@div32 ( x** y** -> q** )
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;_divmod32 JSR2
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;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2
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JMP2r
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z_divmod32 ;z_divmod32/quo0 LDA2 ;z_divmod32/quo1 LDA2 JMP2r
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@mod32 ( x** y** -> r** )
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;_divmod32 JSR2
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;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2
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JMP2r
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z_divmod32 ;z_divmod32/rem0 LDA2 ;z_divmod32/rem1 LDA2 JMP2r
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@divmod32 ( x** y** -> q** r** )
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;_divmod32 JSR2
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;_divmod32/quo0 LDA2 ;_divmod32/quo1 LDA2
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;_divmod32/rem0 LDA2 ;_divmod32/rem1 LDA2
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z_divmod32
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;z_divmod32/quo0 LDA2 ;z_divmod32/quo1 LDA2
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;z_divmod32/rem0 LDA2 ;z_divmod32/rem1 LDA2
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JMP2r
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( calculate and store x / y and x % y )
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@_divmod32 ( x** y** -> )
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@z_divmod32 ( x** y** -> )
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( store y and x for repeated use )
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,&div1 STR2 ,&div0 STR2 ( y -> div )
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,&rem1 STR2 ,&rem0 STR2 ( x -> rem )
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@ -360,7 +249,7 @@
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( if x < y then the answer is 0 )
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,&rem0 LDR2 ,&rem1 LDR2
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,&div0 LDR2 ,&div1 LDR2
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;lt32 JSR2 ,&is-zero JCN ,¬-zero JMP
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lt32 ?&is-zero !¬-zero
|
||||
&is-zero
|
||||
#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 JMP2r
|
||||
|
||||
|
|
@ -369,20 +258,20 @@
|
|||
#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 ( 0 -> quo )
|
||||
|
||||
( bitcount[x] - bitcount[y] determines the largest multiple of y to try )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 ;bitcount32 JSR2 ( rbits^ )
|
||||
,&div0 LDR2 ,&div1 LDR2 ;bitcount32 JSR2 ( rbits^ dbits^ )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 bitcount32 ( rbits^ )
|
||||
,&div0 LDR2 ,&div1 LDR2 bitcount32 ( rbits^ dbits^ )
|
||||
SUB ( shift=rbits-dits )
|
||||
#00 DUP2 ( shift 0 shift 0 )
|
||||
|
||||
( 1<<shift -> cur )
|
||||
#0000 INC2k ROT2 POP
|
||||
;lshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2
|
||||
lshift32 ,&cur1 STR2 ,&cur0 STR2
|
||||
|
||||
( div<<shift -> div )
|
||||
,&div0 LDR2 ,&div1 LDR2 ROT2 POP
|
||||
;lshift32 JSR2 ,&div1 STR2 ,&div0 STR2
|
||||
lshift32 ,&div1 STR2 ,&div0 STR2
|
||||
|
||||
,&loop JMP
|
||||
!&loop
|
||||
|
||||
[ &div0 $2 &div1 $2
|
||||
&rem0 $2 &rem1 $2
|
||||
|
|
@ -391,35 +280,24 @@
|
|||
|
||||
&loop
|
||||
( if rem >= the current divisor, we can subtract it and add to quotient )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 ;lt32 JSR2 ( is rem < div? )
|
||||
,&rem-lt JCN ( if rem < div skip this iteration )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 lt32 ( is rem < div? )
|
||||
?&rem-lt ( if rem < div skip this iteration )
|
||||
|
||||
( since rem >= div, we have found a multiple of y that divides x )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 ;sub32 JSR2 ,&rem1 STR2 ,&rem0 STR2 ( rem -= div )
|
||||
,&quo0 LDR2 ,&quo1 LDR2 ,&cur0 LDR2 ,&cur1 LDR2 ;add32 JSR2 ,&quo1 STR2 ,&quo0 STR2 ( quo += cur )
|
||||
,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 sub32 ,&rem1 STR2 ,&rem0 STR2 ( rem -= div )
|
||||
,&quo0 LDR2 ,&quo1 LDR2 ,&cur0 LDR2 ,&cur1 LDR2 add32 ,&quo1 STR2 ,&quo0 STR2 ( quo += cur )
|
||||
|
||||
&rem-lt
|
||||
,&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 ;non-zero32 JSR2 ,&loop JCN ( if cur>0, loop. else we're done )
|
||||
,&div0 LDR2 ,&div1 LDR2 #01 rshift32 ,&div1 STR2 ,&div0 STR2 ( div >>= 1 )
|
||||
,&cur0 LDR2 ,&cur1 LDR2 #01 rshift32 ,&cur1 STR2 ,&cur0 STR2 ( cur >>= 1 )
|
||||
,&cur0 LDR2 ,&cur1 LDR2 non-zero32 ?&loop ( if cur>0, loop. else we're done )
|
||||
JMP2r
|
||||
|
||||
( greatest common divisor - euclidean algorithm )
|
||||
@gcd32 ( x** y** -> z** )
|
||||
&loop ( x y )
|
||||
OVR2 OVR2 ( x y y )
|
||||
;is-zero32 JSR2 ( x y y=0? )
|
||||
,&done JCN ( x y )
|
||||
OVR2 OVR2 ( x y y )
|
||||
STH2 STH2 ( x y [y] )
|
||||
;mod32 JSR2 ( r=x%y [y] )
|
||||
STH2r ( rhi rlo yhi [ylo] )
|
||||
ROT2 ( rlo yhi rhi [ylo] )
|
||||
ROT2 ( yhi rhi rlo [ylo] )
|
||||
STH2r ( yhi rhi rlo ylo )
|
||||
ROT2 ( yhi rlo ylo rhi )
|
||||
ROT2 ( yhi ylo rhi rlo )
|
||||
,&loop JMP
|
||||
&done
|
||||
POP2 POP2 ( x )
|
||||
JMP2r
|
||||
&loop OVR2 OVR2 is-zero32 ?{ ( x** y** )
|
||||
OVR2 OVR2 STH2 STH2 ( x** y** [y**] )
|
||||
mod32 ( r=x%y** [y**] )
|
||||
STH2r ROT2 ROT2 ( yhi* rhi* rlo* [ylo*] )
|
||||
STH2r ROT2 ROT2 !&loop ( y** r** )
|
||||
} POP2 POP2 JMP2r ( z** )
|
||||
|
|
|
|||
Loading…
Reference in New Issue