Do you mean using two doubles to store the high and low part of a floating point number, the way it is described in this topic:
http://www.fractalforums.com/programming/%28java%29-double-double-library-for-128-bit-precision/That isn't exactly IEEE quad precision, because it has only 104 bits of significand instead of 112. Nevertheless, it is quite useful for fractal calculation. I implemented a double-double library in my Mandelbrot generator, and it allows zooming about twice as deep (because it has twice as many significand bits), while being about 10x slower than double precision. It is still 4x faster than arbitrary (software-based fix point) precision though.
An interesting side-effect is mentioned in that topic:
Even though the double-double has less precision than the quad-precision, it is able to store numbers Quad-precision can't. Consider this number:
1.00000000000000000000000000000000001
which in Quad-precision would just be 1.0, but can be expressed in double-double precision by the tuple (1.0, 1.0-45})
This allows to zoom to the points [0,1] and [0,-1] more deeply. These complex numbers have orbits with a period of 3 ([0,1],[-1,1],[0,0] and [0,-1],[-1,1],[0,0] respectively) and all iterations result in complex numbers with real and imaginary parts of 0, 1, or -1, hence the high part of the double-double representations will always be 0, 1, or -1, and the low part can be arbitrarily small (it is only limited by the minimum exponent of double, -1023).
Botond
August 17, 2008, 03:43:05 PM
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