<div dir="ltr">Even if you do a long multiply, you can still determine whether or not it overflows using at most two multiplies plus a little bit of masking, shifting, and adding.<div><br></div><div>For example, if you want to know if a uint_16 * unit_16 will overflow, and you don't have an overflow flag or any form of 16x16 -> 32 or 16x16 -> hi(16) multiply...</div><div><br></div><div><div>// program to check an algorithm to detect overflow in unsigned multiply</div><div><br></div><div>#include <stdio.h></div><div>#include <stdint.h></div><div><br></div><div>bool umulo(uint16_t a, uint16_t b){</div><div> uint8_t ah = a>>8, al = a & 0xff, bh = b>>8, bl = b & 0xff, mid;</div><div> if (ah == 0){</div><div> if (bh == 0) return false;</div><div> uint16_t albh = al * bh;</div><div> mid = albh & 0xff;</div><div> if (mid != albh) return true;</div><div> } else { // ah != 0</div><div> if (bh != 0) return true;</div><div> uint16_t ahbl = ah * bl;</div><div> mid = ahbl & 0xff;</div><div> if (mid != ahbl) return true;</div><div> }</div><div> uint16_t alblh = (al * bl) >> 8;</div><div> return (mid + alblh) > 0xff;</div><div>}</div><div><br></div><div>int main(){</div><div> int failures = 0;</div><div> for (uint32_t a=0; a<0x10000; ++a){</div><div> for (uint32_t b=0; b<0x10000; ++b){</div><div> bool ov = (a * b) > 0xffff;</div><div> if (ov != umulo(a, b)){</div><div> printf("Error for %d * %d\n", a, b);</div><div> +failures;</div><div> }</div><div> }</div><div> }</div><div> printf("%d failures\n", failures);</div><div> return 0;</div><div>}</div></div><div><br></div><div>That runs an exhaustive test with no failures in 4.25 seconds with -O3 on my machine. Or about 9 seconds with -0, -0s, or -02</div><div><br></div></div><div class="gmail_extra"><br><div class="gmail_quote">On Wed, Feb 28, 2018 at 10:13 PM, via llvm-dev <span dir="ltr"><<a href="mailto:llvm-dev@lists.llvm.org" target="_blank">llvm-dev@lists.llvm.org</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">If your target has a cheap count-leading-zeros instruction, you'd be able to determine whether an unsigned multiply will overflow or not, in most cases, without
doing the long version of the multiplication. This is because an N-bit number times an M-bit number will produce a result that is either N+M bits wide or N+M-1 bits wide. If an N+M bit result will fit in your result type, you are guaranteed the boolean result
is false; if an N+M-1 bit result does not fit in your result type, you are guaranteed the boolean result is true.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">You still need to do the more complicated check in the boundary cases, I think.<u></u><u></u></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d">--paulr<u></u><u></u></span></p>
<p class="MsoNormal"><a name="m_7179216201258576151__MailEndCompose"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1f497d"><u></u> <u></u></span></a></p>
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<p class="MsoNormal"><b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> llvm-dev [mailto:<a href="mailto:llvm-dev-bounces@lists.llvm.org" target="_blank">llvm-dev-bounces@<wbr>lists.llvm.org</a>]
<b>On Behalf Of </b>Bruce Hoult via llvm-dev<br>
<b>Sent:</b> Wednesday, February 28, 2018 5:43 AM<br>
<b>To:</b> </span><span style="font-size:10.0pt;font-family:"MS UI Gothic","sans-serif"">陳韋任</span><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""><br>
<b>Cc:</b> LLVM Developers Mailing List<br>
<b>Subject:</b> Re: [llvm-dev] How to handle UMULO?<u></u><u></u></span></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">I think your users will be very upset if you don't set the boolean return value correctly :-)<u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">Whatever work it takes to determine the correct value for it, if the user code doesn't need/use that value then the dead code will be eliminated later. But if they need that return flag then they will want it to be correct!<u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">You may need to use a multiply instruction that returns a double-register result, or an instruction that returns only the upper half of the result. Or you might need to widen the operands and do a full double-width multiply. Or you might
need to narrow the operands into two halves, do four (or three) multiplies and some shifts and adds (again detecting carry/overflow, but that's easier for addition).<u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">It all depends on what instructions your target has.<u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal">On Wed, Feb 28, 2018 at 4:31 PM, <span style="font-family:"MS Gothic"">
陳韋任</span> via llvm-dev <<a href="mailto:llvm-dev@lists.llvm.org" target="_blank">llvm-dev@lists.llvm.org</a>> wrote:<u></u><u></u></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif"">Hi All,<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif""><u></u> <u></u></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif""> While compiling libgcc, I find I have to deal with UMULO (overflow-aware unsigned multiplication) SDNode. UMULO returns the result of multiplication, and a boolean indicating overflow occurred
or not. Our target's multiply instruction doesn't care (detect) overflow. I am wondering if I can always set the boolean to false. I am not sure about this as I see AArch64 [1] seems trying to emulate the overflow behavior.</span><u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif""> Thanks.</span><u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif"">[1] <a href="https://github.com/llvm-mirror/llvm/blob/master/lib/Target/AArch64/AArch64ISelLowering.cpp" target="_blank">https://github.com/llvm-<wbr>mirror/llvm/blob/master/lib/<wbr>Target/AArch64/<wbr>AArch64ISelLowering.cpp</a></span><u></u><u></u></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif"">Regards,<u></u><u></u></span></p>
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<p class="MsoNormal"><span style="font-family:"Arial","sans-serif"">chenwj<u></u><u></u></span></p>
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<p class="MsoNormal"><u></u> <u></u></p>
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<p class="MsoNormal"><span class="m_7179216201258576151hoenzb"><span style="color:#888888">-- <u></u><u></u></span></span></p>
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<p class="MsoNormal"><span style="color:#888888">Wei-Ren Chen (</span><span style="font-family:"MS Gothic";color:#888888">陳韋任</span><span style="color:#888888">)<br>
Homepage: <a href="https://people.cs.nctu.edu.tw/~chenwj" target="_blank">https://people.cs.nctu.edu.tw/<wbr>~chenwj</a></span><u></u><u></u></p>
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