diff --git a/fix32.tal b/fix32.tal index cf2d48f..3934df0 100644 --- a/fix32.tal +++ b/fix32.tal @@ -7,35 +7,6 @@ %DENOM16 { #03e8 } %DENOM32 { #0000 #03e8 } -|0100 - ( test cases -- compare the two 32-bit values on wst ) - - #0000 #03e8 ( a=1 ) - #0000 #07d0 ( b=2 ) - x32-add ( a+b ) - #0000 #0bb8 ( c=3 ) - #010e DEO POP4 POP4 #0a18 DEO - - #0000 #07d0 ( a=2 ) - #0000 #0bb8 ( b=3 ) - x32-mul ( a*b ) - #0000 #1770 ( c=6 ) - #010e DEO POP4 POP4 #0a18 DEO - - #0000 #4a38 ( a=19 ) - #0000 #6978 ( b=27 ) - x32-mul ( a*b ) - #0007 #d3d8 ( c=513 ) - #010e DEO POP4 POP4 #0a18 DEO - - #0000 #1d4c ( a=7.5 ) - #0000 #05dc ( b=1.5 ) - x32-div ( a/b ) - #0000 #1388 ( c=5.0 ) - #010e DEO POP4 POP4 #0a18 DEO - - #010e DEO #800f DEO BRK ( ensure stack is empty ) - @x32-eq ( x/** y/** -> bool^ ) !u32-eq @x32-ne ( x/** y/** -> bool^ ) !u32-ne @@ -53,6 +24,15 @@ @x32-from-u32 ( x** -> x/** ) DENOM32 !u32-mul +@x32-signed-op ( x** y** f* -> f[x,y]** ) + STH2 LIT2r 0001 ( x** y** [f* 0^ 1^] ) + OVR2 #8000 LTH2 ?{ u32-negate SWPr } ( x** y** [f* ab*] ) + ROT2 STH2 ROT2 STH2r ( y** x** [f* ab*] ) + OVR2 #8000 LTH2 ?{ u32-negate SWPr } ( y** x** [f* cd*] ) + ROT2 STH2 ROT2 STH2r SWP2r ( x** y** [cd* f*] ) + STH2r JSR2 ( f[x,y]** [cd*] ) + NIPr STHr ?{ u32-negate } JMP2r ( z** ) + @x32-prepare-cmp ( x/** y/** -> x/** y/** xp^ yp^ ) OVR2 #8000 LTH2 ,&yp STR STH2 STH2 OVR2 #8000 LTH2 ,&xp STR STH2r STH2r @@ -86,6 +66,9 @@ @x32-gteq ( x/** y/** -> bool^ ) x32-prepare-cmp NEQk ?{ POP2 !u32-gteq } GTH STH POP8 STHr JMP2r +( TODO: support saturation at +/- infinity ) +( TODO: support signed operations ) + @x32-add ( x/** y/** -> z/** ) !u32-add @@ -106,26 +89,46 @@ @x32-scaled-div32 ( x/** y** -> z/** ) !u32-div -( [x * y]/1000 = floor[x/1000] + [[x%1000]*y]/1000 ) @x32-mul ( x/** y/** -> z/** ) - STH2 STH2 DENOM32 ( x/** 1000** [ylo* yhi*] ) - u32-divmod ( q** r** [ylo* yhi*] ) - STH2kr OVR2r STH2r u32-mul ( q** ry** [ylo* yhi*] ) - DENOM32 u32-div ( q** ry1000** [ylo* yhi*] ) - ROT2 STH2 ROT2 STH2r ( ry1000** q** [ylo* yhi*] ) - STH2r STH2r u32-mul ( ry1000** qy** ) - u32-add ( qy+ry/1000** ) - JMP2r ( z/** ) + ;x32-mul-unsigned !x32-signed-op + +( [x * y]/1000 = floor[x/1000] + [[x%1000]*y]/1000 ) +@x32-mul-unsigned ( x/** y/** -> z/** ) + STH2 STH2 DENOM32 ( x** 1000** [ylo* yhi*] ) + u32-divmod ( q=x/1000** r=x%1000** [ylo* yhi*] ) + STH2kr OVR2r STH2r u32-mul ( q** ry** [ylo* yhi*] ) + DENOM32 u32-divmod ( q** rq=ry/1000** rr=ry%1000** [ylo* yhi*] ) + NIP2 ,&r1 STR2 ( q** rq** [ylo* yhi*] ; <-rr1 ) + ROT2 STH2 ROT2 STH2r ( ry/1000** q** [ylo* yhi*] ) + STH2r STH2r u32-mul ( ry/1000** qy** ) + u32-add ( z=qy+ry/1000** ) + DUP2 #0001 AND2 STH2 ( z** [odd*] ) + #0000 LIT2 [ &r1 $2 ] ( z** rr** [odd*] ) + STH2r ADD2 #01f3 ADD2 ( z** rr+odd+499** ) + DENOM32 u32-div ( z** b=rr+odd+499/1000** ) + !u32-add ( z+b** ) + +@x32-div ( x/** y/** -> z/** ) + ;x32-div-unsigned !x32-signed-op ( [x * 1000]/y = floor[x/y]*1000 + [[x%y]*1000]/y ) -@x32-div ( x/** y/** -> z/** ) - STH2k OVR2 STH2 ( x/** y/** [ylo* yhi*] ) - u32-divmod - DENOM32 u32-mul ( q** r1000** [ylo* yhi*] ) - STH2r STH2r u32-div ( q** r1000/y** [ylo* yhi*] ) - ROT2 STH2 ROT2 STH2r ( r1000/y** q** [ylo* yhi*] ) - DENOM32 u32-mul ( r1000/y** q1000** ) - u32-add ( q+r1000/y** ) - JMP2r ( z/** ) +@x32-div-unsigned ( x/** y/** -> z/** ) + STH2k OVR2 STH2 ( x/** y/** [ylo* yhi*] ) + u32-divmod ( q=x/y** r=x%y** [ylo* yhi*] ) + DENOM32 u32-mul ( q** r1000** [ylo* yhi*] ) + STH2kr OVR2r STH2r u32-divmod ( q** rq** rr** [ylo* yhi*] ) + ,&r1 STR2 ,&r0 STR2 ( q** rq** ; <-rr0 <-rr1 [ylo* yhi*] ) + ROT2 STH2 ROT2 STH2r ( rq** q** [ylo* yhi*] ) + DENOM32 u32-mul ( rq** q1000** [ylo* yhi*] ) + u32-add ( z=rq+q1000** [ylo* yhi*] ) + DUP ,&e STR ( z** ; e<-z3^ [ylo* yhi*] ) + LIT2 [ &r0 $2 ] LIT2 [ &r1 $2 ] ( z** rr** [ylo* yhi*] ) + LIT [ &e $1 ] #01 AND ( z** rr** e^ ) + #00 SWP #0000 SWP2 ( z** rr** e** [ylo* yhi*] ) + u32-add ( z** w=rr+e** [ylo* yhi*] ) + STH2kr OVR2r STH2r ( z** w** y** [ylo* yhi*] ) + #0000 #0001 u32-sub ( z** w** y-1** [ylo* yhi*] ) + #01 u32-rshift u32-add ( z** v=w+y-1/2** [ylo* yhi*] ) + STH2r STH2r u32-div !u32-add ( z+v/y** ) ~math32.tal diff --git a/test-fix32.tal b/test-fix32.tal new file mode 100644 index 0000000..2652b37 --- /dev/null +++ b/test-fix32.tal @@ -0,0 +1,60 @@ +( test-fix32.tal ) +( ) +( methods for testing math32 and emitting output ) + +( TODO: consider rounding modes. currently we always round toward zero ) + +( program ) +|0100 + #0000 #03e8 #0000 #07d0 LIT "+ ;x32-add #0000 #0bb8 test-binop ( 1 + 2 = 3 ) + #0a18 DEO + #0000 #03e8 #0000 #03e8 LIT "* ;x32-mul #0000 #03e8 test-binop ( 1 * 1 = 1 ) + #0000 #07d0 #0000 #0bb8 LIT "* ;x32-mul #0000 #1770 test-binop ( 2 * 3 = 6 ) + #0000 #4a38 #0000 #6978 LIT "* ;x32-mul #0007 #d3d8 test-binop ( 19 * 27 = 513 ) + #0000 #0064 #0000 #0064 LIT "* ;x32-mul #0000 #000a