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copied!<p>Using <code>gcc</code> and applying a diff to the generated assembly yields only this difference:</p> <pre><code>73c68,69 < movss LCPI1_0(%rip), %xmm1 --- > movabsq $0, %rcx > cvtsi2ssq %rcx, %xmm1 81d76 < subss %xmm1, %xmm0 </code></pre> <p>The <code>cvtsi2ssq</code> one being 10 times slower indeed.</p> <p>Apparently, the <code>float</code> version uses an <a href="http://en.wikipedia.org/wiki/Streaming_SIMD_Extensions#Registers" rel="noreferrer">XMM</a> register loaded from memory, while the <code>int</code> version converts a real <code>int</code> value 0 to <code>float</code> using the <code>cvtsi2ssq</code> instruction, taking a lot of time. Passing <code>-O3</code> to gcc doesn't help. (gcc version 4.2.1.)</p> <p>(Using <code>double</code> instead of <code>float</code> doesn't matter, except that it changes the <code>cvtsi2ssq</code> into a <code>cvtsi2sdq</code>.)</p> <p><strong>Update</strong> </p> <p>Some extra tests show that it is not necessarily the <code>cvtsi2ssq</code> instruction. Once eliminated (using a <code>int ai=0;float a=ai;</code> and using <code>a</code> instead of <code>0</code>), the speed difference remains. So @Mysticial is right, the denormalized floats make the difference. This can be seen by testing values between <code>0</code> and <code>0.1f</code>. The turning point in the above code is approximately at <code>0.00000000000000000000000000000001</code>, when the loops suddenly takes 10 times as long.</p> <p><strong>Update<<1</strong> </p> <p>A small visualisation of this interesting phenomenon:</p> <ul> <li>Column 1: a float, divided by 2 for every iteration</li> <li>Column 2: the binary representation of this float</li> <li>Column 3: the time taken to sum this float 1e7 times</li> </ul> <p>You can clearly see the exponent (the last 9 bits) change to its lowest value, when denormalization sets in. At that point, simple addition becomes 20 times slower.</p> <pre><code>0.000000000000000000000000000000000100000004670110: 10111100001101110010000011100000 45 ms 0.000000000000000000000000000000000050000002335055: 10111100001101110010000101100000 43 ms 0.000000000000000000000000000000000025000001167528: 10111100001101110010000001100000 43 ms 0.000000000000000000000000000000000012500000583764: 10111100001101110010000110100000 42 ms 0.000000000000000000000000000000000006250000291882: 10111100001101110010000010100000 48 ms 0.000000000000000000000000000000000003125000145941: 10111100001101110010000100100000 43 ms 0.000000000000000000000000000000000001562500072970: 10111100001101110010000000100000 42 ms 0.000000000000000000000000000000000000781250036485: 10111100001101110010000111000000 42 ms 0.000000000000000000000000000000000000390625018243: 10111100001101110010000011000000 42 ms 0.000000000000000000000000000000000000195312509121: 10111100001101110010000101000000 43 ms 0.000000000000000000000000000000000000097656254561: 10111100001101110010000001000000 42 ms 0.000000000000000000000000000000000000048828127280: 10111100001101110010000110000000 44 ms 0.000000000000000000000000000000000000024414063640: 10111100001101110010000010000000 42 ms 0.000000000000000000000000000000000000012207031820: 10111100001101110010000100000000 42 ms 0.000000000000000000000000000000000000006103515209: 01111000011011100100001000000000 789 ms 0.000000000000000000000000000000000000003051757605: 11110000110111001000010000000000 788 ms 0.000000000000000000000000000000000000001525879503: 00010001101110010000100000000000 788 ms 0.000000000000000000000000000000000000000762939751: 00100011011100100001000000000000 795 ms 0.000000000000000000000000000000000000000381469876: 01000110111001000010000000000000 896 ms 0.000000000000000000000000000000000000000190734938: 10001101110010000100000000000000 813 ms 0.000000000000000000000000000000000000000095366768: 00011011100100001000000000000000 798 ms 0.000000000000000000000000000000000000000047683384: 00110111001000010000000000000000 791 ms 0.000000000000000000000000000000000000000023841692: 01101110010000100000000000000000 802 ms 0.000000000000000000000000000000000000000011920846: 11011100100001000000000000000000 809 ms 0.000000000000000000000000000000000000000005961124: 01111001000010000000000000000000 795 ms 0.000000000000000000000000000000000000000002980562: 11110010000100000000000000000000 835 ms 0.000000000000000000000000000000000000000001490982: 00010100001000000000000000000000 864 ms 0.000000000000000000000000000000000000000000745491: 00101000010000000000000000000000 915 ms 0.000000000000000000000000000000000000000000372745: 01010000100000000000000000000000 918 ms 0.000000000000000000000000000000000000000000186373: 10100001000000000000000000000000 881 ms 0.000000000000000000000000000000000000000000092486: 01000010000000000000000000000000 857 ms 0.000000000000000000000000000000000000000000046243: 10000100000000000000000000000000 861 ms 0.000000000000000000000000000000000000000000022421: 00001000000000000000000000000000 855 ms 0.000000000000000000000000000000000000000000011210: 00010000000000000000000000000000 887 ms 0.000000000000000000000000000000000000000000005605: 00100000000000000000000000000000 799 ms 0.000000000000000000000000000000000000000000002803: 01000000000000000000000000000000 828 ms 0.000000000000000000000000000000000000000000001401: 10000000000000000000000000000000 815 ms 0.000000000000000000000000000000000000000000000000: 00000000000000000000000000000000 42 ms 0.000000000000000000000000000000000000000000000000: 00000000000000000000000000000000 42 ms 0.000000000000000000000000000000000000000000000000: 00000000000000000000000000000000 44 ms </code></pre> <p>An equivalent discussion about ARM can be found in Stack Overflow question <em><a href="https://stackoverflow.com/questions/9350810/denormalized-floating-point-in-objective-c/9350820#9350820">Denormalized floating point in Objective-C?</a></em>.</p>

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