w1k #1 Posted September 21, 2009 Hello, where can i found action! support sin/cos functions? thank you Quote Share this post Link to post Share on other sites
invisible kid #2 Posted September 21, 2009 Hello, where can i found action! support sin/cos functions? thank you Greetings, I don't know anything about action! but since you've not had any replies yet, I thought I might post this. Sorry, it's a bit technical and assembly based, hopefully someone with more action! experience can help you out, until then here is some info. In my limited experience, the most common implementation of sin/cos functions are through look-up tables. In one of my programs that's how I implemented it. I used a domain of 0-63 which would coincide with 0-360 degrees. Some programs may require more precision, in my case this was acceptable. I used a calculator program to pre-calculate the values, I saved my worksheet: 0-63 degrees sine cosine 0-63degrees sine cosine 0 0 0 1 32 180.000 0 -1 1 5.625 0.09801714 0.99518473 33 185.625 -0.09801714 -0.99518473 2 11.250 0.19509032 0.98078528 34 191.250 -0.19509032 -0.98078528 3 16.875 0.29028468 0.95694034 35 196.875 -0.29028468 -0.95694034 4 22.500 0.38268343 0.92387953 36 202.500 -0.38268343 -0.92387953 5 28.125 0.47139674 0.88192126 37 208.125 -0.47139674 -0.88192126 6 33.750 0.55557023 0.83146961 38 213.750 -0.55557023 -0.83146961 7 39.375 0.63439328 0.77301045 39 219.375 -0.63439328 -0.77301045 8 45.000 0.70710678 0.70710678 40 225.000 -0.70710678 -0.70710678 9 50.625 0.77301045 0.63439328 41 230.625 -0.77301045 -0.63439328 10 56.250 0.83146961 0.55557023 42 236.250 -0.83146961 -0.55557023 11 61.875 0.88192126 0.47139674 43 241.875 -0.88192126 -0.47139674 12 67.500 0.92387953 0.38268343 44 247.500 -0.92387953 -0.38268343 13 73.125 0.95694034 0.29028468 45 253.125 -0.95694034 -0.29028468 14 78.750 0.98078528 0.19509032 46 258.750 -0.98078528 -0.19509032 15 84.375 0.99518473 0.09801714 47 264.375 -0.99518473 -0.09801714 16 90.000 1 0 48 270.000 -1 0 17 95.625 0.99518473 -0.09801714 49 275.625 -0.99518473 0.09801714 18 101.250 0.98078528 -0.19509032 50 281.250 -0.98078528 0.19509032 19 106.875 0.95694034 -0.29028468 51 286.875 -0.95694034 0.29028468 20 112.500 0.92387953 -0.38268343 52 292.500 -0.92387953 0.38268343 21 118.125 0.88192126 -0.47139674 53 298.125 -0.88192126 0.47139674 22 123.750 0.83146961 -0.55557023 54 303.750 -0.83146961 0.55557023 23 129.375 0.77301045 -0.63439328 55 309.375 -0.77301045 0.63439328 24 135.000 0.70710678 -0.70710678 56 315.000 -0.70710678 0.70710678 25 140.625 0.63439328 -0.77301045 57 320.625 -0.63439328 0.77301045 26 146.250 0.55557023 -0.83146961 58 326.250 -0.55557023 0.83146961 27 151.875 0.47139674 -0.88192126 59 331.875 -0.47139674 0.88192126 28 157.500 0.38268343 -0.92387953 60 337.500 -0.38268343 0.92387953 29 163.125 0.29028468 -0.95694034 61 343.125 -0.29028468 0.95694034 30 168.750 0.19509032 -0.98078528 62 348.750 -0.19509032 0.98078528 31 174.275 0.099753915 -0.99501214 63 354.375 -0.09801714 0.99518473 I then encoded those values in binary in my assembler program: sinlow .byte ~00000000 .byte ~00011001 .byte ~00110010 .byte ~01001010 .byte ~01100010 .byte ~01111001 .byte ~10001110 .byte ~10100010 .byte ~10110101 .byte ~11000110 .byte ~11010101 .byte ~11100010 .byte ~11101101 .byte ~11110101 .byte ~11111011 .byte ~11111111 .byte ~00000000 .byte ~11111111 .byte ~11111011 .byte ~11110101 .byte ~11101101 .byte ~11100010 .byte ~11010101 .byte ~11000110 .byte ~10110101 .byte ~10100010 .byte ~10001110 .byte ~01111001 .byte ~01100010 .byte ~01001010 .byte ~00110010 .byte ~00011001 .byte ~00000000 .byte ~11100111 .byte ~11001110 .byte ~10110110 .byte ~10011110 .byte ~10000111 .byte ~01110010 .byte ~01011110 .byte ~01001011 .byte ~00111010 .byte ~00101011 .byte ~00011110 .byte ~00010011 .byte ~00001011 .byte ~00000101 .byte ~00000001 .byte ~00000000 .byte ~00000001 .byte ~00000101 .byte ~00001011 .byte ~00010011 .byte ~00011110 .byte ~00101011 .byte ~00111010 .byte ~01001011 .byte ~01011110 .byte ~01110010 .byte ~10000111 .byte ~10011110 .byte ~10110110 .byte ~11001110 .byte ~11100111 sinhigh .