add sin/cos/tan/log
This commit is contained in:
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a870fc533a
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fix16.tal
200
fix16.tal
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@ -54,6 +54,24 @@
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( x/y = z = z'/256 )
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( (x'/256)/(y'/256) = (x'*256 / y)/256 )
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( z' = (x' * 256 / y)/256 )
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( )
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( trigonometry, etc: )
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( - sin() and cos() are supported )
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( - tan() is mostly supported )
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( - tan(#0192) and tan(#04b6) throw an error )
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( - a few tan() values are inaccurate due to range )
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( + values "next to" pi/2 and 3pi/2 are affected )
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( + tan(#0191) returns 127.996 not 227.785 )
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( + tan(#0193) returns -127.996 not -292.189 )
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( + etc. )
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( - log() is supported )
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( - log(0) throws an error )
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( - log values farther from zero may be a bit inaccurate )
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( useful macros )
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%x16-is-non-neg { x16-minimum LTH2 }
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%x16-is-neg { x16-maximum GTH2 }
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%x16-emit-dec-digit { #30 ADD #18 DEO }
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( useful constants )
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( )
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@ -74,6 +92,7 @@
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%x16-minus-two { #7e00 } ( -2.0 )
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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-e { #02b8 } ( 2.71828... )
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%x16-phi { #019e } ( 1.61803... )
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@ -84,17 +103,11 @@
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%x16-maximum { #7fff } ( 127.99609... )
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%x16-max-whole { #7f00 } ( 127.0 )
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( useful macros )
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%x16-is-non-neg { x16-minimum LTH2 }
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%x16-is-neg { x16-maximum GTH2 }
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%x16-emit-dec { #30 ADD #18 DEO }
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@x16-emit ( x* -> )
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DUP2 #8000 EQU2 ,&is-min JCN
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DUP2 #8000 GTH2 ,&is-neg JCN
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SWP DUP #64 LTH ,&<100 JCN
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#64 DIVk DUP x16-emit-dec MUL SUB ,&>=10 JMP
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#64 DIVk DUP x16-emit-dec-digit MUL SUB ,&>=10 JMP
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&is-min POP2
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LIT "- #18 DEO LIT "1 #18 DEO LIT "2 #18 DEO LIT "8 #18 DEO
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LIT ". #18 DEO LIT "0 #18 DEO LIT "0 #18 DEO LIT "0 #18 DEO
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@ -102,16 +115,16 @@
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&is-neg
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LIT "- #18 DEO #ffff EOR2 INC2 ,x16-emit JMP
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&<100 DUP #0a LTH ,&<10 JCN
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&>=10 #0a DIVk DUP x16-emit-dec MUL SUB
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&<10 x16-emit-dec
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&>=10 #0a DIVk DUP x16-emit-dec-digit MUL SUB
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&<10 x16-emit-dec-digit
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LIT '. #18 DEO
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( emit fractional part )
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#00 SWP ( lo* )
