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*To*: William Klein <wmklein@xxxxxxxxxxxxx>, IEEE 754 <stds-754@xxxxxxxxxxxxxxxxx>*Subject*: RE: Binary128 - PI and E*From*: Charles Stevens <charles.stevens@xxxxxxxx>*Date*: Wed, 11 May 2011 15:25:30 -0600*Importance*: Normal*In-reply-to*: <005001cc1011$84f244a0$8ed6cde0$@netcom.com>*List-help*: <http://listserv.ieee.org/cgi-bin/wa?LIST=STDS-754>, <mailto:LISTSERV@LISTSERV.IEEE.ORG?body=INFO%20STDS-754>*List-owner*: <mailto:STDS-754-request@LISTSERV.IEEE.ORG>*List-subscribe*: <mailto:STDS-754-subscribe-request@LISTSERV.IEEE.ORG>*List-unsubscribe*: <mailto:STDS-754-unsubscribe-request@LISTSERV.IEEE.ORG>*References*: <COL112-W129FC9BCF42EA29088D5C9839D0@phx.gbl>,<000.08040d00d191bc4d.002@tybor.com>,<002601cc07f1$16e79410$44b6bc30$@netcom.com>,<005001cc1011$84f244a0$8ed6cde0$@netcom.com>*Sender*: stds-754@xxxxxxxx

The answer I got some six years ago, and I have reason to believe it was from Mike Cowlishaw, is that these are best represented in decimal as an arithmetic _expression_ involving the quotient of two integers: For E: (14,114,126,198,520,207,781,233,383,725,636,853 / (2 ** 112)) For PI: (16,312,081,666,030,376,401,667,486,162,748,272 / (2 ** 112)) Given that the entire significand field is "accounted for" in the dividend in this formula, I can't think of a representation of "greater significance". Is there one, or is this as good as it gets? -Chuck Stevens > From: wmklein@xxxxxxxxxxxxx > To: stds-754@xxxxxxxxxxxxxxxxx > CC: charles.stevens@xxxxxxxx > Subject: Binary128 - PI and E > Date: Wed, 11 May 2011 14:27:51 -0500 > > This may be a stupid question and I don't know if I am even expre4ssing it correct, BUT Can anyone tell me or point me to some place that documents what the exact DECIMAL fixed-point value would be for the most accurate values of PI and E that can be stored in a binary128 data item? Would this just be (for PI) PI with 35 digits to the right of the decimal point? > > (I think that I am correct that any decimal item that can be stored in a binary128 item CAN be expressed exactly as a decimal fixed-point number - although the reverse is not true) |

**References**:**Questions on data transfer and non-arithmetic handling rules***From:*Charles Stevens

**Re: Questions on data transfer and non-arithmetic handling rules***From:*Fred J. Tydeman

**"reasonability" check***From:*William M Klein

**Binary128 - PI and E***From:*William M Klein

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