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?
> 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)