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec MUL2 SUB2
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec MUL2 SUB2
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec MUL2 SUB2
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec-digit MUL2 SUB2
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec-digit MUL2 SUB2
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#000a MUL2 #0100 DIV2k DUP2 NIP x16-emit-dec-digit MUL2 SUB2
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#000a MUL2 #0100 DIV2k STH2k MUL2 SUB2 #0080 LTH2 ,&no-round JCN INC2r
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&no-round STH2r NIP x16-emit-dec JMP2r
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&no-round STH2r NIP x16-emit-dec-digit JMP2r
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( comparison between x and y. )
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( - ff: x < y )
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@ -185,3 +198,164 @@
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@x16-remainder ( x* y* -> x%y* )
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DIV2k MUL2 SUB2 JMP2r
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@x16-cos ( x* -> cos(x)* )
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x16-pi/2 ADD2 ,x16-sin JMP
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@x16-sin ( x* -> sin(x)* )
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x16-pi*2 STH2 ( x [2pi] )
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DUP2 STH2kr ;x16-quotient JSR2 ( x x/2pi [2pi] )
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STH2r ;x16-mul JSR2 SUB2 ( x' ; 0 <= x' < 2pi )
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DUP2 x16-3pi/2 LTH2 ,&c1 JCN
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( -sin(2pi - x) ) x16-pi*2 SWP2 SUB2 ,x16-sin-q JSR ;x16-negate JMP2
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&c1 DUP2 x16-pi LTH2 ,&c2 JCN
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( -sin(x - pi) ) x16-pi SUB2 ,x16-sin-q JSR ;x16-negate JMP2
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&c2 DUP2 x16-pi/2 LTH2 ,&c3 JCN
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( sin(pi - x) ) x16-pi SWP2 SUB2 ,x16-sin-q JMP
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&c3
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( sin(x) ) ,x16-sin-q JMP
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( 0 <= x < 2pi )
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@x16-sin-q ( x* -> sin(x) )
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#10 SFT2 ;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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0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 001a 001b 001c 001d 001e 001f
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0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 002a 002b 002c 002d 002e 002f
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0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 003a 003a 003b 003c 003d 003e
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003f 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 004a 004b 004c 004d 004e
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004f 0050 0051 0052 0053 0053 0054 0055 0056 0057 0058 0059 005a 005b 005c 005d
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005e 005f 0060 0061 0061 0062 0063 0064 0065 0066 0067 0068 0069 006a 006b 006c
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006c 006d 006e 006f 0070 0071 0072 0073 0074 0075 0075 0076 0077 0078 0079 007a
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007b 007c 007c 007d 007e 007f 0080 0081 0082 0083 0083 0084 0085 0086 0087 0088
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0089 0089 008a 008b 008c 008d 008e 008e 008f 0090 0091 0092 0093 0093 0094 0095
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0096 0097 0097 0098 0099 009a 009b 009b 009c 009d 009e 009f 009f 00a0 00a1 00a2
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00a2 00a3 00a4 00a5 00a6 00a6 00a7 00a8 00a9 00a9 00aa 00ab 00ac 00ac 00ad 00ae
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00ae 00af 00b0 00b1 00b1 00b2 00b3 00b4 00b4 00b5 00b6 00b6 00b7 00b8 00b8 00b9
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00ba 00bb 00bb 00bc 00bd 00bd 00be 00bf 00bf 00c0 00c1 00c1 00c2 00c3 00c3 00c4
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00c4 00c5 00c6 00c6 00c7 00c8 00c8 00c9 00ca 00ca 00cb 00cb 00cc 00cd 00cd 00ce
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00ce 00cf 00d0 00d0 00d1 00d1 00d2 00d2 00d3 00d4 00d4 00d5 00d5 00d6 00d6 00d7
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00d7 00d8 00d8 00d9 00da 00da 00db 00db 00dc 00dc 00dd 00dd 00de 00de 00df 00df
