4 ms·

"For the special case of the ejection of binary stars, described in Section 6, we employ octuple floating-point precision (~64 digits)." http://arxiv.org/abs/1

"For the special case of the ejection of binary stars, described in Section 6, we employ octuple floating-point precision (~64 digits)." http://arxiv.org/abs/1411.5022 http://arxiv.org/abs/1411.5022

HCIdivision17 12y ago
I don't think I've ever even heard of something needing that level of precision. That's about 18 decimal places, right? I'm adding the paper to my read-later pile just to understand that need. (And I don't doubt it. But man, you can describe the height of man or the plank length in one number!) (And my apologies if it's explained in the paper - I haven't read it yet.)
- throwaway_yy2Di 12y ago
  No, it's 64 decimal digits ~ 213 bits of precision! Octuple precision should have 8 * 32 = 256 bit word size. IEEE 754 single, double, and quadruple precision FP have 32, 64, and 128-bit word sizes, with significand precisions of 24, 53, and 113 bits. https://en.wikipedia.org/wiki/Floating_point#Internal_representation https://en.wikipedia.org/wiki/Floating_point#Internal_repres...
  - HCIdivision17 12y ago
    Even more astounding. In retrospect, the word 'digits' is pretty unambiguous, and I shouldn't have gotten confused. But man, that is some hard-core numerical work. I'll need to bring the paper to the top of my dinner reading stack. The project just seems fascinating.
- Someone 12y ago
  "For the special case of the ejection of binary stars, described in Section 6, we employ octuple floating-point precision (~64 digits)" "That's about 18 decimal places, right?" I would 'guess' it's about 64 decimal places. At 3 digits in 10 bits, that would require 214 bits. Double precision has 53 bits for the mantissa, so that is in the right range.
  - HCIdivision17 12y ago
    You're correct; I had misread that as 64 bit precision, which is vastly smaller. I'll need to be more careful reading the actual paper!
- Houshalter 12y ago
  I can think of some things that would benefit from it. Dealing with probabilities, you often get very small numbers with thousands of 0's in front of them. And summations of a huge number of small numbers can become very inaccurate. Both of these can be accomplished with tricks like doing it in the log domain though. It just makes it more complicated.
  - HCIdivision17 12y ago
    You're absolutely correct - I often forget how much larger probabilistic numbers get. Sort of the difference between "large numbers" and "very large numbers"!

"For the special case of the ejection of binary stars, described in Section 6, we employ octuple floating-point precision (~64 digits)." http://arxiv.org/abs/1411.5022 http://arxiv.org/abs/1411.5022

HCIdivision17 12y ago

I don't think I've ever even heard of something needing that level of precision. That's about 18 decimal places, right? I'm adding the paper to my read-later pile just to understand that need. (And I don't doubt it. But man, you can describe the height of man or the plank length in one number!) (And my apologies if it's explained in the paper - I haven't read it yet.)

throwaway_yy2Di 12y ago
No, it's 64 decimal digits ~ 213 bits of precision! Octuple precision should have 8 * 32 = 256 bit word size. IEEE 754 single, double, and quadruple precision FP have 32, 64, and 128-bit word sizes, with significand precisions of 24, 53, and 113 bits. https://en.wikipedia.org/wiki/Floating_point#Internal_representation https://en.wikipedia.org/wiki/Floating_point#Internal_repres...
- HCIdivision17 12y ago
  Even more astounding. In retrospect, the word 'digits' is pretty unambiguous, and I shouldn't have gotten confused. But man, that is some hard-core numerical work. I'll need to bring the paper to the top of my dinner reading stack. The project just seems fascinating.
Someone 12y ago
"For the special case of the ejection of binary stars, described in Section 6, we employ octuple floating-point precision (~64 digits)" "That's about 18 decimal places, right?" I would 'guess' it's about 64 decimal places. At 3 digits in 10 bits, that would require 214 bits. Double precision has 53 bits for the mantissa, so that is in the right range.
- HCIdivision17 12y ago
  You're correct; I had misread that as 64 bit precision, which is vastly smaller. I'll need to be more careful reading the actual paper!
Houshalter 12y ago
I can think of some things that would benefit from it. Dealing with probabilities, you often get very small numbers with thousands of 0's in front of them. And summations of a huge number of small numbers can become very inaccurate. Both of these can be accomplished with tricks like doing it in the log domain though. It just makes it more complicated.
- HCIdivision17 12y ago
  You're absolutely correct - I often forget how much larger probabilistic numbers get. Sort of the difference between "large numbers" and "very large numbers"!