| 1 | /* Fast and inexact trigonometry routines
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| 2 | * Copyright 2013, Adrien Destugues <pulkomandy@pulkomandy.tk>
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| 3 | *
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| 4 | * This file is distributed under the terms of the MIT licence
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| 5 | */
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| 6 | #include <stdint.h>
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| 7 |
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| 8 |
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| 9 | unsigned char SIN[512];
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| 10 |
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| 11 | // TODO rewrite this in assembler and optimize it ! It should be possible to get
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| 12 | // a very small code for it. Fast doesn't really matter as this is called once
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| 13 | // at demo init.
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| 14 |
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| 15 | /**
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| 16 | * Generate an approximation of a sine wave using a polynomial (x-3)²-1.
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| 17 | * http://codebase64.org/doku.php?id=base:generating_approximate_sines_in_assembly
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| 18 | *
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| 19 | * Output is unsigned 8bit, in the range 0-255.
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| 20 | * Deviates from an actual sinewave by about 6%, which is ok for dirty trig, but
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| 21 | * also more interesting when you derive (get a triangle) or integrate. So this
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| 22 | * adds some distorsion which is nice for plasma curves, and so on.
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| 23 | *
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| 24 | * Call this once, then use the SIN table to lookup your samples. We *should* be
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| 25 | * using a signed char as an offset in the table, which could be used to make
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| 26 | * this code a bit more 6809 optimized. For now we don't...
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| 27 | */
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| 28 | void polysine()
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| 29 | {
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| 30 | // Value is the computed valu of the sine at the current point.
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| 31 | // Delta is the acceleration we use to build the polynomial iteratively
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| 32 | uint16_t value = 0, delta = 0;
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| 33 | // These are indices into the wavetable. We compute only 64 points and the
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| 34 | // others are built by symetry.
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| 35 | uint8_t y = 0x3F, x = 0;
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| 36 |
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| 37 | do
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| 38 | {
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| 39 | // Compute the value for the next point
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| 40 | value += delta;
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| 41 |
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| 42 | // The last half of the sinewave is positive and symetric
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| 43 | SIN[256 + 0xC0 + x] = SIN[0xC0 + x] = value >> 8;
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| 44 | SIN[256 + 0x80 + y] = SIN[0x80 + y] = value >> 8;
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| 45 | // The fist half is negative and a mirror of the last
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| 46 | SIN[256 + 0x40 + x] = SIN[0x40 + x] = (value >> 8) ^ 0xFF;
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| 47 | SIN[256 + y] = SIN[ y] = (value >> 8) ^ 0xFF;
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| 48 |
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| 49 | // Increase delta (else we get a triangle wave)
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| 50 | // Tweak this value if you need the sinewave to have a different amplitude
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| 51 | delta += 0x10;
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| 52 |
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| 53 | // Move on to the next sample
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| 54 | x++;
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| 55 | } while(y-- > 0);
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| 56 | }
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