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00e0 00e0 00e1 00e1 00e2 00e2 00e2 00e3 00e3 00e4 00e4 00e5 00e5 00e6 00e6 00e7
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00e7 00e7 00e8 00e8 00e9 00e9 00ea 00ea 00ea 00eb 00eb 00ec 00ec 00ec 00ed 00ed
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00ed 00ee 00ee 00ef 00ef 00ef 00f0 00f0 00f0 00f1 00f1 00f1 00f2 00f2 00f2 00f3
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00f3 00f3 00f4 00f4 00f4 00f4 00f5 00f5 00f5 00f6 00f6 00f6 00f6 00f7 00f7 00f7
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00f8 00f8 00f8 00f8 00f8 00f9 00f9 00f9 00f9 00fa 00fa 00fa 00fa 00fb 00fb 00fb
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00fb 00fb 00fb 00fc 00fc 00fc 00fc 00fc 00fd 00fd 00fd 00fd 00fd 00fd 00fd 00fe
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00fe 00fe 00fe 00fe 00fe 00fe 00fe 00ff 00ff 00ff 00ff 00ff 00ff 00ff 00ff 00ff
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00ff 00ff 00ff 0100 0100 0100 0100 0100 0100 0100 0100 0100 0100 0100 0100 0100
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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 JSR2 ( x x/2pi [2pi] )
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STH2r ;x16-mul JSR2 SUB2 ( x' ; 0 <= x' < 2pi )
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( tan(pi/2) = tan(3pi/2) = error )
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DUP2 x16-3pi/2 EQU2 ,&error JCN
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DUP2 x16-pi/2 EQU2 ,&error JCN
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DUP2 x16-3pi/2 LTH2 ,&c1 JCN
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( -tan(2pi - x) ) x16-pi*2 SWP2 SUB2 ,x16-tan-q JSR ;x16-negate JMP2
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&c1 DUP2 x16-pi LTH2 ,&c2 JCN
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( tan(x - pi) ) x16-pi SUB2 ,x16-tan-q JMP
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&c2 DUP2 x16-pi/2 LTH2 ,&c3 JCN
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( -tan(pi - x) ) x16-pi SWP2 SUB2 ,x16-tan-q JSR ;x16-negate JMP2
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&c3
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( tan(x) ) ,x16-tan-q JMP
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&error #0000 DIV
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( 0 <= x < 2pi )
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@x16-tan-q ( x* -> sin(x) )
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#10 SFT2 ;x16-tan-table ADD2 LDA2 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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0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 001a 001b 001c 001d 001e 001f
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0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 002a 002b 002c 002d 002f 0030
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0031 0032 0033 0034 0035 0036 0037 0038 0039 003a 003b 003c 003d 003e 003f 0040
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0041 0042 0044 0045 0046 0047 0048 0049 004a 004b 004c 004d 004e 004f 0051 0052
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0053 0054 0055 0056 0057 0058 0059 005b 005c 005d 005e 005f 0060 0061 0062 0064
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0065 0066 0067 0068 0069 006b 006c 006d 006e 006f 0071 0072 0073 0074 0075 0077
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0078 0079 007a 007b 007d 007e 007f 0080 0082 0083 0084 0085 0087 0088 0089 008b
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008c 008d 008e 0090 0091 0092 0094 0095 0096 0098 0099 009a 009c 009d 009f 00a0
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00a1 00a3 00a4 00a6 00a7 00a8 00aa 00ab 00ad 00ae 00b0 00b1 00b3 00b4 00b6 00b7
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00b9 00ba 00bc 00bd 00bf 00c0 00c2 00c4 00c5 00c7 00c8 00ca 00cc 00cd 00cf 00d1
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00d2 00d4 00d6 00d7 00d9 00db 00dc 00de 00e0 00e2 00e4 00e5 00e7 00e9 00eb 00ed
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00ee 00f0 00f2 00f4 00f6 00f8 00fa 00fc 00fe 0100 0102 0104 0106 0108 010a 010c
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010e 0110 0113 0115 0117 0119 011b 011e 0120 0122 0124 0127 0129 012b 012e 0130
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0133 0135 0137 013a 013c 013f 0142 0144 0147 0149 014c 014f 0152 0154 0157 015a
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015d 0160 0162 0165 0168 016b 016e 0171 0175 0178 017b 017e 0181 0185 0188 018b
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018f 0192 0196 0199 019d 01a0 01a4 01a8 01ac 01af 01b3 01b7 01bb 01bf 01c3 01c7
