Timeline for Is floating point math broken?
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Feb 1, 2016 at 14:58 | comment | added | Jeff Y | @DevinJeanpierre I think the point is that "computers" don't have a "specific notion of 'binary' or 'decimal'". Pacerier's point seems to be that it is language designers who have decided to make the jump to "floating point" too early, when storing such numbers as "0.1", "0.2", and "0.3" which can not only be more accurately but also more space-efficiently stored as text (BCD). | |
Aug 26, 2015 at 19:47 | comment | added | supercat | @chux: The difference in precision between binary and decimal types isn't huge, but the 10:1 difference in best-case vs. worst-case precision for decimal types is far greater than the 2:1 difference with binary types. I'm curious whether anyone has built hardware or written software to operate efficiently on either of the decimal types, since neither would seem amenable to efficient implementation in hardware nor software. | |
Aug 26, 2015 at 19:26 | comment | added | chux - Reinstate Monica | @supercat In comparing precision of binary64 and decimal64: the precision are fairly comparable - certainly within a factor of 10 to each other. Granted decimal64 wobbles more than binary64. | |
Apr 24, 2014 at 16:43 | comment | added | supercat | @Pacerier: Neither binary nor decimal floating-point can precisely store 1/3 or 1/13. Decimal floating-point types can precisely represent values of the form M/10^E, but are less precise than similarly-sized binary floating-point numbers when it comes to representing most other fractions. In many applications, it's more useful to have higher precision with arbitrary fractions than to have perfect precision with a few "special" ones. | |
Oct 15, 2011 at 19:45 | comment | added | Devin Jeanpierre | @Pacerier Sure, they could use two unbounded-precision integers to represent a fraction, or they could use quote notation. It's the specific notion of "binary" or "decimal" that makes this impossible -- the idea that you have a sequence of binary/decimal digits and, somewhere in there, a radix point. To get precise rational results we'd need a better format. | |
Feb 25, 2009 at 21:41 | history | answered | Devin Jeanpierre | CC BY-SA 2.5 |