<div dir="ltr"><br><div class="gmail_extra"><br><br><div class="gmail_quote">On Wed, Jun 18, 2014 at 11:12 AM, Owen Anderson <span dir="ltr"><<a href="mailto:resistor@mac.com" target="_blank">resistor@mac.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word"><div class=""><br><div><div>On Jun 18, 2014, at 9:30 AM, Sean Silva <<a href="mailto:chisophugis@gmail.com" target="_blank">chisophugis@gmail.com</a>> wrote:</div>
<br><blockquote type="cite"><span style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">On Tue, Jun 17, 2014 at 10:11 PM, Rafael Avila de Espindola<span> </span></span><span dir="ltr" style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><<a href="mailto:rafael.espindola@gmail.com" target="_blank">rafael.espindola@gmail.com</a>></span><span style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important"> </span><span style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;float:none;display:inline!important">wrote:</span><br style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
<blockquote class="gmail_quote" style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
If we require the host to have sse2 or other IEEE 754 conformant  implementation, would it be possible to use hardware float?<br></blockquote><div style="font-family:Helvetica;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:normal;text-align:start;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">
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I don't think that IEEE 754 actually guarantees bit-exact results in all cases.</div></blockquote></div><br><div><br></div></div><div>IEEE 754 accuracy guarantees are expressed in terms of ULPs: Units-in-the-Last-Place.</div>
</div></blockquote><div><br></div><div>Yeah, that's what I was thinking of, but... <br><br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word">
<div>  Most of the primitive operations are accurate to +/- 0.5 ULPs, which is equivalent to saying that there is a single bit-accurate result (for a given rounding mode).</div></div></blockquote><div><br></div><div>... I wasn't aware that the primitives were spec'd with sufficiently tight ULP bounds for bit-exact results. Good to know!<br>
</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div style="word-wrap:break-word"><div>  Once you get into transcendentals, you start getting operations with much wider ULP bounds.</div>
</div></blockquote><div><br></div><div>Yeah, this was the specific counter-example that I was aware of.<br></div><div> <br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div style="word-wrap:break-word"><span class="HOEnZb"><font color="#888888"><div><br></div><div>—Owen</div></font></span></div></blockquote></div><br></div></div>