Paul, re:explanation of Katmai "double precision" capability.
You say about the inadequacy of single precision:
Even this seems quite adequate, except when you consider division of one SMALL single precision number by another, or subtraction of a very small single precision number from a large one.
Wrong on the division example -- the result of 24-bit precision division will always be accurate to 24 bits, it has nothing to do with the size of the numbers.
Wrong on the subtraction example. Again, if I subtract a small number from a large one, the result of the operation is still accurate to 24 bits. The real inaccuracy in floating point arithmetic creeps in when you subtract two nearly equal floating point numbers. In that case, you can lose "bits of precision," although you will lose just as many bits of precision with 48 bit double precision as with 24 bit single precision.
Unfortunately, no one needs double precision for performing graphics calculations such as lighting, reflection, transmission, projection or position. Even 32 bit color has only 11 bits for each of the primary colors and position on a CRT screen is determined by a pair of 10-12 bit numbers.
Double precision floating point is useful for scientific applications, but for graphics applications its wasteful silicon overkill.
Petz |
