<html><head><meta http-equiv="Content-Type" content="text/html charset=windows-1252"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;"><br><div><div>On Jun 18, 2014, at 9:30 AM, Sean Silva <<a href="mailto:chisophugis@gmail.com">chisophugis@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px; float: none; display: inline !important;">On Tue, Jun 17, 2014 at 10:11 PM, Rafael Avila de Espindola<span class="Apple-converted-space"> </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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 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; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;"><br></div><div style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-stroke-width: 0px;">I don't think that IEEE 754 actually guarantees bit-exact results in all cases.</div></blockquote></div><br><div><br></div><div>IEEE 754 accuracy guarantees are expressed in terms of ULPs: Units-in-the-Last-Place. 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). Once you get into transcendentals, you start getting operations with much wider ULP bounds.</div><div><br></div><div>—Owen</div></body></html>