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01cc 01d0 01d4 01d8 01dd 01e1 01e6 01eb 01ef 01f4 01f9 01fe 0203 0208 020d 0212
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0218 021d 0223 0228 022e 0234 023a 0240 0246 024c 0252 0259 025f 0266 026d 0274
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027b 0282 0289 0291 0299 02a0 02a8 02b1 02b9 02c1 02ca 02d3 02dc 02e5 02ef 02f9
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0302 030d 0317 0322 032d 0338 0343 034f 035b 0368 0374 0382 038f 039d 03ab 03ba
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03c9 03d9 03e9 03f9 040a 041c 042e 0441 0454 0468 047d 0492 04a9 04c0 04d8 04f1
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050b 0526 0542 055f 057d 059d 05bf 05e1 0606 062c 0654 067e 06aa 06d9 070a 073e
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0775 07af 07ed 082f 0876 08c1 0911 0967 09c4 0a28 0a95 0b0a 0b8b 0c17 0cb2 0d5d
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0e1a 0eed 0fdb 10e8 121b 137d 1519 1700 1946 1c0c 1f80 23ed 29cc 31f5 3e13 51f2
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7888 7fff 7fff
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@x16-log ( x* -> log(x)* )
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DUP2 #0000 GTH2 STH
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DUP2 #8000 LTH2 STHr AND ,&0<x<128 JCN
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( error ) #0000 DIV
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&0<x<128 DUP2 #0800 GTH2 ,&8<x<128 JCN
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( 0<x<=8 ) DUP2 #0200 GTH2 ,&2<x<=8 JCN
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( 0<x<=2 ) ,x16-log-q JMP
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&2<x<=8 DUP2 #0400 GTH2 ,&4<x<=8 JCN
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( 2<x<=4 ) #0200 ;x16-div JSR2 ,x16-log-q JSR #00b1 ADD2 JMP2r
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&4<x<=8 #0400 ;x16-div JSR2 ,x16-log-q JSR #0163 ADD2 JMP2r
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&8<x<128 DUP2 #2000 GTH2 ,&32<x<128 JCN
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( 8<x<=32 ) DUP2 #1000 GTH2 ,&16<x<=32 JCN
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( 8<x<=16 ) #0800 ;x16-div JSR2 ,x16-log-q JSR #0214 ADD2 JMP2r
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&16<x<=32 #1000 ;x16-div JSR2 ,x16-log-q JSR #02c6 ADD2 JMP2r
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&32<x<128 DUP2 #4000 GTH2 ,&64<x<128 JCN
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( 32<x<=64 ) #2000 ;x16-div JSR2 ,x16-log-q JSR #0377 ADD2 JMP2r
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&64<x<128 #4000 ;x16-div JSR2 ,x16-log-q JSR #0429 ADD2 JMP2r
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( 0 < x <= 2 )
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@x16-log-q ( x* -> log(x)* )
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#10 SFT2 ;x16-log-table ADD2 LDA2 JMP2r
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( the first entry, i.e. log(0), is invalid and should not be used. )
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( the last entry is log(2). )
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@x16-log-table
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8000 fa74 fb26 fb8e fbd7 fc10 fc3f fc67 fc89 fca7 fcc2 fcda fcf1 fd05 fd18 fd2a
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fd3a fd4a fd58 fd66 fd73 fd80 fd8c fd97 fda2 fdac fdb7 fdc0 fdc9 fdd2 fddb fde4
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fdec fdf4 fdfb fe03 fe0a fe11 fe18 fe1e fe25 fe2b fe31 fe37 fe3d fe43 fe49 fe4e
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fe53 fe59 fe5e fe63 fe68 fe6d fe72 fe76 fe7b fe7f fe84 fe88 fe8d fe91 fe95 fe99
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fe9d fea1 fea5 fea9 fead feb0 feb4 feb8 febb febf fec2 fec6 fec9 fecc fed0 fed3
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fed6 fed9 fedd fee0 fee3 fee6 fee9 feec feef fef2 fef4 fef7 fefa fefd ff00 ff02
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ff05 ff08 ff0a ff0d ff0f ff12 ff14 ff17 ff19 ff1c ff1e ff21 ff23 ff25 ff28 ff2a
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ff2c ff2f ff31 ff33 ff35 ff38 ff3a ff3c ff3e ff40 ff42 ff44 ff46 ff48 ff4b ff4d
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ff4f ff51 ff53 ff54 ff56 ff58 ff5a ff5c ff5e ff60 ff62 ff64 ff65 ff67 ff69 ff6b
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ff6d ff6e ff70 ff72 ff74 ff75 ff77 ff79 ff7b ff7c ff7e ff80 ff81 ff83 ff84 ff86
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ff88 ff89 ff8b ff8c ff8e ff90 ff91 ff93 ff94 ff96 ff97 ff99 ff9a ff9c ff9d ff9f
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ffa0 ffa2 ffa3 ffa4 ffa6 ffa7 ffa9 ffaa ffab ffad ffae ffb0 ffb1 ffb2 ffb4 ffb5
