more issues, more fixes
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fix16.tal
77
fix16.tal
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@ -30,8 +30,8 @@
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( )
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( due to the limited range operations saturate at the )
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( terminal values (i.e. #7fff and #8001). #8000 should )
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( never be generated, and can be considered a Nan value )
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( although this library does not use it as such. )
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( never be generated through valid arithmetic, and can be )
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( considered an error if present. )
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( )
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( many 8.8 operations are equivalent to unsigned int16: )
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( * addition )
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@ -113,21 +113,20 @@
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%x16-pi/2 { #0192 } ( 1.57079... )
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%x16-pi { #0324 } ( 3.14159... )
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%x16-3pi/2 { #04b6 } ( 4.71239... )
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%x16-pi*2 { #0648 } ( 6.28318... )
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%x16-2pi { #0648 } ( 6.28318... )
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%x16-e { #02b8 } ( 2.71828... )
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%x16-phi { #019e } ( 1.61803... )
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%x16-sqrt-2 { #016a } ( 1.41421... )
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%x16-sqrt-3 { #01bb } ( 1.73205... )
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%x16-epsilon { #0001 } ( 0.00390... )
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%x16-minimum { #8000 } ( -128.0 )
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%x16-minimum { #8001 } ( -127.99609... )
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%x16-maximum { #7fff } ( 127.99609... )
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%x16-max-whole { #7f00 } ( 127.0 )
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%x16-error { #8000 } ( not a number )
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( utils )
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@x16-is-non-neg ( x* -> bool^ ) x16-minimum LTH2 JMP2r
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@x16-is-neg ( x* -> bool^ ) x16-maximum GTH2 JMP2r
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@x16-emit-dec-digit ( d^ -> ) #30 ADD #18 DEO JMP2r
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@error [ #0000 DIV ]
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@x16-emit ( x* -> )
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DUP2 #8000 EQU2 ?&is-min
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@ -287,9 +286,10 @@
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@x16-from-s16 ( n* -> x* )
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DUP2 #ff80 GTH2 ?&neg
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DUP2 #007f GTH2 ?error
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DUP2 #007f GTH2 ?&error
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NIP #00 SWP JMP2r
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&neg NIP #ff SWP JMP2r
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&error POP2 #8000 JMP2r
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( 1.5 -> 1, 0.5 -> 0, -1.5 -> -1 )
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@x16-to-s16 ( x* -> whole* )
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@ -343,32 +343,23 @@
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POP2r POP2r NIP2 JMP2r ( s1* )
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@x16-unit-circle ( x* -> x'* )
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x16-pi*2 STH2 ( x [2pi] )
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DUP2 STH2kr x16-quotient ( x x/2pi [2pi] )
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DUP2 #1400 DIV2 STH2 SWP2r ( x x/2pi [adj* 2pi*] )
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STH2r x16-mul STH2r ADD2 SUB2 ( x' ; 0 <= x' < 2pi )
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JMP2r
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x16-2pi STH2 ( x* [2pi*] )
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DUP2 STH2kr x16-quotient ( x* x/2pi* [2pi*] )
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DUP2 #1400 DIV2 STH2 SWP2r ( x* x/2pi* [adj* 2pi*] )
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STH2r x16-mul SUB2 ( x-x/2pi* [adj*] )
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STH2r LTH2k ?{ SUB2 JMP2r } ( x'* ; 0 <= x' < 2pi )
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POP2 POP2 #0000 JMP2r ( x'* ; 0 <= x' < 2pi )
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@x16-cos ( x* -> cos[x]* )
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x16-unit-circle x16-pi/2 ADD2 ( fall-through )
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@x16-sin ( x* -> sin[x]* )
