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POFast equivalent to sin() for DSP referenced in STK
 

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  1. POFast equivalent to sin() for DSP referenced in STK
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    <p>I'm using bits of Perry Cook's Synthesis Toolkit (STK) to generate saw and square waves. STK includes this BLIT-based sawtooth oscillator:</p> <pre><code>inline STKFloat BlitSaw::tick( void ) { StkFloat tmp, denominator = sin( phase_ ); if ( fabs(denominator) &lt;= std::numeric_limits&lt;StkFloat&gt;::epsilon() ) tmp = a_; else { tmp = sin( m_ * phase_ ); tmp /= p_ * denominator; } tmp += state_ - C2_; state_ = tmp * 0.995; phase_ += rate_; if ( phase_ &gt;= PI ) phase_ -= PI; lastFrame_[0] = tmp; return lastFrame_[0]; } </code></pre> <p>The square wave oscillator is broadly similar. At the top, there's this comment:</p> <pre><code>// A fully optimized version of this code would replace the two sin // calls with a pair of fast sin oscillators, for which stable fast // two-multiply algorithms are well known. </code></pre> <p>I don't know where to start looking for these "fast two-multiply algorithms" and I'd appreciate some pointers. I could use a lookup table instead, but I'm keen to learn what these 'fast sin oscillators' are. I could also use an abbreviated Taylor series, but thats way more than two multiplies. Searching hasn't turned up anything much, although I did find this approximation:</p> <pre><code>#define AD_SIN(n) (n*(2.f- fabs(n))) </code></pre> <p>Plotting it out shows that it's not really a close approximation outside the range of -1 to 1, so I don't think I can use it when <code>phase_</code> is in the range -pi to pi:</p> <p><img src="https://i.stack.imgur.com/28scP.png" alt="Plot of Sine vs. approximation"></p> <p>Here, Sine is the blue line and the purple line is the approximation.</p> <p>Profiling my code reveals that the calls to <code>sin()</code> are far and away the most time-consuming calls, so I really would like to optimise this piece.</p> <p>Thanks</p> <p><strong>EDIT</strong> Thanks for the detailed and varied answers. I will explore these and accept one at the weekend.</p> <p><strong>EDIT 2</strong> Would the anonymous close voter please kindly explain their vote in the comments? Thank you.</p>
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    1. USTim Kemp
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      1. USErik Olson
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    1. COI'm surprised that a sawtooth oscillator requires trigonometric calculations.
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      1. USOliver Charlesworth
    2. COOli Charlesworth, they shouldn't. Ideal square-tooth & saw-tooth oscillators are easily modeled with simple algebra. My guess is maybe they're try to model less-ideal physical oscillators. For a saw-tooth, this is generally done as a sum of sine waves.
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      1. USNathan Ernst
    3. CO@NathanErnst the reason you use these functions isn't to do with modelling physical oscillators. Instead, it is because a 'pure' saw wave has infinite harmonics. Any harmonics above half the sampling frequency (44100/2) cause aliasing effects which sound absolutely dreadful. This technique here generates a 'band limited', or anti aliased sawtooth where the harmonics are controlled.
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