clean up fix16
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fix16.tal
53
fix16.tal
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@ -48,14 +48,12 @@
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( MUL2. )
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( MUL2. )
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( )
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( )
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( similarly with division we have: )
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( similarly with division we have: )
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( )
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( )
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( x divided by #0100 -> x )
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( x = x'/256 )
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( x divided by #0001 -> x * 256, with likely overfow )
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( y = y'/256 )
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( #abcd divided by #1000 -> #0abc, rounding with d )
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( x/y = z = z'/256 )
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( x divided by #0200 -> x >> 1 )
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( (x'/256)/(y'/256) = (x'*256 / y)/256 )
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( x divided by #0080 -> x << 1 )
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( z' = (x' * 256 / y)/256 )
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%xyz { ;x16-emit JSR2 #0a #18 DEO }
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( useful constants )
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( useful constants )
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( )
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( )
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@ -92,42 +90,6 @@
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%x16-emit-dec { #30 ADD #18 DEO }
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%x16-emit-dec { #30 ADD #18 DEO }
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( |0100
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x16-zero xyz
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x16-one xyz
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x16-two xyz
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x16-ten xyz
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x16-hundred xyz
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x16-pi/2 xyz
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x16-pi xyz
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x16-pi*2 xyz
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x16-e xyz
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x16-phi xyz
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x16-sqrt-2 xyz
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x16-sqrt-3 xyz
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x16-epsilon xyz
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#0002 xyz
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#1234 xyz
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#7fff xyz
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#8000 xyz
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#8001 xyz
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#ffff xyz
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#0200 xyz
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#0834 #0000 ;x16-add JSR2 xyz
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#0834 #0834 ;x16-add JSR2 xyz
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#0834 #0834 ;x16-mul JSR2 xyz
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#0834 #0200 ;x16-div JSR2 xyz
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#0100 xyz
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#0003 xyz
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#0100 #0003 ;x16-div JSR2 xyz
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#0834 xyz
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#0080 xyz
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#0834 #0080 ;x16-div JSR2 xyz
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#0834 xyz
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#0300 xyz
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#0834 #0300 ;x16-div JSR2 xyz
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BRK )
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@x16-emit ( x* -> )
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@x16-emit ( x* -> )
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DUP2 #8000 EQU2 ,&is-min JCN
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DUP2 #8000 EQU2 ,&is-min JCN
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DUP2 #8000 GTH2 ,&is-neg JCN
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DUP2 #8000 GTH2 ,&is-neg JCN
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@ -201,9 +163,6 @@
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&rhs-whole #08 SFT2 MUL2 JMP2r
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&rhs-whole #08 SFT2 MUL2 JMP2r
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@x16-div ( x* y* -> x/y* )
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@x16-div ( x* y* -> x/y* )
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( DUP ,¬-whole JCN
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#08 SFT2 DIV2 JMP2r ( since y is whole, x/(y>>8) is correct )
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¬-whole )
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DIV2k STH2k ( x y x/y {x/y} )
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DIV2k STH2k ( x y x/y {x/y} )
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LITr 80 SFT2r ( x y x/y {div=(x/y)<<8 )
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LITr 80 SFT2r ( x y x/y {div=(x/y)<<8 )
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OVR2 STH2 ( x y x/y {y div} )
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OVR2 STH2 ( x y x/y {y div} )
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59
fixed.tal
59
fixed.tal
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@ -1,59 +0,0 @@
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( use short as a fixed point number 8.8 )
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( )
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( so #0001 is interpreted as 1/256 )
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( and #ffff is interpreted as 255+255/256 )
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( )
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( x = x0 + x1/256 )
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( y = y0 + y1/256 )
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( )
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( many 8.8 operations are equivalent to u16: )
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( * comparisons/equality )
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( * addition/subtraction )
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( )
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( but due to 16-bit truncation multiplication is different. )
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( )
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( x*y = x0*y0 + x0*y1/256 + x1*y0/256 + x1*y1/65536 )
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( )
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( since we only have 16-bits: )
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( 1. we need to drop the 8 high bits from x0*y0 )
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( 2. we need to drop the 8 low bits from x1*y1 )
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( 3. we need to use all the bits from x0*y1 and x1*y0 )
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%EMIT { #18 DEO }
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%DIGIT { #00 SWP ;digits ADD2 LDA EMIT }
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%SPACE { #20 EMIT }
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%NEWLINE { #0a EMIT }
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%EMIT-BYTE { DUP #04 SFT DIGIT #0f AND DIGIT }
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( program )
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|0100
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#0100 #0100 ;mul-fix JSR2 ;emit-short JSR2 NEWLINE
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#0999 #0100 ;mul-fix JSR2 ;emit-short JSR2 NEWLINE
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#abcd #0100 ;mul-fix JSR2 ;emit-short JSR2 NEWLINE
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#0200 #0200 ;mul-fix JSR2 ;emit-short JSR2 NEWLINE
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#0400 #0200 ;mul-fix JSR2 ;emit-short JSR2 NEWLINE
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BRK
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%LO { NIP #00 SWP }
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%HI { POP #00 SWP }
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@mul-fix ( x* y* -> z* )
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OVR2 OVR2 LO SWP2 LO MUL2 ( x1*y1 )
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#08 SFT2 STH2 ( z = (x1*y1)>>8 )
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OVR2 OVR2 HI SWP2 LO MUL2 ( x0*y1 )
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STH2 ADD2r ( z += x0*y1 )
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OVR2 OVR2 LO SWP2 HI MUL2 ( x1*y0 )
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STH2 ADD2r ( z += x1*y0 )
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HI SWP2 HI MUL2 ( x0*y0 )
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#80 SFT2 STH2r ADD2 ( z += (x0*y0)<<8 )
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JMP2r
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@emit-short SWP EMIT-BYTE EMIT-BYTE JMP2r
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( convenience for less branching when printing hex )
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@digits
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30 31 32 33 34 35 36 37
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38 39 61 62 63 64 65 66
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