Timeline for Does Mathematica have an equivalent of C's nextafter?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
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| Jun 10, 2016 at 7:23 | answer | added | Alexey Popkov | timeline score: 2 | |
| Jun 10, 2016 at 7:05 | answer | added | jkuczm | timeline score: 5 | |
| Aug 15, 2015 at 7:30 | answer | added | J. M.'s missing motivation♦ | timeline score: 6 | |
| May 24, 2015 at 14:01 | history | tweeted | twitter.com/#!/StackMma/status/602474577583853568 | ||
| May 24, 2015 at 12:34 | answer | added | Michael E2 | timeline score: 7 | |
| May 24, 2015 at 6:08 | history | edited | J. M.'s missing motivation♦ |
edited tags
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| May 24, 2015 at 5:52 | history | edited | David Zhang | CC BY-SA 3.0 |
added edit explaining subtleties of floating-point representation
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| May 24, 2015 at 5:43 | comment | added | kirma |
You can also consider doing something like {IntegerPart[#1/$MachineEpsilon], #2} & @@ MantissaExponent[x, 2] to split the floating point number to integer-valued components and working further with those.
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| May 24, 2015 at 5:42 | comment | added | David Zhang |
@ciao Ulp is definitely a step in the right direction, but I'm not sure how to use it to implement nextafter. In particuar, I'm not sure how to handle the transitions between one exponent value and the next; note that 1.0 + Ulp[1.0] == 1.0 while 1.0 - Ulp[1.0] != 1.0.
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| May 24, 2015 at 5:41 | comment | added | David Zhang |
@J. M. I still don't believe it would; the gap between 1.0e300 and the next floating-point value is a lot larger than $MachineEpsilon. In general, the gaps between consecutive floating-point numbers change with the magnitude of the numbers.
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| May 24, 2015 at 5:38 | comment | added | J. M.'s missing motivation♦ | You're right, for numbers in $(-1, 1)$, adding an appropriate signed machine epsilon would not be applicable. But at least for numbers outside that range, the last one would work. | |
| May 24, 2015 at 5:28 | comment | added | ciao |
Have a look at Ulp et al. in the Computer Arithmetic package...
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| May 24, 2015 at 5:01 | comment | added | David Zhang | @J. M. If I understand correctly, incrementing/decrementing a float is a rather nontrivial task using only floating-point arithmetic operations. It's much easier with bit-level access to the internal representation of a number, which I can't figure out how to get in Mathematica. | |
| May 24, 2015 at 4:56 | comment | added | David Zhang |
@J. M. Not quite. $MachineEpsilon is the smallest floating-point number such that 1 + $MachineEpsilon != 1, but for certain values, the distance to the next representable float is much smaller. For example, consider the distance between 1.0e-300 and the next number up.
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| May 24, 2015 at 4:55 | comment | added | J. M.'s missing motivation♦ |
x + Sign[y] $MachineEpsilon should work, yes?
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| May 24, 2015 at 4:43 | history | asked | David Zhang | CC BY-SA 3.0 |