implement mod32, divmod32, etc.
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math32.tal
65
math32.tal
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@ -24,7 +24,9 @@
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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** -> 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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( 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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@ -49,7 +51,7 @@
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( )
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( - shared memory, 16 bytes )
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( - mul32 memory, 12 bytes )
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( - div32 memory, 16 bytes )
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( - _divmod32 memory, 16 bytes )
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%DEBUG { #ff #0e DEO }
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%RTN { JMP2r }
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@ -331,7 +333,6 @@
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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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@ -342,43 +343,66 @@
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&y0 $2 &y1 $2
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&z0 $2 &z1 $2 ]
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( x / y )
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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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@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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@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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( 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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;div32/div1 STA2 ;div32/div0 STA2 ( y -> div )
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;div32/rem1 STA2 ;div32/rem0 STA2 ( x -> rem )
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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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;div32/rem0 LDA2 ;div32/rem1 LDA2
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;div32/div0 LDA2 ;div32/div1 LDA2
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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 #0000 RTN
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#0000 ,&quo0 STR2 #0000 ,&quo1 STR2 RTN
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( x >= y so the answer is >= 1 )
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¬-zero
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#0000 ;div32/quo0 STA2 #0000 ;div32/quo1 STA2 ( 0 -> quo )
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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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;div32/rem0 LDA2 ;div32/rem1 LDA2 ;bitcount32 JSR2 ( rbits^ )
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;div32/div0 LDA2 ;div32/div1 LDA2 ;bitcount32 JSR2 ( rbits^ dbits^ )
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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 ;div32/cur1 STA2 ;div32/cur0 STA2
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;lshift32 JSR2 ,&cur1 STR2 ,&cur0 STR2
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( div<<shift -> div )
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;div32/div0 LDA2 ;div32/div1 LDA2 ROT2 POP
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;lshift32 JSR2 ;div32/div1 STA2 ;div32/div0 STA2
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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
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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 ( rem<div? )
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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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( if rem >= div, then we have found a multiple of y that divides x )
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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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@ -386,9 +410,4 @@
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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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,&quo0 LDR2 ,&quo1 LDR2 ( TODO: consider making this divmod32 )
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RTN
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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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@ -52,6 +52,7 @@ RTN
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;buf LDA LIT '* EQU ;test-mul32 JCN2
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;buf LDA LIT '- EQU ;test-sub32 JCN2
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;buf LDA LIT '/ EQU ;test-div32 JCN2
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;buf LDA LIT '% EQU ;test-mod32 JCN2
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;buf LDA LIT 'L EQU ;test-lshift32 JCN2
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;buf LDA LIT 'R EQU ;test-rshift32 JCN2
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;buf LDA LIT 'B EQU ;test-bitcount32 JCN2
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@ -123,6 +124,7 @@ RTN
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@test-mul32 ;mul32 ;binary-32-test JMP2
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@test-sub32 ;sub32 ;binary-32-test JMP2
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@test-div32 ;div32 ;binary-32-test JMP2
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@test-mod32 ;mod32 ;binary-32-test JMP2
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@test-lshift32 ;lshift32 ;binary-32-8-32-test JMP2
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@test-rshift32 ;rshift32 ;binary-32-8-32-test JMP2
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@test-bitcount32 ;bitcount32 ;unary-32-8-test JMP2
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@ -63,6 +63,7 @@ def main():
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test(p, trials, b'-', [('x', u32), ('y', u32)], u32, lambda x, y: x - y)
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test(p, trials, b'*', [('x', u32), ('y', u32)], u32, lambda x, y: x * y)
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test(p, trials, b'/', [('x', u32), ('y', u32)], u32, lambda x, y: x // y)
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test(p, trials, b'%', [('x', u32), ('y', u32)], u32, lambda x, y: x % y)
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test(p, trials, b'L', [('x', u32), ('y', u5)], u32, lambda x, y: x << y)
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test(p, trials, b'R', [('x', u32), ('y', u5)], u32, lambda x, y: x >> y)
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test(p, trials, b'B', [('x', u32)], u8, bitcount)
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