math clean up
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math32.tal
192
math32.tal
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@ -1,60 +1,59 @@
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( 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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( 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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( 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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%RTN { JMP2r }
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%TOR { ROT ROT } ( a b c -> c a b )
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%COMPLEMENT32 { SWP2 #ffff EOR2 SWP2 #ffff EOR2 }
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%DUP4 { OVR2 OVR2 }
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@ -73,7 +72,7 @@
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,&loop JMP
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&done
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POP ( n )
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RTN
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JMP2r
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@bitcount16 ( x* -> n^ )
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SWP ( xlo xhi )
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@ -81,40 +80,40 @@
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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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RTN
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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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RTN
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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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TOR ;bitcount16 JSR2 ADD RTN ( nhi+nlo )
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TOR ;bitcount16 JSR2 ADD JMP2r ( nhi+nlo )
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&hi-set
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TOR POP2 #10 ADD ( nhi+16 )
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RTN
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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 RTN
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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 RTN
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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 RTN
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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 RTN
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ORA2 #0000 NEQ2 JMP2r
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( comparisons )
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@ -122,51 +121,51 @@
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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 RTN
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LTH2 JMP2r
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<-lo
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GTH2 #00 EQU RTN
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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 RTN
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GTH2 #00 EQU JMP2r
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>-lo
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LTH2 RTN
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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 RTN
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GTH2 JMP2r
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>-lo
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LTH2 #00 EQU RTN
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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 RTN
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LTH2 #00 EQU JMP2r
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<-lo
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GTH2 RTN
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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 RTN
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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 RTN
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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 RTN
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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 RTN
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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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@ -183,7 +182,6 @@
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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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RTN
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( shift right by 0-7 bits )
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@rshift32-0 ( x** n^ -> x<<n )
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@ -192,7 +190,7 @@
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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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RTN
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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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@ -201,7 +199,7 @@
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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 TOR ;m32/z3 LDA
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RTN
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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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@ -209,14 +207,14 @@
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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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RTN
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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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RTN
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JMP2r
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( x << n )
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@lshift32 ( x** n^ -> x<<n )
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@ -224,7 +222,6 @@
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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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RTN
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( shift left by 0-7 bits )
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@lshift32-0 ( x** n^ -> x<<n )
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@ -234,7 +231,7 @@
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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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RTN
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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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@ -244,7 +241,7 @@
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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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RTN
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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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@ -253,14 +250,14 @@
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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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RTN
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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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RTN
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JMP2r
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( arithmetic )
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@ -287,7 +284,7 @@
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( load zhi,zlo )
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;m32/z0 LDA2 ;m32/z2 LDA2
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RTN
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JMP2r
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( -x )
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@negate32 ( x** -> -x** )
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@ -297,11 +294,11 @@
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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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RTN
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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 RTN
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;negate32 JSR2 ;add32 JMP2
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( 16-bit multiplication )
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@mul16 ( x* y* -> z** )
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@ -325,8 +322,7 @@
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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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RTN
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;add32 JMP2
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( x * y )
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@mul32 ( x** y** -> z** )
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@ -339,7 +335,7 @@
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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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RTN
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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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@ -347,18 +343,18 @@
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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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RTN
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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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RTN
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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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RTN
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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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@ -371,7 +367,7 @@
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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 RTN
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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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@ -411,7 +407,7 @@
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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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RTN
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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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@ -431,4 +427,4 @@
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,&loop JMP
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&done
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POP4 ( x )
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RTN
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JMP2r
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@ -32,7 +32,7 @@
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DUP #3a LTH ,&hi-digit JCN
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#57 ,&hi JMP &hi-digit #30
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&hi SUB #40 SFT ORA
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RTN
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JMP2r
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@buf $24 ( buffer used by test-interact )
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@pos $2 ( position in buffer used by test-interact )
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@ -74,14 +74,14 @@ RTN
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@read-byte ( addr* -> x^ )
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LDA2 ;parse-byte JSR2
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RTN
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||||
JMP2r
|
||||
|
||||
@read-long ( addr* -> x** )
|
||||
DUP2 ,&loc STR2 LDA2 ;parse-byte JSR2
|
||||
,&loc LDR2 #0002 ADD2 LDA2 ;parse-byte JSR2
|
||||
,&loc LDR2 #0004 ADD2 LDA2 ;parse-byte JSR2
|
||||
,&loc LDR2 #0006 ADD2 LDA2 ;parse-byte JSR2
|
||||
RTN
|
||||
JMP2r
|
||||
[ &loc $2 ]
|
||||
|
||||
( format: ". xxxxxxxx" -> "zzzzzzzz" )
|
||||
|
|
@ -148,11 +148,11 @@ RTN
|
|||
SWP2
|
||||
SWP EMIT-BYTE EMIT-BYTE
|
||||
SWP EMIT-BYTE EMIT-BYTE
|
||||
RTN
|
||||
JMP2r
|
||||
|
||||
@emit-byte ( x^ -> )
|
||||
EMIT-BYTE
|
||||
RTN
|
||||
JMP2r
|
||||
|
||||
( convenience for less branching when printing hex )
|
||||
@digits
|
||||
|
|
|
|||
Loading…
Reference in New Issue