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000001 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~00000000 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 .byte ~11111111 I only encoded the values for sin, because if you look at the table above, you can get cos values from the sin table by manipulating the look-up index. They are just shifted over. In my case this is how I did it, shifting the index over 48 spots, and wrapping it: ; x = sin(playerangle) ldx playerangle lda sinlow,x sta workbytes lda sinhigh,x sta workbytes+1 <snip> ; y = cos(playerangle) = sin((playerangle+48)&63) txa clc adc #48 and #63 tax lda sinlow,x sta workbytes lda sinhigh,x sta workbytes+1 I am sure there are better/more efficient ways to do this, and it might not help anyway as you are using action!. Either way, good luck, I hope you find something that works. Quote Share this post Link to post Share on other sites
idavis #3 Posted September 21, 2009 You could have either A. better resolution (0-90 in 1 degree steps) or B. a smaller table (only 16 records) if you just went from 0 to 90 degrees and calculated reference angles, then adding the + or - based on quadrant. Quote Share this post Link to post Share on other sites
thorfdbg #4 Posted September 23, 2009 Hello, where can i found action! support sin/cos functions? thank you Greetings, I don't know anything about action! but since you've not had any replies yet, I thought I might post this. Sorry, it's a bit technical and assembly based, hopefully someone with more action! experience can help you out, until then here is some info. In my limited experience, the most common implementation of sin/cos functions are through look-up tables. In one of my programs that's how I implemented it. I used a domain of 0-63 which would coincide with 0-360 degrees. Some programs may require more precision, in my case this was acceptable. ... I am sure there are better/more efficient ways to do this, and it might not help anyway as you are using action!. Either way, good luck, I hope you find something that works. Actually, this is not quite the common implementation. Modern code uses a polynomial approximation, using a minimax-polynomial of sin and cos (minimizing the maximal error over an interval) and the functional equation (periodicity) of sin and cos. Atari Basic uses a pretty stupid Taylor approximation, which is also a polynomial, but isn't very precise. It is slower than necessary, and less precise than possible. A pretty traditional way that uses a lookup table, requires only additions and shifts but is considerably more precise than a direct lookup is the CORDIC algorithm. You'll find it explained at Wikipedia, there to compute the arcus tangens (its traditional approach), but similar approaches are possible for sin and cos. It's the type of code you found in most pocket calculators. Greetings, Thomas Quote Share this post Link to post Share on other sites
+poobah #5 Posted September 23, 2009 Depending on what you are after (speed, precision, memory used, etc), your technique will vary. One of my 8 bit favorites was cutting a circle into 256 angles, and pre-calculating a table for each of those "angles", you can then use the angle with the 6502's indexing modes to quickly get your value. fun stuff Quote Share this post Link to post Share on other sites
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