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copied!<p><code>cos</code> is expensive, especially 4 in a row. You appear to be computing cos(n<em>a+b) where b is a constant and n is a small integer. This means you can precompute cos(b) and sin(b) and at runtime compute just cos(hp) and sin(hp). You can get cos(n</em>a+b) by making repeated use of</p> <pre><code>cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b) </code></pre> <p>You'll be trading a couple of <code>sin</code>s and <code>cos</code>s for some multiplications and additions, almost certainly worthwhile.</p> <p>You can do better if you're feeling ambitious. You're getting <code>hp</code> indirectly from an <code>atan2</code>. The pattern <code>trig-function(rational-function(inverse-trig-function(x)))</code> can frequently be replaced by some combination of polynomials and roots which are faster to evaluate than trig functions.</p> <p>I don't know how <code>pow</code> is implemented in Java, but if it uses logs, you may be better off getting <code>Cp7</code> using <code>Cp2=Cp*Cp;Cp4=Cp2*Cp2;Cp7=Cp4*Cp2*Cp;</code></p> <p>Update: Getting a bit more speculative right now as I don't have time to actually rewrite the code. The power optimization and the trig optimization are actually the same thing in disguise! The trig optimization is a version of the power optimization applied to complex numbers. What's more, the line</p> <pre><code>double dH = 2 * Math.sqrt(CpProd) * Math.sin(dhp / 2); </code></pre> <p>is part of a complex number square root operation. This makes me think that a large chunk of this code could actually be written to use complex numbers eliminating almost all of the trig functions. I don't know how your complex number arithmetic is though...</p>

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