<html>
    <head>
      <base href="http://llvm.org/bugs/" />
    </head>
    <body><table border="1" cellspacing="0" cellpadding="8">
        <tr>
          <th>Bug ID</th>
          <td><a class="bz_bug_link 
          bz_status_NEW "
   title="NEW --- - missed opportunity for associative FP math in summation reduction (pairwise summation)"
   href="http://llvm.org/bugs/show_bug.cgi?id=17305">17305</a>
          </td>
        </tr>

        <tr>
          <th>Summary</th>
          <td>missed opportunity for associative FP math in summation reduction (pairwise summation)
          </td>
        </tr>

        <tr>
          <th>Product</th>
          <td>libraries
          </td>
        </tr>

        <tr>
          <th>Version</th>
          <td>trunk
          </td>
        </tr>

        <tr>
          <th>Hardware</th>
          <td>PC
          </td>
        </tr>

        <tr>
          <th>OS</th>
          <td>All
          </td>
        </tr>

        <tr>
          <th>Status</th>
          <td>NEW
          </td>
        </tr>

        <tr>
          <th>Severity</th>
          <td>normal
          </td>
        </tr>

        <tr>
          <th>Priority</th>
          <td>P
          </td>
        </tr>

        <tr>
          <th>Component</th>
          <td>Scalar Optimizations
          </td>
        </tr>

        <tr>
          <th>Assignee</th>
          <td>unassignedbugs@nondot.org
          </td>
        </tr>

        <tr>
          <th>Reporter</th>
          <td>kkhoo@perfwizard.com
          </td>
        </tr>

        <tr>
          <th>CC</th>
          <td>llvmbugs@cs.uiuc.edu
          </td>
        </tr>

        <tr>
          <th>Classification</th>
          <td>Unclassified
          </td>
        </tr></table>
      <p>
        <div>
        <pre>With the -fassociative-math flag, can the summation below be transformed using
an algorithm like:
<a href="http://en.wikipedia.org/wiki/Pairwise_summation">http://en.wikipedia.org/wiki/Pairwise_summation</a>

?


$ ./clang -v
clang version 3.4 (trunk 190938)
Target: x86_64-apple-darwin11.4.2
Thread model: posix

$ cat no_add_tree.c 
double foo(double x0, double x1, double x2, double x3, double x4, double x5,
double x6, double x7) {
    return x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7;
}

$ ./clang -S -O3 -fassociative-math -fomit-frame-pointer -march=corei7-avx
no_add_tree.c -o -
    .section    __TEXT,__text,regular,pure_instructions
    .globl    _foo
    .align    4, 0x90
_foo:                                   ## @foo
    .cfi_startproc
## BB#0:                                ## %entry
    vaddsd    %xmm1, %xmm0, %xmm0
    vaddsd    %xmm2, %xmm0, %xmm0
    vaddsd    %xmm3, %xmm0, %xmm0
    vaddsd    %xmm4, %xmm0, %xmm0
    vaddsd    %xmm5, %xmm0, %xmm0
    vaddsd    %xmm6, %xmm0, %xmm0
    vaddsd    %xmm7, %xmm0, %xmm0
    ret


Using pairwise addition, we should end up with something like this:
        vaddsd  %xmm1, %xmm0, %xmm0
        vaddsd  %xmm3, %xmm2, %xmm2
        vaddsd  %xmm5, %xmm4, %xmm4
        vaddsd  %xmm7, %xmm6, %xmm6
        vaddsd  %xmm2, %xmm0, %xmm0
        vaddsd  %xmm6, %xmm4, %xmm4
        vaddsd  %xmm4, %xmm0, %xmm0

The equivalent source code hack would be:
        x0 = x0 + x1;
        x2 = x2 + x3;
        x4 = x4 + x5;
        x6 = x6 + x7;
        x0 = x0 + x2;
        x4 = x4 + x6;
        return x0 + x4;

"iaca" (
<a href="http://software.intel.com/en-us/articles/intel-architecture-code-analyzer">http://software.intel.com/en-us/articles/intel-architecture-code-analyzer</a> )
shows that the throughput of the reassociated code is 9 cycles vs. 21 cycles
for the original code on Sandy Bridge; latency is improved to 12 cycles from 21
cycles. 

Real timing on a Sandy Bridge system confirms that the reassociated code runs
faster.</pre>
        </div>
      </p>
      <hr>
      <span>You are receiving this mail because:</span>
      
      <ul>
          <li>You are on the CC list for the bug.</li>
      </ul>
    </body>
</html>