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DUP2 #8000 LTH2 ?&non-negative
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x16-negate x16-sin/non-negative !x16-negate
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&non-negative
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x16-unit-circle
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DUP2 x16-3pi/2 LTH2 ?&c1
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( -sin(2pi - x) ) x16-pi*2 SWP2 SUB2 x16-sin-q !x16-negate
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&c1 DUP2 x16-pi LTH2 ?&c2
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( -sin(x - pi) ) x16-pi SUB2 x16-sin-q !x16-negate
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&c2 DUP2 x16-pi/2 LTH2 ?&c3
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( sin(pi - x) ) x16-pi SWP2 SUB2 !x16-sin-q
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&c3
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( sin[x] ) ( fall-thru )
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( 0 <= x < 2pi )
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@x16-sin-q ( x* -> sin[x] )
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DUP2 ADD2 ;x16-sin-table ADD2 LDA2 JMP2r
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DUP2 #8000 LTH2 ?&positive x16-negate x16-sin/positive !x16-negate
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&positive x16-unit-circle
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DUP2 x16-3pi/2 LTH2 ?{ x16-2pi SWP2 SUB2 x16-sin/q !x16-negate }
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DUP2 x16-pi LTH2 ?{ x16-pi SUB2 x16-sin/q !x16-negate }
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DUP2 x16-pi/2 LTH2 ?{ x16-pi SWP2 SUB2 }
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&q DUP2 ADD2 ;x16-sin-table ADD2 LDA2 JMP2r
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@x16-sin-table
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0000 0001 0002 0003 0004 0005 0006 0007 0008 0009 000a 000b 000c 000d 000e 000f
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@ -399,27 +390,15 @@
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0100 0100 0100
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@x16-tan ( x* -> tan[x]* )
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x16-pi*2 STH2 ( x [2pi] )
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DUP2 STH2kr x16-quotient ( x x/2pi [2pi] )
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DUP2 #1400 DIV2 STH2 SWP2r ( x x/2pi [adj* 2pi*] )
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STH2r x16-mul STH2r ADD2 SUB2 ( x' ; 0 <= x' < 2pi )
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x16-unit-circle
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( tan(pi/2) = tan(3pi/2) = error )
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DUP2 x16-3pi/2 EQU2 ?error
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DUP2 x16-pi/2 EQU2 ?error
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DUP2 x16-3pi/2 LTH2 ?&c1
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( -tan(2pi - x) ) x16-pi*2 SWP2 SUB2 x16-tan-q !x16-negate
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&c1 DUP2 x16-pi LTH2 ?&c2
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( tan(x - pi) ) x16-pi SUB2 !x16-tan-q
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&c2 DUP2 x16-pi/2 LTH2 ?&c3
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( -tan(pi - x) ) x16-pi SWP2 SUB2 x16-tan-q !x16-negate
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&c3
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( tan[x] ) ( fall-thru )
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( 0 <= x < 2pi )
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@x16-tan-q ( x* -> sin[x] )
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DUP2 ADD2 ;x16-tan-table ADD2 LDA2 JMP2r
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DUP2 x16-3pi/2 EQU2 ?&error
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DUP2 x16-pi/2 EQU2 ?&error
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DUP2 x16-3pi/2 LTH2 ?{ x16-2pi SWP2 SUB2 x16-tan/q !x16-negate }
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DUP2 x16-pi LTH2 ?{ x16-pi SUB2 !x16-tan/q }
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DUP2 x16-pi/2 LTH2 ?{ x16-pi SWP2 SUB2 x16-tan/q !x16-negate }
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&q DUP2 ADD2 ;x16-tan-table ADD2 LDA2 JMP2r
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&error POP2 #8000 JMP2r
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@x16-tan-table
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0000 0001 0002 0003 0004 0005 0006 0007 0008 0009 000a 000b 000c 000d 000e 000f
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@ -453,7 +432,7 @@
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[ DUP2 #0000 GTH2 ] STH
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[ DUP2 #8000 LTH2 ] STHr AND ?&0<x<128
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( error ) !error
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( error ) POP2 #8000 JMP2r ( error )
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&0<x<128 DUP2 #0800 GTH2 ?&8<x<128
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( 0<x<=8 ) DUP2 #0200 GTH2 ?&2<x<=8
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