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Thu Mar 7 09:29:07 EST 2013

## Exponentials

I'm running into some interesting problems with the audio synth stuff
I'm working on. At some points in the program, (complex) exponentials
are necessary. Some observations:
- exp / sin / cos from math.h, libm.so seem to be a bit slow.
- straight line curves in the form of complex exponentials, e.g. for
parameter interpolation, can be generated incrementally using just
multiply add.
- for "algorithm" parameter transformation such as initializing
interpolating exponential curves, the accuracy is key.
- for "human" parameter transformation, i.e. things like mapping a
control value to a frequency value, the accuracy of exp probably
doesn't need to be so high, and approximation could be used.
- Some interesting comments on stackexchange[1].
- Maybe this can be split into 2 parts: linear evolution based on
previous coefficient + computation of updated coefficient using some
iteration step, based on some setpoint.
Conclusion seems to be that yes, exp and sin are expensive.
[1] http://math.stackexchange.com/questions/18445/fastest-way-to-calculate-ex-upto-arbitrary-number-of-decimals

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