test-binop ( 0.1 * 0.1 = 0.01 ) + #0000 #01f4 #0000 #0001 LIT "* ;x32-mul #0000 #0000 test-binop ( 0.5 * 0.001 = 0.0 ) + #0000 #01f4 #0000 #0003 LIT "* ;x32-mul #0000 #0002 test-binop ( 0.5 * 0.003 = 0.002 ) + #0000 #01f4 #0000 #0005 LIT "* ;x32-mul #0000 #0002 test-binop ( 0.5 * 0.005 = 0.002 ) + #0000 #01f4 #0000 #0007 LIT "* ;x32-mul #0000 #0004 test-binop ( 0.5 * 0.007 = 0.004 ) + #0000 #01f4 #0000 #0009 LIT "* ;x32-mul #0000 #0004 test-binop ( 0.5 * 0.009 = 0.004 ) + #0000 #0bb8 #ffff #f830 LIT "* ;x32-mul #ffff #e890 test-binop ( 3 * -2 = -6 ) + #ffff #fc18 #ffff #fc18 LIT "* ;x32-mul #0000 #03e8 test-binop ( -1 * -1 = 1 ) + #0a18 DEO + #0000 #1d4c #0000 #05dc LIT "/ ;x32-div #0000 #1388 test-binop ( 7.5 / 1.5 = 5.0 ) + #0000 #03e8 #0000 #0001 LIT "/ ;x32-div #000f #4240 test-binop ( 1.0 / 0.001 = 1000.0 ) + #0000 #03e8 #0000 #0bb8 LIT "/ ;x32-div #0000 #014d test-binop ( 1.0 / 3.0 = 0.333 ) + #0000 #07d0 #0000 #0bb8 LIT "/ ;x32-div #0000 #029b test-binop ( 2.0 / 3.0 = 0.667 ) + #ffff #adf8 #0000 #1b58 LIT "/ ;x32-div #ffff #f448 test-binop ( -21.0 / 7.0 = -3.0 ) + #0000 #0003 #0000 #07d0 LIT "/ ;x32-div #0000 #0002 test-binop ( 0.003 / 2 = 0.002 ) + #0000 #0005 #0000 #07d0 LIT "/ ;x32-div #0000 #0002 test-binop ( 0.005 / 2 = 0.002 ) + #0000 #0007 #0000 #07d0 LIT "/ ;x32-div #0000 #0004 test-binop ( 0.007 / 2 = 0.004 ) + #0000 #0009 #0000 #07d0 LIT "/ ;x32-div #0000 #0004 test-binop ( 0.009 / 2 = 0.004 ) + #0a18 DEO + #800f DEO BRK + +~fix32.tal + +@test-binop ( x** y** op^ f* z** -> x** y** ) + STH2 STH2 ,&f STR2 ,&op STR ( x** y** [z1* z0*] ) + STH2 STH2 OVR2 OVR2 emit/long ( x** [z1* z0* y1* z0*] ; emit x ) + #2018 DEO ( x** [z1* z0* y1* y0*] ; emit space ) + LIT [ &op $1 ] #18 DEO ( x** [z1* z0* y1* y0*] ; emit operator symbol ) + #2018 DEO ( x** [z1* z0* y1* y0*] ; emit space ) + STH2r STH2r OVR2 OVR2 emit/long ( x** y** [z1* z0*] ; emit y ) + #2018 DEO ( x** y** [z1* z0*] ; emit space ) + LIT "= #18 DEO ( x** y** [z1* z0*] ; emit = ) + #2018 DEO ( x** y** [z1* z0*] ; emit space ) + LIT2 [ &f $2 ] JSR2 ( f[x,y]** [z1* z0*] ) + emit/long ( [z1* z0*] ; emit f[x,y] ) + STH2r STH2r #2018 DEO ( z** ; emit space ) + LIT "[ #18 DEO ( z** ; emit [ ) + emit/long ( ; emit z ) + LIT "] #18 DEO ( ; emit ] ) + #0a18 DEO JMP2r ( ; emit newline ) + +@emit + &long SWP2 /short + &short SWP ,&byte JSR + &byte DUP #04 SFT ,&char JSR + &char #0f AND DUP #09 GTH #27 MUL ADD #30 ADD #18 DEO + JMP2r