Am 21.05.2011 23:14, schrieb Stephen:
> On 21/05/2011 10:09 PM, Warp wrote:
>> On 05/19/2011 03:49 PM, gregjohn wrote:
>>> In other words, we now have an artistic way to compare floating point
>>> error
>>> between different machines.
>>
>> The IEEE double-precision floating point format has 52 mantissa bits,
>> and what you are seeing is hitting that limit. In other words, zooming
>> any further would require more mantissa precision than that, and what
>> you are seeing are the rounding errors caused by the mantissa not having
>> enough bits.
>>
>> The IEEE double-precision format is pretty common in most computer
>> architectures, so they will all hit the limit at the same zooming level.
>>
>> If the mandelbrot set were calculated using extended precision floating
>> point numbers, which in the x87 have 64 mantissa bits, you could zoom a
>> bit more (but not a lot) before hitting the artifacts.
>
> How does Fractint's deep zooming work, then?

There's a clue is in the program's name: It computes FRACTals using the 
computer's INTeger instructions - rather than floating point - 
implementing numeric formats with much higher precision than natively 
supported by the computer's architecture.

BTW, when Fractint first entered the scene, hardware floating point 
support was still a luxury on PCs, requiring a dedicated co-processor; 
so on most systems, those custom integer number formats didn't just 
offer higher precision, but were also at least as fast as IEEE double 
precision.

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