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https://git.sr.ht/~rabbits/uxn
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432 lines
12 KiB
Tal
432 lines
12 KiB
Tal
( math32.tal )
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( )
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( This library supports arithmetic on 32-bit unsigned integers, )
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( also known as long values. )
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( )
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( 32-bit long values are represented by two 16-bit short values: )
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( )
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( decimal hexadecimal uxn literals )
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( 0 0x00000000 #0000 #0000 )
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( 1 0x00000001 #0000 #0001 )
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( 4660 0x00001234 #0000 #1234 )
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( 65535 0x0000ffff #0000 #ffff )
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( 65536 0x00010000 #0001 #0000 )
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( 16777215 0x00ffffff #00ff #ffff )
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( 4294967295 0xffffffff #ffff #ffff )
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( )
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( The most significant 16-bit, the "high bits", are stored first. )
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( We document long values as x** -- equivalent to xhi* xlo*. )
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( )
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( Operations supported: )
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( )
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( NAME STACK EFFECT DEFINITION )
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( add32 x** y** -> z** x + y )
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( sub32 x** y** -> z** x - y )
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( mul16 x* y* -> z** x * y )
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( mul32 x** y** -> z** x * y )
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( div32 x** y** -> q** x / y )
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( mod32 x** y** -> r** x % y )
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( divmod32 x** y** -> q** r** x / y, x % y )
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( gcd32 x** y** -> z** gcd(x, y) )
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( negate32 x** -> z** -x )
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( lshift32 x** n^ -> z** x<<n )
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( rshift32 x** n^ -> z** x>>n )
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( and32 x** y** -> z** x & y )
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( or32 x** y** -> z** x | y )
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( xor32 x** y** -> z** x ^ y )
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( complement32 x** -> z** ~x )
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( eq32 x** y** -> bool^ x == y )
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( ne32 x** y** -> bool^ x != y )
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( is-zero32 x** -> bool^ x == 0 )
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( non-zero32 x** -> bool^ x != 0 )
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( lt32 x** y** -> bool^ x < y )
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( gt32 x** y** -> bool^ x > y )
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( lteq32 x** y** -> bool^ x <= y )
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( gteq32 x** y** -> bool^ x >= y )
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( bitcount8 x^ -> bool^ floor(log2(x))+1 )
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( bitcount16 x* -> bool^ floor(log2(x))+1 )
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( bitcount32 x** -> bool^ floor(log2(x))+1 )
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( )
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( In addition to the code this file uses 44 bytes of registers )
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( to store temporary state: )
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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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%COMPLEMENT32 { SWP2 #ffff EOR2 SWP2 #ffff EOR2 }
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%DUP4 { OVR2 OVR2 }
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%POP4 { POP2 POP2 }
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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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@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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SWP POP #08 ADD ( nhi+8 )
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JMP2r
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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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( 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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( 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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( x == 0 )
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@is-zero32 ( x** -> bool^ )
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ORA2 #0000 EQU2 JMP2r
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( x != 0 )
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@non-zero32 ( x** -> bool^ )
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ORA2 #0000 NEQ2 JMP2r
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( comparisons )
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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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( 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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( 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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( 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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( bitwise operations )
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( x & y )
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@and32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
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ROT2 AND2 STH2 AND2 STH2r JMP2r
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( x | y )
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@or32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
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ROT2 ORA2 STH2 ORA2 STH2r JMP2r
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( x ^ y )
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@xor32 ( xhi* xlo* yhi* ylo* -> xhi|yhi* xlo|ylo* )
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ROT2 EOR2 STH2 EOR2 STH2r JMP2r
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( ~x )
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@complement32 ( x** -> ~x** )
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COMPLEMENT32 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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JMP2r
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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 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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( 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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( 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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( 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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JMP2r
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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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( 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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SWP POP ( x0 unused )
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;m32/z1 LDA2 #00
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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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( 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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SWP2 POP2 SWP POP #0000 #00
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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 #0000 ;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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( -x )
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@negate32 ( x** -> -x** )
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COMPLEMENT32
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INC2 ( ~xhi -xlo )
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DUP2 #0000 NEQ2 ( ~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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( x - y )
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@sub32 ( x** y** -> z** )
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;negate32 JSR2 ;add32 JSR2 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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( x1 * y1 => z1z2 )
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#00 ;m32/x1 LDA #00 ;m32/y1 LDA MUL2 ;m32/z2 STA2
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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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( x1 * y0 => w1w2 )
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#00 ;m32/x1 LDA #00 ;m32/y0 LDA MUL2 ;m32/w1 STA2
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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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( 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 JSR2
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JMP2r
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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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( [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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@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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@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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@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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JMP2r
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( calculate and store x / y and x % y )
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@_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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( 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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&is-zero
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#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 JMP2r
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( x >= y so the answer is >= 1 )
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¬-zero
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#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 ( 0 -> quo )
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( bitcount[x] - bitcount[y] determines the largest multiple of y to try )
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,&rem0 LDR2 ,&rem1 LDR2 ;bitcount32 JSR2 ( rbits^ )
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,&div0 LDR2 ,&div1 LDR2 ;bitcount32 JSR2 ( rbits^ dbits^ )
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SUB ( shift=rbits-dits )
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#00 DUP2 ( shift 0 shift 0 )
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( 1<<shift -> cur )
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#0000 #0001 ROT2 POP
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;lshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2
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( div<<shift -> div )
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,&div0 LDR2 ,&div1 LDR2 ROT2 POP
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;lshift32 JSR2 ,&div1 STR2 ,&div0 STR2
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,&loop JMP
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[ &div0 $2 &div1 $2
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&rem0 $2 &rem1 $2
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&quo0 $2 &quo1 $2
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&cur0 $2 &cur1 $2 ]
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&loop
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( if rem >= the current divisor, we can subtract it and add to quotient )
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,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 ;lt32 JSR2 ( is rem < div? )
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,&rem-lt JCN ( if rem < div skip this iteration )
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( since rem >= div, we have found a multiple of y that divides x )
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,&rem0 LDR2 ,&rem1 LDR2 ,&div0 LDR2 ,&div1 LDR2 ;sub32 JSR2 ,&rem1 STR2 ,&rem0 STR2 ( rem -= div )
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,&quo0 LDR2 ,&quo1 LDR2 ,&cur0 LDR2 ,&cur1 LDR2 ;add32 JSR2 ,&quo1 STR2 ,&quo0 STR2 ( quo += cur )
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&rem-lt
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,&div0 LDR2 ,&div1 LDR2 #01 ;rshift32 JSR2 ,&div1 STR2 ,&div0 STR2 ( div >>= 1 )
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,&cur0 LDR2 ,&cur1 LDR2 #01 ;rshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2 ( cur >>= 1 )
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,&cur0 LDR2 ,&cur1 LDR2 ;non-zero32 JSR2 ,&loop JCN ( if cur>0, loop. else we're done )
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JMP2r
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( greatest common divisor - euclidean algorithm )
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@gcd32 ( x** y** -> z** )
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|
&loop ( x y )
|
|
DUP4 ( x y y )
|
|
;is-zero32 JSR2 ( x y y=0? )
|
|
,&done JCN ( x y )
|
|
DUP4 ( 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
|
|
POP4 ( x )
|
|
JMP2r
|