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ffb6 ffb8 ffb9 ffba ffbc ffbd ffbe ffc0 ffc1 ffc2 ffc3 ffc5 ffc6 ffc7 ffc8 ffca
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ffcb ffcc ffcd ffcf ffd0 ffd1 ffd2 ffd3 ffd5 ffd6 ffd7 ffd8 ffd9 ffda ffdc ffdd
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ffde ffdf ffe0 ffe1 ffe2 ffe3 ffe5 ffe6 ffe7 ffe8 ffe9 ffea ffeb ffec ffed ffee
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ffef fff1 fff2 fff3 fff4 fff5 fff6 fff7 fff8 fff9 fffa fffb fffc fffd fffe ffff
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0000 0001 0002 0003 0004 0005 0006 0007 0008 0009 000a 000b 000c 000d 000e 000f
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0010 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 001a 001b 001b 001c 001d
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001e 001f 0020 0021 0022 0023 0023 0024 0025 0026 0027 0028 0029 0029 002a 002b
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002c 002d 002e 002f 002f 0030 0031 0032 0033 0033 0034 0035 0036 0037 0038 0038
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0039 003a 003b 003c 003c 003d 003e 003f 003f 0040 0041 0042 0043 0043 0044 0045
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0046 0046 0047 0048 0049 0049 004a 004b 004c 004c 004d 004e 004f 004f 0050 0051
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0052 0052 0053 0054 0054 0055 0056 0057 0057 0058 0059 0059 005a 005b 005c 005c
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005d 005e 005e 005f 0060 0060 0061 0062 0062 0063 0064 0064 0065 0066 0066 0067
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0068 0068 0069 006a 006a 006b 006c 006c 006d 006e 006e 006f 0070 0070 0071 0072
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0072 0073 0074 0074 0075 0075 0076 0077 0077 0078 0079 0079 007a 007a 007b 007c
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007c 007d 007e 007e 007f 007f 0080 0081 0081 0082 0082 0083 0084 0084 0085 0085
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0086 0087 0087 0088 0088 0089 0089 008a 008b 008b 008c 008c 008d 008e 008e 008f
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008f 0090 0090 0091 0092 0092 0093 0093 0094 0094 0095 0095 0096 0097 0097 0098
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0098 0099 0099 009a 009a 009b 009c 009c 009d 009d 009e 009e 009f 009f 00a0 00a0
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00a1 00a1 00a2 00a3 00a3 00a4 00a4 00a5 00a5 00a6 00a6 00a7 00a7 00a8 00a8 00a9
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00a9 00aa 00aa 00ab 00ab 00ac 00ac 00ad 00ad 00ae 00ae 00af 00af 00b0 00b0 00b1
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00b1
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@ -64,6 +64,10 @@
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;buf LDA LIT "> EQU ;test-x16-gt JCN2
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;buf LDA LIT "{ EQU ;test-x16-lteq JCN2
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;buf LDA LIT "} EQU ;test-x16-gteq JCN2
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;buf LDA LIT "s EQU ;test-x16-sin JCN2
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;buf LDA LIT "c EQU ;test-x16-cos JCN2
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;buf LDA LIT "t EQU ;test-x16-tan JCN2
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;buf LDA LIT "l EQU ;test-x16-log JCN2
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LIT "? #18 DEO #0a #18 DEO ;reset JSR2 BRK
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( set the interpreter to exit now )
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@ -104,6 +108,10 @@
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@test-x16-lteq #04 #01 ;x16-lteq ;test JMP2
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@test-x16-gt #04 #01 ;x16-gt ;test JMP2
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@test-x16-gteq #04 #01 ;x16-gteq ;test JMP2
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@test-x16-sin #02 #02 ;x16-sin ;test JMP2
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@test-x16-cos #02 #02 ;x16-cos ;test JMP2
|
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@test-x16-tan #02 #02 ;x16-tan ;test JMP2
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@test-x16-log #02 #02 ;x16-log ;test JMP2
|
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|
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( reads one byte from ASCII: "13" -> 0x13 )
|
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@read-byte ( c0^ c1^ -> n^ )
|
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|
|
|
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Loading…
Reference in New Issue