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POWhat is the fastest way to compute sin and cos together?
 

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  1. POWhat is the fastest way to compute sin and cos together?
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    <p>I would like to compute both the sine and co-sine of a value together (for example to create a rotation matrix). Of course I could compute them separately one after another like <code>a = cos(x); b = sin(x);</code>, but I wonder if there is a faster way when needing both values.</p> <p><strong>Edit:</strong> To summarize the answers so far:</p> <ul> <li><p><a href="https://stackoverflow.com/a/2683691"><em>Vlad</em></a> said, that there is the asm command <code>FSINCOS</code> computing both of them (in almost the same time as a call to <code>FSIN</code> alone)</p></li> <li><p>Like <a href="https://stackoverflow.com/a/2683963"><em>Chi</em></a> noticed, this optimization is sometimes already done by the compiler (when using optimization flags).</p></li> <li><p><a href="https://stackoverflow.com/a/2687338"><em>caf</em></a> pointed out, that functions <code>sincos</code> and <code>sincosf</code> are probably available and can be called directly by just including <code>math.h</code></p></li> <li><p><a href="https://stackoverflow.com/a/2683613"><em>tanascius</em></a> approach of using a look-up table is discussed controversial. (However on my computer and in a benchmark scenario it runs 3x faster than <code>sincos</code> with almost the same accuracy for 32-bit floating points.)</p></li> <li><p><a href="https://stackoverflow.com/a/2683853"><em>Joel Goodwin</em></a> linked to an interesting approach of an extremly fast approximation technique with quite good accuray (for me, this is even faster then the table look-up)</p></li> </ul>
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    1. COSee also this question about native implementation of sin/cos: http://stackoverflow.com/questions/1640595
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      1. POWhat is the fastest way to compute sin and cos together?
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    2. COtry `sinx ~ x-x^3/6` and `cosx~1-x^2/4` as approximations if you care about speed more than accuracy. You can add on terms in either series as you put more weight on accuracy (http://en.wikipedia.org/wiki/Taylor_series scroll down to trig taylor series.) Note this is a general way to approximate any function you want that is differntiable `n` times. So if you have some bigger function that that sine's and cosine's belong to you will get a much bigger speed up if you approximate it instead of the sin,cos's independently.
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    3. COThis is poor technique with very poor accuracy. See post by Joel Goodwin. Taylor series have been posted below. Please post it as an answer.
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