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Overlapping sin and cos Tables
Submitted by |
In case some people out there aren't doing this, here's a tip to keep your
sin & cos lookup tables smaller saving on memory and thus possible cache
misses. Not to mention initialisation being a fraction faster.
How? Overlap them. As you probably know sin and cos differ only by a phase
shift of 90degrees, so 3/4 of the cos table can be overlapped with the sin
table.
Here is a simple way to do this, which will never run slower than having the
two tables seperate.
Additionally using a Fixed number format (like 16:16) to represent an angle
rather than degrees, radians or gradians makes for a little more speed.
(Unless you absolutely have to convert from degrees in realtime)
i.e. 0-2047 (in fixed 16:16 format) = 0-360degrees.
#define WaveTableSize 2048
//These etc may be useful
#define FullCircle (WaveTableSize<<16)
#define NinetyDegrees (WaveTableSize<<14)
#define FortyFiveDegrees (WaveTableSize<<13)
float sn[(WaveTableSize+(WaveTableSize2))], *cs = &sn[WaveTableSize2];
void initTables()
{
for (int i=0; i<WaveTableTotalSize; ++i)
sn[i]=sin(i * ((pi*2)/WaveTableSize));
}
inline int angleToIndex(int x) {
return (x16) & (WaveTableSize-1);
}
void blah(int angle)
{
int angle2 = angleToIndex(angle);
float cosAngle = cs[angle2], sinAngle = sn[angle2];
...
} |
Before you point it out, of course you can always make the tables smaller by
storing only 90degrees of the sin curve and reflecting it various ways. That
may be good for low memory circumstances.
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